Weiluo Ren

Ruichen Li, Haotian Ye, Du Jiang et al.

Neural network-based variational Monte Carlo (NN-VMC) has emerged as a promising cutting-edge technique of ab initio quantum chemistry. However, the high computational cost of existing approaches hinders their applications in realistic chemistry problems. Here, we report the development of a new NN-VMC method that achieves a remarkable speed-up by more than one order of magnitude, thereby greatly extending the applicability of NN-VMC to larger systems. Our key design is a novel computational framework named Forward Laplacian, which computes the Laplacian associated with neural networks, the bottleneck of NN-VMC, through an efficient forward propagation process. We then demonstrate that Forward Laplacian is not only versatile but also facilitates more developments of acceleration methods across various aspects, including optimization for sparse derivative matrix and efficient neural network design. Empirically, our approach enables NN-VMC to investigate a broader range of atoms, molecules and chemical reactions for the first time, providing valuable references to other ab initio methods. The results demonstrate a great potential in applying deep learning methods to solve general quantum mechanical problems.

Ruichen Li, Yuzhi Liu, Du Jiang et al.

Spin plays a fundamental role in understanding electronic structure, yet many real-space wavefunction methods fail to adequately consider it. We introduce the Spin-Adapted Antisymmetrization Method (SAAM), a general procedure that enforces exact total spin symmetry for antisymmetric many-electron wavefunctions in real space. In the context of neural network-based quantum Monte Carlo (NNQMC), SAAM leverages the expressiveness of deep neural networks to capture electron correlation while enforcing exact spin adaptation via group representation theory. This framework provides a principled route to embed physical priors into otherwise black-box neural network wavefunctions, yielding a compact representation of correlated system with neural network orbitals. Compared with existing treatments of spin in NNQMC, SAAM is more accurate and efficient, achieving exact spin purity without any additional tunable hyperparameters. To demonstrate its effectiveness, we apply SAAM to study the spin ladder of iron-sulfur clusters, a long-standing challenge for many-body methods due to their dense spectrum of nearly degenerate spin states. Our results reveal accurate resolution of low-lying spin states and spin gaps in [Fe$_2$S$_2$] and [Fe$_4$S$_4$] clusters, offering new insights into their electronic structures. In sum, these findings establish SAAM as a robust, hyperparameter-free standard for spin-adapted NNQMC, particularly for strongly correlated systems.