Related Experiment Video
Updated: Mar 7, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Analytic hyperpolarizability and polarizability derivative with fractional occupation numbers for large extended
1Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan.
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.
Related Concept Videos
Potential Due to a Polarized Object
Kohlraush’s Law and its Applications
Bond Polarity, Dipole Moment, and Percent Ionic Character
Debye–Huckel–Onsager Conductance Equation
Susceptibility, Permittivity and Dielectric Constant
The Debye–Hückel Theory of Electrolyte Solutions

