Nanoscience Center, P.O. Box 35, 40014 University of Jyväskylä, Finland.
J Chem Phys. 2012 Mar 7;136(9):094104. doi: 10.1063/1.3687344.
Adiabatic response time-dependent density functional theory (TDDFT) suffers from the restriction to basically an occupied → virtual single excitation formulation. Adiabatic time-dependent density matrix functional theory allows to break away from this restriction. Problematic excitations for TDDFT, viz. bonding-antibonding, double, charge transfer, and higher excitations, are calculated along the bond-dissociation coordinate of the prototype molecules H(2) and HeH(+) using the recently developed adiabatic linear response phase-including (PI) natural orbital theory (PINO). The possibility to systematically increase the scope of the calculation from excitations out of (strongly) occupied into weakly occupied ("virtual") natural orbitals to larger ranges of excitations is explored. The quality of the PINO response calculations is already much improved over TDDFT even when the severest restriction is made, to virtually the size of the TDDFT diagonalization problem (only single excitation out of occupied orbitals plus all diagonal doubles). Further marked improvement is obtained with moderate extension to allow for excitation out of the lumo and lumo+1, which become fractionally occupied in particular at longer distances due to left-right correlation effects. In the second place the interpretation of density matrix response calculations is elucidated. The one-particle reduced density matrix response for an excitation is related to the transition density matrix to the corresponding excited state. The interpretation of the transition density matrix in terms of the familiar excitation character (single excitations, double excitations of various types, etc.) is detailed. The adiabatic PINO theory is shown to successfully resolve the problematic cases of adiabatic TDDFT when it uses a proper PI orbital functional such as the PILS functional.
绝热响应时间相关密度泛函理论（TDDFT）受到基本上仅限于占据→虚拟单激发公式的限制。绝热时间相关密度矩阵泛函理论允许摆脱这种限制。对于 TDDFT，有问题的激发，即成键-反键、双激发、电荷转移和更高激发，沿着原型分子 H(2) 和 HeH(+) 的键离解坐标使用最近开发的绝热线性响应相包含（PI）自然轨道理论（PINO）进行计算。探索了系统地将计算范围从（强）占据的激发扩展到弱占据的“虚拟”自然轨道的可能性，以及更大范围的激发。即使施加最严格的限制，即实质上限制为 TDDFT 对角化问题的大小（仅占据轨道之外的单激发加上所有对角双激发），PINO 响应计算的质量已经比 TDDFT 有了很大的提高。通过适度扩展允许激发占据轨道之外的 lumo 和 lumo+1，可以进一步显著提高，特别是由于左右相关效应，在较长距离处变得部分占据。其次，阐明了密度矩阵响应计算的解释。激发的单粒子约化密度矩阵响应与对应激发态的跃迁密度矩阵有关。详细解释了跃迁密度矩阵在熟悉的激发特征（单激发、各种类型的双激发等）方面的解释。证明绝热 PINO 理论在使用适当的 PI 轨道泛函（如 PILS 泛函）时，成功解决了绝热 TDDFT 的有问题的情况。
