Convergence of Breit-Pauli spin-orbit matrix elements with basis set size and configuration interaction space: The halogen atoms F, Cl, and Br

Systematic sequences of basis sets are used to calculate the spin-orbit splittings of the halogen atoms F, Cl, and Br in the framework of first-order perturbation theory with the Breit-Pauli operator and internally contracted configuration interaction wave functions. The effects of both higher angular momentum functions and the presence of tight functions are studied. By systematically converging the one-particle basis set, an unambiguous evaluation of the effects of correlating different numbers of electrons in the Cl treatment is carried out. Correlation of the 2p-electrons in chlorine increases the spin-orbit splitting by similar to 80 cm(-1), while in bromine we observe incremental increases of 130, 145, and 93 cm(-1), when adding the 3d, 3p, and 2p electrons to the set of explicitly correlated electrons, respectively. For fluorine and chlorine the final basis set limit, all-electrons correlated results match the experimentally observed spin-orbit splittings to within similar to 5 cm(-1), while for bromine the Breit-Pauli operator underestimates the splitting by about 100 cm(-1). More extensive treatment of electron correlation results in only a slight lowering of the spin-orbit matrix elements. Thus, the discrepancy for bromine is proposed to arise from the nonrelativistic character of the underlying wave function. (C) 2000 American Institute of Physics. [S0021-9606(00)31413-1].