Jansik Branislav, Sałek Paweł, Jonsson Dan, Vahtras Olav, Agren Hans
Laboratory of Theoretical Chemistry, The Royal Institute of Technology, SE-10044 Stockholm, Sweden.
J Chem Phys. 2005 Feb 1;122(5):54107. doi: 10.1063/1.1811605.
We present density-functional theory for time-dependent response functions up to and including cubic response. The working expressions are derived from an explicit exponential parametrization of the density operator and the Ehrenfest principle, alternatively, the quasienergy ansatz. While the theory retains the adiabatic approximation, implying that the time-dependency of the functional is obtained only implicitly-through the time dependence of the density itself rather than through the form of the exchange-correlation functionals-it generalizes previous time-dependent implementations in that arbitrary functionals can be chosen for the perturbed densities (energy derivatives or response functions). In particular, general density functionals beyond the local density approximation can be applied, such as hybrid functionals with exchange correlation at the generalized-gradient approximation level and fractional exact Hartree-Fock exchange. With our implementation the response of the density can always be obtained using the stated density functional, or optionally different functionals can be applied for the unperturbed and perturbed densities, even different functionals for different response order. As illustration we explore the use of various combinations of functionals for applications of nonlinear optical hyperpolarizabilities of a few centrosymmetric systems; molecular nitrogen, benzene, and the C(60) fullerene. Considering that vibrational, solvent, and local field factors effects are left out, we find in general that very good experimental agreement can be obtained for the second dynamic hyperpolarizability of these systems. It is shown that a treatment of the response of the density beyond the local density approximation gives a significant effect. The use of different functional combinations are motivated and discussed, and it is concluded that the choice of higher order kernels can be of similar importance as the choice of the potential which governs the Kohn-Sham orbitals.
我们提出了适用于含时响应函数直至并包括三次响应的密度泛函理论。工作表达式源自密度算符的显式指数参数化和埃伦费斯特定理，或者准能量假设。虽然该理论保留了绝热近似，这意味着泛函的时间依赖性仅通过密度本身的时间依赖性隐式获得，而非通过交换关联泛函的形式，但它推广了先前的含时实现方式，即可以为微扰密度（能量导数或响应函数）选择任意泛函。特别是，可以应用超越局域密度近似的一般密度泛函，例如具有广义梯度近似水平的交换关联的杂化泛函以及分数精确哈特里 - 福克交换。通过我们的实现方式，总能使用所述密度泛函获得密度的响应，或者可选地，对于未微扰和微扰密度可以应用不同的泛函，甚至对于不同的响应阶次可以应用不同的泛函。作为示例，我们探索了各种泛函组合在一些中心对称系统（分子氮、苯和C(60)富勒烯）的非线性光学超极化率应用中的使用。考虑到忽略了振动、溶剂和局部场因子的影响，我们总体发现对于这些系统的二阶动态超极化率能够获得非常好的实验一致性。结果表明，对密度响应进行超越局域密度近似的处理会产生显著影响。我们对使用不同泛函组合的动机进行了探讨，并得出结论，高阶核的选择与控制科恩 - 沈轨道的势的选择可能具有相似的重要性。
