Computing observables and correlation functions of molecular systems with auxiliary-field quantum Monte Carlo

The quantitative study of correlated materials requires accurate and efficient calculations of electronic density, forces and correlation functions. To achieve this goal, we formulated and implemented a back-propagation scheme \footnote{S. Zhang, J. Carlson and J. E. Gubernatis, {\em{Phys. Rev. B}} {\bf{55}}, 7464 (1997);} for auxiliary-field quantum Monte Carlo \footnote{S. Zhang and H. Krakauer, {\em{Phys. Rev. Lett.}} {\bf{90}}, 136401 (2003)} electronic structure calculations. We discuss the numerical stability and computational complexity of the technique, and assess its performance computing ground-state properties for a broad set of molecules, including constituents of the primordial terrestrial atmoshpere and medium-sized organic molecules. Accurate estimates for electronic density and dipole moment of molecular systems are obtained.