Beyond single-reference fixed-node approximation in ab initio Diffusion Monte Carlo using antisymmetrized geminal power applied to systems with hundreds of electrons

Abstract

Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in fermionic systems the projection needs to be carried out while imposing anti-symmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds, or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as {\emph{single reference}}. In this paper, we propose a new approach, applicable to systems as large as the C$_{60}$ fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (Antisymmetrized Geminal power wavefunction constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.