Infinite-order quasirelativistic density functional method based on the exact matrix quasirelativistic theory

The exact one-electron matrix quasirelativistic theory [Kutzelnigg and Liu, J. Chem. Phys. 123, 241102 (2005)] is extended to the effective one-particle Kohn-Sham scheme of density functional theory. Several variants of the resultant theory are discussed. Although they are in principle equivalent, consideration of computational efficiency strongly favors the one (F(+)) in which the effective potential remains untransformed. Further combined with the atomic approximation for the matrix X relating the small and large components of the Dirac spinors as well as a simple ansatz for correcting the two-electron picture change errors, a very elegant, accurate, and efficient infinite-order quasirelativistic approach is obtained, which is far simpler than all existing quasirelativistic theories and must hence be regarded as a breakthrough in relativistic quantum chemistry. In passing, it is also shown that the Dirac-Kohn-Sham scheme can be made as efficient as two-component approaches without compromising the accuracy. To demonstrate the performance of the new methods, atomic calculations on Hg and E117 are first carried out. The spectroscopic constants (bond length, vibrational frequency, and dissociation energy) of E117(2) are then reported. All the results are in excellent agreement with those of the Dirac-Kohn-Sham calculations.