Polarizability zero-point vibrational average

There are two ways in which molecular vibrations affect non-linear optical properties. The first, which is well understood, is zero-point-vibrational averaging of the calculated electronic properties. This need not delay us long. The second comes about from the effect that the electromagnetic radiation has on the vibrational motions themselves and this leads to the vibrational polarizabilities and hyperpolarizabilities which are the exact counterparts of the electronic ones which stem from the effect that the radiation has on the electronic motions. This phenomenon is now receiving long overdue attention and will be the main subject of this section. A more extensive review is available elsewhere [2]. 

Santiago et a/. ° have calculated at the Time-Dependent Hartree-Fock level the vibrational contributions to the dynamic (hyper)polarizabilities of H2O2 and have demonstrated that, though smaller than their electronic counterparts, the zero-point vibrational average contributions increase faster with the frequency. 

For the vibrational ground state with quantum number u = 0 the averaged polarizabilities are often expressed as e sum of the polarizability at an equilibrium geometry, i e, and a zero-point-vibrational correction (ZPVC)... 

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