在这项工作中,我们使用从头算方法和机器学习(ML)模型实现了一种近似算法,用于计算多原子系统的非绝热耦合矩阵元素(NACME)。利用这个算法,人们可以仅使用势能面(PES)的信息来计算NACME,即,能量,和梯度以及Hessian矩阵元素。我们使用了一个现实的系统,即CH2NH,比较这种基于PES的近似算法和基于波函数的精确算法计算的NACME。我们的结果表明,除了能量退化点之外,这种基于PES的近似算法可以给出与基于波函数的算法相当的非常准确的结果,即,锥形相交。我们还使用这种基于PES的近似算法测试了机器学习(ML)训练模型,它也提供了同样准确的NACME,但效率更高。这种基于PES的算法的优点是其与不实现基于波函数的算法的电子结构方法相结合的巨大潜力,基于能量的低尺度分段方法,等。,特别是高效的机器学习模型,计算NACME。目前的工作可以鼓励进一步研究通过从头算非绝热动力学模拟方法模拟的大型系统的非绝热过程,其中总是需要NACME。
In this work, we implemented an approximate algorithm for calculating nonadiabatic coupling matrix elements (NACMEs) of a polyatomic system with ab initio methods and machine learning (ML) models. Utilizing this algorithm, one can calculate NACMEs using only the information of potential energy surfaces (PESs), i.e., energies, and gradients as well as Hessian matrix elements. We used a realistic system, namely CH2NH, to compare NACMEs calculated by this approximate PES-based algorithm and the accurate wavefunction-based algorithm. Our results show that this approximate PES-based algorithm can give very accurate results comparable to the wavefunction-based algorithm except at energetically degenerate points, i.e., conical intersections. We also tested a machine learning (ML)-trained model with this approximate PES-based algorithm, which also supplied similarly accurate NACMEs but more efficiently. The advantage of this PES-based algorithm is its significant potential to combine with electronic structure methods that do not implement wavefunction-based algorithms, low-scaling energy-based fragment methods, etc., and in particular efficient ML models, to compute NACMEs. The present work could encourage further research on nonadiabatic processes of large systems simulated by ab initio nonadiabatic dynamics simulation methods in which NACMEs are always required.