Kjønstad Eirik F, Koch Henrik
Department of Chemistry, Norwegian University of Science and Technology, Trondheim 7491, Norway.
Scuola Normale Superiore, Piazza dei Cavalieri, 7, Pisa PI 56126, Italy.
J Chem Theory Comput. 2021 Jan 12;17(1):127-138. doi: 10.1021/acs.jctc.0c00730. Epub 2020 Dec 18.
In coupled cluster theory, 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 electronic wave functions. Calculating normalization factors that scale as full configuration interaction is not necessary, contrary to claims in the literature. For nonadiabatic nuclear dynamics, we need expressions for the derivative couplings in the biorthonormal formalism. These are derived in a Lagrangian framework.
在耦合簇理论中，电子态是双正交归一的，即左态与右态正交归一。在此，我们将这种形式体系扩展到左右总分子波函数。从左右玻恩 - 黄展开式出发，我们推导出左右核波函数的投影薛定谔方程。可观测量可以使用标准表达式从所得的波函数对中提取。该形式体系在电子基变换下是不变的，例如电子态的归一化。因此，非绝热耦合元可以用双正交归一的电子波函数来表示。与文献中的说法相反，计算按完全组态相互作用缩放的归一化因子并非必要。对于非绝热核动力学，我们需要双正交归一形式体系中导数耦合的表达式。这些表达式是在拉格朗日框架下推导出来的。
