Electron density in the ground states of atoms and molecules

Abstract

The ground-state energy E of an atom or molecule is known to be a unique functional of the electron density ϱ( r). Unfortunately the functional, to date, is unknown except in the limiting cases of large and small numbers of electrons N. In this article, therefore, emphasis is first placed on the fact that, for an atomic ion having nuclear charge Ze, the Hamiltonian is fixed by specifying Z and N and hence E[ϱ] becomes E( Z, N). The 1/ Z expansion of this quantity is first set out and linked with the Thomas-Fermi statistical limit, in which both Z and N become large such that 0 < N/Z ⩽ 1. Partial summation of the 1/ Z expansion then leads to essential corrections in the Thomas-Fermi energy from (i) density gradients and (ii) exchange. The resulting formula is brought into close contact with numerical Hartree-Fock energies. This theory is then extended to apply to simple homonuclear diatomic molecules. Using scaling properties at the internuclear equilibrium distance, the above formula for atomic ions is generalized to such neutral molecules. By subtraction, the structure of the dissociation energy D is exposed in relation to (a) the number of electrons N and (b) the lowest-order density gradient kinetic energy correction T 2. In particular, D/N 2 will be shown to depend on the one-sixth power of T 2 ; contact will also be made with an empirical relation previously exposed. Finally, a discussion will be given of the effects on the ground states, especially for atomic ions, of both intense magnetic and electric fields; the electron density theory is again used, but now working within a statistical-mechanical context.