Exchange integral matrices and cohesive energies of transition metal atoms

A variational theorem is used to obtain an expression for the spin polarisation (or exchange) energy of a free atom directly, rather than as the difference between two large numbers, and a numerical demonstration is provided for a nickel atom. The spin polarisation energy of several open shells, and the coupling between them, is then expressed as a quadratic form in the spins of the occupied valence orbitals, with local exchange integral matrix elements as coefficients. The authors have evaluated these matrix elements for all d transition metal and light actinide atoms. The spin polarisation energies of transition metal atoms are added to the measured cohesive energies to obtain valence bond energies.