Mössbauer spectroscopy is a spectroscopic technique based on the Mössbauer effect. This effect, discovered by Rudolf Mössbauer in 1958, consists in the nearly recoil-free, resonant absorption and emission of gamma rays in solids. Like nuclear magnetic resonance spectroscopy, Mössbauer spectroscopy probes tiny changes in the energy levels of an atomic nucleus in response to its environment. Three types of nuclear interactions may be observed: isomer shift called chemical shift in the older literature. Due to the high energy and narrow line widths of gamma rays, Mössbauer spectroscopy is a sensitive technique in terms of energy resolution, capable of detecting changes in just a few parts per 1011. Just as a gun recoils when a bullet is fired, conservation of momentum requires a nucleus to recoil during emission or absorption of a gamma ray. If a nucleus at rest emits a gamma ray, the energy of the gamma ray is less than the natural energy of the transition, but in order for a nucleus at rest to absorb a gamma ray, the gamma ray's energy must be greater than the natural energy, because in both cases energy is lost to recoil.
This means that nuclear resonance is unobservable with free nuclei, because the shift in energy is too great and the emission and absorption spectra have no significant overlap. Nuclei in a solid crystal, are not free to recoil because they are bound in place in the crystal lattice; when a nucleus in a solid emits or absorbs a gamma ray, some energy can still be lost as recoil energy, but in this case it always occurs in discrete packets called phonons. Any whole number of phonons can be emitted, including zero, known as a "recoil-free" event. In this case conservation of momentum is satisfied by the momentum of the crystal as a whole, so no energy is lost. Mössbauer found that a significant fraction of emission and absorption events will be recoil-free, quantified using the Lamb–Mössbauer factor; this fact is what makes Mössbauer spectroscopy possible, because it means that gamma rays emitted by one nucleus can be resonantly absorbed by a sample containing nuclei of the same isotope, this absorption can be measured.
The recoil fraction of the Mössbauer absorption is analyzed by nuclear resonance vibrational spectroscopy. In its most common form, Mössbauer absorption spectroscopy, a solid sample is exposed to a beam of gamma radiation, a detector measures the intensity of the beam transmitted through the sample; the atoms in the source emitting the gamma rays must be of the same isotope as the atoms in the sample absorbing them. If the emitting and absorbing nuclei were in identical chemical environments, the nuclear transition energies would be equal and resonant absorption would be observed with both materials at rest; the difference in chemical environments, causes the nuclear energy levels to shift in a few different ways, as described below. Although these energy shifts are tiny, the narrow spectral linewidths of gamma rays for some radionuclides make the small energy shifts correspond to large changes in absorbance. To bring the two nuclei back into resonance it is necessary to change the energy of the gamma ray and in practice this is always done using the Doppler shift.
During Mössbauer absorption spectroscopy, the source is accelerated through a range of velocities using a linear motor to produce a Doppler effect and scan the gamma ray energy through a given range. A typical range of velocities for 57Fe, for example, may be ±11 mm/s. In the resulting spectra, gamma ray intensity is plotted as a function of the source velocity. At velocities corresponding to the resonant energy levels of the sample, a fraction of the gamma rays are absorbed, resulting in a drop in the measured intensity and a corresponding dip in the spectrum; the number and intensities of the dips provide information about the chemical environment of the absorbing nuclei and can be used to characterize the sample. Suitable gamma-ray sources consist of a radioactive parent. Example, the source for 57Fe consists of 57Co, which decays by electron capture to an excited state of 57Fe, which in turn decays to a ground state emitting a gamma-ray of the appropriate energy; the radioactive cobalt is prepared on a foil of rhodium.
Ideally the parent isotope will have a convenient half-life. The gamma-ray energy should be low, otherwise the system will have a low recoil-free fraction resulting in a poor signal-to-noise ratio and requiring long collection times; the periodic table below indicates those elements having an isotope suitable for Mössbauer spectroscopy. Of these, 57Fe is by far the most common element studied using the technique, although 129I, 119Sn, 121Sb are frequently studied; as described above, Mössbauer spectroscopy has an fine energy resolution and can detect subtle changes in the nuclear environment of the relevant atoms. There are three types of nuclear interactions that are observed: isomeric shift, quadrupole splitting, hyperfine splitting. Isomer shift is a relative measure describing a shift in the resonance energy of a nucleus due to the transition of electrons within its s orbitals; the whole spectrum is shifted in either a positive or negative direction dep
Electron paramagnetic resonance
Electron paramagnetic resonance or electron spin resonance spectroscopy is a method for studying materials with unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance, but it is electron spins that are excited instead of the spins of atomic nuclei. EPR spectroscopy is useful for studying metal complexes or organic radicals. EPR was first observed in Kazan State University by Soviet physicist Yevgeny Zavoisky in 1944, was developed independently at the same time by Brebis Bleaney at the University of Oxford; every electron has a magnetic moment and spin quantum number s = 1 2, with magnetic components m s = + 1 2 and m s = − 1 2. In the presence of an external magnetic field with strength B 0, the electron's magnetic moment aligns itself either parallel or antiparallel to the field, each alignment having a specific energy due to the Zeeman effect: E = m s g e μ B B 0, where g e is the electron's so-called g-factor, g e = 2.0023 for the free electron, μ B is the Bohr magneton.
Therefore, the separation between the lower and the upper state is Δ E = g e μ B B 0 for unpaired free electrons. This equation implies 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 move between the two energy levels by either absorbing or emitting a photon of energy h ν such that the resonance condition, h ν = Δ E, is obeyed; this leads to the fundamental equation of EPR spectroscopy: h ν = g e μ 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 region, with fields corresponding to about 3500 G. 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 the frequency, 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 and m s = − 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 are more electrons in the lower state, due to the Maxwell–Boltzmann distribution, there is a net absorption of energy, it is this absorption, 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 publish continuous wave EPR spectra. For the microwave frequency of 9388.2 MHz, the predicted resonance occurs at a magnetic field of about B 0 = h ν / g e μ B = 0.3350 teslas = 3350 gausses. Because of electron-nuclear mass differences, the magnetic moment of an electron is 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 at the right, 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 where g N and
Astrophysical X-ray source
Astrophysical X-ray sources are astronomical objects with physical properties which result in the emission of X-rays. There are a number of types of astrophysical objects which emit X-rays, from galaxy clusters, through black holes in active galactic nuclei to galactic objects such as supernova remnants and binary stars containing a white dwarf, neutron star or black hole; some solar system bodies emit X-rays, the most notable being the Moon, although most of the X-ray brightness of the Moon arises from reflected solar X-rays. A combination of many unresolved X-ray sources is thought to produce the observed X-ray background; the X-ray continuum can arise from bremsstrahlung, either magnetic or ordinary Coulomb, black-body radiation, synchrotron radiation, inverse Compton scattering of lower-energy photons by relativistic electrons, knock-on collisions of fast protons with atomic electrons, atomic recombination, with or without additional electron transitions. Furthermore, celestial entities in space are discussed as celestial X-ray sources.
The origin of all observed astronomical X-ray sources is in, near to, or associated with a coronal cloud or gas at coronal cloud temperatures for however long or brief a period. Clusters of galaxies are formed by the merger of smaller units of matter, such as galaxy groups or individual galaxies; the infalling material gains kinetic energy as it falls into the cluster's gravitational potential well. The infalling gas collides with gas in the cluster and is shock heated to between 107 and 108 K depending on the size of the cluster; this hot gas emits X-rays by thermal bremsstrahlung emission, line emission from metals. The galaxies and dark matter are collisionless and become virialised, orbiting in the cluster potential well. At a statistical significance of 8σ, it was found that the spatial offset of the center of the total mass from the center of the baryonic mass peaks cannot be explained with an alteration of the gravitational force law. A quasi-stellar radio source is a energetic and distant galaxy with an active galactic nucleus.
QSO 0836 +7107 is a Quasi-Stellar Object. This radio emission is caused by electrons spiraling along magnetic fields producing cyclotron or synchrotron radiation; these electrons can interact with visible light emitted by the disk around the AGN or the black hole at its center. These photons accelerate the electrons, which emit X- and gamma-radiation via Compton and inverse Compton scattering. On board the Compton Gamma Ray Observatory is the Burst and Transient Source Experiment which detects in the 20 keV to 8 MeV range. QSO 0836+7107 or 4C 71.07 was detected by BATSE as a source of soft gamma rays and hard X-rays. "What BATSE has discovered is that it can be a soft gamma-ray source", McCollough said. QSO 0836 +7107 is the most distant object to be observed in soft gamma rays, it has been observed in gamma rays by the Energetic Gamma Ray Experiment Telescope aboard the Compton Gamma Ray Observatory. Seyfert galaxies are a class of galaxies with nuclei that produce spectral line emission from ionized gas.
They are a subclass of active galactic nuclei, are thought to contain supermassive black holes. The following early-type galaxies have been observed to be X-ray bright due to hot gaseous coronae: 315, 1316, 1332, 1395, 2563, 4374, 4382, 4406, 4472, 4594, 4636, 4649, 5128; the X-ray emission can be explained as thermal bremsstrahlung from hot gas. Ultraluminous X-ray sources are pointlike, nonnuclear X-ray sources with luminosities above the Eddington limit of 3 × 1032 W for a 20 M☉ black hole. Many ULXs may be black hole binaries. To fall into the class of intermediate-mass black holes, their luminosities, thermal disk emissions, variation timescales, surrounding emission-line nebulae must suggest this. However, when the emission is beamed or exceeds the Eddington limit, the ULX may be a stellar-mass black hole; the nearby spiral galaxy NGC 1313 has two compact ULXs, X-1 and X-2. For X-1 the X-ray luminosity increases to a maximum of 3 × 1033 W, exceeding the Eddington limit, enters a steep power-law state at high luminosities more indicative of a stellar-mass black hole, whereas X-2 has the opposite behavior and appears to be in the hard X-ray state of an IMBH.
Black holes give off radiation because matter falling into them loses gravitational energy which may result in the emission of radiation before the matter falls into the event horizon. The infalling matter has angular momentum, which means that the material cannot fall in directly, but spins around the black hole; this material forms an accretion disk. Similar luminous accretion disks can form around white dwarfs and neutron stars, but in these the infalling gas releases additional energy as it slams against the high-density surface with high speed. In case of a neutron star, the infall speed can be a sizeable fraction of the speed of light. In some neutron star or white dwarf systems, the magnetic field of the star is strong enough to prevent the formation of an accretion disc; the material in the disc gets hot because of friction, emits X-rays. The material in the disc loses its angular momentum and falls into the compact star. In neutron stars and white dwarfs, additional X-rays are generated when the material hits their surfaces.
X-ray emission from black holes is variable, varying in luminosity in short timescales. The variation in luminosity can provi
Extended X-ray absorption fine structure
X-ray Absorption Spectroscopy includes both Extended X-Ray Absorption Fine Structure and X-ray Absorption Near Edge Structure. XAS is the measurement of the x-ray absorption coefficient of a material as a function of energy. X-rays of a narrow energy resolution are shone on the sample and the incident and transmitted x-ray intensity is recorded as the incident x-ray energy is incremented; the number of x-ray photons that are transmitted through a sample is equal to the number of x-ray photons shone on the sample multiplied by a decreasing exponential that depends on the type of atoms in the sample, the absorption coefficient μ, the thickness of the sample x. I t = I 0 e − μ x The absorption coefficient is obtained by taking the log ratio of the incident x-ray intensity to the transmitted x-ray intensity. Μ = − l n x When the incident x-ray energy matches the binding energy of an electron of an atom within the sample, the number of x-rays absorbed by the sample increases causing a drop in the transmitted x-ray intensity.
This results in an absorption edge. Each element on the periodic table has a set of unique absorption edges corresponding to different binding energies of its electrons, giving XAS element selectivity. XAS spectra are most collected at synchrotrons; because X-rays are penetrating, XAS samples can be gases, solids or liquids. And because of the brilliance of synchrotron X-ray sources the concentration of the absorbing element can be as low as a few ppm. EXAFS spectra are displayed as graphs of the absorption coefficient of a given material versus energy in a 500 – 1000 eV range beginning before an absorption edge of an element in the sample; the x-ray absorption coefficient is normalized to unit step height. This is done by regressing a line to the region before and after the absorption edge, subtracting the pre-edge line from the entire data set and dividing by the absorption step height, determined by the difference between the pre-edge and post-edge lines at the value of E0; the normalized absorption spectra are called XANES spectra.
These spectra can be used to determine the average oxidation state of the element in the sample. The XANES spectra are sensitive to the coordination environment of the absorbing atom in the sample. Finger printing methods have been used to match the XANES spectra of an unknown sample to those of known "standards". Linear combination fitting of several different standard spectra can give an estimate to the amount of each of the known standard spectra within an unknown sample. X-ray absorption spectra are produced over the range of 200 – 35,000 eV; the dominant physical process is one where the absorbed photon ejects a core photoelectron from the absorbing atom, leaving behind a core hole. The atom with the core hole is now excited; the ejected photoelectron's energy will be equal to that of the absorbed photon minus the binding energy of the initial core state. The ejected photoelectron interacts with electrons in the surrounding non-excited atoms. If the ejected photoelectron is taken to have a wave-like nature and the surrounding atoms are described as point scatterers, it is possible to imagine the backscattered electron waves interfering with the forward-propagating waves.
The resulting interference pattern shows up as a modulation of the measured absorption coefficient, thereby causing the oscillation in the EXAFS spectra. A simplified plane-wave single-scattering theory has been used for interpretation of EXAFS spectra for many years, although modern methods have shown that curved-wave corrections and multiple-scattering effects can not be neglected; the photelectron scattering amplitude in the low energy range of the photoelectron kinetic energy become much larger so that multiple scattering events become dominant in the XANES spectra. The wavelength of the photoelectron is dependent on the energy and phase of the backscattered wave which exists at the central atom; the wavelength changes as a function of the energy of the incoming photon. The phase and amplitude of the backscattered wave are dependent on the type of atom doing the backscattering and the distance of the backscattering atom from the central atom; the dependence of the scattering on atomic species makes it possible to obtain information pertaining to the chemical coordination environment of the original absorbing atom by analyzing these EXAFS data.
Since EXAFS requires a tunable x-ray source, data are always collected at synchrotrons at beamlines which are optimized for the purpose. The utility of a particular synchrotron to study a particular solid depends on the brightness of the x-ray flux at the absorption edges of the relevant elements. XAS is an interdisciplinary technique and its unique properties, as compared to x-ray diffraction, have been exploited for understanding the details of local structure in: glass and liquid systems solid solutions Doping and ionic implantation of materials for electronics local distortions of crystal lattices organometallic compounds metalloproteins metal clusters vibrational dynamics ions in solutions speciation of elements EXAFS is, like XANE
Rotational–vibrational spectroscopy is a branch of molecular spectroscopy concerned with infrared and Raman spectra of molecules in the gas phase. Transitions involving changes in both vibrational and rotational states can be abbreviated as rovibrational transitions; when such transitions emit or absorb photons, the frequency is proportional to the difference in energy levels and can be detected by certain kinds of spectroscopy. Since changes in rotational energy levels are much smaller than changes in vibrational energy levels, changes in rotational state are said to give fine structure to the vibrational spectrum. For a given vibrational transition, the same theoretical treatment as for pure rotational spectroscopy gives the rotational quantum numbers, energy levels, selection rules. In linear and spherical top molecules, rotational lines are found as simple progressions at both higher and lower frequencies relative to the pure vibration frequency. In symmetric top molecules the transitions are classified as parallel when the dipole moment change is parallel to the principal axis of rotation, perpendicular when the change is perpendicular to that axis.
The ro-vibrational spectrum of the asymmetric rotor water is important because of the presence of water vapor in the atmosphere. Ro-vibrational spectroscopy concerns molecules in the gas phase. There are sequences of quantized rotational levels associated with both the ground and excited vibrational states; the spectra are resolved into lines due to transitions from one rotational level in the ground vibrational state to one rotational level in the vibrationally excited state. The lines corresponding to a given vibrational transition form a band. In the simplest cases the part of the infrared spectrum involving vibrational transitions with the same rotational quantum number in ground and excited states is called the Q-branch. On the high frequency side of the Q-branch the energy of rotational transitions is added to the energy of the vibrational transition; this is known as the R-branch of the spectrum for ΔJ = +1. The P-branch for ΔJ = −1 lies on the low wavenumber side of the Q branch; the appearance of the R-branch is similar to the appearance of the pure rotation spectrum, the P-branch appears as a nearly mirror image of the R-branch.
The appearance of rotational fine structure is determined by the symmetry of the molecular rotors which are classified, in the same way as for pure rotational spectroscopy, into linear molecules, spherical-, symmetric- and asymmetric- rotor classes. The quantum mechanical treatment of rotational fine structure is the same as for pure rotation. A general convention is to label quantities that refer to the vibrational ground and excited states of a transition with double prime and single prime, respectively. For example, the rotational constant for the ground state is written as B ′ ′, that of the excited state as B ′; these constants are expressed in the molecular spectroscopist's units of cm−1. So that B in this article corresponds to B ¯ = B / h c in the definition of rotational constant at Rigid rotor. Numerical analysis of ro-vibrational spectral data would appear to be complicated by the fact that the wavenumber for each transition depends on two rotational constants, B ′ ′ and B ′; however combinations which depend on only one rotational constant are found by subtracting wavenumbers of pairs of lines which have either the same lower level or the same upper level.
For example, in a diatomic molecule the line denoted P is due to the transition →, the line R is due to the transition →. The difference between the two wavenumbers corresponds to the energy difference between the and levels of the lower vibrational state and denoted by Δ 2 since it is the difference between levels differing by two units of J. If centrifugal distortion is included, it is given by Δ 2 ′ ′ F = ν ¯ − ν ¯ = − D ′ ′ 3 The rotational constant of the ground vibrational state B′′ and centrifugal distortion constant, D′′ can be found by least-squares fitting this difference as a function of J; the constant B′′ is used to determine the internuclear distance in the ground state as in pure rotational spectroscopy. The difference R − P depends only on the constants B′ and D′ for the excited vibrational state, B′ can be used to
Photoemission spectroscopy known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in a substance. The term refers to various techniques, depending on whether the ionization energy is provided by an X-ray photon, an EUV photon, or an ultraviolet photon. Regardless of the incident photon beam, all photoelectron spectroscopy revolves around the general theme of surface analysis by measuring the ejected electrons. X-ray photoelectron spectroscopy was developed by Kai Siegbahn starting in 1957 and is used to study the energy levels of atomic core electrons in solids. Siegbahn referred to the technique as "electron spectroscopy for chemical analysis", since the core levels have small chemical shifts depending on the chemical environment of the atom, ionized, allowing chemical structure to be determined. Siegbahn was awarded the Nobel Prize in 1981 for this work.
XPS is sometimes referred to as PESIS, whereas the lower-energy radiation of UV light is referred to as PESOS because it cannot excite core electrons. In the ultraviolet and visible region, the method is referred to as photoelectron spectroscopy for the study of gases, photoemission spectroscopy for solid surfaces. Ultraviolet photoelectron spectroscopy is used to study valence energy levels and chemical bonding the bonding character of molecular orbitals; the method was developed for gas-phase molecules in 1961 by Feodor I. Vilesov and in 1962 by David W. Turner, other early workers included David C. Frost, J. H. D. Eland and K. Kimura. Richard Smalley modified the technique and used a UV laser to excite the sample, in order to measure the binding energy of electrons in gaseous molecular clusters. Two-photon photoelectron spectroscopy extends the technique to optically excited electronic states through the introduction of a pump-and-probe scheme. Extreme-ultraviolet photoelectron spectroscopy lies in between XPS and UPS.
It is used to assess the valence band structure. Compared to XPS, it gives better energy resolution, compared to UPS, the ejected electrons are faster, resulting in less space charge and mitigated final state effects; the physics behind the PES technique is an application of the photoelectric effect. The sample is exposed to a beam of XUV light inducing photoelectric ionization; the energies of the emitted photoelectrons are characteristic of their original electronic states, depend on vibrational state and rotational level. For solids, photoelectrons can escape only from a depth on the order of nanometers, so that it is the surface layer, analyzed; because of the high frequency of the light, the substantial charge and energy of emitted electrons, photoemission is one of the most sensitive and accurate techniques for measuring the energies and shapes of electronic states and molecular and atomic orbitals. Photoemission is among the most sensitive methods of detecting substances in trace concentrations, provided the sample is compatible with ultra-high vacuum and the analyte can be distinguished from background.
Typical PES instruments use helium gas sources of UV light, with photon energy up to 52 eV. The photoelectrons that escaped into the vacuum are collected, energy resolved retarded and counted, which results in a spectrum of electron intensity as a function of the measured kinetic energy; because binding energy values are more applied and understood, the kinetic energy values, which are source dependent, are converted into binding energy values, which are source independent. This is achieved by applying Einstein's relation E k = h ν − E B; the h ν term of this equation is due to the energy of the UV light. Photoemission spectra are measured using synchrotron radiation sources; the binding energies of the measured electrons are characteristic of the chemical structure and molecular bonding of the material. By adding a source monochromator and increasing the energy resolution of the electron analyzer, peaks appear with full width at half maximum less than 5–8 meV. Angle resolved photoemission spectroscopy AR-PES Inverse photoemission spectroscopy IPS Ultra high vacuum UHV X-ray photoelectron spectroscopy XPS Ultraviolet photoelectron spectroscopy UPS Two-photon photoelectron spectroscopy 2PPE Vibronic spectroscopy Reinert, Friedrich.
"Photoemission spectroscopy—from early days to recent applications". New Journal of Physics. 7: 97. Bibcode:2005NJPh....7...97R. Doi:10.1088/1367-2630/7/1/097. ISSN 1367-2630. Presentation on principle of ARPES
Resonance Raman spectroscopy
Resonance Raman spectroscopy is a Raman spectroscopy technique in which the incident photon energy is close in energy to an electronic transition of a compound or material under examination. The frequency coincidence can lead to enhanced intensity of the Raman scattering, which facilitates the study of chemical compounds present at low concentrations. Raman scattering is extremely weak, of the order of 1 in 10 million photons that hit a sample are scattered with the loss or gain of energy because of changes in vibrational energy of the molecules in the sample. Resonance enhancement of Raman scattering requires that the wavelength of the laser used is close to that of an electronic transition. In larger molecules the change in electron density can be confined to one part of the molecule, a chromophore, in these cases the Raman bands that are enhanced are from those parts of the molecule in which the electronic transition leads to a change in bond length or force constant in the excited state of the chromophore.
For large molecules such as proteins, this selectivity helps to identify the observed bands as originating from vibrational modes of specific parts of the molecule or protein, such as the heme unit within myoglobin. Raman spectroscopy and RR spectroscopy provide information about the vibrations of molecules, can be used for identifying unknown substances. RR spectroscopy has found wide application to the analysis of bioinorganic molecules; the technique measures the energy required to change the vibrational state of a molecule as does infrared spectroscopy. The mechanism and selection rules are different in each technique, band positions are identical and therefore the two methods provide complementary information. Infrared spectroscopy involves measuring the direct absorption of photons with the appropriate energy to excite molecular bond vibrational modes and phonons; the wavelengths of these photons lie in the infrared region of the spectrum, hence the name of the technique. Raman spectroscopy measures the excitation of bond vibrations by an inelastic scattering process, in which the incident photons are more energetic and lose only part of their energy to the sample.
The two methods are complementary because some vibrational transitions that are observed in IR spectroscopy are not observed in Raman spectroscopy, vice versa. RR spectroscopy is an extension of conventional Raman spectroscopy that can provide increased sensitivity to specific compounds that are present at low in an otherwise complex mixture of compounds. An advantage of resonance Raman spectroscopy over Raman spectroscopy is that the intensity of bands can be increased by several orders of magnitude. An application that illustrates this advantage is the study of the dioxygen unit in cytochrome c oxidase. Identification of the band associated with the O–O stretching vibration was confirmed by using 18O–16O and 16O–16O isotopologues; the frequencies of molecular vibrations range from less than 1012 to 1014 Hz. These frequencies correspond to radiation in the infrared region of the electromagnetic spectrum. At any given instant, each molecule in a sample has a certain amount of vibrational energy.
However, the amount of vibrational energy that a molecule has continually changes due to collisions and other interactions with other molecules in the sample. At room temperature, most molecules are in the lowest energy state—known as the ground state. A few molecules are in higher energy states—known as excited states; the fraction of molecules occupying a given vibrational mode at a given temperature can be calculated using the Boltzmann distribution. Performing such a calculation shows that, for low temperatures, most of the molecules occupy the ground vibrational state; such a molecule can be excited to a higher vibrational mode through the direct absorption of a photon of the appropriate energy. This is the mechanism by which IR spectroscopy operates: infrared radiation is passed through the sample, the intensity of the transmitted light is compared with that of the incident light. A reduction in intensity at a given wavelength of light indicates the absorption of energy by a vibrational transition.
The energy, E, of a photon is E = h ν where h is Planck's constant and ν is the frequency of the radiation. Thus, the energy required for such transition may be calculated if the frequency of the incident radiation is known, it is possible to observe molecular vibrations by an inelastic scattering process. In inelastic scattering, an absorbed photon is reemitted with lower energy. In Raman scattering, the difference in energy between the absorbed and reemitted photons corresponds to the energy required to excite a molecule to a higher vibrational mode. In Raman spectroscopy high intensity laser radiation with wavelengths in either the visible or near-infrared regions of the spectrum is passed through a sample. Photons from the laser beam are absorbed by the molecules. If the molecules relax back to the vibrational state that they started in, the reemitted photon has the same energy as the original photon; this leads to scattering of the laser light, but with no change in energy between the incoming photons and the reemitted/scattered photons.
This type of scattering is known as Rayleigh scattering. However, it is possible for the mo