Vibrational interactions

Tokmakoff A, Lang M J, Larsen D S, Fleming G R, Chernyak V and Mukamel S 1997 Two-dimensional Raman spectroscopy of vibrational interactions in liquids Phys. Rev. Lett. 79 2702-5... 

R. E. Pennington and K. A. Kobe. Contributions of Vibrational Anharmonicity and Rotation-Vibration Interaction to Thermodynamic Functions". J. Client. Plus., 22. 1442-1447 (1954). 

Using the impact approximation presented in Chapter 6, they may easily be found for any rotational band even if rotational-vibrational interaction is nonlinear in J. In 1954 R W. Anderson proved as a theorem [104] that expansion of the spectral wings in inverse powers of frequency is controlled by successive odd derivatives of the correlation function at the origin. In impact approximation the lowest non-zero derivative of this type is the third and therefore asymptotics G/(co) is described by the power expansion [20]... 

One possibility for this was demonstrated in Chapter 3. If impact theory is still valid in a moderately dense fluid where non-model stochastic perturbation theory has been already found applicable, then evidently the continuation of the theory to liquid densities is justified. This simplest opportunity of unified description of nitrogen isotropic Q-branch from rarefied gas to liquid is validated due to the small enough frequency scale of rotation-vibration interaction. The frequency scales corresponding to IR and anisotropic Raman spectra are much larger. So the common applicability region for perturbation and impact theories hardly exists. The analysis of numerous experimental data proves that in simple (non-associated) systems there are three different scenarios of linear rotator spectral transformation. The IR spectrum in rarefied gas is a P-R doublet with either resolved or unresolved rotational structure. In the process of condensation the following may happen. 

The probability that J has a wave vector K relative to I in HD + is given by the momentum transform of the wave function for the vibrational and rotational interactions in HD +. The probability that I is captured by X with a wave vector k is given by the momentum transform of the wave function for the rotational and vibrational interactions in XI+. 

Persson BNJ, Ryberg R. 1981. Vibrational interaction between molecules adsorbed on a metal surface The dipole-dipole interaction. Phys Rev B 24 6954-6970. 

A number of other models were considered and tested (for example, direct B—H bonding). The most significant test was the IR vibrational spectrum, where a sharp absorption band at 1875 cm-1 was found, corresponding to the Si—H stretch mode softened by the proximity of the B-atom. Had the hydrogen been bonded to boron, a sharp absorption band at 2560 cm-1 would have been expected. Also, Johnson (1985) showed that deuteration produced the expected isotopic shift. The most definitive and elegant proof of the correctness of the Si-H-B bonding model was provided by Watkins and coworkers (1990), on the basis of a parametric vibrational interaction between the isotopes D and 10B. 

The book covers a variety of questions related to orientational mobility of polar and nonpolar molecules in condensed phases, including orientational states and phase transitions in low-dimensional lattice systems and the theory of molecular vibrations interacting both with each other and with a solid-state heat bath. Special attention is given to simple models which permit analytical solutions and provide a qualitative insight into physical phenomena. 

The electrons produced during the first and subsequent collisions may be energetic enough to cause further ionisation and excitation (delta rays) until they reach the subionisation and suhexcitation levels characteristic of the material. Finally, they undergo rotational-vibrational interactions until they reach thermal energies. 

The rotational Herman-Wallis factor Fv< v(m) of the operator (2.140) is still that of a rigid rotor. In order to describe rotational-vibrational interactions, one must introduce explicitly the angular momentum J. To lowest order, the dipole operator that includes rotational-vibrational interactions is... 

We have discussed up to now vibrational spectra of linear and bent triatomic molecules. We address here the problem of rotational spectra and rotation-vibration interactions.3 At the level of Hamiltonians discussed up to this point we only have two contributions to rotational energies, coming from the operators C(0(3]2)) and IC(0(412))I2. The eigenvalues of these operators are... 

We begin our study of rotation-vibration interactions by considering the class of operators h2,2- In this class we can distinguish two types of operators (1) diagonal and (2) nondiagonal operators. 

The most general expression for type (1) rotation-vibration interactions is... 

The most general expression for type (1) rotation-vibration interactions is still given by (4.118) but with hRV given by Eq. (4.96) with the coefficients... 

Similar expressions hold for +2,11 and T222. The most general nondiagonal rotation-vibration interaction can be written as... 

Properties of nondiagonal rotation-vibration interactions Linear molecules... 

The rotation-vibration interaction of the previous section can be rewritten in terms of the usual quantum numbers of linear molecules vav hbv,.JM > by making use of Eq. (4.53). By explicit evaluation, one can show that, for fixed values of va, vh,vc, the matrix elements of Eq. (4.127) have selection rules... 

Diagonalization of the rotation-vibration interaction produces splittings of the individual (degenerate) levels, as shown schematically in Figure 4.22. It is interesting to note that the matrix elements of Eq. (4.124a) can be approximately written as... 

The rotation-vibration interaction of Section 4.32 produces different effects in nonlinear molecules than those discussed in the previous section. In nonlinear molecules the quantum numbers are vavhvcKJM >. The connection between the group quantum numbers Ico , co2> xi > 2 -A 3/ > and the usual quantum numbers is given by Eq. (4.85). The different effect can be traced to the different nature of the rotational spectrum. In lowest order, the spectrum of a bent molecule is given by Eq. (4.107) and Figure 4.21. The rotation-vibration interaction introduces terms with selection rules... 

For fixed va,vb,vc and 7, there are 27 + 1 initially degenerate states with /IT = 0, 1, 2,..., 7. The rotation-vibration interaction splits these states. The matrices to diagonalize are of the type ... 

Iachello, F., Oss, S., and Viola, L. (1993b), Rotation-Vibration Interaction and Fermi Resonances of HCCF in the Vibron Model, Mol. Phys. 78, 561. 

I have predicted that the very unusual low-frequency IR behavior for the Creutz-Taube ion calculated by Piepho, Schatz and Krausz [Piepho, S. B. Krausz, E. R. Schatz, P. N. J. Am. Chem. Soc. 1978, 100, 2996] on the assumption of only antisymmetric mode involvement in electron-vibrational interaction would not be found, and that it was an artifact of the method. The failure of experiments designed to locate such IR bands has subsequently been reported by Krausz, et al. 

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