Raman anharmonicity

Raman anharmonicities can be introduced as the infrared anharmonicities of the previous sections. The appropriate operator is... 

Electric Raman anharmonicities can also be introduced by considering, for example, operators of the form... 

Equations (6.5) and (6.12) contain terms in x to the second and higher powers. If the expressions for the dipole moment /i and the polarizability a were linear in x, then /i and ot would be said to vary harmonically with x. The effect of higher terms is known as anharmonicity and, because this particular kind of anharmonicity is concerned with electrical properties of a molecule, it is referred to as electrical anharmonicity. One effect of it is to cause the vibrational selection mle Au = 1 in infrared and Raman spectroscopy to be modified to Au = 1, 2, 3,. However, since electrical anharmonicity is usually small, the effect is to make only a very small contribution to the intensities of Av = 2, 3,. .. transitions, which are known as vibrational overtones. 

One effect of mechanical anharmonicity is to modify the Au = t infrared and Raman selection rule to Au = 1, 2, 3,. .., but the overtone transitions with Au = 2, 3,... are usually weak compared with those with Au = t. Since electrical anharmonicity also has this effect both types of anharmonicity may contribute to overtone intensities. 

Thus far we have discussed the direct mechanism of dissipation, when the reaction coordinate is coupled directly to the continuous spectrum of the bath degrees of freedom. For chemical reactions this situation is rather rare, since low-frequency acoustic phonon modes have much larger wavelengths than the size of the reaction complex, and so they cannot cause a considerable relative displacement of the reactants. The direct mechanism may play an essential role in long-distance electron transfer in dielectric media, when the reorganization energy is created by displacement of equilibrium positions of low-frequency polarization phonons. Another cause of friction may be anharmonicity of solids which leads to multiphonon processes. In particular, the Raman processes may provide small energy losses. 

Raman spectra of S2 in its triplet ground state have been recorded both in sulfur vapor and after matrix isolation using various noble gases. The stretching mode was observed at 715 cm in the gas phase [46], and at 716 cm in an argon matrix [71]. From UV absorption and fluorescence spectra of sulfur vapor the harmonic fundamental mode of the S2 ground state was derived as t e = 726 cm . The value corrected for anharmonicity is 720 cm [26, 27]. Earlier reports on the infrared absorption spectrum of 2 in matrix isolated sulfur vapor [72] are in error the observed bands at 660, 668 and 680 cm are due to S4 [17] and other species [73]. 

Contents Lattice Dynamics. - Symmetry. - Inter-molecular Potentials. - Anharmonic Interactions. - Two-Phonon Spectra of Molecular Crystals. -Infrared and Raman Intensities in Molecular Crystals. 

In our discussion the usual Born-Oppenheimer (BO) approximation will be employed. This means that we assume a standard partition of the effective Hamiltonian into an electronic and a nuclear part, as well as the factorization of the solute wavefunction into an electronic and a nuclear component. As will be clear soon, the corresponding electronic problem is the main source of specificities of QM continuum models, due to the nonlinearity of the effective electronic Hamiltonian of the solute. The QM nuclear problem, whose solution gives information on solvent effects on the nuclear structure (geometry) and properties, has less specific aspects, with respect the case of the isolated molecules. In fact, once the proper potential energy surfaces are obtained from the solution of the electronic problem, such a problem can be solved using the standard methods and approximations (mechanical harmonicity, and anharmonicity of various order) used for isolated molecules. The QM nuclear problem is mainly connected with the vibrational properties of the nuclei and the corresponding spectroscopic observables, and it will be considered in more detail in the contributions in the book dedicated to the vibrational spectroscopies (IR/Raman). This contribution will be focused on the QM electronic problem. 

The resonance Raman spectrum of K4[Mo2C18] has been reinvestigated using 488.0 and 514.5 nm excitation. An enormous enhancement of the intensity of the Mo—Mo stretching mode relative to the intensity of other fundamentals was observed and an overtone progression in Vj to 5vj identified. From these data the harmonic frequency and anharmonicity constant X, were calculated as 347.1 + 0.5 cm -1... 

The sensitivity of the phonon frequencies to temperature shows quite clearly the importance of their anharmonicity.42 The width of the Raman peaks, very small at low temperature ( 1cm-1), evolves in parallel with the frequency shift with temperature, which is still a consequence of the phonon-phonon interactions due to the anharmonicity. The fundamental reason for this strong anharmonicity, as well as the importance of the equilibrium-position shifts between 4 and 300 K,45 resides in the weakness of the van der Waals cohesive forces in the molecular crystal. 

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