The Behaviour of the First-Order Density Matrix at the Coulomb Singularities of the Schrödinger Equation

Abstract

The cusp conditions of KATO for a spinless n-electron wave function at the COULOMB Singularities of the SCHRÖDINGER Equation are used to derive corresponding conditions for the first-order density matrix. These results are applied to the united-atom expansion of the electronic energy of polyatomic molecules resulting in an exact relation between the coefficients of the quadratic and cubic terms in this expansion. Finally it is shown how the cusp condition for the first-order density matrix is modified if the wave function includes electron spin in a proper way.