Anharmonic shift

The results for various alcohol solutions are compiled in Table 2. The data refer to room temperature except for methanol in C5CI6, which was measured at 333 K. A few spectroscopic parameters are shown in the first four lines. There is evidence for inhomogeneous broadening of the monomeric OH-stretching vibration for the various investigated alcohols with a width of the observed spectral holes as small as 50% of the conventional absorption band (DMEP). The anharmonic shift of the OH mode is indicated in the table to amount to 170 cm-1, independent of solute or solvent within experimental accuracy. The large anharmonicity of the monomeric alcohols is noteworthy. The population lifetime Ti of the mode... 

All data are taken at room temperature besides the one shown for methanol diluted in C5CI6 (T = 333 K). vc peak position of the OH stretch Ar>h, AV12 spectral width of the transient hole and the excited-state absorption, respectively anharmonic shift vc — V12 Ti, T10, ror time constants for the vibrational lifetime of the OH, ground state filling and reorientation, respectively. 

In order to calculate the response function of the Feynman diagram R3, it is further assumed that the transition frequency co 12 is anharmonically shifted with respect to the ground states transition frequency so that, u>n = >oi -A. Another assumption that can be made (see later for a discussion of these assumptions) is that the fluctuations between both level pairs are strictly correlated <5co12 = <5 j0i. This implies that only the harmonic part of the potential surface is perturbed by the bath fluctuations and the anharmonicity of the vibrator is unaffected. We then obtain for R3 ... 

State at the bottom of the band resembles that of the local anharmonic state, whereas the states at the higher-energy side of the exciton band appear more harmonic. The two diagonal dashed lines in Fig. 8 represent the local anharmonic shift. 

In Equation (8), A represents the anharmonic shift and F the anharmonic broadening. Both A and F are proportional to nj, the Bose phonon occupation numbers - 1)" ], and at temperatures such that kT fi(jjj, rij is propor-... 

Table 6.3 Anharmonic shift of the r phonon frequency in diamond...

Avj (K, co) is the so called anharmonic shift of the fundamental frequency of mode k, the computationally most demanding part of the calculations, requiring the evaluation of the numerical third and fourth derivatives of the PES and the treatment of the Fermi resonances. The anharmonic shifts can be seen as corrections with respect to the harmonic frequencies, in most cases not exceeding 5%, but are very important when vibrational frequencies need to be computed with a high accuracy, or even for a qualitative analysis for example, for a C-H stretching mode typically at about 3000 cm", an anharmonic correction... 

Regardingthe intensities, the transition dipole moment for a generic fundamental transition (Eq. 10.27) can be split into a doubly harmonic term (i.e., depending only on and co) and an anharmonic shift (depending also on and K),... 

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