Analytical TDHF second derivatives of dynamic electronic polarizability with respect to nuclear coordinates. Application to the dynamic ZPVA correction

Analytical calculation of second derivatives of the dynamic electronic polarizability with respect to vibrational normal coordinates has been implemented at the TDHF level of approximation. Important simplifications are obtained by using the 2n + 1 rule and interchange relations. In application to small molecules the first-order ZPVA correction is found to have greater frequency dispersion than the electronic polarizability, but the former remains small in comparison. For the linear polyenes, C_2nH_2n+2 (n = 1-3), the percentage ZPVA correction decreases with chain length for all ℏω < 0.10 a.u.