Classical many-body model for atomic collisions incorporating the Heisenberg and Pauli principles

A novel, classical many-body model, previously introduced for nuclear collisions, has been extended to atomic and molecular structure, with the goal of providing a framework for atomic collisions. In addition to the usual kinetic and Coulomb potential terms, a momentum-dependent two-body potential acts between electron pairs of identical spin in order to approximate the Pauli constraint $r_{\mathrm{ij}}{p}_{\mathrm{ij}}\ge \hslash \xi p$, where $\xi$ is a dimensionless parameter here set equal to 2.767. A similar potential is introduced to simulate the Heisenberg constraint, $r_{\mathrm{iN}}{p}_{\mathrm{iN}}=h$, where $N$ refers to each nucleus. Because of these constraints, the atomic and molecular ground-state configurations are stable. The hydrogen ground state is given exactly. Calculations in ${\mathrm{H}}^{-}$, He, Li, Ne, and Ar reproduce total ground-state energies to better than 15%; this is considerably better than the Thomas-Fermi model, in which the errors are approximately 28% for neon and 23% for argon. The resulting electrostatic potential is in general intermediate between Thomas-Fermi and Hartree-Fock calculations. ${\mathrm{H}}_2^{+}$ and ${\mathrm{H}}_2$ molecules are overbound; in contrast, the Thomas-Fermi model does not bind neutral molecules.