Wang Mengsa, Hou Enze, Wang Han
Machine learning-based methods have advanced electronic structure calculations in groundstate, excited-state, and time-dependent multi-electron systems. For ground states, neural network wave functions with Slater-Jastrow-Backflow forms, trained via variational Monte Carlo, accurately capture electron correlation, achieving precision comparable to or exceeding coupled-cluster approaches. In excited-state calculations, techniques such as state-averaged penalties and natural excited-state variational principles enforce orthogonality and enable accurate prediction of excitation energies and oscillator strengths for atoms and molecules. For time-dependent systems, the time-dependent variational Monte Carlo method, which evolves parameterized wave functions, precisely simulates electron dynamics under strong fields and captures non-equilibrium effects. Integrating pseudopotential with neural networks improves computational efficiency while maintaining accuracy in complex systems, including those with transition metals. These developments highlight the strong representational capacity of neural quantum states and their applicability across diverse quantum chemistry problems, offering effective tools for high-accuracy simulations in physical and chemical sciences.
