Use of Electrostatic Variation Principles in Molecular Energy Calculations

The Thomson and Dirichlet principles of electrostatics have been applied to the evaluation of electron-interaction terms occurring in molecular-energy calculations. A suitable choice of certain trial electric fields and electrostatic potentials permits these terms to be approximated both from above and from below. These approximate calculations of electronic interaction terms may often be considerably easier to perform than the exact evaluations required when molecular energies are obtained in the usual way through the minimum-energy principle. At the same time, when the upper and lower bounds obtained by the present method are properly inserted into the total-energy expression, the validity of the minimum-energy principle is preserved, so that any parameters appearing in the trial wave function can still be evaluated by the usual energy minimization procedure. For illustration, the method has been applied to the calculation of the ground-state energy of molecular hydrogen.