Section Theoretical Chemistry, VU University, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands.
J Chem Phys. 2010 Nov 7;133(17):174119. doi: 10.1063/1.3499601.
The adiabatic approximation is problematic in time-dependent density matrix functional theory. With pure density matrix functionals (invariant under phase change of the natural orbitals) it leads to lack of response in the occupation numbers, hence wrong frequency dependent responses, in particular α(ω→0)≠α(0) (the static polarizability). We propose to relinquish the requirement that the functional must be a pure one-body reduced density matrix (1RDM) functional, and to introduce additional variables which can be interpreted as phases of the one-particle states of the independent particle reference system formed with the natural orbitals, thus obtaining so-called phase-including natural orbital (PINO) functionals. We also stress the importance of the correct choice of the complex conjugation in the two-electron integrals in the commonly used functionals (they should not be of exchange type). We demonstrate with the Löwdin-Shull energy expression for two-electron systems, which is an example of a PINO functional, that for two-electron systems exact responses (polarizabilities, excitation energies) are obtained, while writing this energy expression in the usual way as a 1RDM functional yields erroneous responses.
在含时密度矩阵泛函理论中，绝热近似是有问题的。对于纯密度矩阵泛函（在自然轨道相位变化下不变），它会导致占据数没有响应，因此频率相关的响应是错误的，特别是α(ω→0)≠α(0)（静态极化率）。我们建议放弃泛函必须是纯单粒子约化密度矩阵（1RDM）泛函的要求，并引入其他变量，这些变量可以被解释为独立粒子参考系中单粒子态的相位，从而得到所谓的包含相位的自然轨道（PINO）泛函。我们还强调了在常用泛函中正确选择双电子积分的复共轭的重要性（它们不应是交换类型）。我们用 Löwdin-Shull 双电子系统的能量表达式（它是 PINO 泛函的一个例子）证明，对于双电子系统，得到了精确的响应（极化率、激发能），而以通常的方式将这个能量表达式写成 1RDM 泛函则会得到错误的响应。
