  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
H2 that is very close to the exact potential curve. Moreover, we have
re-derived all the important equations of the FCCS-I method.
