Quantum Monte Carlo calculations of the potential energy curve of the helium dimer

We report results of both the Diffusion Quantum Monte Carlo (DMC) and Reptation Quantum Monte Carlo (RMC) methods 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 the recently developed Reptation Quantum Monte Carlo (RMC) method, yield particularly accurate results with reduced statistical error, which gives very excellent agreement across the whole potential curve. For the equilibrium internuclear distance of 5.6 bohr, the calculated total energy with Reptation Quantum Monte Carlo (RMC) method is -5.807483599$\pm$0.000000016 hartrees and the corresponding well depth is -11.003$\pm$0.005 K.