Effective quantum potentials for molecular dynamics simulation of non-ideal plasmas

Molecular dynamics simulation of electron-ion systems are prone to the so-called “Coulomb catastrophe” which is due to the infinitely deep Coulomb potential of the ion without any stabilizing effect in a classical framework. Quantum mechanically this is forbidden by the Heisenberg Uncertainty Principle. In addition, many electron systems need to satisfy the Pauli Exclusion Principle as well. Fermion Molecular Dynamics¹ accommodates the two effects in a quasi-classical treatment through the momentum-dependent pseudo-potentials that exclude the regions of phase space forbidden by the quantum principles. The extent of exclusion is determined by a set of parameters which need to be chosen carefully to include the quantum effects specific to the system. Initial attempts to determine these parameters were ad-hoc² followed by accurate calculation of the Heisenberg parameters for Hydrogen or Helium-like systems³. The results so far do not suffice to study plasmas where multi-electron effects are important in atomic processes. We report the first attempt to accurately determine the Heisenberg and Pauli parameters for a set of atoms. The parameters are found to take a set of correlated values and the correlation is elliptic for all the atoms we studied. It is possible that the coefficients of the ellipse could be functions of atomic number indicating a possible connection with a quantum mechanical treatment in the limiting case.