'Partitions' in the perturbation theory of n-electron systems. III. The third-order energy

Abstract

For pt.II, see ibid., vol.19, p.1863 (1986). In the perturbation theory of the general n-electron system, H(n)= Sigma nf(i)+ lambda Sigma ng(i,j), the subsystem method provides a finite decomposition (termed 'partition') in each order of the perturbation eigenfunctions and energies. The author shows that the third-order energy E(3)(n) is a weighted sum of third-order energies E(3)(n1) belonging to electronic states (most of them highly excited) of the n1=four-, three- and two-particle subsystems. The proof uses a parentage expansion of the second-order n-electron eigenfunction. The energy partitions can be regarded as the rigorous derivation of the important 'atomic energy relations' intuitively derived by Bacher and Goudsmit (1934).