Li Zhendong, Liu Wenjian
Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People's Republic of China.
J Chem Phys. 2014 Jul 7;141(1):014110. doi: 10.1063/1.4885817.
Analytic expressions for the first-order nonadiabatic coupling matrix elements between electronically excited states are first formulated exactly via both time-independent equation of motion and time-dependent response theory, and are then approximated at the configuration interaction singles, particle-hole/particle-particle random phase approximation, and time-dependent density functional theory/Hartree-Fock levels of theory. Note that, to get the Pulay terms arising from the derivatives of basis functions, the standard response theory designed for electronic perturbations has to be extended to nuclear derivatives. The results are further recast into a Lagrangian form that is similar to that for excited-state energy gradients and allows to use atomic orbital based direct algorithms for large molecules.
首先通过含时运动方程和含时响应理论精确地推导出电子激发态之间一阶非绝热耦合矩阵元的解析表达式，然后在组态相互作用单激发、粒子-空穴/粒子-粒子随机相位近似以及含时密度泛函理论/哈特里-福克理论水平上进行近似。需要注意的是，为了得到由基函数导数产生的普利项，专门为电子微扰设计的标准响应理论必须扩展到核导数。结果进一步转化为一种拉格朗日形式，该形式类似于激发态能量梯度的形式，并允许对大分子使用基于原子轨道的直接算法。
