title: Analytic hyperpolarizability and polarizability derivative with fractional occupation numbers for large extended systems.
abstract: The analytic hyperpolarizability and polarizability derivative with fractional occupation numbers are derived using Wigner's 2n + 1 rule. The formulation contains no terms that blow up for quasi-degenerate systems. The density-functional tight-binding method is used for implementation, which makes it possible to compute these third-order derivatives for systems containing up to one thousand atoms within 8 h using 24 CPU cores. A comparison between analytic and numerical non-resonance Raman activity spectra indicates that the numerical differentiation approach can give a significant deviation unless the strength of perturbative electric field is carefully chosen. With extremely high electronic temperatures, the polarizability and hyperpolarizability should converge to zero.
authors.affiliation: Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan.
authors.forename: Yoshio
authors.identifier: 0000000155814712
authors.initials: Y
authors.lastname: Nishimoto