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== History == The ammonia molecule NH3 is shaped like a pyramid 0.38 Å in height, with an equilateral triangle of hydrogens forming the base.The nitrogen situated on the axis has two equivalent equilibrium positions above and below the triangle of hydrogens, and this raises the possibility of the nitrogen tunneling up and down, through the plane of the H-atoms. In 1932 Dennison et al. ... analyzed the vibrational energy of this molecule and concluded that the vibrational energy would be split into pairs by the presence of these two equilibrium positions. The next year Wright and Randall observed ... a splitting of 0.67 cm–1 in far infrared lines, corresponding to ν = 20 GHz, the value predicted by theory.In 1934 Cleeton and Williams ... constructed a grating echelette spectrometer in order to measure this splitting directly, thereby beginning the field of microwave spectroscopy. They observed a somewhat asymmetric absorption line with a maximum at 24 GHz and a full width at half height of 12 GHz. == In molecular physics == In the field of molecular physics, microwave spectroscopy is commonly used to probe the rotation of molecules. == In condensed matter physics == In the field of condensed matter physics, microwave spectroscopy is used to detect dynamic phenomena of either charges or spins at GHz frequencies (corresponding to nanosecond time scales) and energy scales in the µeV regime. Matching to these energy scales, microwave spectroscopy on solids is often performed as a function of temperature (down to cryogenic regimes of a few K or even lower) and/or magnetic field (with fields up to several T). Spectroscopy traditionally considers the frequency-dependent response of materials, and in the study of dielectrics microwave spectroscopy often covers a large frequency range. In contrast, for conductive samples as well as for magnetic resonance, experiments at a fixed frequency are common (using a highly sensitive microwave resonator), but frequency-dependent measurements are also possible. === Probing charges in condensed matter physics === For insulating materials (both solid and liquid), probing charge dynamics with microwaves is a part of dielectric spectroscopy. Amongst the conductive materials, superconductors are a material class that is often studied with microwave spectroscopy, giving information about penetration depth (governed by the superconducting condensate), energy gap (single-particle excitation of Cooper pairs), and quasiparticle dynamics.Another material class that has been studied using microwave spectroscopy at low temperatures are heavy fermion metals with Drude relaxation rates at GHz frequencies. === Probing spins in condensed matter physics === Microwaves impinging on matter usually interact with charges as well as with spins (via electric and magnetic field components, respectively), with the charge response typically much stronger than the spin response. But in the case of magnetic resonance, spins can be directly probed using microwaves. For paramagnetic materials, this technique is called electron spin resonance (ESR) and for ferromagnetic materials ferromagnetic resonance (FMR). In the paramagnetic case, such an experiment probes the Zeeman splitting, with a linear relation between the static external magnetic field and the frequency of the probing microwave field. A popular combination, as implemented in commercial X-band ESR spectrometers, is approximately 0.3 T (static field) and 10 GHz (microwave frequency) for a typical material with electron g-factor close to 2. == References ==

Microwave spectroscopy is the spectroscopy method that employs microwaves, i.e. electromagnetic radiation at GHz frequencies, for the study of matter.

Microwave spectroscopy

== History == Credit for the discovery of NMR goes to Isidor Isaac Rabi, who received the Nobel Prize in Physics in 1944. The Purcell group at Harvard University and the Bloch group at Stanford University independently developed NMR spectroscopy in the late 1940s and early 1950s. Edward Mills Purcell and Felix Bloch shared the 1952 Nobel Prize in Physics for their discoveries. == Basic NMR techniques == === Resonant frequency === When placed in a magnetic field, NMR active nuclei (such as 1H or 13C) absorb electromagnetic radiation at a frequency characteristic of the isotope. The resonant frequency, energy of the radiation absorbed, and the intensity of the signal are proportional to the strength of the magnetic field. For example, in a 21 Tesla magnetic field, hydrogen nuclei (commonly referred to as protons) resonate at 900 MHz. It is common to refer to a 21 T magnet as a 900 MHz magnet since hydrogen is the most common nucleus detected, however different nuclei will resonate at different frequencies at this field strength in proportion to their nuclear magnetic moments. === Sample handling === An NMR spectrometer typically consists of a spinning sample-holder inside a very strong magnet, a radio-frequency emitter, and a receiver with a probe (an antenna assembly) that goes inside the magnet to surround the sample, optionally gradient coils for diffusion measurements, and electronics to control the system. Spinning the sample is usually necessary to average out diffusional motion, however some experiments call for a stationary sample when solution movement is an important variable. For instance, measurements of diffusion constants (diffusion ordered spectroscopy or DOSY) are done using a stationary sample with spinning off, and flow cells can be used for online analysis of process flows. === Deuterated solvents === The vast majority of molecules in a solution are solvent molecules, and most regular solvents are hydrocarbons and so contain NMR-active protons. In order to avoid detecting only signals from solvent hydrogen atoms, deuterated solvents are used where 99+% of the protons are replaced with deuterium (hydrogen-2). The most widely used deuterated solvent is deuterochloroform (CDCl3), although other solvents may be used for various reasons, such as solubility of a sample, desire to control hydrogen bonding, or melting or boiling points. The chemical shifts of a molecule will change slightly between solvents, and the solvent used will almost always be reported with chemical shifts. NMR spectra are often calibrated against the known solvent residual proton peak instead of added tetramethylsilane. === Shim and lock === To detect the very small frequency shifts due to nuclear magnetic resonance, the applied magnetic field must be constant throughout the sample volume. High resolution NMR spectrometers use shims to adjust the homogeneity of the magnetic field to parts per billion (ppb) in a volume of a few cubic centimeters. In order to detect and compensate for inhomogeneity and drift in the magnetic field, the spectrometer maintains a "lock" on the solvent deuterium frequency with a separate lock unit, which is essentially an additional transmitter and RF processor tuned to the lock nucleus (deuterium) rather than the nuclei of the sample of interest. In modern NMR spectrometers shimming is adjusted automatically, though in some cases the operator has to optimize the shim parameters manually to obtain the best possible resolution === Acquisition of spectra === Upon excitation of the sample with a radio frequency (60–1000 MHz) pulse, a nuclear magnetic resonance response - a free induction decay (FID) - is obtained. It is a very weak signal, and requires sensitive radio receivers to pick up. A Fourier transform is carried out to extract the frequency-domain spectrum from the raw time-domain FID. A spectrum from a single FID has a low signal-to-noise ratio, but it improves readily with averaging of repeated acquisitions. Good 1H NMR spectra can be acquired with 16 repeats, which takes only minutes. However, for elements heavier than hydrogen, the relaxation time is rather long, e.g. around 8 seconds for 13C. Thus, acquisition of quantitative heavy-element spectra can be time-consuming, taking tens of minutes to hours.Following the pulse, the nuclei are, on average, excited to a certain angle vs. the spectrometer magnetic field. The extent of excitation can be controlled with the pulse width, typically ca. 3-8 µs for the optimal 90° pulse. The pulse width can be determined by plotting the (signed) intensity as a function of pulse width. It follows a sine curve, and accordingly, changes sign at pulse widths corresponding to 180° and 360° pulses.Decay times of the excitation, typically measured in seconds, depend on the effectiveness of relaxation, which is faster for lighter nuclei and in solids, and slower for heavier nuclei and in solutions, and they can be very long in gases. If the second excitation pulse is sent prematurely before the relaxation is complete, the average magnetization vector has not decayed to ground state, which affects the strength of the signal in an unpredictable manner. In practice, the peak areas are then not proportional to the stoichiometry; only the presence, but not the amount of functional groups is possible to discern. An inversion recovery experiment can be done to determine the relaxation time and thus the required delay between pulses. A 180° pulse, an adjustable delay, and a 90° pulse is transmitted. When the 90° pulse exactly cancels out the signal, the delay corresponds to the time needed for 90° of relaxation. Inversion recovery is worthwhile for quantitative 13C, 2D and other time-consuming experiments. === Chemical shift === A spinning charge generates a magnetic field that results in a magnetic moment proportional to the spin. In the presence of an external magnetic field, two spin states exist (for a spin 1/2 nucleus): one spin up and one spin down, where one aligns with the magnetic field and the other opposes it. The difference in energy (ΔE) between the two spin states increases as the strength of the field increases, but this difference is usually very small, leading to the requirement for strong NMR magnets (1-20 T for modern NMR instruments). Irradiation of the sample with energy corresponding to the exact spin state separation of a specific set of nuclei will cause excitation of those set of nuclei in the lower energy state to the higher energy state.For spin 1/2 nuclei, the energy difference between the two spin states at a given magnetic field strength is proportional to their magnetic moment. However, even if all protons have the same magnetic moments, they do not give resonant signals at the same frequency values. This difference arises from the differing electronic environments of the nucleus of interest. Upon application of an external magnetic field, these electrons move in response to the field and generate local magnetic fields that oppose the much stronger applied field. This local field thus "shields" the proton from the applied magnetic field, which must therefore be increased in order to achieve resonance (absorption of rf energy). Such increments are very small, usually in parts per million (ppm). For instance, the proton peak from an aldehyde is shifted ca. 10 ppm compared to a hydrocarbon peak, since as an electron-withdrawing group, the carbonyl deshields the proton by reducing the local electron density. The difference between 2.3487 T and 2.3488 T is therefore about 42 ppm. However a frequency scale is commonly used to designate the NMR signals, even though the spectrometer may operate by sweeping the magnetic field, and thus the 42 ppm is 4200 Hz for a 100 MHz reference frequency (rf). However, given that the location of different NMR signals is dependent on the external magnetic field strength and the reference frequency, the signals are usually reported relative to a reference signal, usually that of TMS (tetramethylsilane). Additionally, since the distribution of NMR signals is field dependent, these frequencies are divided by the spectrometer frequency. However, since we are dividing Hz by MHz, the resulting number would be too small, and thus it is multiplied by a million. This operation therefore gives a locator number called the "chemical shift" with units of parts per million. In general, chemical shifts for protons are highly predictable since the shifts are primarily determined by simpler shielding effects (electron density), but the chemical shifts for many heavier nuclei are more strongly influenced by other factors including excited states ("paramagnetic" contribution to shielding tensor). The chemical shift provides information about the structure of the molecule. The conversion of the raw data to this information is called assigning the spectrum. For example, for the 1H-NMR spectrum for ethanol (CH3CH2OH), one would expect signals at each of three specific chemical shifts: one for the CH3 group, one for the CH2 group and one for the OH group. A typical CH3 group has a shift around 1 ppm, a CH2 attached to an OH has a shift of around 4 ppm and an OH has a shift anywhere from 2–6 ppm depending on the solvent used and the amount of hydrogen bonding. While the O atom does draw electron density away from the attached H through their mutual sigma bond, the electron lone pairs on the O bathe the H in their shielding effect.In paramagnetic NMR spectroscopy, measurements are conducted on paramagnetic samples. The paramagnetism gives rise to very diverse chemical shifts. In 1H NMR spectroscopy, the chemical shift range can span up to thousands of ppm.Because of molecular motion at room temperature, the three methyl protons average out during the NMR experiment (which typically requires a few ms). These protons become degenerate and form a peak at the same chemical shift. The shape and area of peaks are indicators of chemical structure too. In the example above—the proton spectrum of ethanol—the CH3 peak has three times the area of the OH peak. Similarly the CH2 peak would be twice the area of the OH peak but only 2/3 the area of the CH3 peak. Software allows analysis of signal intensity of peaks, which under conditions of optimal relaxation, correlate with the number of protons of that type. Analysis of signal intensity is done by integration—the mathematical process that calculates the area under a curve. The analyst must integrate the peak and not measure its height because the peaks also have width—and thus its size is dependent on its area not its height. However, it should be mentioned that the number of protons, or any other observed nucleus, is only proportional to the intensity, or the integral, of the NMR signal in the very simplest one-dimensional NMR experiments. In more elaborate experiments, for instance, experiments typically used to obtain carbon-13 NMR spectra, the integral of the signals depends on the relaxation rate of the nucleus, and its scalar and dipolar coupling constants. Very often these factors are poorly known - therefore, the integral of the NMR signal is very difficult to interpret in more complicated NMR experiments. === J-coupling === Some of the most useful information for structure determination in a one-dimensional NMR spectrum comes from J-coupling or scalar coupling (a special case of spin–spin coupling) between NMR active nuclei. This coupling arises from the interaction of different spin states through the chemical bonds of a molecule and results in the splitting of NMR signals. For a proton, the local magnetic field is slightly different depending on whether an adjacent nucleus points towards or against the spectrometer magnetic field, which gives rise to two signals per proton instead of one. These splitting patterns can be complex or simple and, likewise, can be straightforwardly interpretable or deceptive. This coupling provides detailed insight into the connectivity of atoms in a molecule.Coupling to n equivalent (spin ½) nuclei splits the signal into a n+1 multiplet with intensity ratios following Pascal's triangle as described on the right. Coupling to additional spins will lead to further splittings of each component of the multiplet e.g. coupling to two different spin ½ nuclei with significantly different coupling constants will lead to a doublet of doublets (abbreviation: dd). Note that coupling between nuclei that are chemically equivalent (that is, have the same chemical shift) has no effect on the NMR spectra and couplings between nuclei that are distant (usually more than 3 bonds apart for protons in flexible molecules) are usually too small to cause observable splittings. Long-range couplings over more than three bonds can often be observed in cyclic and aromatic compounds, leading to more complex splitting patterns.For example, in the proton spectrum for ethanol described above, the CH3 group is split into a triplet with an intensity ratio of 1:2:1 by the two neighboring CH2 protons. Similarly, the CH2 is split into a quartet with an intensity ratio of 1:3:3:1 by the three neighboring CH3 protons. In principle, the two CH2 protons would also be split again into a doublet to form a doublet of quartets by the hydroxyl proton, but intermolecular exchange of the acidic hydroxyl proton often results in a loss of coupling information. Coupling to any spin-1/2 nuclei such as phosphorus-31 or fluorine-19 works in this fashion (although the magnitudes of the coupling constants may be very different). But the splitting patterns differ from those described above for nuclei with spin greater than ½ because the spin quantum number has more than two possible values. For instance, coupling to deuterium (a spin 1 nucleus) splits the signal into a 1:1:1 triplet because the spin 1 has three spin states. Similarly, a spin 3/2 nucleus such as 35Cl splits a signal into a 1:1:1:1 quartet and so on. Coupling combined with the chemical shift (and the integration for protons) tells us not only about the chemical environment of the nuclei, but also the number of neighboring NMR active nuclei within the molecule. In more complex spectra with multiple peaks at similar chemical shifts or in spectra of nuclei other than hydrogen, coupling is often the only way to distinguish different nuclei. ==== Second-order (or strong) coupling ==== The above description assumes that the coupling constant is small in comparison with the difference in NMR frequencies between the inequivalent spins. If the shift separation decreases (or the coupling strength increases), the multiplet intensity patterns are first distorted, and then become more complex and less easily analyzed (especially if more than two spins are involved). Intensification of some peaks in a multiplet is achieved at the expense of the remainder, which sometimes almost disappear in the background noise, although the integrated area under the peaks remains constant. In most high-field NMR, however, the distortions are usually modest and the characteristic distortions (roofing) can in fact help to identify related peaks. Some of these patterns can be analyzed with the method published by John Pople, though it has limited scope. Second-order effects decrease as the frequency difference between multiplets increases, so that high-field (i.e. high-frequency) NMR spectra display less distortion than lower frequency spectra. Early spectra at 60 MHz were more prone to distortion than spectra from later machines typically operating at frequencies at 200 MHz or above. Furthermore, as in the figure to the right, J-coupling can be used to identify ortho-meta-para substitution of a ring. Ortho coupling is the strongest at 15 Hz, Meta follows with an average of 2 Hz, and finally para coupling is usually insignificant for studies. ==== Magnetic inequivalence ==== More subtle effects can occur if chemically equivalent spins (i.e., nuclei related by symmetry and so having the same NMR frequency) have different coupling relationships to external spins. Spins that are chemically equivalent but are not indistinguishable (based on their coupling relationships) are termed magnetically inequivalent. For example, the 4 H sites of 1,2-dichlorobenzene divide into two chemically equivalent pairs by symmetry, but an individual member of one of the pairs has different couplings to the spins making up the other pair. Magnetic inequivalence can lead to highly complex spectra which can only be analyzed by computational modeling. Such effects are more common in NMR spectra of aromatic and other non-flexible systems, while conformational averaging about C−C bonds in flexible molecules tends to equalize the couplings between protons on adjacent carbons, reducing problems with magnetic inequivalence. == Correlation spectroscopy == Correlation spectroscopy is one of several types of two-dimensional nuclear magnetic resonance (NMR) spectroscopy or 2D-NMR. This type of NMR experiment is best known by its acronym, COSY. Other types of two-dimensional NMR include J-spectroscopy, exchange spectroscopy (EXSY), Nuclear Overhauser effect spectroscopy (NOESY), total correlation spectroscopy (TOCSY), and heteronuclear correlation experiments, such as HSQC, HMQC, and HMBC. In correlation spectroscopy, emission is centered on the peak of an individual nucleus; if its magnetic field is correlated with another nucleus by through-bond (COSY, HSQC, etc.) or through-space (NOE) coupling, a response can also be detected on the frequency of the correlated nucleus. Two-dimensional NMR spectra provide more information about a molecule than one-dimensional NMR spectra and are especially useful in determining the structure of a molecule, particularly for molecules that are too complicated to work with using one-dimensional NMR. The first two-dimensional experiment, COSY, was proposed by Jean Jeener, a professor at Université Libre de Bruxelles, in 1971. This experiment was later implemented by Walter P. Aue, Enrico Bartholdi and Richard R. Ernst, who published their work in 1976. == Solid-state nuclear magnetic resonance == A variety of physical circumstances do not allow molecules to be studied in solution, and at the same time not by other spectroscopic techniques to an atomic level, either. In solid-phase media, such as crystals, microcrystalline powders, gels, anisotropic solutions, etc., it is in particular the dipolar coupling and chemical shift anisotropy that become dominant to the behaviour of the nuclear spin systems. In conventional solution-state NMR spectroscopy, these additional interactions would lead to a significant broadening of spectral lines. A variety of techniques allows establishing high-resolution conditions, that can, at least for 13C spectra, be comparable to solution-state NMR spectra. Two important concepts for high-resolution solid-state NMR spectroscopy are the limitation of possible molecular orientation by sample orientation, and the reduction of anisotropic nuclear magnetic interactions by sample spinning. Of the latter approach, fast spinning around the magic angle is a very prominent method, when the system comprises spin 1/2 nuclei. Spinning rates of ca. 20 kHz are used, which demands special equipment. A number of intermediate techniques, with samples of partial alignment or reduced mobility, is currently being used in NMR spectroscopy. Applications in which solid-state NMR effects occur are often related to structure investigations on membrane proteins, protein fibrils or all kinds of polymers, and chemical analysis in inorganic chemistry, but also include "exotic" applications like the plant leaves and fuel cells. For example, Rahmani et al. studied the effect of pressure and temperature on the bicellar structures' self-assembly using deuterium NMR spectroscopy. == Biomolecular NMR spectroscopy == === Proteins === Much of the innovation within NMR spectroscopy has been within the field of protein NMR spectroscopy, an important technique in structural biology. A common goal of these investigations is to obtain high resolution 3-dimensional structures of the protein, similar to what can be achieved by X-ray crystallography. In contrast to X-ray crystallography, NMR spectroscopy is usually limited to proteins smaller than 35 kDa, although larger structures have been solved. NMR spectroscopy is often the only way to obtain high resolution information on partially or wholly intrinsically unstructured proteins. It is now a common tool for the determination of Conformation Activity Relationships where the structure before and after interaction with, for example, a drug candidate is compared to its known biochemical activity. Proteins are orders of magnitude larger than the small organic molecules discussed earlier in this article, but the basic NMR techniques and some NMR theory also applies. Because of the much higher number of atoms present in a protein molecule in comparison with a small organic compound, the basic 1D spectra become crowded with overlapping signals to an extent where direct spectral analysis becomes untenable. Therefore, multidimensional (2, 3 or 4D) experiments have been devised to deal with this problem. To facilitate these experiments, it is desirable to isotopically label the protein with 13C and 15N because the predominant naturally occurring isotope 12C is not NMR-active and the nuclear quadrupole moment of the predominant naturally occurring 14N isotope prevents high resolution information from being obtained from this nitrogen isotope. The most important method used for structure determination of proteins utilizes NOE experiments to measure distances between atoms within the molecule. Subsequently, the distances obtained are used to generate a 3D structure of the molecule by solving a distance geometry problem. NMR can also be used to obtain information on the dynamics and conformational flexibility of different regions of a protein. === Nucleic acids === Nucleic acid NMR is the use of NMR spectroscopy to obtain information about the structure and dynamics of polynucleic acids, such as DNA or RNA. As of 2003, nearly half of all known RNA structures had been determined by NMR spectroscopy.Nucleic acid and protein NMR spectroscopy are similar but differences exist. Nucleic acids have a smaller percentage of hydrogen atoms, which are the atoms usually observed in NMR spectroscopy, and because nucleic acid double helices are stiff and roughly linear, they do not fold back on themselves to give "long-range" correlations. The types of NMR usually done with nucleic acids are 1H or proton NMR, 13C NMR, 15N NMR, and 31P NMR. Two-dimensional NMR methods are almost always used, such as correlation spectroscopy (COSY) and total coherence transfer spectroscopy (TOCSY) to detect through-bond nuclear couplings, and nuclear Overhauser effect spectroscopy (NOESY) to detect couplings between nuclei that are close to each other in space.Parameters taken from the spectrum, mainly NOESY cross-peaks and coupling constants, can be used to determine local structural features such as glycosidic bond angles, dihedral angles (using the Karplus equation), and sugar pucker conformations. For large-scale structure, these local parameters must be supplemented with other structural assumptions or models, because errors add up as the double helix is traversed, and unlike with proteins, the double helix does not have a compact interior and does not fold back upon itself. NMR is also useful for investigating nonstandard geometries such as bent helices, non-Watson–Crick basepairing, and coaxial stacking. It has been especially useful in probing the structure of natural RNA oligonucleotides, which tend to adopt complex conformations such as stem-loops and pseudoknots. NMR is also useful for probing the binding of nucleic acid molecules to other molecules, such as proteins or drugs, by seeing which resonances are shifted upon binding of the other molecule. === Carbohydrates === Carbohydrate NMR spectroscopy addresses questions on the structure and conformation of carbohydrates. The analysis of carbohydrates by 1H NMR is challenging due to the limited variation in functional groups, which leads to 1H resonances concentrated in narrow bands of the NMR spectrum. In other words, there is poor spectral dispersion. The anomeric proton resonances are segregated from the others due to fact that the anomeric carbons bear two oxygen atoms. For smaller carbohydrates, the dispersion of the anomeric proton resonances facilitates the use of 1D TOCSY experiments to investigate the entire spin systems of individual carbohydrate residues. === Drug Discovery === Knowledge of energy minima and rotational energy barriers of small molecules in solution can be found using NMR, e.g. looking at free ligand conformational preferences and conformational dynamics, respectively. This can be used to guide drug design hypotheses, since experimental and calculated values are comparable. For example, AstraZeneca uses NMR for its oncology research & development. == NMR spectroscopy and rechargeable batteries == Rechargeable batteries are complex and heterogeneous devices with numerous interfaces, which are essential as they are at the core of the battery function. The redox reactions used to store and release energy necessitate the (triple) contact of electrons, redox centres, and ions (commonly lithium) for charge balance. Side reaction also take place at interfaces and they are therefore of key importance for the battery lifetime. Two main families of measurements, ex situ and in situ, can be performed to study the solid interphases in batteries. For ex situ NMR, the part of interest is extracted from the battery in an argon glovebox and transferred into the NMR sample holder. Magic Angle Spinning (MAS) is a great tool to record resolved NMR spectra of solids and it is the main asset of ex-situ NMR for the characterization of the solid components of a battery, especially for positive paramagnetic electrodes-electrodes containing transition metal ions with localized unpaired electron such as Co2+, Ni2/3+, Mn4+, Fe2/3+ ... Ex situ NMR is traditionally performed to study the bulk changes in the solid parts for various state of charge of the battery and more recently, it was applied to gain insight into the interface components of Lithium-ion battery, especially the solid electrode-electrolyte interface (SEI) for the anode, the solid electrolyte reactivity and dynamics and the cathode-electrolyte interface (CEI) for the cathode, but also for Sodium-ion battery. The liquid electrolyte stability (decomposition products on the surface) and the plating and stripping of metal (lithium, sodium) on negative electrodes were of particular interest. The main issue for NMR studies of interphases is the small amount of material so that the signals for the interphase are often hidden or negligible compared to the intense signals of the bulkier parts, such as the electrolyte or electrode. For in situ NMR, the full battery is placed within the NMR magnet and radiofrequency coil for the measurement. Unfortunately, in situ NMR suffers from lower resolution, so that in situ approaches concentrate on batteries with materials displaying strong variations in the NMR shifts upon charge-discharge, or in combination with ex situ studies. In situ NMR is advantageous as it is non-destructive - the battery does not need a destructive opening for the measurement - and it allows measuring the spectra for several states of charge on the same battery. Operando spectroscopy (while the current is flowing for the charge/discharge) enables detecting transient phases in real-time which is of particular interest in batteries because of the strongly reducing environment, especially at the negative electrode on top of charge. == See also == Related methods of nuclear spectroscopy: Mössbauer effect Muon spin spectroscopy Perturbed angular correlation == References == == Further reading == John D. Roberts (1959). Nuclear Magnetic Resonance : applications to organic chemistry. McGraw-Hill Book Company. ISBN 9781258811662. J.A.Pople; W.G.Schneider; H.J.Bernstein (1959). High-resolution Nuclear Magnetic Resonance. McGraw-Hill Book Company. A. Abragam (1961). The Principles of Nuclear Magnetism. Clarendon Press. ISBN 9780198520146. Charles P. Slichter (1963). Principles of magnetic resonance: with examples from solid state physics. Harper & Row. ISBN 9783540084761. John Emsley; James Feeney; Leslie Howard Sutcliffe (1965). High Resolution Nuclear Magnetic Resonance Spectroscopy. Pergamon. ISBN 9781483184081. == External links == James Keeler. "Understanding NMR Spectroscopy" (reprinted at University of Cambridge). University of California, Irvine. Retrieved 2007-05-11. The Basics of NMR - A non-technical overview of NMR theory, equipment, and techniques by Dr. Joseph Hornak, Professor of Chemistry at RIT GAMMA and PyGAMMA Libraries - GAMMA is an open source C++ library written for the simulation of Nuclear Magnetic Resonance Spectroscopy experiments. PyGAMMA is a Python wrapper around GAMMA. relax Software for the analysis of NMR dynamics Vespa - VeSPA (Versatile Simulation, Pulses and Analysis) is a free software suite composed of three Python applications. These GUI based tools are for magnetic resonance (MR) spectral simulation, RF pulse design, and spectral processing and analysis of MR data.

Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. This spectroscopy is based on the measurement of absorption of electromagnetic radiations in the radio frequency region from roughly 4 to 900 MHz. Absortion of radio waves in the presence of magnetic field is accompanied by a special type of nuclear transition, and for this reason, such type of spectroscopy is known as Nuclear Magnetic Resonance Spectroscopy. The sample is placed in a magnetic field and the NMR signal is produced by excitation of the nuclei sample with radio waves into nuclear magnetic resonance, which is detected with sensitive radio receivers. The intramolecular magnetic field around an atom in a molecule changes the resonance frequency, thus giving access to details of the electronic structure of a molecule and its individual functional groups. As the fields are unique or highly characteristic to individual compounds, in modern organic chemistry practice, NMR spectroscopy is the definitive method to identify monomolecular organic compounds. The principle of NMR usually involves three sequential steps: The alignment (polarization) of the magnetic nuclear spins in an applied, constant magnetic field B0. The perturbation of this alignment of the nuclear spins by a weak oscillating magnetic field, usually referred to as a radio-frequency (RF) pulse. Detection and analysis of the electromagnetic waves emitted by the nuclei of the sample as a result of this perturbation.Similarly, biochemists use NMR to identify proteins and other complex molecules. Besides identification, NMR spectroscopy provides detailed information about the structure, dynamics, reaction state, and chemical environment of molecules. The most common types of NMR are proton and carbon-13 NMR spectroscopy, but it is applicable to any kind of sample that contains nuclei possessing spin. NMR spectra are unique, well-resolved, analytically tractable and often highly predictable for small molecules. Different functional groups are obviously distinguishable, and identical functional groups with differing neighboring substituents still give distinguishable signals. NMR has largely replaced traditional wet chemistry tests such as color reagents or typical chromatography for identification. A disadvantage is that a relatively large amount, 2–50 mg, of a purified substance is required, although it may be recovered through a workup. Preferably, the sample should be dissolved in a solvent, because NMR analysis of solids requires a dedicated magic angle spinning machine and may not give equally well-resolved spectra. The timescale of NMR is relatively long, and thus it is not suitable for observing fast phenomena, producing only an averaged spectrum. Although large amounts of impurities do show on an NMR spectrum, better methods exist for detecting impurities, as NMR is inherently not very sensitive - though at higher frequencies, sensitivity is higher. Correlation spectroscopy is a development of ordinary NMR. In two-dimensional NMR, the emission is centered around a single frequency, and correlated resonances are observed. This allows identifying the neighboring substituents of the observed functional group, allowing unambiguous identification of the resonances. There are also more complex 3D and 4D methods and a variety of methods designed to suppress or amplify particular types of resonances. In nuclear Overhauser effect (NOE) spectroscopy, the relaxation of the resonances is observed. As NOE depends on the proximity of the nuclei, quantifying the NOE for each nucleus allows for construction of a three-dimensional model of the molecule. NMR spectrometers are relatively expensive; universities usually have them, but they are less common in private companies. Between 2000 and 2015, an NMR spectrometer cost around 500,000 - 5 million USD. Modern NMR spectrometers have a very strong, large and expensive liquid helium-cooled superconducting magnet, because resolution directly depends on magnetic field strength. Less expensive machines using permanent magnets and lower resolution are also available, which still give sufficient performance for certain applications such as reaction monitoring and quick checking of samples. There are even benchtop nuclear magnetic resonance spectrometers. NMR can be observed in magnetic fields less than a millitesla. Low-resolution NMR produces broader peaks which can easily overlap one another causing issues in resolving complex structures. The use of higher strength magnetic fields result in clear resolution of the peaks and is the standard in industry.

Nuclear magnetic resonance spectroscopy

== Calculation == Molecular masses are calculated from the atomic masses of each nuclide present in the molecule, while relative molecular masses are calculated from the standard atomic weights of each element. The standard atomic weight takes into account the isotopic distribution of the element in a given sample (usually assumed to be "normal"). For example, water has a relative molecular mass of 18.0153(3), but individual water molecules have molecular masses which range between 18.010 564 6863(15) Da (1H216O) and 22.027 7364(9) Da (2H218O). Atomic and molecular masses are usually reported in daltons which is defined relative to the mass of the isotope 12C (carbon 12). Relative atomic and molecular mass values as defined are dimensionless. However, the "unit" Dalton is still used in common practice. For example, the relative molecular mass and molecular mass of methane, whose molecular formula is CH4, are calculated respectively as follows: The uncertainty in molecular mass reflects variance (error) in measurement not the natural variance in isotopic abundances across the globe. In high-resolution mass spectrometry the mass isotopomers 12C1H4 and 13C1H4 are observed as distinct molecules, with molecular masses of approximately 16.031 Da and 17.035 Da, respectively. The intensity of the mass-spectrometry peaks is proportional to the isotopic abundances in the molecular species. 12C 2H 1H3 can also be observed with molecular mass of 17 Da. == Determination == === Mass spectrometry === In mass spectrometry, the molecular mass of a small molecule is usually reported as the monoisotopic mass, that is, the mass of the molecule containing only the most common isotope of each element. Note that this also differs subtly from the molecular mass in that the choice of isotopes is defined and thus is a single specific molecular mass of the many possibilities. The masses used to compute the monoisotopic molecular mass are found on a table of isotopic masses and are not found on a typical periodic table. The average molecular mass is often used for larger molecules since molecules with many atoms are unlikely to be composed exclusively of the most abundant isotope of each element. A theoretical average molecular mass can be calculated using the standard atomic weights found on a typical periodic table, since there is likely to be a statistical distribution of atoms representing the isotopes throughout the molecule. The average molecular mass of a sample, however, usually differs substantially from this since a single sample average is not the same as the average of many geographically distributed samples. === Mass photometry === Mass photometry (MP) is a rapid, in-solution, label-free method of obtaining the molecular mass of proteins, lipids, sugars & nucleic acids at the single-molecule level. The technique is based on interferometric scattered light microscopy. Contrast from scattered light by a single binding event at the interface between the protein solution and glass slide is detected and is linearly proportional to the mass of the molecule. This technique is also capable of measuring sample homogeneity, detecting protein oligomerisation state, characterisation of complex macromolecular assemblies (ribosomes, GroEL, AAV) and protein interactions such as protein-protein interactions. Mass photometry can measure molecular mass to an accurate degree over a wide range of molecular masses (40kDa – 5MDa). === Hydrodynamic methods === To a first approximation, the basis for determination of molecular mass according to Mark–Houwink relations is the fact that the intrinsic viscosity of solutions (or suspensions) of macromolecules depends on volumetric proportion of the dispersed particles in a particular solvent. Specifically, the hydrodynamic size as related to molecular mass depends on a conversion factor, describing the shape of a particular molecule. This allows the apparent molecular mass to be described from a range of techniques sensitive to hydrodynamic effects, including DLS, SEC (also known as GPC when the eluent is an organic solvent), viscometry, and diffusion ordered nuclear magnetic resonance spectroscopy (DOSY). The apparent hydrodynamic size can then be used to approximate molecular mass using a series of macromolecule-specific standards. As this requires calibration, it's frequently described as a "relative" molecular mass determination method. === Static light scattering === It is also possible to determine absolute molecular mass directly from light scattering, traditionally using the Zimm method. This can be accomplished either via classical static light scattering or via multi-angle light scattering detectors. Molecular masses determined by this method do not require calibration, hence the term "absolute". The only external measurement required is refractive index increment, which describes the change in refractive index with concentration. == See also == Cryoscopy and cryoscopic constant Ebullioscopy and ebullioscopic constant Dumas method of molecular weight determination François-Marie Raoult Standard atomic weight Mass number Absolute molar mass Molar mass distribution Dalton (unit) SDS-PAGE == References == == External links == A Free Android application for molecular and reciprocal weight calculation of any chemical formula Stoichiometry Add-In for Microsoft Excel for calculation of molecular weights, reaction coefficients and stoichiometry.

The molecular mass (m) is the mass of a given molecule: it is measured in daltons or atomic mass (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quantity relative molecular mass, as defined by IUPAC, is the ratio of the mass of a molecule to the unified atomic mass unit (also known as the dalton) and is unitless. The molecular mass and relative molecular mass are distinct from but related to the molar mass. The molar mass is defined as the mass of a given substance divided by the amount of a substance and is expressed in g/mol. That makes the molar mass an average of many particles or molecules, and the molecular mass the mass of one specific particle or molecule. The molar mass is usually the more appropriate figure when dealing with macroscopic (weigh-able) quantities of a substance. The definition of molecular weight is most authoritatively synonymous with relative molecular mass; however, in common practice, it is highly variable. When the molecular weight is used with the units Da or u, it is frequently as a weighted average similar to the molar mass but with different units. In molecular biology, the mass of macromolecules is referred to as their molecular weight and is expressed in kDa, although the numerical value is often approximate and representative of an average. The terms molecular mass, molecular weight, and molar mass are often used interchangeably in areas of science where distinguishing between them is unhelpful. In other areas of science, the distinction is crucial. The molecular mass is more commonly used when referring to the mass of a single or specific well-defined molecule and less commonly than molecular weight when referring to a weighted average of a sample. Prior to the 2019 redefinition of SI base units quantities expressed in daltons (Da or u) were by definition numerically equivalent to otherwise identical quantities expressed in the units g/mol and were thus strictly numerically interchangeable. After the 20 May 2019 redefinition of units, this relationship is only nearly equivalent. The molecular mass of small to medium size molecules, measured by mass spectrometry, can be used to determine the composition of elements in the molecule. The molecular masses of macromolecules, such as proteins, can also be determined by mass spectrometry; however, methods based on viscosity and light-scattering are also used to determine molecular mass when crystallographic or mass spectrometric data are not available.

Molecular mass

== Scientific career == Bright started his higher education at Princeton in 1926, where he received both his bachelor's and master's degree in 1930 and 1931 respectively. He then went to the California Institute of Technology where he worked with Linus Pauling on crystal structure determinations and finished his PhD. During this time, he also wrote a textbook with Pauling, called Introduction to Quantum Mechanics, which was published in 1935. This textbook was still in print in the year 2000, some 70 years after its initial publication. In 1934, Bright was elected to the Society of Fellows at Harvard for his work done at the California Institute of Technology. His election meant he had a 3-year junior fellowship at Harvard during which he studied molecular motion and symmetry analysis. In 1936 the Harvard Chemistry department appointed Bright as an assistant professor during his third year of his fellowship. He taught courses in chemistry and quantum mechanics and was promoted to an associate professor with tenure after three years. From 1934 to 1941, Bright, along with Harold Gershinowitz, constructed an automatic infrared spectrometer which was used to measure vibrational absorption spectra of various molecules.After the start of World War II Bright started research on explosives with the National Defense Research Committee (NDRC) where he studied shock waves in water. In 1942 an Underwater Explosives Research Laboratory (UERL) was opened at the Woods Hole Oceanographic Institution which Bright led. The US navy, exasperated by the continual harassment of Nazi U-boats on allied shipping vessels had a strong interest in the UERL and its research with depth charges and other anti-submarine weapons. To facilitate this research, the laboratory acquired an old fishing vessel, the Reliance, which was fitted to record electronic signals from pressure sensors deep underwater.After the end of the war Bright returned to Harvard. In 1947 Bright and Richard Hughes invented and built a Stark-effect microwave spectrometer which could measure different radio waves and became an important tool in spectroscopy. From 1949 to 1950, Bright took a sabbatical in Oxford during which he mainly worked on his book Introduction to Scientific Research which was published in 1952.In 1952–1953, during the Korean War, Bright became the Research director and deputy director of the Weapons Evaluation Group (WSEG), where he only stayed for 18 months. He later began accepting assignments in the mid-1960's in Washington during the Vietnam war.In 1955 Bright published a book Molecular Vibrations along with co-authors J.C Decius and P.C. Cross which discussed infrared and Raman spectra of polyatomic molecules. In 1955 Bright studied the internal rotation of single bonds in molecules using microwave spectroscopy. In 1965 Bright studied the rotational energy transfer in inelastic molecular collisions. In 1970, Bright began to study hydrogen bonding and the structure of hydrogen bonds using low resolution microwave spectroscopy.In 1979, Bright retired and was named an emeritus professor. The E. Bright Wilson Award in Spectroscopy was established in 1994 by the American Chemical Society. == Personal life == Wilson was born in Gallatin, Tennessee to mother Alma Lackey and father E. B. Wilson, a lawyer. His family soon moved to Yonkers, New York.He was married to Emily Buckingham from 1935 until she died in 1954. He remarried to Therese Bremer in 1955, a distinguished photochemist. Wilson had a total of 4 sons and 2 daughters, one of whom was Kenneth Wilson, a Nobel Laureate in physics.In his final years, Wilson suffered from Parkinson's disease. He died on July 12, 1992, in Cambridge, Massachusetts of pneumonia. == References == == External links == Linus Pauling and E. Bright Wilson Jr., Introduction to Quantum Mechanics With Applications to Chemistry (1935). Introduction to Quantum Mechanics With Applications to Chemistry. Dover Books, New York. ISBN 0-07-048960-2. E. Bright Wilson Jr. (1952). An Introduction to Scientific Research. McGraw-Hill, New York. ISBN 0-486-66545-3. Wilson, Edgar Bright (January 1990). 13-digit. ISBN 978-0-486-66545-0.

Edgar Bright Wilson Jr. (December 18, 1908 – July 12, 1992) was an American chemist.Wilson was a prominent and accomplished chemist and teacher, recipient of the National Medal of Science in 1975, Guggenheim Fellowships in 1949 and 1970, the Elliott Cresson Medal in 1982, and a number of honorary doctorates. He was a member of both the American Academy of Arts and Sciences, the American Philosophical Society, and the United States National Academy of Sciences. He was also the Theodore William Richards Professor of Chemistry, Emeritus at Harvard University. One of his sons, Kenneth G. Wilson, was awarded the Nobel Prize in physics in 1982. E. B. Wilson was a student and protégé of Nobel laureate Linus Pauling and was a coauthor with Pauling of Introduction to Quantum Mechanics, a graduate level textbook in Quantum Mechanics. Wilson was also the thesis advisor of Nobel laureate Dudley Herschbach. Wilson was elected to the first class of the Harvard Society of Fellows. Wilson made major contributions to the field of molecular spectroscopy. He developed the first rigorous quantum mechanical Hamiltonian in internal coordinates for a polyatomic molecule. He developed the theory of how rotational spectra are influenced by centrifugal distortion during rotation. He pioneered the use of group theory for the analysis and simplification normal mode analysis, particularly for high symmetry molecules, such as benzene. In 1955, Wilson published Molecular Vibrations along with J.C. Decius and Paul C. Cross. Following the Second World War, Wilson was a pioneer in the application of microwave spectroscopy to the determination of molecular structure. Wilson wrote an influential introductory text Introduction to Scientific Research that provided an introduction of all the steps of scientific research, from defining a problem through the archival of data after publication. Starting in 1997, the American Chemical Society has annually awarded the E. Bright Wilson Award in Spectroscopy, named in honor of Wilson.

Edgar Bright Wilson

== Origins == An atomic transition is associated with a specific amount of energy, E. However, when this energy is measured by means of some spectroscopic technique, the line is not infinitely sharp, but has a particular shape. Numerous factors can contribute to the broadening of spectral lines. Broadening can only be mitigated by the use of specialized techniques, such as Lamb dip spectroscopy. The principal sources of broadening are: Lifetime broadening. According to the uncertainty principle the uncertainty in energy, ΔE and the lifetime, Δt, of the excited state are related by Δ E Δ t ⪆ ℏ {\displaystyle \Delta E\Delta t\gtrapprox \hbar } This determines the minimum possible line width. As the excited state decays exponentially in time this effect produces a line with Lorentzian shape in terms of frequency (or wavenumber).Doppler broadening. This is caused by the fact that the velocity of atoms or molecules relative to the observer follows a Maxwell distribution, so the effect is dependent on temperature. If this were the only effect the line shape would be Gaussian. Pressure broadening (Collision broadening). Collisions between atoms or molecules reduce the lifetime of the upper state, Δt, increasing the uncertainty ΔE. This effect depends on both the density (that is, pressure for a gas) and the temperature, which affects the rate of collisions. The broadening effect is described by a Lorentzian profile in most cases. Proximity broadening. The presence of other molecules close to the molecule involved affects both line width and line position. It is the dominant process for liquids and solids. An extreme example of this effect is the influence of hydrogen bonding on the spectra of protic liquids.Observed spectral line shape and line width are also affected by instrumental factors. The observed line shape is a convolution of the intrinsic line shape with the instrument transfer function.Each of these mechanisms, and others, can act in isolation or in combination. If each effect is independent of the other, the observed line profile is a convolution of the line profiles of each mechanism. Thus, a combination of Doppler and pressure broadening effects yields a Voigt profile. == Line shape functions == === Lorentzian === A Lorentzian line shape function can be represented as L = 1 1 + x 2 , {\displaystyle L={\frac {1}{1+x^{2}}},} where L signifies a Lorentzian function standardized, for spectroscopic purposes, to a maximum value of 1; x {\displaystyle x} is a subsidiary variable defined as x = p − p 0 w / 2 , {\displaystyle x={\frac {p-p_{0}}{w/2}},} where p 0 {\displaystyle p_{0}} is the position of the maximum (corresponding to the transition energy E), p is a position, and w is the full width at half maximum (FWHM), the width of the curve when the intensity is half the maximum intensity (this occurs at the points p = p 0 ± w 2 {\displaystyle p=p_{0}\pm {\frac {w}{2}}} ). The unit of p 0 {\displaystyle p_{0}} , p {\displaystyle p} and w {\displaystyle w} is typically wavenumber or frequency. The variable x is dimensionless and is zero at p = p 0 {\displaystyle p=p_{0}} . === Gaussian === The Gaussian line shape has the standardized form, G = e − ( ln ⁡ 2 ) x 2 . {\displaystyle G=e^{-(\ln 2)x^{2}}.} The subsidiary variable, x, is defined in the same way as for a Lorentzian shape. Both this function and the Lorentzian have a maximum value of 1 at x = 0 and a value of 1/2 at x=±1. === Voigt === The third line shape that has a theoretical basis is the Voigt function, a convolution of a Gaussian and a Lorentzian, V ( x ; σ , γ ) = ∫ − ∞ ∞ G ( x ′ ; σ ) L ( x − x ′ ; γ ) d x ′ , {\displaystyle V(x;\sigma ,\gamma )=\int _{-\infty }^{\infty }G(x';\sigma )L(x-x';\gamma )\,dx',} where σ and γ are half-widths. The computation of a Voigt function and its derivatives are more complicated than a Gaussian or Lorentzian. === Spectral fitting === A spectroscopic peak may be fitted to multiples of the above functions or to sums or products of functions with variable parameters. The above functions are all symmetrical about the position of their maximum. Asymmetric functions have also been used. == Instances == === Atomic spectra === For atoms in the gas phase the principal effects are Doppler and pressure broadening. Lines are relatively sharp on the scale of measurement so that applications such as atomic absorption spectroscopy (AAS) and Inductively coupled plasma atomic emission spectroscopy (ICP) are used for elemental analysis. Atoms also have distinct x-ray spectra that are attributable to the excitation of inner shell electrons to excited states. The lines are relatively sharp because the inner electron energies are not very sensitive to the atom's environment. This is applied to X-ray fluorescence spectroscopy of solid materials. === Molecular spectra === For molecules in the gas phase, the principal effects are Doppler and pressure broadening. This applies to rotational spectroscopy, rotational-vibrational spectroscopy and vibronic spectroscopy. For molecules in the liquid state or in solution, collision and proximity broadening predominate and lines are much broader than lines from the same molecule in the gas phase. Line maxima may also be shifted. Because there are many sources of broadening, the lines have a stable distribution, tending towards a Gaussian shape. === Nuclear magnetic resonance === The shape of lines in a nuclear magnetic resonance (NMR) spectrum is determined by the process of free induction decay. This decay is approximately exponential, so the line shape is Lorentzian. This follows because the Fourier transform of an exponential function in the time domain is a Lorentzian in the frequency domain. In NMR spectroscopy the lifetime of the excited states is relatively long, so the lines are very sharp, producing high-resolution spectra. === Magnetic resonance imaging === Gadolinium-based pharmaceuticals alter the relaxation time, and hence spectral line shape, of those protons that are in water molecules that are transiently attached to the paramagnetic atoms, resulting contrast enhancement of the MRI image. This allows better visualisation of some brain tumours. == Applications == === Curve decomposition === Some spectroscopic curves can be approximated by the sum of a set of component curves. For example, when Beer's law I λ = ∑ k ϵ k , λ c k {\displaystyle I_{\lambda }=\sum _{k}\epsilon _{k,\lambda }c_{k}} applies, the measured intensity, I, at wavelength λ, is a linear combination of the intensity due to the individual components, k, at concentration, ck. ε is an extinction coefficient. In such cases the curve of experimental data may be decomposed into sum of component curves in a process of curve fitting. This process is also widely called deconvolution. Curve deconvolution and curve fitting are completely different mathematical procedures.Curve fitting can be used in two distinct ways. The line shapes and parameters p 0 {\displaystyle p_{0}} and w {\displaystyle w} of the individual component curves have been obtained experimentally. In this case the curve may be decomposed using a linear least squares process simply to determine the concentrations of the components. This process is used in analytical chemistry to determine the composition of a mixture of the components of known molar absorptivity spectra. For example, if the heights of two lines are found to be h1 and h2, c1 = h1 / ε1 and c2 = h2 / ε2. Parameters of the line shape are unknown. The intensity of each component is a function of at least 3 parameters, position, height and half-width. In addition one or both of the line shape function and baseline function may not be known with certainty. When two or more parameters of a fitting curve are not known the method of non-linear least squares must be used. The reliability of curve fitting in this case is dependent on the separation between the components, their shape functions and relative heights, and the signal-to-noise ratio in the data. When Gaussian-shaped curves are used for the decomposition of set of Nsol spectra into Npks curves, the p 0 {\displaystyle p_{0}} and w {\displaystyle w} parameters are common to all Nsol spectra. This allows to calculated the heights of each Gaussian curve in each spectrum (Nsol·Npks parameters) by a (fast) linear least squares fitting procedure, while the p 0 {\displaystyle p_{0}} and w parameters (2·Npks parameters) can be obtained with a non-linear least-square fitting on the data from all spectra simultaneously, thus reducing dramatically the correlation between optimized parameters. === Derivative spectroscopy === Spectroscopic curves can be subjected to numerical differentiation. When the data points in a curve are equidistant from each other the Savitzky–Golay convolution method may be used. The best convolution function to use depends primarily on the signal-to-noise ratio of the data. The first derivative (slope, d y d x {\displaystyle {\frac {dy}{dx}}} ) of all single line shapes is zero at the position of maximum height. This is also true of the third derivative; odd derivatives can be used to locate the position of a peak maximum.The second derivatives, d 2 y d x 2 {\displaystyle {\frac {d^{2}y}{dx^{2}}}} , of both Gaussian and Lorentzian functions have a reduced half-width. This can be used to apparently improve spectral resolution. The diagram shows the second derivative of the black curve in the diagram above it. Whereas the smaller component produces a shoulder in the spectrum, it appears as a separate peak in the 2nd. derivative. Fourth derivatives, d 4 y d x 4 {\displaystyle {\frac {d^{4}y}{dx^{4}}}} , can also be used, when the signal-to-noise ratio in the spectrum is sufficiently high. === Deconvolution === Deconvolution can be used to apparently improve spectral resolution. In the case of NMR spectra, the process is relatively straight forward, because the line shapes are Lorentzian, and the convolution of a Lorentzian with another Lorentzian is also Lorentzian. The Fourier transform of a Lorentzian is an exponential. In the co-domain (time) of the spectroscopic domain (frequency) convolution becomes multiplication. Therefore, a convolution of the sum of two Lorentzians becomes a multiplication of two exponentials in the co-domain. Since, in FT-NMR, the measurements are made in the time domain division of the data by an exponential is equivalent to deconvolution in the frequency domain. A suitable choice of exponential results in a reduction of the half-width of a line in the frequency domain. This technique has been rendered all but obsolete by advances in NMR technology. A similar process has been applied for resolution enhancement of other types of spectra, with the disadvantage that the spectrum must be first Fourier transformed and then transformed back after the deconvoluting function has been applied in the spectrum's co-domain. == See also == Fano resonance Holtsmark distribution Zero-phonon line and phonon sideband == Notes == == References == == Further reading == == External links == Curve Fitting in Raman and IR Spectroscopy: Basic Theory of Line Shapes and Applications 21st International Conference on Spectral Line Shapes, St. Petersburg (2012)

Spectral line shape describes the form of a feature, observed in spectroscopy, corresponding to an energy change in an atom, molecule or ion. This shape is also referred to as the spectral line profile. Ideal line shapes include Lorentzian, Gaussian and Voigt functions, whose parameters are the line position, maximum height and half-width. Actual line shapes are determined principally by Doppler, collision and proximity broadening. For each system the half-width of the shape function varies with temperature, pressure (or concentration) and phase. A knowledge of shape function is needed for spectroscopic curve fitting and deconvolution.

Spectral line shape

== Theory == === Origin of an EPR signal === Every electron has a magnetic moment and spin quantum number s = 1 2 {\displaystyle s={\tfrac {1}{2}}} , with magnetic components m s = + 1 2 {\displaystyle m_{\mathrm {s} }=+{\tfrac {1}{2}}} or m s = − 1 2 {\displaystyle m_{\mathrm {s} }=-{\tfrac {1}{2}}} . In the presence of an external magnetic field with strength B 0 {\displaystyle B_{\mathrm {0} }} , the electron's magnetic moment aligns itself either antiparallel ( m s = − 1 2 {\displaystyle m_{\mathrm {s} }=-{\tfrac {1}{2}}} ) or parallel ( m s = + 1 2 {\displaystyle m_{\mathrm {s} }=+{\tfrac {1}{2}}} ) to the field, each alignment having a specific energy due to the Zeeman effect: E = m s g e μ B B 0 , {\displaystyle E=m_{s}g_{e}\mu _{\text{B}}B_{0},} where g e {\displaystyle g_{e}} is the electron's so-called g-factor (see also the Landé g-factor), g e = 2.0023 {\displaystyle g_{\mathrm {e} }=2.0023} for the free electron, μ B {\displaystyle \mu _{\text{B}}} is the Bohr magneton.Therefore, the separation between the lower and the upper state is Δ E = g e μ B B 0 {\displaystyle \Delta E=g_{e}\mu _{\text{B}}B_{0}} for unpaired free electrons. This equation implies (since both g e {\displaystyle g_{e}} and μ B {\displaystyle \mu _{\text{B}}} are constant) that the splitting of the energy levels is directly proportional to the magnetic field's strength, as shown in the diagram below. An unpaired electron can change its electron spin by either absorbing or emitting a photon of energy h ν {\displaystyle h\nu } such that the resonance condition, h ν = Δ E {\displaystyle h\nu =\Delta E} , is obeyed. This leads to the fundamental equation of EPR spectroscopy: h ν = g e μ B B 0 {\displaystyle h\nu =g_{e}\mu _{\text{B}}B_{0}} . Experimentally, this equation permits a large combination of frequency and magnetic field values, but the great majority of EPR measurements are made with microwaves in the 9000–10000 MHz (9–10 GHz) region, with fields corresponding to about 3500 G (0.35 T). Furthermore, EPR spectra can be generated by either varying the photon frequency incident on a sample while holding the magnetic field constant or doing the reverse. In practice, it is usually the frequency that is kept fixed. A collection of paramagnetic centers, such as free radicals, is exposed to microwaves at a fixed frequency. By increasing an external magnetic field, the gap between the m s = + 1 2 {\displaystyle m_{\mathrm {s} }=+{\tfrac {1}{2}}} and m s = − 1 2 {\displaystyle m_{\mathrm {s} }=-{\tfrac {1}{2}}} energy states is widened until it matches the energy of the microwaves, as represented by the double arrow in the diagram above. At this point the unpaired electrons can move between their two spin states. Since there typically are more electrons in the lower state, due to the Maxwell–Boltzmann distribution (see below), there is a net absorption of energy, and it is this absorption that is monitored and converted into a spectrum. The upper spectrum below is the simulated absorption for a system of free electrons in a varying magnetic field. The lower spectrum is the first derivative of the absorption spectrum. The latter is the most common way to record and publish continuous wave EPR spectra. For the microwave frequency of 9388.4 MHz, the predicted resonance occurs at a magnetic field of about B 0 = h ν / g e μ B {\displaystyle B_{0}=h\nu /g_{e}\mu _{\text{B}}} = 0.3350 T = 3350 G Because of electron-nuclear mass differences, the magnetic moment of an electron is substantially larger than the corresponding quantity for any nucleus, so that a much higher electromagnetic frequency is needed to bring about a spin resonance with an electron than with a nucleus, at identical magnetic field strengths. For example, for the field of 3350 G shown above, spin resonance occurs near 9388.2 MHz for an electron compared to only about 14.3 MHz for 1H nuclei. (For NMR spectroscopy, the corresponding resonance equation is h ν = g N μ N B 0 {\displaystyle h\nu =g_{\mathrm {N} }\mu _{\mathrm {N} }B_{0}} where g N {\displaystyle g_{\mathrm {N} }} and μ N {\displaystyle \mu _{\mathrm {N} }} depend on the nucleus under study.) === Field modulation === As previously mentioned an EPR spectrum is usually directly measured as the first derivative of the absorption. This is accomplished by using field modulation. A small additional oscillating magnetic field is applied to the external magnetic field at a typical frequency of 100 kHz. By detecting the peak to peak amplitude the first derivative of the absorption is measured. By using phase sensitive detection only signals with the same modulation (100 kHz) are detected. This results in higher signal to noise ratios. Note field modulation is unique to continuous wave EPR measurements and spectra resulting from pulsed experiments are presented as absorption profiles. The same idea underlies the Pound-Drever-Hall technique for frequency locking of lasers to a high-finesse optical cavity. === Maxwell–Boltzmann distribution === In practice, EPR samples consist of collections of many paramagnetic species, and not single isolated paramagnetic centers. If the population of radicals is in thermodynamic equilibrium, its statistical distribution is described by the Maxwell–Boltzmann equation: n upper n lower = exp ⁡ ( − E upper − E lower k T ) = exp ⁡ ( − Δ E k T ) = exp ⁡ ( − ϵ k T ) = exp ⁡ ( − h ν k T ) {\displaystyle {\frac {n_{\text{upper}}}{n_{\text{lower}}}}=\exp {\left(-{\frac {E_{\text{upper}}-E_{\text{lower}}}{kT}}\right)}=\exp {\left(-{\frac {\Delta E}{kT}}\right)}=\exp {\left(-{\frac {\epsilon }{kT}}\right)}=\exp {\left(-{\frac {h\nu }{kT}}\right)}} where n upper {\displaystyle n_{\text{upper}}} is the number of paramagnetic centers occupying the upper energy state, k {\displaystyle k} is the Boltzmann constant, and T {\displaystyle T} is the thermodynamic temperature. At 298 K, X-band microwave frequencies ( ν {\displaystyle \nu } ≈ 9.75 GHz) give n upper / n lower {\displaystyle n_{\text{upper}}/n_{\text{lower}}} ≈ 0.998, meaning that the upper energy level has a slightly smaller population than the lower one. Therefore, transitions from the lower to the higher level are more probable than the reverse, which is why there is a net absorption of energy. The sensitivity of the EPR method (i.e., the minimal number of detectable spins N min {\displaystyle N_{\text{min}}} ) depends on the photon frequency ν {\displaystyle \nu } according to N min = k 1 V Q 0 k f ν 2 P 1 / 2 , (Eq. 2) {\displaystyle N_{\text{min}}={\frac {k_{1}V}{Q_{0}k_{f}\nu ^{2}P^{1/2}}},\qquad {\text{(Eq. 2)}}} where k 1 {\displaystyle k_{1}} is a constant, V {\displaystyle V} is the sample's volume, Q 0 {\displaystyle Q_{0}} is the unloaded quality factor of the microwave cavity (sample chamber), k f {\displaystyle k_{f}} is the cavity filling coefficient, and P {\displaystyle P} is the microwave power in the spectrometer cavity. With k f {\displaystyle k_{f}} and P {\displaystyle P} being constants, N min {\displaystyle N_{\text{min}}} ~ ( Q 0 ν 2 ) − 1 {\displaystyle (Q_{0}\nu ^{2})^{-1}} , i.e., N min {\displaystyle N_{\text{min}}} ~ ν − α {\displaystyle \nu ^{-\alpha }} , where α {\displaystyle \alpha } ≈ 1.5. In practice, α {\displaystyle \alpha } can change varying from 0.5 to 4.5 depending on spectrometer characteristics, resonance conditions, and sample size. A great sensitivity is therefore obtained with a low detection limit N min {\displaystyle N_{\text{min}}} and a large number of spins. Therefore, the required parameters are: A high spectrometer frequency to minimize the Eq. 2. Common frequencies are discussed below A low temperature to decrease the number of spin at the high level of energy as shown in Eq. 1. This condition explains why spectra are often recorded on sample at the boiling point of liquid nitrogen or liquid helium. == Spectral parameters == In real systems, electrons are normally not solitary, but are associated with one or more atoms. There are several important consequences of this: An unpaired electron can gain or lose angular momentum, which can change the value of its g-factor, causing it to differ from g e {\displaystyle g_{e}} . This is especially significant for chemical systems with transition-metal ions. Systems with multiple unpaired electrons experience electron–electron interactions that give rise to "fine" structure. This is realized as zero field splitting and exchange coupling, and can be large in magnitude. The magnetic moment of a nucleus with a non-zero nuclear spin will affect any unpaired electrons associated with that atom. This leads to the phenomenon of hyperfine coupling, analogous to J-coupling in NMR, splitting the EPR resonance signal into doublets, triplets and so forth. Additional smaller splittings from nearby nuclei is sometimes termed "superhyperfine" coupling. Interactions of an unpaired electron with its environment influence the shape of an EPR spectral line. Line shapes can yield information about, for example, rates of chemical reactions. These effects (g-factor, hyperfine coupling, zero field splitting, exchange coupling) in an atom or molecule may not be the same for all orientations of an unpaired electron in an external magnetic field. This anisotropy depends upon the electronic structure of the atom or molecule (e.g., free radical) in question, and so can provide information about the atomic or molecular orbital containing the unpaired electron. === The g factor === Knowledge of the g-factor can give information about a paramagnetic center's electronic structure. An unpaired electron responds not only to a spectrometer's applied magnetic field B 0 {\displaystyle B_{0}} but also to any local magnetic fields of atoms or molecules. The effective field B eff {\displaystyle B_{\text{eff}}} experienced by an electron is thus written B eff = B 0 ( 1 − σ ) , {\displaystyle B_{\text{eff}}=B_{0}(1-\sigma ),} where σ {\displaystyle \sigma } includes the effects of local fields ( σ {\displaystyle \sigma } can be positive or negative). Therefore, the h ν = g e μ B B eff {\displaystyle h\nu =g_{e}\mu _{\text{B}}B_{\text{eff}}} resonance condition (above) is rewritten as follows: h ν = g e μ B B eff = g e μ B B 0 ( 1 − σ ) . {\displaystyle h\nu =g_{e}\mu _{B}B_{\text{eff}}=g_{e}\mu _{\text{B}}B_{0}(1-\sigma ).} The quantity g e ( 1 − σ ) {\displaystyle g_{e}(1-\sigma )} is denoted g {\displaystyle g} and called simply the g-factor, so that the final resonance equation becomes h ν = g μ B B 0 . {\displaystyle h\nu =g\mu _{\text{B}}B_{0}.} This last equation is used to determine g {\displaystyle g} in an EPR experiment by measuring the field and the frequency at which resonance occurs. If g {\displaystyle g} does not equal g e {\displaystyle g_{e}} , the implication is that the ratio of the unpaired electron's spin magnetic moment to its angular momentum differs from the free-electron value. Since an electron's spin magnetic moment is constant (approximately the Bohr magneton), then the electron must have gained or lost angular momentum through spin–orbit coupling. Because the mechanisms of spin–orbit coupling are well understood, the magnitude of the change gives information about the nature of the atomic or molecular orbital containing the unpaired electron. In general, the g factor is not a number but a 3×3 matrix. The principal axes of this tensor are determined by the local fields, for example, by the local atomic arrangement around the unpaired spin in a solid or in a molecule. Choosing an appropriate coordinate system (say, x,y,z) allows one to "diagonalize" this tensor, thereby reducing the maximal number of its components from 9 to 3: gxx, gyy and gzz. For a single spin experiencing only Zeeman interaction with an external magnetic field, the position of the EPR resonance is given by the expression gxxBx + gyyBy + gzzBz. Here Bx, By and Bz are the components of the magnetic field vector in the coordinate system (x,y,z); their magnitudes change as the field is rotated, so does the frequency of the resonance. For a large ensemble of randomly oriented spins (as in a fluid solution), the EPR spectrum consists of three peaks of characteristic shape at frequencies gxxB0, gyyB0 and gzzB0. In first-derivative spectrum, the low-frequency peak is positive, the high-frequency peak is negative, and the central peak is bipolar. Such situations are commonly observed in powders, and the spectra are therefore called "powder-pattern spectra". In crystals, the number of EPR lines is determined by the number of crystallographically equivalent orientations of the EPR spin (called "EPR center"). At higher temperatures, the three peaks coalesce to a singlet, corresponding to giso, for isotropic. The relationship between giso and the components is: ( g i s o ) 2 = ( g x x ) 2 + ( g y y ) 2 + ( g z z ) 2 {\displaystyle (g_{\mathrm {iso} })^{2}=(g_{xx})^{2}+(g_{yy})^{2}+(g_{zz})^{2}} One elementary step in analyzing an EPR spectrum is to compare giso with the g-factor for the free electron, ge. Metal-based radicals giso is typically well above ge whereas organic radicals, giso ~ ge. The determination of the absolute value of the g factor is challenging due to the lack of a precise estimate of the local magnetic field at the sample location. Therefore, typically so-called g factor standards are measured together with the sample of interest. In the common spectrum, the spectral line of the g factor standard is then used as a reference point to determine the g factor of the sample. For the initial calibration of g factor standards, Herb et al. introduced a precise procedure by using double resonance techniques based on the Overhauser shift. === Hyperfine coupling === Since the source of an EPR spectrum is a change in an electron's spin state, the EPR spectrum for a radical (S = 1/2 system) would consist of one line. Greater complexity arises because the spin couples with nearby nuclear spins. The magnitude of the coupling is proportional to the magnetic moment of the coupled nuclei and depends on the mechanism of the coupling. Coupling is mediated by two processes, dipolar (through space) and isotropic (through bond). This coupling introduces additional energy states and, in turn, multi-lined spectra. In such cases, the spacing between the EPR spectral lines indicates the degree of interaction between the unpaired electron and the perturbing nuclei. The hyperfine coupling constant of a nucleus is directly related to the spectral line spacing and, in the simplest cases, is essentially the spacing itself.Two common mechanisms by which electrons and nuclei interact are the Fermi contact interaction and by dipolar interaction. The former applies largely to the case of isotropic interactions (independent of sample orientation in a magnetic field) and the latter to the case of anisotropic interactions (spectra dependent on sample orientation in a magnetic field). Spin polarization is a third mechanism for interactions between an unpaired electron and a nuclear spin, being especially important for π {\displaystyle \pi } -electron organic radicals, such as the benzene radical anion. The symbols "a" or "A" are used for isotropic hyperfine coupling constants, while "B" is usually employed for anisotropic hyperfine coupling constants.In many cases, the isotropic hyperfine splitting pattern for a radical freely tumbling in a solution (isotropic system) can be predicted. ==== Multiplicity ==== For a radical having M equivalent nuclei, each with a spin of I, the number of EPR lines expected is 2MI + 1. As an example, the methyl radical, CH3, has three 1H nuclei, each with I = 1/2, and so the number of lines expected is 2MI + 1 = 2(3)(1/2) + 1 = 4, which is as observed. For a radical having M1 equivalent nuclei, each with a spin of I1, and a group of M2 equivalent nuclei, each with a spin of I2, the number of lines expected is (2M1I1 + 1) (2M2I2 + 1). As an example, the methoxymethyl radical, H2C(OCH3) has two equivalent 1H nuclei, each with I = 1/2 and three equivalent 1H nuclei each with I = 1/2, and so the number of lines expected is (2M1I1 + 1) (2M2I2 + 1) = [2(2)(1/2) + 1] [2(3)(1/2) + 1] = 3×4 = 12, again as observed. The above can be extended to predict the number of lines for any number of nuclei.While it is easy to predict the number of lines, the reverse problem, unraveling a complex multi-line EPR spectrum and assigning the various spacings to specific nuclei, is more difficult. In the often encountered case of I = 1/2 nuclei (e.g., 1H, 19F, 31P), the line intensities produced by a population of radicals, each possessing M equivalent nuclei, will follow Pascal's triangle. For example, the spectrum at the right shows that the three 1H nuclei of the CH3 radical give rise to 2MI + 1 = 2(3)(1/2) + 1 = 4 lines with a 1:3:3:1 ratio. The line spacing gives a hyperfine coupling constant of aH = 23 G for each of the three 1H nuclei. Note again that the lines in this spectrum are first derivatives of absorptions. As a second example, the methoxymethyl radical, H3COCH2. the OCH2 center will give an overall 1:2:1 EPR pattern, each component of which is further split by the three methoxy hydrogens into a 1:3:3:1 pattern to give a total of 3×4 = 12 lines, a triplet of quartets. A simulation of the observed EPR spectrum is shown and agrees with the 12-line prediction and the expected line intensities. Note that the smaller coupling constant (smaller line spacing) is due to the three methoxy hydrogens, while the larger coupling constant (line spacing) is from the two hydrogens bonded directly to the carbon atom bearing the unpaired electron. It is often the case that coupling constants decrease in size with distance from a radical's unpaired electron, but there are some notable exceptions, such as the ethyl radical (CH2CH3). === Resonance linewidth definition === Resonance linewidths are defined in terms of the magnetic induction B and its corresponding units, and are measured along the x axis of an EPR spectrum, from a line's center to a chosen reference point of the line. These defined widths are called halfwidths and possess some advantages: for asymmetric lines, values of left and right halfwidth can be given. The halfwidth Δ B h {\displaystyle \Delta B_{h}} is the distance measured from the line's center to the point in which absorption value has half of maximal absorption value in the center of resonance line. First inclination width Δ B 1 / 2 {\displaystyle \Delta B_{1/2}} is a distance from center of the line to the point of maximal absorption curve inclination. In practice, a full definition of linewidth is used. For symmetric lines, halfwidth Δ B 1 / 2 = 2 Δ B h {\displaystyle \Delta B_{1/2}=2\Delta B_{h}} , and full inclination width Δ B max = 2 Δ B 1 s {\displaystyle \Delta B_{\text{max}}=2\Delta B_{1s}} . == Applications == EPR/ESR spectroscopy is used in various branches of science, such as biology, chemistry and physics, for the detection and identification of free radicals in the solid, liquid, or gaseous state, and in paramagnetic centers such as F-centers. === Chemical reactions === EPR is a sensitive, specific method for studying both radicals formed in chemical reactions and the reactions themselves. For example, when ice (solid H2O) is decomposed by exposure to high-energy radiation, radicals such as H, OH, and HO2 are produced. Such radicals can be identified and studied by EPR. Organic and inorganic radicals can be detected in electrochemical systems and in materials exposed to UV light. In many cases, the reactions to make the radicals and the subsequent reactions of the radicals are of interest, while in other cases EPR is used to provide information on a radical's geometry and the orbital of the unpaired electron. EPR is useful in homogeneous catalysis research for characterization of paramagnetic complexes and reactive intermediates. EPR spectroscopy is a particularly useful tool to investigate their electronic structures, which is fundamental to understand their reactivity. EPR/ESR spectroscopy can be applied only to systems in which the balance between radical decay and radical formation keeps the free radicals concentration above the detection limit of the spectrometer used. This can be a particularly severe problem in studying reactions in liquids. An alternative approach is to slow down reactions by studying samples held at cryogenic temperatures, such as 77 K (liquid nitrogen) or 4.2 K (liquid helium). An example of this work is the study of radical reactions in single crystals of amino acids exposed to x-rays, work that sometimes leads to activation energies and rate constants for radical reactions. === Medical and biological === Medical and biological applications of EPR also exist. Although radicals are very reactive, so they do not normally occur in high concentrations in biology, special reagents have been developed to attach "spin labels", also called "spin probes", to molecules of interest. Specially-designed nonreactive radical molecules can attach to specific sites in a biological cell, and EPR spectra then give information on the environment of the spin labels. Spin-labeled fatty acids have been extensively used to study dynamic organisation of lipids in biological membranes, lipid-protein interactions and temperature of transition of gel to liquid crystalline phases. Injection of spin-labeled molecules allows for electron resonance imaging of living organisms. A type of dosimetry system has been designed for reference standards and routine use in medicine, based on EPR signals of radicals from irradiated polycrystalline α-alanine (the alanine deamination radical, the hydrogen abstraction radical, and the (CO−(OH))=C(CH3)NH+2 radical). This method is suitable for measuring gamma and X-rays, electrons, protons, and high-linear energy transfer (LET) radiation of doses in the 1 Gy to 100 kGy range.EPR can be used to measure microviscosity and micropolarity within drug delivery systems as well as the characterization of colloidal drug carriers.The study of radiation-induced free radicals in biological substances (for cancer research) poses the additional problem that tissue contains water, and water (due to its electric dipole moment) has a strong absorption band in the microwave region used in EPR spectrometers. === Material characterization === EPR/ESR spectroscopy is used in geology and archaeology as a dating tool. It can be applied to a wide range of materials such as organic shales, carbonates, sulfates, phosphates, silica or other silicates. When applied to shales, the EPR data correlates to the maturity of the kerogen in the shale.EPR spectroscopy has been used to measure properties of crude oil, such as determination of asphaltene and vanadium content. The free-radical component of the EPR signal is proportional to the amount of asphaltene in the oil regardless of any solvents, or precipitants that may be present in that oil. When the oil is subject to a precipitant such as hexane, heptane, pyridine however, then much of the asphaltene can be subsequently extracted from the oil by gravimetric techniques. The EPR measurement of that extract will then be function of the polarity of the precipitant that was used. Consequently, it is preferable to apply the EPR measurement directly to the crude. In the case that the measurement is made upstream of a separator (oil production), then it may also be necessary determine the oil fraction within the crude (e.g., if a certain crude contains 80% oil and 20% water, then the EPR signature will be 80% of the signature of downstream of the separator). EPR has been used by archaeologists for the dating of teeth. Radiation damage over long periods of time creates free radicals in tooth enamel, which can then be examined by EPR and, after proper calibration, dated. Similarly, material extracted from the teeth of people during dental procedures can be used to quantify their cumulative exposure to ionizing radiation. People (and other mammals) exposed to radiation from the atomic bombs, from the Chernobyl disaster, and from the Fukushima accident have been examined by this method.Radiation-sterilized foods have been examined with EPR spectroscopy, aiming to develop methods to determine whether a food sample has been irradiated and to what dose. === Other applications === In the field of quantum computing, pulsed EPR is used to control the state of electron spin qubits in materials such as diamond, silicon and gallium arsenide. == High-field high-frequency measurements == High-field high-frequency EPR measurements are sometimes needed to detect subtle spectroscopic details. However, for many years the use of electromagnets to produce the needed fields above 1.5 T was impossible, due principally to limitations of traditional magnet materials. The first multifunctional millimeter EPR spectrometer with a superconducting solenoid was described in the early 1970s by Prof. Y. S. Lebedev's group (Russian Institute of Chemical Physics, Moscow) in collaboration with L. G. Oranski's group (Ukrainian Physics and Technics Institute, Donetsk), which began working in the Institute of Problems of Chemical Physics, Chernogolovka around 1975. Two decades later, a W-band EPR spectrometer was produced as a small commercial line by the German Bruker Company, initiating the expansion of W-band EPR techniques into medium-sized academic laboratories. The EPR waveband is stipulated by the frequency or wavelength of a spectrometer's microwave source (see Table). EPR experiments often are conducted at X and, less commonly, Q bands, mainly due to the ready availability of the necessary microwave components (which originally were developed for radar applications). A second reason for widespread X and Q band measurements is that electromagnets can reliably generate fields up to about 1 tesla. However, the low spectral resolution over g-factor at these wavebands limits the study of paramagnetic centers with comparatively low anisotropic magnetic parameters. Measurements at ν {\displaystyle \nu } > 40 GHz, in the millimeter wavelength region, offer the following advantages: EPR spectra are simplified due to the reduction of second-order effects at high fields. Increase in orientation selectivity and sensitivity in the investigation of disordered systems. The informativity and precision of pulse methods, e.g., ENDOR also increase at high magnetic fields. Accessibility of spin systems with larger zero-field splitting due to the larger microwave quantum energy h ν {\displaystyle \nu } . The higher spectral resolution over g-factor, which increases with irradiation frequency ν {\displaystyle \nu } and external magnetic field B0. This is used to investigate the structure, polarity, and dynamics of radical microenvironments in spin-modified organic and biological systems through the spin label and probe method. The figure shows how spectral resolution improves with increasing frequency. Saturation of paramagnetic centers occurs at a comparatively low microwave polarizing field B1, due to the exponential dependence of the number of excited spins on the radiation frequency ν {\displaystyle \nu } . This effect can be successfully used to study the relaxation and dynamics of paramagnetic centers as well as of superslow motion in the systems under study. The cross-relaxation of paramagnetic centers decreases dramatically at high magnetic fields, making it easier to obtain more-precise and more-complete information about the system under study.This was demonstrated experimentally in the study of various biological, polymeric and model systems at D-band EPR. == Hardware components == === Microwave bridge === The microwave bridge contains both the microwave source and the detector. Older spectrometers used a vacuum tube called a klystron to generate microwaves, but modern spectrometers use a Gunn diode. Immediately after the microwave source there is an isolator which serves to attenuate any reflections back to the source which would result in fluctuations in the microwave frequency. The microwave power from the source is then passed through a directional coupler which splits the microwave power into two paths, one directed towards the cavity and the other the reference arm. Along both paths there is a variable attenuator that facilitates the precise control of the flow of microwave power. This in turn allows for accurate control over the intensity of the microwaves subjected to the sample. On the reference arm, after the variable attenuator there is a phase shifter that sets a defined phase relationship between the reference and reflected signal which permits phase sensitive detection. Most EPR spectrometers are reflection spectrometers, meaning that the detector should only be exposed to microwave radiation coming back from the cavity. This is achieved by the use of a device known as the circulator which directs the microwave radiation (from the branch that is heading towards the cavity) into the cavity. Reflected microwave radiation (after absorption by the sample) is then passed through the circulator towards the detector, ensuring it does not go back to the microwave source. The reference signal and reflected signal are combined and passed to the detector diode which converts the microwave power into an electrical current. ==== Reference arm ==== At low energies (less than 1 μW) the diode current is proportional to the microwave power and the detector is referred to as a square-law detector. At higher power levels (greater than 1 mW) the diode current is proportional to the square root of the microwave power and the detector is called a linear detector. In order to obtain optimal sensitivity as well as quantitative information the diode should be operating within the linear region. To ensure the detector is operating at that level the reference arm serves to provide a "bias". === Magnet === In an EPR spectrometer the magnetic assembly includes the magnet with a dedicated power supply as well as a field sensor or regulator such as a Hall probe. EPR spectrometers use one of two types of magnet which is determined by the operating microwave frequency (which determine the range of magnetic field strengths required). The first is an electromagnet which are generally capable of generating field strengths of up to 1.5 T making them suitable for measurements using the Q-band frequency. In order to generate field strengths appropriate for W-band and higher frequency operation superconducting magnets are employed. The magnetic field is homogeneous across the sample volume and has a high stability at static field. === Microwave resonator (cavity) === The microwave resonator is designed to enhance the microwave magnetic field at the sample in order to induce EPR transitions. It is a metal box with a rectangular or cylindrical shape that resonates with microwaves (like an organ pipe with sound waves). At the resonance frequency of the cavity microwaves remain inside the cavity and are not reflected back. Resonance means the cavity stores microwave energy and its ability to do this is given by the quality factor Q, defined by the following equation: Q = 2 π ( energy stored ) ( energy dissipated ) {\displaystyle Q={\frac {2\pi ({\text{energy stored}})}{({\text{energy dissipated}})}}} The higher the value of Q the higher the sensitivity of the spectrometer. The energy dissipated is the energy lost in one microwave period. Energy may be lost to the side walls of the cavity as microwaves may generate currents which in turn generate heat. A consequence of resonance is the creation of a standing wave inside the cavity. Electromagnetic standing waves have their electric and magnetic field components exactly out of phase. This provides an advantage as the electric field provides non-resonant absorption of the microwaves, which in turn increases the dissipated energy and reduces Q. To achieve the largest signals and hence sensitivity the sample is positioned such that it lies within the magnetic field maximum and the electric field minimum. When the magnetic field strength is such that an absorption event occurs, the value of Q will be reduced due to the extra energy loss. This results in a change of impedance which serves to stop the cavity from being critically coupled. This means microwaves will now be reflected back to the detector (in the microwave bridge) where an EPR signal is detected. == Pulsed electron paramagnetic resonance == The dynamics of electron spins are best studied with pulsed measurements. Microwave pulses typically 10–100 ns long are used to control the spins in the Bloch sphere. The spin–lattice relaxation time can be measured with an inversion recovery experiment. As with pulsed NMR, the Hahn echo is central to many pulsed EPR experiments. A Hahn echo decay experiment can be used to measure the dephasing time, as shown in the animation below. The size of the echo is recorded for different spacings of the two pulses. This reveals the decoherence, which is not refocused by the π {\displaystyle \pi } pulse. In simple cases, an exponential decay is measured, which is described by the T 2 {\displaystyle T_{2}} time. Pulsed electron paramagnetic resonance could be advanced into electron nuclear double resonance spectroscopy (ENDOR), which utilizes waves in the radio frequencies. Since different nuclei with unpaired electrons respond to different wavelengths, radio frequencies are required at times. Since the results of the ENDOR gives the coupling resonance between the nuclei and the unpaired electron, the relationship between them can be determined. == See also == == References == == External links == Electron Magnetic Resonance Program National High Magnetic Field Laboratory Electron Paramagnetic Resonance (Specialist Periodical Reports) Published by the Royal Society of Chemistry Using ESR to measure free radicals in used engine oil

Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the spins excited are those of the electrons instead of the atomic nuclei. EPR spectroscopy is particularly useful for studying metal complexes and organic radicals. EPR was first observed in Kazan State University by Soviet physicist Yevgeny Zavoisky in 1944, and was developed independently at the same time by Brebis Bleaney at the University of Oxford.

Electron paramagnetic resonance

== Detailed description == Cavity ring-down spectroscopy is a form of laser absorption spectroscopy. In CRDS, a laser pulse is trapped in a highly reflective (typically R > 99.9%) detection cavity. The intensity of the trapped pulse will decrease by a fixed percentage during each round trip within the cell due to absorption, scattering by the medium within the cell, and reflectivity losses. The intensity of light within the cavity is then determined as an exponential function of time. I ( t ) = I 0 exp ⁡ ( − t / τ ) {\displaystyle I(t)=I_{0}\exp \left(-t/\tau \right)} The principle of operation is based on the measurement of a decay rate rather than an absolute absorbance. This is one reason for the increased sensitivity over traditional absorption spectroscopy, as the technique is then immune to shot-to-shot laser fluctuations. The decay constant, τ, which is the time taken for the intensity of light to fall to 1/e of the initial intensity, is called the ring-down time and is dependent on the loss mechanism(s) within the cavity. For an empty cavity, the decay constant is dependent on mirror loss and various optical phenomena like scattering and refraction: τ 0 = n c ⋅ l 1 − R + X {\displaystyle \tau _{0}={\frac {n}{c}}\cdot {\frac {l}{1-R+X}}} where n is the index of refraction within the cavity, c is the speed of light in vacuum, l is the cavity length, R is the mirror reflectivity, and X takes into account other miscellaneous optical losses. This equation uses the approximation that ln(1+x) ≈ x for x close to zero, which is the case under cavity ring-down conditions. Often, the miscellaneous losses are factored into an effective mirror loss for simplicity. An absorbing species in the cavity will increase losses according to the Beer-Lambert law. Assuming the sample fills the entire cavity, τ = n c ⋅ l 1 − R + X + α l {\displaystyle \tau ={\frac {n}{c}}\cdot {\frac {l}{1-R+X+\alpha l}}} where α is the absorption coefficient for a specific analyte concentration at the cavity's resonance wavelength. The decadic absorbance, A, due to the analyte can be determined from both ring-down times. A = n c ⋅ l 2.303 ⋅ ( 1 τ − 1 τ 0 ) {\displaystyle A={\frac {n}{c}}\cdot {\frac {l}{2.303}}\cdot \left({\frac {1}{\tau }}-{\frac {1}{\tau _{0}}}\right)} Alternatively, the molar absorptivity, ε, and analyte concentration, C, can be determined from the ratio of both ring-down times. If X can be neglected, one obtains τ 0 τ = 1 + α l 1 − R = 1 + 2.303 ϵ l C ( 1 − R ) {\displaystyle {\frac {\tau _{0}}{\tau }}=1+{\frac {\alpha l}{1-R}}=1+{\frac {2.303\epsilon lC}{(1-R)}}} When a ratio of species' concentrations is the analytical objective, as for example in carbon-13 to carbon-12 measurements in carbon dioxide, the ratio of ring-down times measured for the same sample at the relevant absorption frequencies can be used directly with extreme accuracy and precision. == Advantages of CRDS == There are two main advantages to CRDS over other absorption methods: First, it is not affected by fluctuations in the laser intensity. In most absorption measurements, the light source must be assumed to remain steady between blank (no analyte), standard (known amount of analyte), and sample (unknown amount of analyte). Any drift (change in the light source) between measurements will introduce errors. In CRDS, the ringdown time does not depend on the intensity of the laser, so fluctuations of this type are not a problem. Independency from laser intensity makes CRDS needless to any calibration and comparison with standards.Second, it is very sensitive due to its long pathlength. In absorption measurements, the smallest amount that can be detected is proportional to the length that the light travels through a sample. Since the light reflects many times between the mirrors, it ends up traveling long distances. For example, a laser pulse making 500 round trips through a 1-meter cavity will effectively have traveled through 1 kilometer of sample. Thus, the advantages include: High sensitivity due to the multipass nature (i.e. long pathlength) of the detection cell. Immunity to shot variations in laser intensity due to the measurement of a rate constant. Wide range of use for a given set of mirrors; typically, ±5% of the center wavelength. High throughput, individual ring down events occur on the millisecond time scale. No need for a fluorophore, which makes it more attractive than laser-induced fluorescence (LIF) or resonance-enhanced multiphoton ionization (REMPI) for some (e.g. rapidly predissociating) systems. Commercial systems available. == Disadvantages of CRDS == Spectra cannot be acquired quickly due to the monochromatic laser source which is used. Having said this, some groups are now beginning to develop the use of broadband LED or supercontinuum sources for CRDS, the light of which can then be dispersed by a grating onto a CCD, or Fourier transformed spectrometer (mainly in broadband analogues of CRDS). Perhaps more importantly, the development of CRDS based techniques have now been demonstrated over the range from the near UV to the mid-infrared. In addition, the frequency-agile rapid scanning (FARS) CRDS technique has been developed to overcome the mechanical or thermal frequency tuning which typically limits CRDS acquisition rates. The FARS method utilizes an electro-optic modulator to step a probe laser side band to successive cavity modes, eliminating tuning time between data points and allowing for acquisition rates about 2 orders of magnitude faster than traditional thermal tuning. Analytes are limited both by the availability of tunable laser light at the appropriate wavelength and also the availability of high reflectance mirrors at those wavelengths. Expense: the requirement for laser systems and high reflectivity mirrors often makes CRDS orders of magnitude more expensive than some alternative spectroscopic techniques. == See also == Absorption spectroscopy Laser absorption spectrometry Noise-Immune Cavity-Enhanced Optical-Heterodyne Molecular Spectroscopy (NICE-OHMS) Tunable Diode Laser Absorption Spectroscopy (TDLAS) == References == Anthony O'Keefe; David A.G. Deacon (1988). "Cavity ring-down Optical Spectrometer for absorption measurements using pulsed laser sources". Review of Scientific Instruments. 59 (12): 2544. Bibcode:1988RScI...59.2544O. doi:10.1063/1.1139895. S2CID 6033311. Piotr Zalicki; Richard N. Zare (15 February 1995). "Cavity ring-down spectroscopy for quantitative absorption measurements". The Journal of Chemical Physics. 102 (7): 2708–2717. Bibcode:1995JChPh.102.2708Z. doi:10.1063/1.468647. Giel Berden; Rudy Peeters; Gerard Meijer (2000). "Cavity ring-down spectroscopy: Experimental schemes and applications". International Reviews in Physical Chemistry. 19 (4): 565–607. Bibcode:2000IRPC...19..565B. doi:10.1080/014423500750040627. S2CID 98510055.

Cavity ring-down spectroscopy (CRDS) is a highly sensitive optical spectroscopic technique that enables measurement of absolute optical extinction by samples that scatter and absorb light. It has been widely used to study gaseous samples which absorb light at specific wavelengths, and in turn to determine mole fractions down to the parts per trillion level. The technique is also known as cavity ring-down laser absorption spectroscopy (CRLAS). A typical CRDS setup consists of a laser that is used to illuminate a high-finesse optical cavity, which in its simplest form consists of two highly reflective mirrors. When the laser is in resonance with a cavity mode, intensity builds up in the cavity due to constructive interference. The laser is then turned off in order to allow the measurement of the exponentially decaying light intensity leaking from the cavity. During this decay, light is reflected back and forth thousands of times between the mirrors giving an effective path length for the extinction on the order of a few kilometers. If a light-absorbing material is now placed in the cavity, the mean lifetime decreases as fewer bounces through the medium are required before the light is fully absorbed, or absorbed to some fraction of its initial intensity. A CRDS setup measures how long it takes for the light to decay to 1/e of its initial intensity, and this "ringdown time" can be used to calculate the concentration of the absorbing substance in the gas mixture in the cavity.

Cavity ring-down spectroscopy

== See also == Chemical structure == References ==

Structural chemistry is a part of chemistry and deals with spatial structures of molecules (in the gaseous, liquid or solid state) and solids (with extended structures that cannot be subdivided into molecules).The main tasks are: The formulation of general laws for structure-property relationships; and The derivation of general rules on how the chemical and physical properties of the constituents of matter determine the resulting structures (e.g. the relationship between the electron configuration of the crystal building blocks and the symmetry of the resulting crystal lattice).For structure elucidation a range of different methods are used. One has to distinguish between methods that elucidate solely the connectivity between atoms (constitution) and such that provide precise three dimensional information such as atom coordinates, bond lengths and angles and torsional angles. The latter methods include (mainly): for the gaseous state: gas electron diffraction and microwave spectroscopy for the liquid state: NMR spectroscopy (note, obtaining precise structural information from liquids and solutions is still rather difficult compared to gases and crystalline solids) for the solid state: X-ray, electron and neutron diffractionTo identify connectivity and the presence of functional groups a variety of methods of molecular spectroscopy and solid state spectroscopy can be used.

Structural chemistry

== History == In 1964, the Kerala Government announced the need to start more junior colleges in the state. In response, Bishop Rt. Rev. M.M. John of the CSI Madhya Kerala Diocese made the decision to establish the college, renaming it in honor of the late Edward Moore, the fourth Anglican Bishop of Travancore and Cochin of the Church Missionary Society. In 1964, the college began operations as a Junior College offering a two-year-long Pre-Degree course for the University of Kerala. The founding Principal was Rev. K C Mathew. In 1968, the University of Kerala sanctioned the provision of undergraduate courses. The first postgraduate course started in 1982. After the de-linking of Pre-Degree courses from the university education system in 2000, the college now offers ten undergraduate and three postgraduate programs. Post-graduate classes started in the Department of Physics in 1983. The center for Nonlinear studies started in 2000. The University of Kerala approved the Department of Physics as a research department in 2013. == Courses == Degree Courses B.A English Language and Literature B.A Malayalam B.A Economics B.Sc Mathematics B.Sc Physics B.Sc Chemistry B.Sc Zoology B.Sc Biotechnology Bachelor of Commerce (B.Com.Finance and B.Com.Computer Application )Post Graduate Courses M.Sc Physics M.Sc Analytical Chemistry M.A English M.A Economics M.Sc Botany M.A Behavioural Economics and Data Science (New Generation Course)Research Departments 1. Department of Physics Theoretical Physics- Nonlinear dynamics, Quantum Computations, Nanomaterials, Spectroscopy, Research Guides Dr. Thomas Kuruvilla, Dr. D Sajan 2. Department of Chemistry Spectroscopy == Notable alumni == Saji Cheriyan, Former Minister of Fisheries, Culture and Kerala State Film Development Corporation Justice CT.Ravikumar , Judge, Supreme Court of India M. S. Arun Kumar, MLA Pramod Narayanan, MLA M Murali, ex-MLA Dr. Valson Thampu, an academic and a social thinker of national repute. Former principal, St. Stephen's College, New Delhi. Adv. B Babu Prasad, ex-MLA B. Aburaj, Director, State Institute of Educational Technology, Kerala and Gen. Secretary, Indian Philosophical Society. == Notable conferences and seminars == === Refresher course in theoretical physics === Bishop Moore College on 07 – 19 December 2009 Sponsored by the Indian Academy of Sciences, Coordinator Dr. Thomas Kuruvilla, Department of Physics. Dr. Thomas Kuruvilla was the Principal of Bishop Moore College from 2012 to 2014. During his tenure, the Department of Physics was upgraded as a Research Department. === Molecular Spectroscopy of Advanced Materials and Biomolecules === IMSAB 2012 from 7 to 9 August 2012 International Conference in the Department of Physics Organised by Dr. D Sajan === National seminar-Inclusive Growth and Indian Economy - 20 Years of Liberation === A national seminar with the financial help of UGC was conducted in the Economics Department. The topic was on Inclusive Growth and Indian Economy - 20 Years of Liberation. Kerala planning board member Sri C. P. John inaugurated the function. Eminent scholars and academicians from various parts of India have participated. === International Conference on Marxism === Organised by post-graduation Department of English in 2019 == Principals and achievements == Rev. K.C. Mathew was the founding principal of Bishop Moore College. He served the college from 1964 to 1989. During this period, he played an important role in college's offering of postgraduate studies. Below is a list of principals that succeeded him after his retirement. Prof. M.K. Cherian (8 years) Prof. Mammen Varkey Varkey (5 years) Prof. Victor Sam (4 years) Prof. Koshy Ninan (4 years) Prof. Matthew Koshy (2 years) Prof. Kurien Thomas (1 year) Dr. Thomas Kuruvilla Dr. Leelamma George Dr. Sabu GeorgeDr. Thomas Kuruvilla was the principal of Bishop Moore College from 2012 to 2014. During his tenure, the college received four first ranks for degree examinations and one second rank for the PG examination of the University of Kerala, as well as conducting two international seminars in Physics. All departments conducted national seminars. The college won many prizes in sports, games, and university youth festivals. Bishop Moore hosted the University Youth festival. The college auditorium was renovated and made echo-proof. A grant was received for the basketball and volleyball courts, as well as one for a generator. The college was granted ten million rupees by UGC-FIST. Five new classrooms and prayer centers were built. The M.Sc. Course in Botany and B.Com. was equipped with a computer and applications began. Bishop Moore had the best results in the University Examinations of 2013 and 2014. The college girl's hostel was renovated. Golden Jubilee celebrations were inaugurated by the Honorable Governor of Kerala in a grand function.The current principal is Dr. Jacob Chandy from the Department of Zoology. He is an alumnus of Bishop Moore College. == References == == External links == Kerala University

Bishop Moore College is an aided college in Mavelikkara, Alappuzha, Kerala, India, affiliated with the University of Kerala. The college is ranked 58 in NIRF 2022, 89 in NIRF 2021, 76 in NIRF 2020, in the rank band 101–150 in NIRF (National Institutional Ranking Framework) 2019, and ranked 92 in NIRF 2018. The college was accredited by NAAC with an "A" Grade in 2017 (Third Cycle of Accreditation). The college is managed by the Madhya Kerala Diocese of the Church of South India, and offers 11 undergraduate programs, five postgraduate programs, and two research programs. It is located at Kallumala, Mavelikara. The current principal of the college is Dr. Jacob Chandy.

Bishop Moore College

== Early life and family == Herzberg was born in Hamburg, Germany on December 25, 1904 to Albin H. Herzberg and Ella Biber. He had an older brother, Walter, who was born in January 1904. Herzberg started Vorschule (pre-school) late, after contracting measles. Gerhard and his family were atheists and kept this fact hidden. His father died in 1914, at 43 years of age, after having suffered from dropsy and complications due to an earlier heart condition. Herzberg graduated Vorschule shortly after his father's death. He married Luise Oettinger, a spectroscopist and fellow researcher in 1929. (Luise Herzberg, died in 1971.) == Nazi Persecution and Immigration to Canada == In 1933, the Nazi Party introduced a law banning men with Jewish wives from teaching at universities. Herzberg was working as a lecturer at the university in Darmstadt. His wife and fellow researcher, Luise Herzberg, was Jewish so they began making plans to leave Germany near the end of 1933. Leaving Germany was a daunting task as many barriers faced the thousands of Germans trying to flee Nazi persecution. However Herzberg had earlier worked with a visiting physical chemist named John Spinks, from the University of Saskatchewan. Spinks helped Herzberg get a job at the university in Saskatoon. When Herzberg and his wife left Germany in 1935, the Nazis let them take only the equivalent of $2.50 each and personal belongings. == Education and career == Initially, Herzberg considered a career in astronomy, but his application to the Hamburg Observatory was returned advising him not to pursue a career in the field without private financial support. After completing high school at the Gelehrtenschule des Johanneums, Herzberg continued his education at Darmstadt University of Technology with the help of a private scholarship. Herzberg completed his Dr.-Ing. degree under Hans Rau in 1928. 1928–30 Post-doctoral work at the University of Göttingen and Bristol University under James Franck, Max Born, John Lennard-Jones 1930 Darmstadt University of Technology: Privatdozent (lecturer) and senior assistant in Physics 1935 Guest professor, University of Saskatchewan (Saskatoon, Canada) 1936–45 Professor of Physics, University of Saskatchewan 1939 Fellow of the Royal Society of Canada 1945–8 Professor of spectroscopy, Yerkes Observatory, University of Chicago (Chicago, United States) 1948 Director of the Division of Pure Physics, National Research Council of Canada 1951 Fellow of the Royal Society of London 1957–63 Vice President of the International Union of Pure and Applied Physics 1956–7 President of the Canadian Association of Physicists 1960 gives Bakerian Lecturer of the Royal Society of London 1965 Member of the American Academy of Arts and Sciences 1966–7 President of the Royal Society of Canada 1968 Member of the United States National Academy of Sciences 1968 Companion of the Order of Canada 1968 George Fisher Baker Non-Resident Lecturer in Chemistry at Cornell University (Ithaca, United States) 1969 Willard Gibbs Award 1969 Distinguished Research Scientist in the recombined Division of Physics, at the National Research Council of Canada 1970 Lecturer of the Chemical Society of London, receives Faraday Medal 1971 Nobel Prize in Chemistry "for his contributions to the knowledge of electronic structure and geometry of molecules, particularly free radicals" 1971 Royal Medal from Royal Society of London 1972 Member of the American Philosophical Society 1973-1980 Chancellor of Carleton University (Ottawa, Ontario, Canada) 1981 Founding member of the World Cultural Council. 1992 Sworn into the Queen's Privy Council for Canada 1999 Died aged 94 == Honours and awards == Herzberg's most significant award was the 1971 Nobel Prize in Chemistry, which he was awarded "for his contributions to the knowledge of electronic structure and geometry of molecules, particularly free radicals". During the presentation speech, it was noted that at the time of the award, Herzberg was "generally considered to be the world's foremost molecular spectroscopist."Herzberg was honoured with memberships or fellowships by a very large number of scientific societies, received many awards and honorary degrees in different countries. The NSERC Gerhard Herzberg Canada Gold Medal for Science and Engineering, Canada's highest research award, was named in his honour in 2000. The Canadian Association of Physicists also has an annual award named in his honour. The Herzberg Institute of Astrophysics is named for him. He was made a member of the International Academy of Quantum Molecular Science. Asteroid 3316 Herzberg is named after him. In 1964 he was awarded the Frederic Ives Medal by the OSA. At Carleton University, there is a building named after him that belongs to the Physics and Mathematics/Statistics Departments, Herzberg Laboratories. Herzberg was elected a Fellow of the Royal Society (FRS) in 1951.The main building of John Abbott College in Montreal is named after him. Carleton University named the Herzberg Laboratories building after him. A public park in the College Park neighbourhood of Saskatoon also bears his name. == Books and publications == Herzberg authored some classic works in the field of spectroscopy, including Atomic Spectra and Atomic Structure and the encyclopaedic four volume work: Molecular Spectra and Molecular Structure, which is often called the spectroscopist's bible. The three volumes of Molecular Spectra and Molecular Structure were re-issued by Krieger in 1989, including extensive new footnotes by Herzberg. Volume IV of the series, "Constants of diatomic molecules" is purely a reference work, a compendium of known spectroscopic constants (and therefore a bibliography of molecular spectroscopy) of diatomic molecules up until 1978. Atomic Spectra and Atomic Structure. (Dover Books, New York, 2010, ISBN 0-486-60115-3) The spectra and structures of simple free radicals: An introduction to molecular spectroscopy. (Dover Books, New York, 1971, ISBN 0-486-65821-X). Molecular Spectra and Molecular Structure: I. Spectra of Diatomic Molecules. (Krieger, 1989, ISBN 0-89464-268-5) Molecular Spectra and Molecular Structure: II. Infrared and Raman Spectra of Polyatomic Molecules. (Krieger, 1989, ISBN 0-89464-269-3) Molecular Spectra and Molecular Structure: III. Electronic Spectra and Electronic Structure of Polyatomic Molecules. (Krieger, 1989, ISBN 0-89464-270-7) Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules, K. P. Huber and G. Herzberg, (Van nostrand Reinhold company, New York, 1979, ISBN 0-442-23394-9). == Archives == There are Gerhard Herzberg fonds at Library and Archives Canada and at National Research Council Canada. == See also == Herzeberg bands Collision-induced absorption and emission Methylene (compound) Pseudo Jahn–Teller effect Triatomic hydrogen Vibronic coupling List of German Canadians == References == == Further reading == == External links == Gerhard Herzberg on Nobelprize.org including the Nobel Lecture, December 11, 1971 Spectroscopic Studies of Molecular Structure Canadian Science and Technology Museum Hall of Fame Encyclopædia Britannica entry Order of Canada citation

Gerhard Heinrich Friedrich Otto Julius Herzberg, (German: [ˈɡeːɐ̯.haʁt ˈhɛʁt͡sˌbɛʁk] (listen); December 25, 1904 – March 3, 1999) was a German-Canadian pioneering physicist and physical chemist, who won the Nobel Prize for Chemistry in 1971, "for his contributions to the knowledge of electronic structure and geometry of molecules, particularly free radicals". Herzberg's main work concerned atomic and molecular spectroscopy. He is well known for using these techniques that determine the structures of diatomic and polyatomic molecules, including free radicals which are difficult to investigate in any other way, and for the chemical analysis of astronomical objects. Herzberg served as Chancellor of Carleton University in Ottawa, Ontario, Canada from 1973 to 1980.

Gerhard Herzberg

== Molecular Structure == In a molecule, both the electrons and nuclei experience similar-scale forces from the Coulomb interaction. However, the nuclei remain at nearly fixed locations in the molecule while the electrons move significantly. This picture of a molecule is based on the idea that nucleons are much heavier than electrons, so will move much less in response to the same force. Neutron scattering experiments on molecules have been used to verify this description. === Molecular Energy Levels and Spectra === When atoms join into molecules, their inner electrons remain bound to their original nucleus while the outer valence electrons are distributed around the molecule. The charge distribution of these valence electrons determines the electronic energy level of a molecule, and can be described by molecular orbital theory, which closely follows the atomic orbital theory used for single atoms. Assuming that the momenta of the electrons are on the order of ħ/a (where ħ is the reduced Planck's constant and a is the average internuclear distance within a molecule, ~1Å), the magnitude of the energy spacing for electronic states can be estimated at a few electron volts. This is the case for most low-lying molecular energy states, and corresponds to transitions in the visible and ultraviolet regions of the electromagnetic spectrum.In addition to the electronic energy levels shared with atoms, molecules have additional quantized energy levels corresponding to vibrational and rotational states. Vibrational energy levels refer to motion of the nuclei about their equilibrium positions in the molecule. The approximate energy spacing of these levels can be estimated by treating each nucleus as a quantum harmonic oscillator in the potential produced by the molecule, and comparing its associated frequency to that of an electron experiencing the same potential. The result is a is an energy spacing about 100x smaller than that for electronic levels. In agreement with this estimate, vibrational spectra show transitions in the near infrared (about 1 - 5 μm). Finally, rotational energy states describe semi-rigid rotation of the entire molecule and produce transition wavelengths in the far infrared and microwave regions (about 100-10,000 μm in wavelength). These are the smallest energy spacings, and their size can be understood by comparing the energy of a diatomic molecule with internuclear spacing ~1Å to the energy of a valence electron (estimated above as ~ħ/a).Actual molecular spectra also show transitions which simultaneously couple electronic, vibrational, and rotational states. For example, transitions involving both rotational and vibrational states are often referred to as rotational-vibrational or rovibrational transitions. Vibronic transitions combine electronic and vibrational transitions, and rovibronic transitions combine electronic, rotational, and vibrational transitions. Due to the very different frequencies associated with each type of transition, the wavelengths associated with these mixed transitions vary across the electromagnetic spectrum. == Experiments == In general, the goals of molecular physics experiments are to characterize shape and size, electric and magnetic properties, internal energy levels, and ionization and dissociation energies for molecules. In terms of shape and size, rotational spectra and vibrational spectra allow for the determination of molecular moments of inertia, which allows for calculations of internuclear distances in molecules. X-ray diffraction allows determination of internuclear spacing directly, especially for molecules containing heavy elements. All branches of spectroscopy contribute to determination of molecular energy levels due to the wide range of applicable energies (ultraviolet to microwave regimes). === Current Research === Within atomic, molecular, and optical physics, there are numerous studies using molecules to verify fundamental constants and probe for physics beyond the Standard Model. Certain molecular structures are predicted to be sensitive to new physics phenomena, such as parity and time-reversal violation. Molecules are also considered a potential future platform for trapped ion quantum computing, as their more complex energy level structure could facilitate higher efficiency encoding of quantum information than individual atoms. From a chemical physics perspective, intramolecular vibrational energy redistribution experiments use vibrational spectra to determine how energy is redistributed between different quantum states of a vibrationally excited molecule. == See also == == Sources == ATOMIC, MOLECULAR AND OPTICAL PHYSICS: NEW RESEARCH by L.T. Chen ; Nova Science Publishers, Inc. New York == References ==

Molecular physics is the study of the physical properties of molecules and molecular dynamics. The field overlaps significantly with physical chemistry, chemical physics, and quantum chemistry. It is often considered as a sub-field of atomic, molecular, and optical physics. Research groups studying molecular physics are typically designated as one of these other fields. Molecular physics addresses phenomena due to both molecular structure and individual atomic processes within molecules. Like atomic physics, it relies on a combination of classical and quantum mechanics to describe interactions between electromagnetic radiation and matter. Experiments in the field often rely heavily on techniques borrowed from atomic physics, such as spectroscopy and scattering.

Molecular physics

== Franchise history == === Building the first dynasty of the WNBA (1997–2000) === The Comets were one of the founding teams in the WNBA. They capped off the league's inaugural season in 1997 with a win over the New York Liberty in the WNBA championship game to win the WNBA's first championship. When the league expanded the next season, the Comets were moved from the Eastern Conference to the Western Conference. In 1998, they put together a win loss record of 27-3 for a .900 winning percentage – a WNBA record that still stands. They went on to repeat as champions, defeating the Phoenix Mercury in the first-ever WNBA Finals that year due to the championship game being extended into a three-game championship series. In 1999, led by what was already known as the Big Three, (Cynthia Cooper, Sheryl Swoopes and Tina Thompson), the Comets survived a highlight-film, last-second, court-to-court, game-winning shot by the Liberty's Teresa Weatherspoon in Game 2 of the finals to beat the Liberty in three games and win their third straight title, this one after the death of teammate Kim Perrot, who died of cancer. In 2000, behind league MVP Sheryl Swoopes and eventual WNBA Finals MVP Cynthia Cooper, the Comets beat the New York Liberty in two games to win their fourth title in a row cementing themselves as the greatest WNBA team ever assembled. 2000 was the Comets' last championship and last WNBA Finals appearance in franchise history. === The years of change and rebuilding (2001–2006) === After Cooper retired in 2001, Houston clinched the playoffs with a 19–13 record, but lost in the first round in a sweep to the 2001 eventual champion Los Angeles Sparks. In 2002, when Swoopes was injured most of the year with a torn ACL, the Comets were able to qualify for the playoffs with a 24–8 record, but lost to the Utah Starzz in 3 games. In 2003, they qualified to the playoffs for the 7th straight year, but they lost in the first round to the Sacramento Monarchs in 3 games. They missed the playoffs for the first time in franchise history with a record of 13–21 in 2004, but returned to the playoffs with a 19–15 record, finishing 3rd. In the first round, the Comets knocked out the 2004 defending champion Seattle Storm in 3 games, but lost in the conference finals to the Sacramento Monarchs in a sweep, which Sacramento later became WNBA Champions in 2005. Houston would return to the playoffs with an 18–16 record, but lost to the 2005 defending champion Sacramento Monarchs in another sweep. 2006 was the last playoff appearance for the Houston Comets. After the Comets' season ended in 2006, the Comets underwent major front-office changes during the off-season. In October 2006, team owner Leslie Alexander (who also owned the NBA's Houston Rockets) announced he was selling the Comets, and longtime head coach Van Chancellor resigned in January 2007. === New ownership and a new home (2007) === On January 31, 2007, the WNBA Board of Governors approved the sale of the team to Hilton Koch, a Houston-based mattress and furniture businessman. Two weeks later, Comets assistant coach Karleen Thompson was named to become the team's new head coach and general manager for the 2007 season. For the 2007 season, they would miss the playoffs for the second time in franchise history after starting the season 0-10, resulting in a 13–21 record. On December 12, 2007, team owner Hilton Koch announced that the Comets would be moving from the Toyota Center to Reliant Arena for the 2008 WNBA season. This resulted in a loss of fans. The Toyota Center drew 13,000 fans, but the Reliant Arena could only house 7,200. In 2008, the Comets' final year, they only drew an average 6,000 fans per game and sold out four games. === End of the era (2008) === In 2008, Koch put the team up for sale, with an asking price of $10 million. No investors stepped up. The WNBA took over management of the Comets and disbanded the team in December 2008. They stated that they would only be suspending operations in 2009, which some people saw as a sign that the franchise could be revived if an investor came in. Comets players were sent off to other teams in a dispersal draft.League president Donna Orender said that the collapse of the Comets was not a sign that the WNBA was in trouble. Former player Cynthia Cooper-Dyke said that the loss of the Comets was "disturbing news" and that the Comets were integral to the WNBA.The Comets played their final home game on September 15, 2008 at the Strahan Coliseum on the campus of Texas State due to Hurricane Ike. They defeated the Sacramento Monarchs 90–81. They finished the season 17-17 and missed the playoffs for the third time in their history. == Season-by-season records == === Team owners === Leslie Alexander (1997–2006) Hilton Koch (2007–2008) WNBA (2008) == Players of note == === Final roster === === Retired numbers === === Former Comets === Tiffani Johnson Matee Ajavon Janeth Arcain Octavia Blue Latasha Byears Dominique Canty Cynthia Cooper, now the head coach of the Texas Southern Women's Basketball Team Tamecka Dixon Ukari Figgs Nekeshia Henderson Sonja Henning Tammy Jackson Shannon Johnson Amanda Lassiter Edwige Lawson Tynesha Lewis Rebecca Lobo Sancho Lyttle Mwadi Mabika Hamchétou Maïga Kim Perrot Jennifer Rizzotti, now the head coach of the George Washington Colonials Women's Basketball Team Michelle Snow Dawn Staley, now the head coach of the South Carolina Gamecocks Women's Basketball Team Sheryl Swoopes, now assistant coach of Texas Tech Women's Basketball Team Lindsay Taylor Tina Thompson, formerly the head coach of Virginia Cavaliers Women's Basketball Team Amaya Valdemoro Coquese Washington, now assistant head coach of Notre Dame Fighting Irish Women's Basketball Team Kara Wolters Monica Lamb-Powell === FIBA Hall of Fame === == Coaches and others == Head coaches: Van Chancellor (1997–2007) (served as the women's head basketball coach at Louisiana State University from 2007 to 2011) Karleen Thompson (2007–2008)General managers Carroll Dawson (1997-2007) Karleen Thompson (2007–08) == References == == External links ==

The Houston Comets were a Women's National Basketball Association (WNBA) team based in Houston. Formed in 1997, the team was one of the original eight WNBA teams and won the first four championships of the league's existence. They are one of two teams in the WNBA that are undefeated in the WNBA Finals; the Seattle Storm are the other. The Comets were the first dynasty of the WNBA and are tied with the Minnesota Lynx and Seattle Storm for the most championships of any WNBA franchise. The team was folded and disbanded by the league in 2008 during the height of the Great Recession because new ownership could not be found.The Comets were known for courting great women's basketball stars. The team had among its members Cynthia Cooper (the WNBA's first MVP); college and national team standout Sheryl Swoopes; Kim Perrot, who succumbed to cancer in 1999; and college stars Michelle Snow and Tina Thompson.

Houston Comets

== Early history == In around the mid-1940s, Bill Haley performed with the Down Homers and formed a group called the Four Aces of Western Swing. The group that later became the Comets initially formed as "Bill Haley and the Saddlemen" c. 1949–1952, and performed mostly country and western songs, though occasionally with a bluesy feel. During those years Haley was considered one of the top cowboy yodelers in America. Many Saddlemen recordings were not released until the 1970s and 1980s, and highlights included romantic ballads such as "Rose of My Heart" and western swing tunes such as "Yodel Your Blues Away." The original members of this group were Haley, pianist and accordion player Johnny Grande and steel guitarist Billy Williamson. Al Thompson was the group's first bass player, followed by Al Rex and Marshall Lytle. During the group's early years, it recorded under several other names, including Johnny Clifton and His String Band and Reno Browne and Her Buckaroos (although Browne, a female matinee idol of the time, did not actually appear on the record). Haley began his rock and roll career with what is now recognized as a rockabilly style in a cover of "Rocket 88" recorded for the Philadelphia-based Holiday Records label in 1951. It sold well and was followed in 1952 by a cover of a 1940s rhythm and blues song called "Rock the Joint" (this time for Holiday's sister company, Essex Records). "Rock the Joint" and its immediate follow-ups were released under the increasingly incongruous Saddlemen name. It soon became apparent that a new name was needed to fit the new musical style. A friend of Haley's, making note of the common alternative pronunciation of the name Halley's Comet to rhyme with Bailey, suggested that Haley call his band the Comets. This event is cited in the Haley biographies Sound and Glory by John Haley and John von Hoelle; Bill Haley by John Swenson; and in Still Rockin' Around the Clock, a memoir by Comets bass player Marshall Lytle. The new name was adopted in the fall of 1952. Members of the group at that time were Haley, Johnny Grande, Billy Williamson and Marshall Lytle. Grande usually played piano on records but switched to accordion for live shows as it was more portable than a piano and easier to deal with during musical numbers that involved a lot of dancing around. Soon after renaming the band Haley hired his first drummer, Earl Famous. Displeased with the lineup, Haley sought out Dick Boccelli (also known as Dick Richards), who turned down the job but recommended a young drummer Charlie Higler. Soon after, Haley asked Richards again, who then accepted the role. During this time (and as late as the fall of 1955), Haley did not have a permanent lead guitar player, choosing to use session musicians on records and either playing lead guitar himself or having Williamson play steel solos. Even before the release of more successful records, the group had achieved greatness in some respects: "No one had blended country and R&B on a single before the Comets' "Rock the Joint" in 1952. No one had scored an American Top 20 hit with anything that could really qualify as rock'n'roll before their single "Crazy Man Crazy" in 1953". == National success and "Rock Around the Clock" == In 1953, Haley scored his first national success with an original song called "Crazy Man, Crazy", a phrase Haley said he heard from his teenage audience, again released on Essex. Haley later claimed the recording sold a million copies, but this is considered an exaggeration. Some sources indicate that the recording—a blend of R&B, western and pop music—is a contender for the title of "first rock'n'roll record" while others state that it was merely "the first rock and roll song to be a hit on the pop charts". It was also said to be the first rock'n'roll recording to be played on national television in the United States (in an episode of Omnibus (American TV program) in 1953).On their last release from Essex, new band member Joey Ambrose is heard on the B-side, "Straight Jacket." In the spring of 1954, Haley and His Comets left Essex for New York-based Decca Records, where they were placed under the auspices of veteran producer Milt Gabler, who would produce all of the band's recordings for the label and who had been involved in creating many proto-rock and roll recordings by the likes of the Andrews Sisters and Louis Jordan dating back to the 1940s. One of Jordan's records, Saturday Night Fish Fry (1949), is considered to be a contender for the title of "first rock'n' roll record. Gabler later commented that "all the tricks I used with Louis Jordan, I used with Bill Haley".The group's first session, on April 12, 1954, yielded "Rock Around the Clock", which would become Haley's biggest hit and one of the most important records in rock and roll history. Sales of "Rock Around the Clock" started slowly, since it was the B-side of the single, but it performed well enough that a second Decca session was commissioned. "Shake, Rattle and Roll" followed, a somewhat bowdlerized cover version of the Big Joe Turner recording released earlier in 1954. The single was one of Decca's best-selling records of 1954 and the seventh-best-selling record in November 1954.In March 1955, the group had four songs in Cash Box magazine's top 50 songs: "Dim, Dim the Lights (I Want Some Atmosphere)", "Birth of the Boogie", "Mambo Rock", and "Shake, Rattle and Roll."Haley's "Shake, Rattle and Roll" never achieved the same level of historical importance as "Rock Around the Clock" but it predated it as the first international rock and roll hit. It did not attain the Number 1 position on the American charts, but it became Haley's first gold record. Elvis Presley recorded the song in 1956, combining Haley's arrangement with Turner's original lyrics, but his version was not a substantial hit. Late in 1954, Haley recorded another hit, "Dim, Dim The Lights", which was one of the first R&B songs recorded by a white group to cross over to the R&B charts. Johnnie Ray had reached Number 1 with "Cry" in 1952. The belated success of "Rock Around the Clock" is attributed to its use in the soundtrack of the film Blackboard Jungle, which was released on March 19, 1955. The song was re-released to coincide with the film and shifted to the single's A-side. Haley's recording became an anthem for rebellious 1950s youth and reached Number 1 on the pop charts, remaining there for eight weeks, and went to Number 3 on the R&B chart. According to The Guardian, the group was "the first rock'n'roll band" and the song was particularly "important because it was the first rock'n'roll record heard by millions of people worldwide".Ambrose's acrobatic saxophone playing, along with Lytle on the double bass – literally on it, riding it like a pony, and holding it over his head – were highlights of the band's live performances during this time. Their music and their act were part of a tradition in jazz and rhythm and blues, but it all came like a thunderclap to most of their audience. In late 1954, Haley and His Comets appeared in a short subject entitled Round Up of Rhythm, performing three songs. This was the earliest known theatrical rock and roll film release. In 1955, Lytle, Richards and Ambrose quit the Comets in a salary dispute and formed their own group, the Jodimars. Haley hired several new musicians to take their place: Rudy Pompilli on sax, Al Rex (a former member of the Saddlemen) on double bass, and Ralph Jones on drums. In addition, lead guitarist Franny Beecher, who had been a session musician for Haley since Danny Cedrone's death in the spring of 1954, became a full-time Comet and Haley's first performing lead guitarist (Cedrone had played the guitar solo on the original recording of "Rock Around the Clock" and died shortly after the recording session for "Shake, Rattle and Roll" in the summer of 1954). This version of the band became more popular than the earlier manifestation and appeared in several motion pictures over the next few years. Other hits recorded by the band included "See You Later, Alligator" in which Haley's frantic delivery contrasted with the Louisiana languor of the original by Bobby Charles, "Don't Knock the Rock", "Rock-a-Beatin' Boogie", "Rudy's Rock" (the first instrumental hit of the rock and roll era), and "Skinny Minnie." Bill Haley and the Comets performed "Rock Around the Clock" in an a cappella and a lip-synched version on the NBC television program Texaco Star Theater hosted by Milton Berle on May 31, 1955. Berle predicted that the song would go to Number 1, calling the band "A group of entertainers who are going right to the top." Berle also sang and danced to the song, which was performed by the entire cast of the show. This was one of the earliest nationally televised performances by a rock and roll band and provided the new musical genre a much wider audience. Bill Haley and the Comets were the first rock and roll performers to appear on the CBS television musical variety program The Ed Sullivan Show, or Toast of the Town on Sunday, August 7, 1955, in a broadcast from the Shakespeare Festival Theater in Stratford, Connecticut. They performed a live version of "Rock Around the Clock" featuring Franny Beecher on lead guitar and Dick Richards on drums. The group made a second and final appearance on the Ed Sullivan Show on Sunday, April 28, 1957, performing "Rudy's Rock" and "Forty Cups of Coffee." Bill Haley and the Comets appeared on American Bandstand hosted by Dick Clark on ABC television twice in 1957, on the prime-time show on October 28 and on the regular daytime show on November 27. The band also appeared on Dick Clark's Saturday Night Beechnut Show (also known as The Dick Clark Show), a prime-time TV series from New York on March 22, 1958, during the first season (performing "Rock Around the Clock" and "Ooh, Look-a There, Ain't She Pretty") and on February 20, 1960 (performing "Rock Around the Clock" and "Tamiami"). In 1956, the group appeared in two of the earliest full-length rock and roll movies with Alan Freed: Rock Around the Clock and Don't Knock the Rock. The Platters were co-stars in the first movie, and Little Richard appeared in the second. Rock Around the Clock was produced by Sam Katzman (who would produce several Elvis Presley films in the 1960s) and directed by Fred F. Sears. == Decline in popularity == The band's popularity in the United States began to wane in 1956–57 as sexier, wilder acts such as Elvis Presley, Jerry Lee Lewis and Little Richard began to dominate the record charts (although Haley's cover version of Little Richard's "Rip It Up", released in direct competition with Little Richard's original recording, outsold the original). After "Skinny Minnie" hit the charts in 1958, Haley had little further success in the United States, although a spin-off group made up of Comets musicians dubbed The Kingsmen (no relation to the later group of "Louie, Louie" fame) had a hit with an instrumental, "Weekend", that same year. Overseas, however, Haley and his band continued to be popular, touring the United Kingdom in February 1957, when Haley and his crew were mobbed by thousands of fans at Waterloo station in London at an incident which the media dubbed the "Second Battle of Waterloo". The group also toured Australia in 1957, and in 1958 enjoyed a successful (if riot-dominated) tour of the European mainland. Bill Haley & His Comets were the first major American rock and roll act to tour the world in this way. Elvis, who was on military duty in Germany, visited them backstage at some shows. On a free day in Berlin they performed two songs in the Caterina Valente movie Hier Bin ich Hier Bleib Ich (Here I Am Here I Stay). Back in the U.S., Haley attempted to start his own record label, Clymax, and establish his own stable of performers, notably Sally Starr (the hostess of a Philadelphia television children's program) and the Matys Brothers. Members of the Comets were commissioned to work as session musicians on many of these recordings, many of which were written or co-written by Haley and members of the Comets. The Clymax experiment only lasted about a year. In 1959, Haley's relationship with Decca collapsed; after a final set of instrumental-only recordings in the fall, Haley announced he was leaving Decca for the new Warner Bros. Records label, which released two more albums in 1960, which were moderately successful. In 1960 Franny Beecher and Rudi Pompilli left the Comets to start their own record label. Replacing Beecher was a 20-year-old guitarist, Johnny Kay, from Chester, Pennsylvania. Beecher later returned briefly to play with the Comets, when his record label failed to take off, sharing guitar duties with Kay. Kay left the band in 1966 but returned in the early 1970s for an aborted world tour. He appeared in the Wembley show, which was filmed and released as the London Rock and Roll Show. == Mexico and the late 1960s == In 1961–1962, Bill Haley y sus Cometas (as the band was known in Hispanic America) signed with the Orfeón label of Mexico and scored an unexpected hit with "Twist Español", a Spanish-language recording based on the twist dance craze, which was sweeping America at the time. Haley followed up with "Florida Twist" (#3 MEX, according to Billboard Hits Of The World 04.21.62), which was for a time the biggest-selling single in Mexican history. Although Chubby Checker and Hank Ballard were credited with starting the twist craze in America, in Mexico and Latin America, Bill Haley and His Comets were proclaimed the Kings of the Twist. Thanks to the success of "Twist Español" and "Florida Twist", among others, the band had continued success in Mexico and Latin America over the next few years, selling many recordings of Spanish and Spanish-flavored material and simulated live performances (overdubbed audience over studio recordings) on the Orfeon label and its subsidiary, Dimsa. They hosted a television series, Orfeon a Go-Go, and made cameo appearances in several movies, lip-synching some of their old hits. Haley, who was fluent in Spanish, recorded a number of songs in the language, but most of the band's output during these years was instrumental recordings, many utilizing local session musicians playing trumpet. There was also some experimentation with Haley's style during this time; one single for Orfeon was a folk ballad, "Jimmy Martinez", which Haley recorded without the Comets. In 1966, the Comets (without Bill Haley) cut an album for Orfeon as session musicians for Big Joe Turner, who had always been an idol to Haley; no joint performance of "Shake, Rattle and Roll" was recorded, however. In a 1974 interview with BBC Radio, Haley said Turner's career was in a slump at this time, so he used his then-considerable influence with Orfeon to get Turner a recording session. The Comets' association with Orfeon/Dimsa ended later that year. By 1967, as related by Haley in an interview with radio host Red Robinson in that year, the group was "a free agent" without any recording contracts at all, although the band continued to perform regularly in North America and Europe. During this year, Haley—without the Comets—recorded a pair of demos in Phoenix, Arizona: a country-western song, "Jealous Heart", on which he was backed by a local mariachi band (similar in style to the earlier "Jimmy Martinez"), and a late-60s-style rocker, "Rock on Baby", backed by a group called Superfine Dandelion. Neither recording would be released for 30 years. In 1968, Haley and the Comets recorded a single for the United Artists label, a version of Tom T. Hall's "That's How I Got to Memphis", but no long-term association with the label resulted. In order to revive his recording career, Haley turned to Europe. == Revival == By the late 1960s, Haley and the Comets were considered an "oldies" act. The band's popularity never waned in Europe. The group signed a lucrative deal with Sonet Records of Sweden in 1968 and recorded in a new version of "Rock Around the Clock", which hit the European charts that year. The band recorded a mixture of live and studio albums for the label over the next decade. In the United States in 1969, promoter Richard Nader launched a series of rock and roll revival concert tours featuring artists of the 1950s and 1960s. At one of the first of these shows, held at the Felt Forum at Madison Square Garden in New York City, Haley received an eight-and-a-half-minute standing ovation following his performance, as Nader related in his recorded introduction to Haley's live album Bill Haley Scrapbook, which was recorded a few weeks later at the Bitter End club in New York. The band appeared in several concert films in the early 1970s, including The London Rock and Roll Show (for which Haley's 1960–66 lead guitarist, John Kay, briefly rejoined the band) and Let the Good Times Roll. After 1974, tax and management problems prevented Haley from performing in the United States, so he performed in Europe almost exclusively, though he also toured South America in 1975. The band was also kept busy in the studio, recording numerous albums for Sonet and other labels in the 1970s, several with a country music flavor. In 1974, Haley's original Decca recording of "Rock Around the Clock" hit the American sales charts once again, thanks to its use in the film American Graffiti and for two years, on the television program Happy Days. == Late career == In February 1976, Haley's saxophone player and best friend, Rudy Pompilli, died of cancer after a nearly 20-year career with the Comets. Haley continued to tour for the next year with a succession of new sax players, but his popularity was waning again, and his 1976 performance in London was critically lambasted in the music media, such as Melody Maker. That year, the group also recorded an album, R-O-C-K at Muscle Shoals Sound Studio for Sonet Records. In early 1977, Haley announced his retirement from performing and settled down at his home in Mexico. According to the John Swenson biography of Haley, the musician was quoted as saying that he and Pompilli had an agreement that if one died, the other would retire. The Comets continued to tour on their own during this period. In 1979, Haley was persuaded to return to performing with the offer of a lucrative contract to tour Europe. An almost completely new group of musicians, mostly British, including saxophonist Pete Thomas, were assembled to perform as the Comets. Haley appeared on numerous television shows and in the movie Blue Suede Shoes, filmed at one of his London concerts in March 1979. A few days later, a performance in Birmingham was videotaped and aired on UK television; it was released on DVD in 2005. During the March tour, Haley recorded several tracks in London for his next album for Sonet, completing the work that summer in Muscle Shoals; the album, Everyone Can Rock & Roll, issued later in 1979, was the last release of new recordings by Haley before his death. In November 1979, Haley and the Comets performed for Queen Elizabeth II, a moment Haley considered the proudest of his career. It was also the last time he performed in Europe and the last time most fans saw him perform "Rock Around the Clock". In 1980, Bill Haley and His Comets toured South Africa, but Haley's health was failing, and it was reported that he had a brain tumor. The tour was critically lambasted, but surviving recordings of a performance in Johannesburg show Haley in good spirits and good voice. Nonetheless, according to the Haley News fan club newsletter and the Haley biography Sound and Glory, planned concerts (such as a fall 1980 tour of Germany) and proposed recording sessions in New York and Memphis were cancelled, including a potential reunion with past members of the Comets. Haley returned to his home in Harlingen, Texas, where he died in his sleep of an apparent heart attack on February 9, 1981, at the age of 55.In April 1981, Bill Haley & His Comets returned to the British musical charts once again when MCA Records (inheritors of the Decca catalogue) released "Haley's Golden Medley", a hastily compiled edit of the band's best-known hits in the style of the then-popular "Stars on 45" format. The single reached Number 50 in the UK but was not released in the United States. In 1987, Bill Haley was inducted into the Rock and Roll Hall of Fame. At that time, supporting bands were not also named to the Hall of Fame. This policy was subsequently changed, and in 2012 a special committee of the Hall of Fame inducted the Comets. Bill Haley and His Comets were also inducted into the Rockabilly Hall of Fame. In June 2005, Bill Haley And His Comets were inducted into the Michigan Rock and Roll Legends Hall of Fame. In July 2005, the surviving members of the 1954–55 Comets (see below) represented Haley when Bill Haley and His Comets were inducted into Hollywood's Rockwalk, a ceremony also attended by Haley's second wife and youngest daughter. The Comets placed their handprints in cement; a space was left blank for Haley. == The Comets == More than 100 musicians performed with Bill Haley & His Comets between 1952 and Haley's death in 1981, many becoming fan favorites along the way. Several short-lived Comets reunions were attempted in the 1970s and 1980s, including one contingent (organized by Baltimore-based piano player Joey Welz, who played piano for the Comets from 1962 to 1965) that appeared on The Tomorrow Show, and another run by an Elvis Presley impersonator, Joey Rand (this group later lost a legal action over the right to use the Comets name). Only one group was sent out to perform by Haley himself and his management and production company, consisting of musicians who had played with Haley throughout the 1960s and 1970s—lead guitarist "Nick Masters" (Mathias Nicholas Nastos), bassist Ray Cawley, singer Ray "Pudge" Parsons, and drummer Buddy Dee—and who had continued to perform as the Comets between gigs and during Haley's retirement. This group rerecorded "Rock Around the Clock" for the television series Happy Days.The Comets, featuring musicians who performed with Haley in 1954–1955, reunited in 1987 and are still touring the world as of 2007, playing showrooms in the United States and Europe. They have also recorded a half-dozen albums for small labels in Europe and the United States. This version of the group has also been credited as Bill Haley's Original Comets and, in circumstances in which the use of the Comets name is in dispute, A Tribute to Bill Haley and The Original Band. The basic lineup of this group from 1987 to May 2006 was Marshall Lytle (bass), Joey Ambrose (sax), Johnny Grande (piano), Dick Richards (drums) and Franny Beecher (guitar). British singer Jacko Buddin augmented the group on vocals during most of their European tours, with Lytle taking over on vocals for US and Canadian tours beginning in 2000 and full-time in Europe in the mid-2000s. Since they connected with Klaus Kettner's Rock It Concerts (Germany) in 1991, they have played hundreds of shows all over Europe and have appeared on dozens of television shows. In March 2007 they opened the Bill-Haley-Museum in Munich, Germany. Two additional groups claim the name Bill Haley's Comets and have extensively toured in the United States since forming in the 1980s: one originally led by Haley's 1965–68 drummer John "Bam-Bam" Lane, the other run by Al Rappa, who played bass for Haley off and on between late 1959 and early 1969. (The 1959 album "Strictly Instrumental" on Decca was Rappa's first recording session with Bill Haley & His Comets. Haley had used Rappa as a fill-in player on live gigs for several years prior to that.) Both these musicians claim trademark ownership of the name "Bill Haley's Comets"; this dates back to Lane and Rappa (during a period when they worked together as one band) winning a trademark infringement lawsuit against the aforementioned Joey Rand group in 1989. Both Rappa's and Lane's bands have, from time to time, recruited other former Comets for their lineups (for example, in 2005, Rappa joined forces with Joey Welz), but for the most part the bandleaders are the only regular members who have worked with Bill Haley directly. Lane died in 2007, but his group continues to perform, led by bandleader Lenny Longo, who has no direct connection with Bill Haley. Rappa incorporated numerous professional musicians from the southern Indiana area (Guitarist Warren Batts, Joe Esarey, Dave Matthews, Joe Denton, saxophonist John Urbina, bassist Jody Hamilton Miley (previous bassist with the George Jones Show), and others) to make a full band. Rappa performed his Upright Bass show before thousands in audiences all over the country. Members of Rappa's "Comets" went on to form the LocoMotion Showband and continued touring the United States without Rappa adding Galen Deig (Drums) and Jimmy Baze (Bass) before eventually disbanding. Esarey went on to graduate from Cedarville University and Luther Rice Theological Seminary. He has since pastored churches and produced his own saxophone instrumental albums. Several of the members are now active in a very popular Southern Indiana 50's / 60's band called The Duke Boys. In March and July 2005, the members of the 1954–55 group, now billed as simply the Comets after decades of controversy over the use of the name, made several high-profile concert appearances in New York City and Los Angeles organized by Martin Lewis as part of celebrations marking the 50th anniversary of rock and roll, the release of Blackboard Jungle, the 50th anniversary of "Rock Around the Clock" hitting Number 1, and the 80th birthday of Bill Haley. During a concert at the Viper Room in West Hollywood on July 6, 2005, the Comets were joined on stage for one song by Gina Haley, the youngest daughter of Bill Haley; at a similar appearance in March they were joined by Haley's eldest son, John W. Haley. The 1954–55 Comets were also joined on stage by Bill Haley Jr. during several appearances in 2005 at Bubba Mac's in Somers Point, New Jersey, and at a 2005 concert recognizing the tenure of Bill Haley and the Saddlemen at the Twin Bars in Gloucester City, New Jersey. In 2006, the 1954–55 Comets spent much of the year in residence at Dick Clark's American Bandstand Theater in Branson, Missouri. Meanwhile, the John Lane edition of Bill Haley's Comets recorded an album in Tennessee in early 2006, which has yet to be released. On June 2, 2006, Johnny Grande, keyboardist with the 1954–55 Comets and a founding member of the band, died after a short illness. The following month, 85-year-old guitarist Franny Beecher announced his retirement, though he was at one point announced as participating in an early 2007 tour of Germany. The three remaining original Comets (Lytle, Richards, and Ambrose) continued to perform in Branson with new musicians taking over the keyboard and lead guitar positions. During September 2006, PBS in the United States aired a series of programs videotaped in Branson during the spring of 2006; these shows include the last recorded performances of the complete Original Comets lineup, including Grande. Lytle died in 2013, Beecher in 2014. The last remaining members of the 1954–55 Comets, Dick Richards and Joey Ambrose, continued to perform as the Comets as of mid-2018, sometimes augmented by 1970s-era Comet Bill Turner on lead guitar. John "Bam-Bam" Lane died on February 18, 2007 but his edition of Bill Haley's Comets is expected to continue touring, with the 2006 recordings to be released in Lane's memory. On October 27, 2007, ex-Comets guitar player Bill Turner opened the aforementioned Bill-Haley-Museum in Munich, Germany. He will also join the New Comets during their Remember Bill Haley Tour 2011 with Haley's daughter Gina Haley.Several bands patterning themselves after the Comets are also active in Europe, including Bill Haley's New Comets in Germany.In 2011, Haley's son Bill Jr. formed the band Bill Haley Jr. and the Comets, and created a "Rock 'N' Roll History Show."On July 12, 2019, drummer Dick Richards died at age 95 in Ocean City, New Jersey. He was born Richard Marley Boccelli on February 12, 1924, in Yeadon, Pennsylvania.On May 24, 2020, ex-Comet bassist, Albert 'Al Rex' Piccirilli, died.Al Rappa died on July 25, 2021, aged 94.Original saxophone player Joseph Frank D'Ambrosio (stage name Joey Ambrose)(March 23, 1934 – August 9, 2021), played on the hit recording of Rock Around the Clock in 1954 but from September 1955 was replaced long-term by Rudy Pompilli until Rudy's death 20 years later. Joey Ambrose remained a musician and was the last Comet to expire, at 87, on August 9, 2021. == Discography == === Studio albums === 1954 – Rock with Bill Haley and the Comets (compilation) 1955 – Shake, Rattle And Roll (compilation) 1955 – Rock Around The Clock (compilation) 1956 – Rock 'n' Roll Stage Show (Decca 1945) 1957 – Rockin' the Oldies (Decca 1969) 1958 – Rockin' Around the World (Decca 1992) 1959 – Bill Haley's Chicks (Decca 1921) 1959 – Strictly Instrumental (Decca 1964) 1960 – Bill Haley and His Comets (Warner Bros. 1978) 1960 – Haley's Juke Box (Warner Bros. 1991) 1961 – Twist (Dimsa 1955) 1961 – Bikini Twist (Dimsa 8259) 1962 – Twist Vol. 2 (Dimsa 8275) 1962 – Twist en Mexico (Dimsa 8290) 1963 – Rock Around the Clock King (Guest Star 1454) 1963 – Madison (Orfeon 12339) 1963 – Carnaval de Ritmos Modernos (Orfeon 12340) 1964 – Surf Surf Surf (Orfeon 12354) 1966 – Whiskey a Go-Go (Orfeon 12478) 1966 – Bill Haley a Go-Go (re-recordings) (Dimsa 8381) 1971 – Rock Around the Country (Sonet 623); issued in North America by GNP-Crescendo (LP 2097) and as Travelin' Band on Janus (JLS 3035) 1973 – Just Rock 'n' Roll Music (Sonet 645); issued in North America by GNP-Crescendo (LP 2077) 1979 – Everyone Can Rock and Roll (Sonet 808) == Grammy Hall of Fame == "Rock Around the Clock" was inducted into the Grammy Hall of Fame, a Grammy award established in 1973 to honor recordings that are at least 25 years old and that have "qualitative or historical significance." == Notes == == References == Jim Dawson, Rock Around the Clock: The Record That Started the Rock Revolution! (San Francisco: Backbeat Books, 2005) John W. Haley and John von Hoelle, Sound and Glory (Wilmington, Delaware: Dyne-American, 1990) John Swenson, Bill Haley (London: W.H. Allen, 1982) Discography information from Bill Haley Central and Bill Haley & His Comets, etc.: A Discography, an unpublished reference work by Herbert Kamitz What Was the First Rock 'n' Roll Record? ISBN 0-571-12939-0 (paper) Charlie Gillette and SImon Frith, eds., Rock File 4 (Panther Books, 1976) ISBN 0-586-04370-5 Billboard magazine Cash Box magazine == External links == Bill Haley at IMDb Bill Haley & His Comets discography at Discogs Rockabilly Hall of Fame – Biography of Bill Haley Archived May 27, 2010, at the Wayback Machine Rockabilly Hall of Fame – List of Comets musicians Archived October 11, 2011, at the Wayback Machine Bill Haley Central Web Portal – dead link "Bill Haley & His Comets". Rock and Roll Hall of Fame.

Bill Haley & His Comets was an American rock and roll band formed in 1947 and continuing until Haley's death in 1981. The band was also known as Bill Haley and the Comets and Bill Haley's Comets. From late 1954 to late 1956, the group recorded nine Top 20 singles, one of which was number one and three that were Top Ten. The single "Rock Around the Clock" was the best-selling rock single in the history of the genre and maintained that position for several years.Band leader Bill Haley had previously been a Western swing performer; after recording a rockabilly version of Ike Turner and his Kings of Rhythm's "Rocket 88", one of the first rock and roll recordings, Haley changed his band's musical direction to rock music. Though the group was considered to be at the forefront of rock and roll during the genre's formative years, the arrival of more risqué acts such as Elvis Presley and Little Richard by 1956 led the more clean-cut Haley and his Comets to decline in popularity. Haley would remain popular in Europe and go on to have a comeback as a nostalgia act in the 1970s, along with many of his contemporaries. Following Haley's death, no fewer than seven different groups have existed under the Comets name, all claiming (with varying degrees of authority) to be the continuation of Haley's group. As of the end of 2014, four such groups were still performing in the United States and internationally.

Bill Haley & His Comets