Expectation values in spin-averaged Douglas-Kroll and infinite-order relativistic methods

The change of picture for the r(-1) operator which occurs on passing from the four component relativistic schemes to two component theories is investigated for the spin-averaged Douglas-Kroll approximation and the recently proposed infinite-order approach. For nuclei already with moderately large values of the nuclear charge the change of picture contribution is found to be relatively important. Its neglect significantly affects the calculated values of the total relativistic contribution to the expectation value of r(-1). A numerical method for the calculation of the total relativistic contribution to the expectation values of r(-1), which avoids the explicit use of the appropriately transformed r(-1) operator, is devised and tested. Also the differences between the Douglas-Kroll approximation and the infinite-order scheme are investigated.