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General analytical nuclear force and molecular potential energy surface from full configuration interaction quantum Monte Carlo

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 {\em 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 force 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 force calculations. After numerical check of this procedure on the binding curve of N$_2$ molecule, we use the FCIQMC energy and force to obtain the full-dimensional ground state PES of water molecule via Gaussian processes regression. The new water FCIQMC PES can be used as the basis for H$_2$O ground state nuclear dynamics, structure optimization, and rotation-vibrational spectrum calculation.