论文标题
非绝热耦合群集动力学的生物表格形式主义
A biorthonormal formalism for nonadiabatic coupled cluster dynamics
论文作者
论文摘要
在耦合群集方法中，电子状态是生物三角的，因为左边状态与右态是正直的。在这里，我们将这种形式主义扩展到左右分子波函数。从左右出现的人扩展开始，我们为左右核波功能提供了预测的Schrödinger方程。可以使用标准表达式从最终的波函数对中提取可观察物。形式主义被证明是在电子基础转换下是不变的，例如电子状态的归一化。因此，非绝热耦合元件可以用生物三个规范的波函数表示。因此，与文献中的主张相反，计算规模为全CI的归一化因素。因此，对于核动力学，我们需要在生物表达形式上的载体和标量耦合的表达。我们使用拉格朗日形式主义得出这些表达。
In coupled cluster methods, the electronic states are biorthonormal in the sense that the left states are orthonormal to the right states. Here we present an extension of this formalism to a left and right total molecular wave function. Starting from left and right Born-Huang expansions, we derive projected Schrödinger equations for the left and right nuclear wave functions. Observables may be extracted from the resulting wave function pair using standard expressions. The formalism is shown to be invariant under electronic basis transformations, such as normalization of the electronic states. Consequently, the nonadiabatic coupling elements can be expressed with biorthonormal wave functions. Calculating normalization factors that scale as full-CI is therefore not necessary, contrary to claims in the literature. For nuclear dynamics, we therefore need expressions for the vector and scalar couplings in the biorthonormal formalism. We derive these expressions using a Lagrangian formalism.
