Quantum Monte Carlo calculated potential energy curve for the helium dimer

TL;DR

This paper demonstrates highly accurate potential energy curves for the helium dimer using advanced Quantum Monte Carlo methods, achieving excellent agreement with theoretical benchmarks and reducing statistical errors.

Contribution

It introduces an improved stochastic reconfiguration technique and applies both DMC and RMC methods to accurately compute the helium dimer's potential energy curve.

Findings

RMC yields highly accurate results with reduced statistical error.

The calculated equilibrium energy closely matches theoretical values.

The potential energy curve shows excellent agreement across all ranges.

Abstract

We report results of both Diffusion Quantum Monte Carlo(DMC) method and Reptation Quantum Monte Carlo(RMC) method on the potential energy curve of the helium dimer. We show that it is possible to obtain a highly accurate description of the helium dimer. An improved stochastic reconfiguration technique is employed to optimize the many-body wave function, which is the starting point for highly accurate simulations based on the Diffusion Quantum Monte Carlo(DMC) and Reptation Quantum Monte Carlo (RMC) methods. We find that the results of these methods are in excellent agreement with the best theoretical results at short range, especially recently developed Reptation Quantum Monte Carlo(RMC) method, yield practically accurate results with reduced statistical error, which gives very excellent agreement across the whole potential. For the equilibrium internuclear distance of 5.6 bohr, the calculated electronic energy with Reptation Quantum Monte Carlo(RMC) method is 5.807483599$\pm$0.000000015 hartrees and the corresponding well depth is -11.003$\pm$0.005 K.