Vibrational Contributions to Electric Polarizabilities

In this section, we shall present the results of calculations of vibrational contributions to a and (3 performed at the HF/6-31G level of theory for 1, 2, 3 (Fig.3.1) and 11 (Fig. 3.5). Due to the computational limitations, the nuclear relaxation (NR) contributions were evaluated only for 11. Since the diagonal components (along cartesian X axis) of electronic contributions to a and / were found to be dominant, we 

It was found for 11 that = 11.78 a.u. and is significantly smaller than the electronic counterpart (501.28 a.u.). However, the opposite trend was observed in the case of the static first-order hyperpolarizability. The electronic was found to be -35.8 a.u., while - -608.7 a.u. Thus, the ratio P xx l xx is equal to 17. In order to explain the origin of the large value, the analysis of contributing terms was performed. The value of the harmonic term is 128.7 a.u. which 

In Table3.9, the vibrational contributions for 11, 1, 2 and 3, calculated within the double-harmonic oscillator approximation are presented. The calculations were performed seminumerically, i.e. second derivatives of energy were calculated by differentiation of analytic first derivatives. Thus, the values of harmonic terms presented in Table 3.9 may serve as a reference point for numerical accuracy assessment of NR contributions discussed above. The relative error for [/uq ] ) term for 11 does not exceed 10%. It follows from Table3.9 that diagonal vibrational contributions to a 

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