Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State
This work addresses the scalability challenge for quantum chemistry simulations, offering a more efficient method for modeling excited states across molecules, though it is incremental in improving existing neural-network wave function approaches.
The paper tackles the computational cost of accurately representing multiple quantum states in Variational Monte Carlo by introducing Multi-State Importance Sampling (MSIS) and Excited Pfaffians, achieving a >200x faster training speed and modeling 50% more states on the carbon dimer, and enabling the first neural-network-based discovery of all distinct energy levels in the beryllium atom.
Neural-network wave functions in Variational Monte Carlo (VMC) have achieved great success in accurately representing both ground and excited states. However, achieving sufficient numerical accuracy in state overlaps requires increasing the number of Monte Carlo samples, and consequently the computational cost, with the number of states. We present a nearly constant sample-size approach, Multi-State Importance Sampling (MSIS), that leverages samples from all states to estimate pairwise overlap. To efficiently evaluate all states for all samples, we introduce Excited Pfaffians. Inspired by Hartree-Fock, this architecture represents many states within a single neural network. Excited Pfaffians also serve as generalized wave functions, allowing a single model to represent multi-state potential energy surfaces. On the carbon dimer, we match the $O(N_s^4)$-scaling natural excited states while training $>200\times$ faster and modeling 50\% more states. Our favorable scaling enables us to be the first to use neural networks to find all distinct energy levels of the beryllium atom. Finally, we demonstrate that a single wave function can represent excited states across various molecules.