Relativistic corrections to the partial wave expansion of two‐electron atoms

The asymptotic behavior of the partial wave expansion (or the CI expansion in terms of AOs with angular quantum number l ) of the leading relativistic correction for two‐electron atomic ions in a 1 S state is studied analytically. In agreement with earlier numerical findings, the partial wave increments of the leading relativistic correction go as ( l + 1/2) −2 , whereas the nonrelativistic increments go as ( l + 1/2) −4 . The coefficient of the leading term is 2 α 2 π 2 ∫   0 ∞| ψ( r,r ,0)| 2 r 3 dr for the Dirac Coulomb operator, and surprisingly also the full Dirac‐Breit operator, while the Gaunt term gives a contribution of −4α 2 π 2 ∫   0 ∞ |ψ( r,r ,0)| 2 r 3 dr . The results obtained here rely entirely on the nonrelativistic correlation cusp, and do not require assumptions on a no‐pair projection or a short‐range regularization of the electron interaction. They do not give any information on what happens beyond the leading order of relativistic corrections. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008