We report a linear-scaling computation method for evaluating the dynamic first hyperpolarizability based on the divide-and-conquer (DC) method. In the present scheme, we utilized the quasi-density-matrix expression derived from Wigners (2n 1) rule for , 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)10.1016/j.cplett.2009.12.043]. Numerical evaluation of -conjugated and saturated organic chain systems verified that the present scheme considerably reduces the computational time for the 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.
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