The direct calculation of the first-order density matrix for atoms

Abstract

The theory of isoelectronic sequences of atoms has been developed as a perturbation theory and is extended here to the calculation of the first-order density matrix. It is shown that the calculation of the first-order contribution to this matrix can be reduced to the solution of a number of one-electron equations. These equations have been solved for the helium ground state, the helium 3 S state and the lithium ground state. From the density matrix, mean values of one-electron operators can be derived by integration. A variety of these mean values is quoted and the significance of the stable values discussed. From the density matrix the natural orbitals can be derived and these are found to be identical with the unrestricted molecular orbitals to terms of zero and first order.