 
Summary: A quantum Monte Carlo calculation of the ground state energy
of the hydrogen molecule
Carol A. Traynor and James B. Anderson
Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802
Bruce M. Boghosian
Thinking Machines Corporation, Cambridge, Massachusetts 021421264
(Received 20 August 1990; accepted 6 November 1990)
We have calculated the ground state energy of the hydrogen molecule using the quantum
Monte Carlo (QMC) method of solving the Schrodinger equation, without the use of the
BornOppenheimer or any other adiabatic approximations. The wave function sampling was
carried out in the full 12dimensional configuration space of the four particles (two electrons
and two protons). Two different methods were employed: the diffusion quantum Monte Carlo
(DQMC) method and the Green's function quantum Monte Carlo (GFQMC) method. This
computation is very demanding because the configurations must be evolved on the time scale
of the electronic motion, whereas the finite nuclear mass effects are resolved accurately only
after equilibration on the much slower time scale of the nuclear motion. Thus, a very large
number of iterations is required. The calculations were performed on the CM2 Connection
Machine computer, a massively parallel supercomputer. The enormous speedup afforded by
the massive parallelism allowed us to complete the computation in a reasonable amount of
time. The total energy from the DQMC calculations is  1.163 97 + 0.000 05 a.u. A more
