Chemical potential, ionization energies, and electron correlation in atoms

Abstract

The total energy E(Z,N) of an atomic ion with nuclear charge Ze and N electrons is expanded in a Taylor series about the neutral atom energy E(Z,Z). By truncating the Taylor expansion, the chemical potential μ of the neutral atom is expressed in terms of the nth ionization potential I_n = E(Z,Z−n)−E(Z, Z−n+1), the most refined formula given being to fifth order, and involving up to and including I₄. As an approximate test of the validity of this expression, one can then make use of the empirical relation that I_n∼nI₁, in which case, with the electron affinity consistently taken as small, one obtains μ∼−I₁/2, consistent with Mulliken’s electronegativity. The relation of the present work to that of March and Bader, which involves the potential energy of the electron correlations, is briefly discussed.