Departamento de Química, Laboratório Computacional de Espectroscopia e Cinética, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, 14040-901 Ribeirão Preto, São Paulo, Brazil.
J Chem Theory Comput. 2021 Feb 9;17(2):1106-1116. doi: 10.1021/acs.jctc.0c01110. Epub 2021 Jan 6.
Simulations of electronically nonadiabatic processes may employ either the adiabatic or diabatic representation. Direct dynamics calculations are usually carried out in the adiabatic basis because the energy, force, and state coupling can be evaluated directly by many electronic structure methods. However, although its straightforwardness is appealing, direct dynamics is expensive when combined with quantitatively accurate electronic structure theories. This generates interest in analytically fitted surfaces to cut the expense, but the cuspidal ridges of the potentials and the singularities and vector nature of the couplings at high-dimensional, nonsymmetry-determined intersections in the adiabatic representation make accurate fitting almost impossible. This motivates using diabatic representations, where the surfaces are smooth and the couplings are also smooth and-importantly-scalar. In a recent previous work, we have developed a method called diabatization by deep neural network (DDNN) that takes advantage of the smoothness and nonuniqueness of diabatic bases to obtain them by machine learning. The diabatic potential energy matrices (DPEMs) learned by the DDNN method yield not only diabatic potential energy surfaces (PESs) and couplings in an analytic form useful for dynamics calculations, but also adiabatic surfaces and couplings in the adiabatic representation can be calculated inexpensively from the transformation. In the present work, we show how to extend the DDNN method to produce good approximations to global permutationally invariant adiabatic PESs simultaneously with DPEMs. The extended method is called permutationally restrained DDNN.
模拟非绝热过程可以采用绝热或非绝热表示。直接动力学计算通常在绝热基中进行，因为许多电子结构方法可以直接评估能量、力和态耦合。然而，尽管直接动力学方法简单直接，但与定量准确的电子结构理论结合使用时成本很高。这就产生了对分析拟合表面以降低成本的兴趣，但在绝热表示中的高维、非对称确定交点处的势能的尖峰脊和耦合的奇点以及向量性质使得准确拟合几乎不可能。这就促使使用非绝热表示，其中表面是平滑的，耦合也是平滑的，并且重要的是标量。在最近的一项前期工作中，我们开发了一种称为通过深度神经网络的非绝热化（DDNN）的方法，该方法利用非绝热基的平滑性和非唯一性通过机器学习来获得它们。DDNN 方法学习的非绝热势能矩阵（DPEM）不仅提供了用于动力学计算的解析形式的非绝热势能表面（PES）和耦合，而且还可以从变换中廉价地计算出绝热表示中的绝热表面和耦合。在本工作中，我们展示了如何扩展 DDNN 方法以同时生成 DPEM 的全局置换不变绝热 PES 的良好近似。扩展方法称为置换约束 DDNN。
