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.

完全组态相互作用量子蒙特卡洛（Full Configuration Interaction Quantum Monte Carlo, FCIQMC）是当前顶尖的随机电子结构计算方法，可在量子化学基组下计算分子体系的完全组态相互作用级态能量。然而，若要在该方法层面探究分子动力学，则亟需设计更高效的方案，以从该方法中提取核力与势能面（Potential Energy Surface, PES）。本研究推导了完全组态相互作用量子蒙特卡洛方法下核力的通用表达式，并阐明了总核力的各项不同贡献来源。该核力提取方法破除了既往的限制条件，可结合冻核近似与任意轨道选择方案使用，有望实现更高效的核力计算。我们先以氮气分子的结合曲线对该流程进行了数值验证，随后借助高斯过程回归，利用完全组态相互作用量子蒙特卡洛的能量与核力数据，构建了水分子的全维基态势能面。这套全新的水分子完全组态相互作用量子蒙特卡洛势能面，可作为水分子基态核动力学、结构优化以及转动振动光谱计算的研究基础。