title: Dynamic hyperpolarizability calculations of large systems: the linear-scaling divide-and-conquer approach.
abstract: We report a linear-scaling computation method for evaluating the dynamic first hyperpolarizability β based on the divide-and-conquer (DC) method. In the present scheme, we utilized the quasi-density-matrix expression derived from Wigner's (2n + 1) rule for β, where the quasi-density matrices are constructed from the solution obtained via the DC time-dependent self-consistent field (TD-SCF) method [T. Touma, M. Kobayashi, and H. Nakai, Chem. Phys. Lett. 485, 247 (2010)]. Numerical evaluation of π-conjugated and saturated organic chain systems verified that the present scheme considerably reduces the computational time for the β evaluation with a slight loss of accuracy, even around the singular frequency appearing at the electronic excitation energy. This evaluation indicates that the present linear-scaling TD-SCF scheme can also be used to estimate the molecular excitation energy. Furthermore, we succeeded in accurately evaluating the macroscopic second-harmonic generation coefficient of the polyvinylidene fluoride from the molecular (hyper)polarizabilities.
authors.affiliation: Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555, Japan.
authors.forename: Masato
authors.initials: M
authors.lastname: Kobayashi
authors.forename: Tsuguki
authors.initials: T
authors.lastname: Touma
authors.forename: Hiromi
authors.initials: H
authors.lastname: Nakai