  The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used
to calculate the ab initio ground state energies for multiple geometries of the
H$_{2}$O, N$_2$, and F$_2$ molecules. The method is based on Feynman's path
integral formulation of quantum mechanics and has two stages. The first stage
is called the learning stage and reduces the well-known QMC minus sign problem
by optimizing the linear combinations of Slater determinants which are used in
the second stage, a conventional QMC simulation. The method is tested using
different vector spaces and compared to the results of other quantum chemical
methods and to exact diagonalization. Our findings demonstrate that the SiLK
method is accurate and reduces or eliminates the minus sign problem.
