Wang Fan, Yam Chi Yung, Chen GuanHua
Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong.
J Chem Phys. 2007 Jun 28;126(24):244102. doi: 10.1063/1.2746034.
Time-dependent density-functional theory/localized density matrix method (TDDFT/LDM) was developed to calculate the excited state energy, absorption spectrum and dynamic polarizability. In the present work we generalize it to calculate the dynamic hyperpolarizabilities in both time and frequency domains. We show that in the frequency domain the 2n+1 rule can be derived readily and the dynamic hyperpolarizabilities are thus calculated efficiently. Although the time-domain TDDFT/LDM is time consuming, its implementation is straightforward because the evaluation of the derivatives of exchange-correlation potential with respect to electron density is avoided. Moreover, the time-domain method can be used to simulate higher order response which is very difficult to be calculated with the frequency-domain method.
含时密度泛函理论/定域密度矩阵方法（TDDFT/LDM）被开发用于计算激发态能量、吸收光谱和动态极化率。在本工作中，我们将其推广以计算时域和频域中的动态超极化率。我们表明，在频域中可以很容易地导出2n + 1规则，从而高效地计算动态超极化率。虽然时域TDDFT/LDM耗时，但由于避免了交换关联势相对于电子密度的导数的计算，其实现很直接。此外，时域方法可用于模拟高阶响应，而这用频域方法很难计算。
