A new version of fermion coupled coherent states method: Theory and applications in simulation of two-electron systems

Highlights: • FCCS-II increase the speed of computations significantly. • FCCS-II with a relatively low number of CS gives a very good potential energy curve for H. • The diffusion Monte-Carlo part does not need any grid refinement algorithm. • FCCS-II does not need any exclusion of high energy coherent states from the grid. • All the important equations of the FCCS-I are re-derived. We report a new version of fermion coupled coherent states method (FCCS-II) to simulate two-electron systems based on a self-symmetrized six-dimensional (6D) coherent states grid. Unlike the older fermion coupled coherent states method (FCCS-I), FCCS-II does not need any new equations in comparison with the coupled coherent states method. FCCS-II uses a simpler and more efficient approach for symmetrizing the spatial wave function in the simulation of fermionic systems. This method, has significantly increased the speed of computations and give us the capability to simulate the quantum systems with the larger CS grids. We apply FCCS-II to simulate the Helium atom and the Hydrogen molecule based on grids with a large numbers of coherent states. FCCS-II with a relatively low number of CS gives a potential energy curve for H₂that is very close to the exact potential curve. Moreover, we have re-derived all the important equations of the FCCS-I method.