The exact one-electron matrix quasirelativistic theory [W. Kutzelnigg and W. 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 effciency 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 effcient innite-order quasirelativistic approach is obtained, which is far simpler than all existing uasirelativistic 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 effcient as two-component approaches without compromising the accuracy. To demonstrate the performance of the new methods atomic calculations on Hg and E117 are rst carried out. The spectroscopic constants (bond length, vibrational frequency, and dissociation energy) of E1172 are then reported. All the results are in excellent agreement with those of the Dirac-Kohn-Sham calculations.

A four-component density functional program package (Beijing Density Functional), suitable for the calculation of total-energy-related chemical properties of systems containing heavy atoms, was developed. The code is based on modern sophisticated exchange-corre-lation functionals and was applied to calculate the spectroscopic constants of the lanthanide diatomic molecules of EuO, EuS, YbO and YbS. It is suggested that the experimental bond lengths for EuS and YbS, derived from empirical interpolations, need to be revised. Relativistic effects on the electronic structure are discussed and compared with results from previous work. The involvement of the lanthanide valence orbit-als in chemical bonding is investigated with a newly developed population and bonding analysis approach.

Fully relativistic density functional calculations using the recently developed Beijing 4-component density functional program package (BDF) were performed for a large number of excited states of the ytterbium atom and the spectroscopic constants of the ground and some excited states of the diatomic molecules YbH, YbF and YbO. It is shown that in a relativistic framework based on the Dirac-Coulomb Hamiltonian modern (nonrelativistic) density functionals work fairly well even for the rather compact 4 f shell, i.e., they quantitatively reproduce the excitation energies due to the occupation changes in the 4 f shell, in contrast to previous statements made by other authors. The nondegeneracy induced by the approximate density functionals to the degenerate open 4 f shell is found to be almost independent of the occupancy of outer shells as well as Hund's coupling and of the same order as that for the first transition metals. After subtracting the unphysical nondegeneracy we obtain reasonable patterns of excited states due to different occupations of the 4 f spinors for the molecules studied here. Although the spectroscopic constants for YbH and YbF obtained by this and other theoretical work are all in good agreement with available experimental data, the theoretical results for YbO show remarkable disagreement with each other and experiment. The present calculations favor a V501 ground state with a leading f 14s0 configuration, which is in agreement with the interpretation of experimental data.

Relativistic MC-SCF (multiconfiguration self-consistent field) in terms of quasidegenerate direct perturbation theory (DPT) of relativistic effects is formulated based on a recently presented theory of effective Hamiltonians for electrons in a model space. The appropriately defined diagonal and nondiagonal parts of operators play a key role in this context. Their definition is based on stationary conditions for the MC-SCF wave function. The formalism starts from nonrelativistic MC-SCF theory. The leading relativistic correction appears as an expectation value in terms of the nonrelativistic MC-SCF function, while the higher-order relativistic corrections require a coupled-MC-SCF type approach.

A time-dependent quasirelativistic density-functional theory for excitation energies of systems containing heavy elements is developed, which is based on the zeroth-order regular approximation (ZORA) for the relativistic Hamiltonian and a noncollinear form for the adiabatic exchange-correlation kernel. To avoid the gauge dependence of the ZORA Hamiltonian a model atomic potential, instead of the full molecular potential, is used to construct the ZORA kinetic operator in ground-state calculations. As such, the ZORA kinetic operator no longer responds to changes in the density in response calculations. In addition, it is shown that, for closed-shell ground states, time-reversal symmetry can be employed to simplify the eigenvalue equation into an approximate form that is similar to that of time-dependent nonrelativistic density-functional theory. This is achieved by invoking an independent-particle approximation for the induced density matrix. The resulting theory is applied to investigate the global potential-energy curves of low-lying Sand-coupled electronic states of the AuH molecule. The derived spectroscopic parameters, including the adiabatic and vertical excitation energies, equilibrium bond lengths, harmonic and anharmonic vibrational constants, fundamental frequencies, and dissociation energies, are in good agreement with those of time-dependent four-component relativistic density-functional theory and ab initio multireference second-order perturbation theory. Nonetheless, this two-component relativistic version of time-dependent density-functional theory is only moderately advantageous over the four-component one as far as computational efforts are concerned.