University of Nebraska-Lincoln, Lincoln, Nebraska 68583, USA.
J Phys Chem A. 2013 Jun 6;117(22):4698-708. doi: 10.1021/jp4022079. Epub 2013 May 29.
Intuition suggests that a molecular system in the electronic ground state Φ0 should exhibit an electronic flux density (EFD) in response to the motion of its nuclei. If that state is described by the Born-Oppenheimer approximation (BOA), however, a straightforward calculation of the EFD yields zero, since the electrons are in a stationary state, regardless of the state of the nuclear motion. Here an alternative pathway to a nonzero EFD from a knowledge of only the BOA ground-state wave function is proposed. Via perturbation theory a complete set of approximate vibronic eigenfunctions of the whole Hamiltonian is generated. If the complete non-BOA wave function is expressed in the basis of these vibronic eigenfunctions, the ground-state contribution to the EFD is found to involve a summation over excited states. Evaluation of this sum through the so-called "average excitation energy approximation" produces a nonzero EFD. An explicit formula for the EFD for the prototypical system, namely, oriented H2+ vibrating in the electronic ground state, is derived.
直觉表明，处于电子基态 Φ0 的分子系统应该会对其核运动产生电子通量密度（EFD）。然而，如果该状态由 Born-Oppenheimer 近似（BOA）描述，则直接计算 EFD 会得到零，因为电子处于静止状态，与核运动的状态无关。本文提出了一种仅从 BOA 基态波函数知识出发获得非零 EFD 的替代途径。通过微扰理论，生成了整个哈密顿量的完整的一组近似振子本征函数。如果完整的非 BOA 波函数用这些振子本征函数来表示，那么对 EFD 的基态贡献就会涉及到对激发态的求和。通过所谓的“平均激发能近似”来评估这个和，就会得到非零的 EFD。对于原型系统，即处于电子基态振动的定向 H2+，推导出了 EFD 的显式公式。
