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The Beijing Density Functional (BDF) program package is such a code that can perform nonrelativistic, one-, two-, and four-component relativistic density functional calculations on medium-sized molecular systems with various functionals in most compact and yet sufficient basis set expansions. The mergence of different approaches in a single code facilitates direct and systematic comparisons between different Hamiltonians, since they share all the same numerical and technical issues. In this account, the methodologies adopted in the code will be discussed in great detail and some applications of the code will be briefly presented.

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A method based on first-order density matrices is proposed to define an atom in a molecule, which is in accord with a previously given definition using density functional theory. The promotion energy Ep is expressed in terms of a defined division function α(r). By minimizing Ep with respect to α(r), one can obtain α(r), by which an atom in a molecule is uniquely determined. It is shown that such an ‘‘atom’’ satisfies a local virial theorem, depicted intuitively, Some other properties of the atom in a molecule are also discussed. Comparison is made with a definition due to Bader, and an approximate but simple approach to determine an atom in a molecule is proposed.

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 4f shell, i.e., they quantitatively reproduce the excitation energies due to the occupation changes in the 4f shell, in contrast to previous statements made by other authors. The nondegeneracy induced by the approximate density functionals to the degenerate open 4f 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 4f 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 Ω=0+ ground state with a leading f14σ0 configuration, which is in agreement with the interpretation of experimental data.

A new method for constructing nonorthogonal localized molecular orbitals (NOLMOs) is presented. The set of highly localized NOLMOs is obtained by minimization of the spread functional starting from an initial set of canonical orthogonal molecular orbitals. To enhance the stability and efficiency, the centroids of the NOLMOs are constrained to be those of the corresponding orthogonal localized molecular orbitals (OLMOs), which are obtained with the Boys criterion in advance. In particular, these centroid constraints make the optimization for each NOLMO independent of the others, which is an attractive feature for application to large systems. The minimization with the constraints incorporated through the multiplier-penalty function method is stable and efficient in convergence. While exhibiting the classical bonding pattern in chemistry and sharing a spatial distribution similar to that of the corresponding OLMOs, the obtained NOLMOs are more compact than the corresponding OLMOs with about 10%-28% reduction in the value of the spread functional and devoid of the troublesome "orthogonalization tails."

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