Luo Kai, Fuks Johanna I, Sandoval Ernesto D, Elliott Peter, Maitra Neepa T
Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA.
Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, 06120 Halle (Saale), Germany.
J Chem Phys. 2014 May 14;140(18):18A515. doi: 10.1063/1.4867002.
The exact exchange-correlation (xc) potential of time-dependent density functional theory has been shown to have striking features. For example, step and peak features are generically found when the system is far from its ground-state, and these depend nonlocally on the density in space and time. We analyze the xc potential by decomposing it into kinetic and interaction components and comparing each with their exact-adiabatic counterparts, for a range of dynamical situations in model one-dimensional two-electron systems. We find that often, but not always, the kinetic contribution is largely responsible for these features that are missed by the adiabatic approximation. The adiabatic approximation often makes a smaller error for the interaction component, which we write in two parts, one being the Coulomb potential due to the time-dependent xc hole. Non-adiabatic features of the kinetic component were also larger than those of the interaction component in cases that we studied when there is negligible step structure. In ground-state situations, step and peak structures arise in cases of static correlation, when more than one determinant is essential to describe the interacting state. We investigate the time-dependent natural orbital occupation numbers and find the corresponding relation between these and the dynamical step is more complex than for the ground-state case.
含时密度泛函理论中精确的交换关联（xc）势已被证明具有显著特征。例如，当系统远离其基态时，通常会发现阶跃和峰值特征，并且这些特征非局部地依赖于空间和时间中的密度。对于模型一维双电子系统中的一系列动力学情况，我们通过将xc势分解为动能和相互作用分量，并将每个分量与其精确绝热对应物进行比较，来分析xc势。我们发现，通常但并非总是如此，动能贡献在很大程度上导致了绝热近似所遗漏的这些特征。绝热近似对于相互作用分量通常产生较小的误差，我们将相互作用分量分为两部分，其中一部分是由于含时xc空穴产生的库仑势。在我们研究的步长结构可忽略不计的情况下，动能分量的非绝热特征也大于相互作用分量的非绝热特征。在基态情况下，当多个行列式对于描述相互作用态至关重要时，在静态关联的情况下会出现阶跃和峰值结构。我们研究了含时自然轨道占据数，并发现这些与动力学步长之间的相应关系比基态情况更为复杂。
