Auxiliary Field Quantum Monte Carlo Study of Ground State Properties of Atoms and Molecules

We apply a recently developed quantum Monte Carlo (QMC) method \footnote{Shiwei Zhang, Henry Krakauer, Phys. Rev. Lett. {\bf 90}. 136401 (2003).} to calculate the ground state properties of several atoms and molecules. The QMC method projects the many-body ground state from a trial state by random walks in the space of Slater determants. The Hubbard-Stratonovich transformation is employed to decouple the Coulomb interaction between electrons. A trial wave function $|\Psi_T\rangle$ is used in the approximation to control the phase problem in QMC. We also carry out Hartree-Fock (HF) and density functional theory (with the local density approximation (LDA)) calculations. The generated single Slater determinant wave functions are used as $|\Psi_T\rangle$ in QMC. The dissociation and ionization energies are calculated for Aluminum, Silicon, Phosphorous, Sulfur, Chlorine and Arsenic atoms and molecules. The results are in good agreement with experimental values.