Practical Schemes for Accurate Forces in Quantum Monte Carlo.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Calculating interatomic forces is crucial in computational chemistry, but accurate methods like Fixed-Node Diffusion Monte Carlo (DMC) are computationally expensive for force calculations.
• Existing exact DMC force calculations are often impractical due to high computational costs.
• Variational Monte Carlo (VMC) offers a more computationally feasible alternative but with lower accuracy for forces.

Purpose of the Study:

• To investigate the accuracy and efficiency of an approximate method, the Variational Drift-Diffusion (VD) approach, for computing interatomic forces within DMC.
• To assess the robustness of the VD method against different trial wave functions.
• To compare the performance of VD forces with VMC forces and exact DMC energy derivatives.

Main Methods:

• The study revisits and applies the Variational Drift-Diffusion (VD) approach, an approximate method for calculating forces in Diffusion Monte Carlo (DMC).
• Accuracy was tested by comparing VD forces with the derivative of the DMC potential energy surface for SiH and C2 molecules.
• The robustness was assessed using various wave functions optimized with Variational Monte Carlo (VMC).

Main Results:

• The VD approximation shows high accuracy, with discrepancies in equilibrium bond lengths less than 0.004 atomic units (au) compared to DMC energy derivatives.
• VD forces derived from DMC calculations exhibit smaller errors and yield equilibrium distances closer to experimental values than VMC forces, especially with partially optimized wave functions.
• The computational cost of VD forces is only slightly higher than that of calculating the DMC energy.

Conclusions:

• The Variational Drift-Diffusion (VD) approximation provides a robust, efficient, and accurate method for computing interatomic forces using Diffusion Monte Carlo (DMC).
• VD forces offer a significant improvement in accuracy over Variational Monte Carlo (VMC) forces, particularly for molecular structure determination.
• This method presents a practical route to leverage the accuracy of DMC for force calculations in quantum mechanical simulations.