General Analytical Nuclear Forces and Molecular Potential Energy Surface from Full Configuration Interaction Quantum Monte Carlo

The full configuration interaction quantum Monte Carlo
(FCIQMC)
is a state-of-the-art stochastic electronic structure method, providing
a methodology to compute FCI-level state energies of molecular systems
within a quantum chemical basis. However, especially to probe dynamics at the FCIQMC level, it is necessary to devise
more efficient schemes to produce nuclear forces and potential energy
surfaces (PES) from FCIQMC. In this work, we derive the general formula
for nuclear forces from FCIQMC, and clarify different contributions
of the total force. This method to obtain FCIQMC forces eliminates
previous restrictions and can be used with frozen core approximation
and free selection of orbitals, making it promising for more efficient
nuclear forces calculations. After some numerical checks of this procedure
on the binding curve of N2 molecule, we use the FCIQMC
energy and force to obtain the full-dimensional ground state PES of
the water molecule via Gaussian processes regression. The new water
FCIQMC PES can be used as the basis for H2O ground state
nuclear dynamics, structure optimization, and rotation-vibrational
spectrum calculation.