Calculation of ab initio dynamic hyperpolarizabilities of polymers

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Abstract
The coupled Hartree–Fock (CHF) equations in second order are derived to calculate dynamic polarizabilities and hyperpolarizabilities for infinite periodic chains. The analytical expressions for the second derivatives of the perturbed crystal orbitals with respect to the quasimomentum k are developed. The first and second derivatives are required on behalf of the definition of the perturbation operator describing the effect of the time-dependent electric field on the electronic structure of the polymer. The computer program has been applied to calculate the tensor elements of the second-harmonic generation and the optical rectification for the model chain poly(water) and the conjugated π-electron system poly(carbonitrile), respectively. The CHF-results are compared with uncoupled Hartree–Fock (UCHF) calculations.