Geminal-based statistics for the energies of many-electron molecular systems
Adam E. Rothman and David A. Mazziotti

In 1959, F. Bopp developed a lower bound to atomic and molecular ground-state energies by summing the lowest eigenvalues of the two-particle reduced Hamiltonian, \Ktwo. His approximation is only accurate for very small systems (fewer than about 4 electrons), with the results degenerating rapidly for larger problems. In this paper, we extend and improve Bopp's work by introducing a flexible distribution function, guided by familiar Fermi-Dirac statistics, in order to generate occupation numbers for the energy levels of \Ktwo. The distribution function and the resulting energy are parameterized by a correlation temperature $T$. For a given system, characteristic temperatures may be identified that yield the true energy or any other benchmark energy of the system. Using a geometric argument and the empirical properties of the energy vs temperature curve, the two-electron statistics are investigated as a predictive tool for a variety of small atoms and molecules.

© 2008 The American Physical Society.