  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.
