非绝热耦合团簇动力学的双正交正规形式
A biorthonormal formalism for nonadiabatic coupled cluster dynamics
摘要：
在耦合团簇方法中，电子态是双正交的，即左侧态与右侧态正交。在这里，我们提出了一个扩展，这种形式主义的左，右总分子波函数。从左、右Born-Huang展开式出发，导出了左、右核波函数的投影薛定谔方程。可以使用标准表达式从所得到的波函数对中提取观测量。的形式主义被证明是不变的电子基础变换下，如归一化的电子状态。因此，非绝热耦合元可以用双正交波函数表示。因此，与文献中的声明相反，计算作为全CI缩放的归一化因子是不必要的。因此，对于核动力学，我们需要用双正交规范形式表示矢量和标量耦合。我们推导出这些表达式使用拉格朗日形式主义。
英文摘要：
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.
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