Spectroscopy, vibrational

IR spectroscopy has been specifically used in the investigation of the nature of 

FTIR and Raman spectra of polydialkoxyphosphazenes, [P(OCmH2m+i)2-N]n, for m=l—9, have been studied between —100 and + 100 and demonstrate that the temperature-dependent conformational 

Although vibrational frequencies have been calculated and compared with experimental data since the early days of molecular mechanics refinements using full-matrix second-derivative procedures196,971, there are few reports on the application of this method in the field of transition metal chemistry. One of the few examples is a recent study on linear metallocenes [981. Here, the molecular mechanics force constants were obtained by adjusting initially assumed values by fitting the calculated vibrations to thoroughly analyzed experimental spectra. The average difference (rms) between experimental and calculated vibrations were of the order of ca. 30 cm-1.2 Table 

1 shows the observed and calculated frequencies associated with the skeletal modes of ferrocene (see Fig. 9.1 for the representation of these modes). A comparison between experimental and calculated spectroscopic parameters for various cyclopenta-dienyl (Cp) compounds indicated drat the internal Cp modes are transferable while the skeletal modes are dependent on the nature of the metal-Cp bonds. The skeletal force constants for a number of metallocenes are given in Table 9.2. 

2 A similar accuracy was obtained in calculated vibrations of organic molecules 

In recent studies, involving the prediction of electronic and EPR spectra of hex-aamine complexes of chromium(III), low spin iron(II), cobalt(III), nickel(II) and copper(II)[90,166,197,3021 with a combination of molecular mechanics and AOM (angular overlap model) calculations, the two effects could be separated (Table 10.4 see also text below) because the structural factors (steric crowding molecular mechanics) and the electronic factors (inductive effects AOM) are parameterized separately. 

The MM-AOM approach - AOM calculations based on molecular mechanics refined structures - was used to predict d-electron transitions of chromium(III), 

Infrared spectroscopy is a widely available technique and has been applied extensively in the study of microporous solids. Using Fourier Transform analysis, sensitive detectors and operating either in transmission or in diffuse reflectance (DRIFT) mode, powders can give spectra with high resolution and sensitivity. The method is most valuable when analysing the interaction of molecules with adsorption sites (acid or base) - this is described in Chapters 7 and 8. It does give some structural insights, however, for example on the environment of protons and on the presence of framework and non-framework cations. 

A typical infrared spectrum is collected between 400 and 4000cm , which enables most of the fundamental bands from the framework and hydroxyls to be measured. Some spectrometers permit measurement in the near IR (up to 7000cm ), so that overtones and eombination bands (much weaker than the fundamental resonances) ean also be measured. For porous inorganic solids empty of adsorbed speeies, fundamental hydroxyl stretches are observed in the range 3200-3800 cm and framework vibrations are observed in the range 400-1200 cm Organic species present (such as templates or the organic parts 

For microporous solids, the bands from framework vibrations depend on both the structure type and the composition. For zeolites, substitution of framework aluminium results in broadening of these bands and a shift to lower wavenumber, which is attributable to the Al-O bonds being weaker than Si-O bonds. As a result, and once the variation of frequency with composition of a certain framework stretching vibration (symmetric or asymmetric 

Vibrational spectroscopy is a very powerful method for the study of hydroxyl species present. For zeolitic solids, these divide into three broad categories silanol groups, (SiO)3SiOH, hydroxyl groups bound to metal cations such as aluminium, AlOH, and bridging hydroxyls, Si-OH-Al. 

Bridging hydroxyls, which are responsible for Bronsted acidity, have stretching and in-plane bending frequencies in the ranges 3250-3660cm and 

Vibrational spectroscopy of water probes the effeets of the environment on the 0-H (or the 0-D) stretching mode of water molecules and therefore exhibits exeeptional sensitivity towards hydrogen-bonding. This teehnique has been used for probing solute-solvent interactions, for example, the influenee of Na and CF ions on solvent stmcture in electrolyte solutions. IR and near-IR vibrational speetroscopy 

The use of vibrational spectroscopy for the qualitative analysis of absorbed surface species is first considered, and a Table is then included which summarises a number of the key features of the various quantitative techniques. We then proceed to summarize these in groups depending not upon the probe used (as in the preceding chapters), but in terms of the signal emitted by the specimen which is used in each identification process. 

We have not included Atom Probe Microanalysis in this scheme. It constitutes the ultimate in local analysis - in that individual atoms can be selected and identified by TOF spectroscopy. Chapter 1 gives an account of the range of applications of the technique at the present time the development in atom-probe methods has allowed the continuing increase of both the volume of material that can be mapped at the atomic scale and the quality of the data obtained. 

This is a standard method of identifying molecular species adsorbed on a surface, as well as species generated by surface reaction. We have considered three such techniques. 

Raman microscopy has the ability to investigate regions down to 1 pm, and, by the aid of fibre optics, remote sampling is possible. The molecular information 

Infra-red (IR) spectroscopy functions to probe vibrational transitions (2000-50 000 nm 5000-200 cm i.e. wave number - typical IR spectroscopy units) in the singlet ground electronic state of molecules. The absorption principles of IR spectroscopy are identical to those of UV-visible and CD spectroscopy. Hence the Beer-Lambert law (Equation (4.3)) applies. Moreover, absorption band intensities are determined by the transition dipole moment and there are extensive perturbation and coupling effects. Overall though, values of molar extinction coefficients for vibrational transitions, are up to 10 times lower in magnitude 

In general, there has been some misunderstanding about the nature of the vibrational transitions being observed, given the way IR spectroscopy is frequently referred to in terms of functional group vibrations. In fact, observed vibrational transitions are associated with normal vibrational modes. Each normal vibrational mode will in effect include contributions 

IR spectroscopy of proteins is often seen as a technique complementary to CD spectroscopy for proteins. The IR spectroscopy of peptide links is particularly rich and useful given the extensive way in which the energies of vibrational transitions associated with the normal vibrational modes centred on atom motions within peptide links can vary substantially. 

Raman spectroscopy seeks to analyse vibrational transitions in biological macromolecnles in a complementary way to IR spectroscopy. The physical basis of the technique is somewhat different as well. Initially, an intense beam of light of frequency Vy is used to irradiate a sample of molecules of interest in order classically to induce oscillating dipoles of equivalent frequency in the polarisable clouds of electrons. The time dependent magnitude of the induced dipole, /rind(t) obeys 

The molecular singlet ground state Sa is promoted to singlet excited state Sb at a rate of photon absorption, Bab related to the transition dipole moment (see Expression (4.2)) by 

In infra-red spectroscopy, a molecule is irradiated with infra-red light, which excites the vibrational transitions, and the absorbance of this light is measured directly. 

In Raman spectroscopy, a molecule is irradiated with monochromatic light. 

Most of the light scattered by the molecule is at the same wavelength as the irradiating light, but scattering also occurs at wavelengths above and below that of the incident beam, but at much lower intensity. This is known as Raman scattering, and it arises from the modulatory effects of molecular vibrations on the incident beam. 

For light to be absorbed by a molecule it must have the right frequency with respect to the molecular energy levels and also it must have a direct effect on the molecule. 

Infra-red spectroscopy can be carried out using dry samples (e.g., in films) or with non-aqueous solvent. Neither of these conditions is particularly suitable for the study of biomolecules and this limits the application of the technique. 

The intention in this chapter is to provide the reader with a balanced picture of the complementary roles of Raman and infrared spectroscopy in polymer characterisation. The emphasis chosen is towards practical applications, particularly those of significant industrial or analytical relevance. An attempt has been made to target as wide a range as possible, and to give examples of the many chemical and physical characterisations regularly undertaken. In doing this the intention is to provide as well exampled and referenced a text as could reasonably be accommodated, and to have provided those interested in more detail with a short route to important texts. Unfortunately, space constraints have inevitably necessitated the omission of certain important classes of materials such as biomolecules and conducting polymers. 

The two techniques most commonly used to observe vibrational spectra are infrared (IR) and Raman spectroscopy, although other techniques such as neutron scattering [8] can also be employed. Methods for obtaining IR and Raman data are considered in section 4.3, and comprehensive reviews have been given elsewhere [9, 10]. The IR spectrum arises from the absorption of radiation the frequency of which is resonant with a vibrational transition, while the Raman effect results from inelastic scattering of photons to leave a molecule or crystal in a vibrationally excited state. The shift in frequency of the scattered photon corresponds to the frequency of the normal mode that has been excited. 

Vibrational spectroscopies are particularly useful for the analysis of the adsorbed layers on metallic particles. Among them, infrared spectroscopy is of widespread use and provides a powerful tool in the study of metal-based catalysts under reaction conditions. Under the approximation of vibrational and rotational coordinate separation, the vibrational wavefunction by is a function of the internal coordinates (Qk) and is a solution of the vibrational hamiltonian. Assuming a quadratic approximation of the potential energy in terms of the internal coordinates, then  

Under the dipole approximation of the molecule radiation field interaction (see previous section), the coefficient of absorption under vibrational excitation between initial and final vibrational states is given by  

The main drawback of infrared spectroscopy can be interference from the gas phase and bulk contributions (for example of supporting oxides) which result in the loss of information in several key regions of the spectrum. 

One point to mention is that SFG is not fully independent of the gaseous environment. At pressures above 1 Torr, a significant energy dependent 

These and previous studies were in agreement with the belief that the CO oxidation reaction is essentially structure insensitive and thus independent of particle size, but IRAS studies using model Pd catalysts were able to show in fact that such reaction displays a weak structure sensitivity.154 When the temperature-ramp (light-off) experiment was repeated using different O2 CO ratios, a relationship was observed between the temperature at which this invariance in the carbonyl stretching frequency was initiated, and attainment of ca. 80% CO to CO2 conversion (Fig. 3.8). 

Vibrational spectroscopies are particularly useful for the analysis of the adsorbed layers on metallic particles. Among them, infrared spectroscopy is of widespread use and provides a powerful tool in the study of metal-based catalysts under reaction conditions. Under the 

Another point in interpreting infrared spectra of adsorbed layers is the coupling interaction between adsorbates. This primarily depends on the nature of the adsorbate-adsorbent bond. For CO this bond is mainly covalent-dative, while for NO it is mostly 

One point to mention is that SFG is not fully independent of the gaseous environment. At pressures above 1 Torr, a significant energy-dependent infrared absorption occurs via vibrational and rotational excitation of gas phase molecules. Since the intensity of the SFG depends on the input infrared beam intensity, gas pressure indirectly influences the outcome of SFG. To compensate for such an effect, several strategies have been proposed. Another point is that the SFG phenomenon depends on both infrared and Raman absorption coefficients and therefore correlation of band intensity with adsorbate concentration is not straightforward. 

While IR-based techniques can be considered as a whole as the most widely available tool used for analysis of catalytic samples, it is apparent that its use under real, in situ conditions is not as widely employed as might be expected. The use of SFG is even more scarce with regard to real catalysts. A detailed review of the use of infrared in catalysts up to 2001 has been published by Ryczkowky. More recent, in iito-type of studies involve the preparation of catalysts, the presence of poisons during the preparation step, or 

Phosgene has attracted a tremendous amount of attention, both experimental and theoretical, because of its essentially simple structure. Indeed, it has become a classical aid for teaching vibrational analysis and group theory. It possesses C2v symmetry (see Appendix A4), and the fundamental vibrational modes, their symmetry and activity are illustrated in Fig. 7.2. 

The results of infrared and Raman studies of phosgene are summarized in Tables 7.2 and 7.3, respectively. In addition, the infrared spectrum of gaseous phosgene has been included in standard catalogues of common molecules [1462a,1463,1615,1859]. Bands originally 

The absorption coefficients, a, for phosgene have been measured at three different CO 

The vibration-rotation spectra of the v, and v bands of CO C1 j have been measured (using a tunable semiconductor-diode laser), and assigned with the aid of Stark modulation spectra [2224]. The precise values of these bands were determined to be 1828.2012 and 851.0105 cm , respectively, and the equilibrium rotational constants for CO Clj were calculated as = 7950.35, Bg = 3490.22, and Cg = 2425.44 MHz cf. 

There have been a large number of determinations of molecular force constants, mean amplitudes of vibration, bond asymmetry parameters, Coriolis coupling constants (and inertia defects) and centrifugal distortion constants [146,152,259,271,304,581,840,1221,1222,1278,1312, 1416,1448,1449,1549,1550,1575-1578,1587,1618,1671,1682,1806,1807,1858,1931,1961,1984,2021,2045, 2108,2109-2111,2167a], as well as a determination of the atomic potential energy distribution 

As we have seen, a molecule can be approximated as a collection of atoms held together by bonds. In describing the vibrations in a molecule, we can compare the bond between a given pair of atoms to a spring attached to two masses. As the atoms move apart in a vibrational motion, the bond—like a spring—provides a restoring force that pulls the atoms back toward each other. 

The potential curve for a diatomic molecule (blue) where / e represents the equilibrium bond distance and De is the bond dissociation energy. The parabolic curve (red) represents the behavior of a true harmonic oscillator. 

This equation assumes harmonic behavior where the vibrational levels are equally spaced (separated by an energy equivalent to v0). However, bonds do 

For purposes of determining the force constant for a particular bond, the energy required for the v = 0 to u = 1 transition is used (this is assumed to be v0). This procedure is illustrated in Example 14.9. Vibrational transitions in molecules typically require energies that correspond to the infrared region of the electromagnetic spectrum. The data are often represented in wave numbers a wave number is the reciprocal of the wavelength (in cm) required to cause the vibrational transition. 

The infrared spectrum of gaseous HC1 (1H3SC1) shows the v = 0 to v = 1 transition at 2885 cm-1. Calculate the vibrational force constant for the HC1 molecule. 

V = the vibrational quantum number, which can assume only the values 0, 1, 2, 3,. . .  

This equation assumes harmonic behavior where the vibrational levels are equally spaced (separated by an energy equivalent to np). However, bonds do not behave exactly like springs (for example, the restoring force is weaker for a bond than is predicted for a spring at greatly stretched bond lengths). The actual potential energy curve (called the Morse potential) for a bond is represented by the blue curve in Fig. 14.58 and is shown in detail in Fig. 14.59. 

Note that the vibrational energy spacings on the Morse potential get smaller with increasing n, leading to anharmonic behavior. 

The essential signature of a molecule is tiiat it vibrates. For a molecule composed of N atoms, there are 3N mechanical degrees of freedom associated with the motions of the system. Three degrees of freedom are determined by the translational motions of the center of mass, and for a nonlinear molecule there are three degrees of freedom connected with the overall rotational motion of the molecule. For a macromolecule, some of the remaining 3N - 6 degrees of freedom are associated with isomerizations of the chain backbone and the side chains. Finally, there exists a set of quantized vibrational states for the molecule. If the frequencies of the vibrational states depend on the conformational state of the molecule, the measurement of the vibrational spectrum can be used to infer the conformational composition of the ensemble of macromolecules. The frequencies of quantized molecular vibrations greatly exceed the frequencies associated with isomerization of the chain backbone. 

The motion of atoms relative to one another in molecules and crystals involves changes in energy. The frequencies of these vibrations 

Here we are studying the absorption of infra-red radiation from a continuous source. The spectrum is a plot of the absorbance of the sample as a function of the frequency of the incident radiation. Each peak (or band) in the spectrum corresponds to the absorption of a photon with the concomitant excitation of a normal mode of vibration -, some relatively weak bands (overtones) involve the double excitation of a vibrational mode, while the simultaneous excitation of two different modes may appear as a combination band, but these need not concern us further. 

A molecule - ring TV atoms has 37V - 6 normal modes of vibration (or 37V - 5 if it is linear). Each can be represented by a set of arrows, one on each atom, giving the direction along which the atom moves back and forth as the mode is executed. For example, the three normal modes of a bent AB2 molecule can be represented as  

At the most empirical level, IR spectra provide valuable fingerprints of substances since the spectrum is so sensitive to structural details. At a slightly higher level of elaboration, we can identify specific bonds or groupings of atoms whose stretching and deformation frequencies fall 

IR spectroscopy is not confined to stable substances. In recent years, matrix isolation IR spectroscopy has become important in the investigation of short-lived, unstable molecular species. A gas containing such highly-reactive molecules - produced by photolysis of a reaction mixture, or in a high-temperature furnace - is suddenly cooled by contact with an inert solid (e.g. argon at c. 40 K). The matrix-isolated molecules are protected by the low temperature from unimolecular decomposition, and - by sheer isolation, if the dilution is sufficient - from bimolecular processes such as dimerisation or disproportionation. For example, the photolysis of Mn(CO)5H by a laser produces the otherwise unstable Mn(CO)5 and Mn(CO)4H molecules whose IR spectra can be measured in an argon matrix. Because of the low temperature, the lack of inter-molecular interactions and the rigidity with which the molecules are trapped in the matrix, such spectra are often very well resolved, better than can be achieved by conventional methods. Thus matrix isolation spectroscopy is widely used in the study of stable species, in preference to conventional techniques. 

The frequency, v, of a stretching vibration between two atoms of mass Mx and My is given by the formula  

Steven M. Howdle, Michael W. George and Martyn Poliakoff 

Supercritical fluids (SCFs) have proved to be versatile media for a wide range of chemical processes [1] from stereoselective organic chemistry [2] through catalytic hydrogenation [3], polymer synthesis [4] and polymer modification [5] to the preparation of novel inorganic materials [6] and organometallic complexes [7]. IR and Raman spectroscopy have played a significant role [8] in many of these developments. 

An additional complication with SCF processes is the possibility of complex phase behavior. A thorough understanding of the phase behavior of each reaction mixture is desirable, but not always possible. There is an extensive literature devoted to the investigation and prediction of phase behavior of SCFs [11], and the subject is introduced in chapter 1.2. Spectroscopic monitoring can provide at least an indication of phase behavior for example, which compounds are dissolved in which phase, as well as a method for monitoring the progress of reactions and identifying intermediates and products. It is best to resist the temptation to treat a supercritical reactor as a black box, and simply 

There are already several excellent reviews and multiauthored books that describe various designs for high pressure spectroscopic vessels [10,12-16]. This chapter demonstrates the use of vibrational spectroscopy for in situ monitoring of chemical reactions in SCFs. 

A key consideration in vibrational spectroscopy is to ensure the effective delivery of the IR beam to the SCF and the subsequent collection of the light. This involves choosing the correct window materials and ensuring that the spectroscopic features of interest are not so weak that they cannot easily be detected, nor so strong that they become totally absorbing. 

These lead to the following corrected ranges for linear complexes  

The narrower ranges when combined with isotope shifts for and (NO) have been used to distinguish linear and bent nitrosyl complexes, and it was noted that isotope shift differences are more discriminating than isotope frequency ratios. The review also analyses the data for bridging nitrosyl and analyses environmental and solvent effects. Infrared spectroscopy has proved particularly useful for identifying complexes which have structural isomers in the sohd state. For example. 

3 Effects of Ions on Water Structure and Vice Versa 

One of the major ideas in quantum mechanics is that you can know things only within certain limits. (Do I really need quantum mechanics to tell me this ) 

Specifically, a statement known as the principle of uncertainty - or Heisenbergs Uncertainty Principle - tells us that once you know the interaction energy of two atoms in a molecule you cannot know their positions very accurately. This relation, named in honor of the German physicist Werner Heisenberg, can be expressed in the following way  

Here v is the vibrational quantum number, h and c are of course Planck s constant and speed of light, in this order, and a is something new. People who measure the motions of atoms in molecules call it wavenumber its unit is a reciprocal centimeter, cm The range of observed atomic vibrations in most molecules is typically between 250 and 3650 cm The vibrational quantum number v takes positive integer values 0, 1, 2, 3. similar to the quantum number n in the infinite potential well model. Note that when v = 0 vibrational energy does not go to zero, Eo = 1/2 X h c a this is known as zero potential energy, ZPE. 

Make a note ZPE - zero potential (vibrational) energy, Eq = 1/2 x he a 

According to harmonic approximation the H- CI molecule vibrates with a force constant k = 480.6 [N m ]. Assuming that the harmonic model holds for this molecule, and keeping in mind that the average H—Cl bond energy is 451 kJ mol , predict the vibrational quantum level at which the H-CI molecule will dissociate. 

1 The normal modes of vibration of C2H4 are shown below. By inspection of the D2h character table, deduce the symmetry species to which the normal modes belong. The coordinate system adopted is shown on the right. 

2 Phosphorus oxychloride, OPCI3, is a colorless, moisture-sensitive liquid. This molecule has C3v symmetry and its infrared and Raman spectra exhibit the following bands (in cm )  

3 The noble gas compound Xe03p2 has a trigonal bipyramidal structure with Dsh 

4 Consider the square pyramidal molecule xenon oxide tetrafluoride, XeOp4, with C4V symmetry. A convenient coordinate system for this molecule is shown on the right. In our convention, each symmetryplane 7v passes through two F atoms, while the aa planes do not. 

Note N.O. denotes not observed (but expected ) s for strong w for weak m for medium v for very . In the Raman spectrum, one more band is expected, but not observed. 

CIS isomer is indicative of a band splitting which is not resolved in the spectrum). Another origin of band splitting which may conveniently be mentioned at this point is that which occurs in a ligand mode when there is a decrease in ligand symmetry on coordination. For instance, the infrared active v(S-O) stretches of the isolated (tetrahedral, T ) sulfate anion appear as a single band (the mode is of T2 symmetry), which splits, loses degeneracy, on coordination. 

The higher frequency bands in both spectra are the (totally symmetric, breathing mode) and the lower Eg, the components of which are split apart. This latter splitting—and all the frequency differences between the two spectra—show the importance of solid-state effects, in which they originate. (Adapted and reproduced with permission from T. N. Day, 

Bonner and Jumper [37], corresponding to hydrogen-bonded and non-bonded water gronps. Cations increased the fraction of the hydrogen-bonded water relative to that in pnre water whereas anions decreased it, but it is not clear how the observed changes were allocated to cations and anions. 

Pulsed two-color mid-infrared ultra-fast spectroscopy was used to study the effect of ions on the structural dynamics of their aqueous solutions by Bakker s group [44]. The pump pulse that excited the 0-H (or 0-D) stretch vibration to the first excited state was provided first, and then after a short delay, the probe pulse, which was red-shifted with respect to the first, probed the decay of this state. Solutions of 0.5 to 

10 M of lithium, sodium, and magnesium halides and of KF, NaClO, MgCClO ), and Na SO in 0.1 to 0.5 M HDO in D O were studied by this technique. The rotational anisotropy 

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M. L. Hair, Vibrational Spectroscopies for Adsorbed Species, ACS Symposium Series No. 137, A. T. Bell and M. L. Hair, eds., American Chemical Society, Washington, DC, 1980. 

Vibrational Spectroscopy. Infrared absorption spectra may be obtained using convention IR or FTIR instrumentation the catalyst may be present as a compressed disk, allowing transmission spectroscopy. If the surface area is high, there can be enough chemisorbed species for their spectra to be recorded. This approach is widely used to follow actual catalyzed reactions see, for example. Refs. 26 (metal oxide catalysts) and 27 (zeolitic catalysts). Diffuse reflectance infrared reflection spectroscopy (DRIFT S) may be used on films [e.g.. Ref. 28—Si02 films on Mo(llO)]. Laser Raman spectroscopy (e.g.. Refs. 29, 30) and infrared emission spectroscopy may give greater detail [31]. 

STM has also been adapted for perfonning single-atom vibrational spectroscopy [73],... 

Stipe B C, Rezaei M A and Flo W 1998 Single-molecule vibrational spectroscopy and microscopy Science 280 1732... 

Raduge C, Pfiumio V and Shen Y R 1997 Surface vibrational spectroscopy of sulfuric acid-water mixtures at the liquid-vapor interface Chem. Phys. Lett. 274 140... 

Shen Y R 1998 Sum frequency generation for vibrational spectroscopy applications to water interfaces and films of water and ice Solid State Commun. 108 399... 

The secondary hydration sheath has also been studied using vibrational spectroscopy. In the presence of... 

Miller R E 1988 The vibrational spectroscopy and dynamics of weakly bound neutral complexes Scianca 240 447-53... 

Vibrational spectroscopy provides detailed infonnation on both structure and dynamics of molecular species. Infrared (IR) and Raman spectroscopy are the most connnonly used methods, and will be covered in detail in this chapter. There exist other methods to obtain vibrational spectra, but those are somewhat more specialized and used less often. They are discussed in other chapters, and include inelastic neutron scattering (INS), helium atom scattering, electron energy loss spectroscopy (EELS), photoelectron spectroscopy, among others. 

Vibrational spectroscopy is an enomiously large subject area spamiing many scientific disciplines. The methodology, both experimental and theoretical, was developed primarily by physical chemists and has branched far and wide over the last 50 years. This chapter will mainly focus on its importance with regard to physical chemistry. 

Raman scattering has been discussed by many authors. As in the case of IR vibrational spectroscopy, the interaction is between the electromagnetic field and a dipole moment, however in this case the dipole moment is induced by the field itself The induced dipole is pj j = a E, where a is the polarizability. It can be expressed in a Taylor series expansion in coordinate isplacement... 

There are thousands of scientists whose work can be classified as vibrational spectroscopy. The following examples are meant to show the breadth of the field, but cannot be expected to constitute a complete representation of all the fields where vibrational spectroscopy is important. 

The temi action spectroscopy refers to those teclmiques that do not directly measure die absorption, but rather the consequence of photoabsorption. That is, there is some measurable change associated with the absorption process. There are several well known examples, such as photoionization spectroscopy [47], multi-photon ionization spectroscopy [48], photoacoustic spectroscopy [49], photoelectron spectroscopy [, 51], vibrational predissociation spectroscopy [ ] and optothemial spectroscopy [53, M]. These teclmiques have all been applied to vibrational spectroscopy, but only the last one will be discussed here. 

Vibrational spectroscopy has been, and will continue to be, one of the most important teclmiques in physical chemistry. In fact, the vibrational absorption of a single acetylene molecule on a Cu(lOO) surface was recently reported [ ]. Its endurance is due to the fact that it provides detailed infonnation on structure, dynamics and enviromnent. It is employed in a wide variety of circumstances, from routine analytical applications, to identifying novel (often transient) species, to providing some of the most important data for advancing the understanding of intramolecular and intemiolecular interactions. 

Mathies R A 1995 Biomolecular vibrational spectroscopy Biochemical Spectroscopy Methods Enzymol. vol 246, ed K Sauer (San Diego, CA Academic) pp 377-89... 

Ayotte P, Bailey C G, Weddle G FI and Johnson M A 1998 Vibrational spectroscopy of small Br (Fl20) and I Fl20) clusters infrared characterization of the ionic hydrogen bond J. Phys. Chem. A 102 3067-71... 

Comprehensive treatment of vibrational spectroscopy, including data for a wide variety of molecules. 

The general task is to trace the evolution of the third order polarization of the material created by each of the above 12 Raman field operators. For brevity, we choose to select only the subset of eight that is based on two colours only—a situation that is connnon to almost all of the Raman spectroscopies. Tliree-coloiir Raman studies are rather rare, but are most interesting, as demonstrated at both third and fifth order by the work in Wright s laboratory [21, 22, 23 and 24]- That work anticipates variations that include infrared resonances and the birth of doubly resonant vibrational spectroscopy (DOVE) and its two-dimensional Fourier transfomi representations analogous to 2D NMR [25]. 

Wright J C, Labuda M J, Zilian A, Chen P C and Hamilton J P 1997 New selective nonlinear vibrational spectroscopies J. Luminesc. 72-74 799-801... 

Labuda M J and Wright J C 1997 Measurement of vibrationally resonant and the feasibility of new vibrational spectroscopies Phys. Rev. Lett. 79 2446-9... 

Khidekel V and Mukamel S 1995 High-order echoes in vibrational spectroscopy of liquids Chem. Phys. Lett. 240 304-14... 

We now present one of the many examples of interfacial vibrational spectroscopy using SFG. Figure Bl.5.15 shows the surface vibrational spectrum of the water/air interface at a temperature of 40 °C [83]. Notice that... 

Dumas P, Weldon M K, Chabal Y J and Williams G P 1999 Molecules at surfaces and interfaces studied using vibrational spectroscopies and related techniques Surf. Rev. Lett. 6 225-55... 

Bain C D 1995 Sum-frequency vibrational spectroscopy of the solid-liquid interface J. Chem. See. Faraday Trans. 91 1281-96... 

Richmond G L 1997 Vibrational spectroscopy of molecules at liquid/liquid interfaces Ana/. Chem. 69 A536-43... 

Zhu X D, Suhr H and Shen Y R 1987 Surface vibrational spectroscopy by infrared-visible sum frequency generation Phys. Rev. B 35 3047-59... 

Du Q, Superfine R, Freysz E and Shen Y R 1993 Vibrational spectroscopy of water at the vapor-water interface Phys. Rev. Lett. 70 2313-16... 

The major role of TOF-SARS and SARIS is as surface structure analysis teclmiques which are capable of probing the positions of all elements with an accuracy of <0.1 A. They are sensitive to short-range order, i.e. individual interatomic spacings that are <10 A. They provide a direct measure of the interatomic distances in the first and subsurface layers and a measure of surface periodicity in real space. One of its most important applications is the direct determination of hydrogen adsorption sites by recoiling spectrometry [12, 4T ]. Most other surface structure teclmiques do not detect hydrogen, with the possible exception of He atom scattering and vibrational spectroscopy. 

Zhu L, Wang W, Sage J T and Champion P M 1995 Femtosecond time-resolved vibrational spectroscopy of heme proteins J. Raman Spectrosc. 26 527-34... 

As with the uncoupled case, one solution involves diagonalizing the Liouville matrix, iL+R+K. If U is the matrix with the eigenvectors as cohmms, and A is the diagonal matrix with the eigenvalues down the diagonal, then (B2.4.32) can be written as (B2.4.33). This is similar to other eigenvalue problems in quantum mechanics, such as the transfonnation to nonnal co-ordinates in vibrational spectroscopy. 

Molecular clusters are weakly bound aggregates of stable molecules. Such clusters can be produced easily using supersonic expansion, and have been extensively studied by both electronic and vibrational spectroscopy [146,... 

Handschuh H, Gantefor G and Eberhardt W 1995 Vibrational spectroscopy of clusters using a magnetic bottle electron spectrometer Rev. Sci. Instnim. 66 3838... 

Cwrutsky J C, Li M, Culver J P, Sarisky M J, Yodh A G and Hoohstrasser R M 1993 Vibrational dynamios of oondensed phase moleoules studied by ultrafast infrared speotrosoopy Time Resolved Vibrational Spectroscopy VI (Springer Proc. in Physics 74) ed A Lau (New York Springer) pp 63-7... 

As mentioned, we also carried out IR studies (a fast vibrational spectroscopy) early in our work on carbocations. In our studies of the norbornyl cation we obtained Raman spectra as well, although at the time it was not possible to theoretically calculate the spectra. Comparison with model compounds (the 2-norbornyl system and nortri-cyclane, respectively) indicated the symmetrical, bridged nature of the ion. In recent years, Sunko and Schleyer were able, using the since-developed Fourier transform-infrared (FT-IR) method, to obtain the spectrum of the norbornyl cation and to compare it with the theoretically calculated one. Again, it was rewarding that their data were in excellent accord with our earlier work. 

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