Basis-free neural-network geminal and Jastrow factors for variational Monte Carlo

TL;DR

This paper introduces a basis-free neural-network approach combining AGP determinants and Jastrow factors for variational Monte Carlo, improving accuracy in modeling many-electron wave functions.

Contribution

It presents a novel basis-free neural-network ansatz that separates static and dynamical correlation treatment, enhancing wave function accuracy.

Findings

Achieves sub-millihartree accuracy for hydrogen molecules

Separates static and dynamical correlation errors

Identifies residual nodal limitations in large-radius geometries

Abstract

Neural-network quantum states offer a flexible route to compact many-electron wave functions, but their practical accuracy depends strongly on how fermionic antisymmetry, electron correlation, and optimization noise are treated. Here we combine an antisymmetrized geminal power (AGP) determinant with feed-forward neural networks that replace conventional basis-set expansions in the geminal and in two Jastrow-factor constructions. The resulting basis-free Jastrow--AGP ansatz is optimized by variational Monte Carlo and is designed to separate two tasks: the AGP part defines the nodal surface, while the neural-network Jastrow factor recovers dynamical correlation at fixed nodes. This separation makes it possible to distinguish errors associated with dynamical correlation from those caused by static, multireference correlation. Applications to the hydrogen molecule and the rectangular hydrogen tetramer show sub-millihartree accuracy when the AGP nodes are adequate, and expose the residual nodal limitation near the large-radius square geometry of the hydrogen tetramer. These results clarify where neural-network building blocks can improve a compact geminal ansatz and where additional nodal flexibility is required.