Advanced Mathematical and Computational Methods in Quantum Chemistry

Wave-function based ab initio calculation methods have been gaining significant atten- tion from chemists due to their ability to provide insights into experimental results. However, their application to large systems is limited by the considerable computational cost involved, especially when dealing with high-dimensional tensors inherent to these calculations. To address these challenges, two primary strategies have been explored in this study. First, advancements in hardware architecture and algorithmic development. Graphics Processing Units (GPUs) have facilitated parallel computation, leading to a significant acceleration of these calculations. In this work, we propose a method for evaluating two-electron repulsion integrals (ERIs)—a key component of quantum chemistry—on GPUs. Regarding to the algorithm development, we propose a series of new algorithms for skew symmetric matrix LTLT decomposition,andimplementedhighperformanceCPUimplementationtoaccelerate these matrix operations in Quantum Monte Carlo (QMC) simulation./="/">Second, the development of approximation methods, such as tensor hypercontraction (THC), specifically least-squares tensor (LS-THC), has been introduced to reduce the high- dimensional tensors commonly encountered in computational chemistry, which allows wave- function methods to be applied to larger systems. However, the accuracy of LS-THC depends on the grid points. In this work, we proposed a pair of grid point schemes to account for missing interactions for grid points. In addition, we propose a novel energy pivoting algorithm to select grid points to prune unnecessary ones, which demonstrates good performance over the traditional pruning algorithm.