The Exact Boundary Condition to Solve the Schrodinger Equation of Many Electron System

Abstract

In an attempt to bypass the sign problem in quantum Monte Carlo simulation of electronic systems within the framework of fixed node approach, we derive the exclusion principle "Two electrons can't be at the same external isopotential surface simultaneously" using the first postulate of quantum mechanics. We propose the exact Coulomb-Exchange nodal surface i.e. the exact boundary condition to solve the non-relativistic Schrodinger equation for the non-degenerate ground state of atoms and molecules. This boundary condition was applied to compute the ground state energies of N, Ne, Li2, Be2, B2, C2, N2, O2, F2, and H2O systems using diffusion Monte Carlo method. The ground state energies thus obtained agree well with the exact estimate of non-relativistic energies.