Orbital-Dependent Exchange-Correlation

Hock, A. and Engel, E. (1998). Pseudopotentials from orbital-dependent exchange-correlation functionals, Phys. Rev. A 58, 3578-3581. 

The Pair Density. Orbital-dependent Exchange-correlation Functionals... 

In the next subsection we consider two orbital-dependent exchange-correlation functionals used for soMds with the strong electron correlation. These functionals are used mainly with non-LCAO (PW, LMTO) basis and from this point of view are not quantum-chemical approaches. Therefore, we discuss them only briefly. 

This chapter is devoted to orbital-dependent exchange-correlation (xc) functionals, a concept that has attracted more and more attention during the last ten years. After a few preliminary remarks, which clarify the scope of this review and introduce the basic notation, some motivation will be given why such implicit density functionals are of definite interest, in spite of the fact that one has to cope with additional complications (compared to the standard xc-functionals). The basic idea of orbital-dependent xc-functionals is then illustrated by the simplest and, at the same time, most important functional of this type, the exact exchange of density functional theory (DFT for a review see e.g. [1], or the chapter by J. Perdew and S. Kurth in this volume). 

Semi-empirical Orbital-Dependent Exchange-Correlation Functionals... 

Eds., NATO ASI Series B, Plenum, New York, 1995, pp. 191-216. Recent Developments in Kohn-Sham Theory for Orbital Dependent Exchange-Correlation Energy Functionals. 

The general idea of using different orbitals for different spins" seems thus to render an important extension of the entire framework of the independent-particle model. There seem to be essential physical reasons for a comparatively large orbital splitting depending on correlation, since electrons with opposite spins try to avoid each other because of their mutual Coulomb repulsion, and, in systems with unbalanced spins, there may further exist an extra exchange polarization of the type emphasized by Slater. 

The dependence of the DFT results on the basis set used to expand the Kohn-Sham orbitals is illustrated in Table 4.3, which collects equilibrium geometry properties of water dimer obtained with the same exchange-correlation functional (B88/P86) but with different basis sets. 

The quality of the TD-DFT results is determined by the quality of the KS molecular orbitals and the orbital energies for the occupied and virtual states. These in turn depend on the exchange-correlation potential. In particular, excitations to Rydberg and valence states are sensitive to the behavior of the exchange-correlation potential in the asymptotic region. If the exchange-correla-... 

To perform excited-state calculations, one has to approximate the exchange-correlation potential. Local self-interaction-free approximate exchange-correlation potentials have been proposed for this purpose [73]. We can try to construct these functionals as orbital-dependent functionals. There are different exchange-correlation functionals for the different excited states, and we suppose that the difference between the excited-state functionals can be adequately modeled through the occupation numbers (i.e., the electron configuration). Both the OPM and the KLI methods have been generalized for degenerate excited states [37,40]. 

In summary, the original Thomas-Fermi-Dirac DFT was unable to give binding in molecules. This was corrected by Kohn-Sham, [11] who chose to use an orbital rather than density evaluation of the kinetic energy. By the virial theorem, = —E, so this was a necessity to obtain realistic results for energies. Next, it was shown that the exact exchange requires an orbital-dependent form, too. [47,48] The future seems to demand an orbital-dependent form for the correlation. 

Ec = E c - Ex have been employed. On the one hand, LDA and GGA type correlation functionals have been used [14], However, the success of the LDA (and, to a lesser extent, also the GGA) partially depends on an error cancellation between the exchange and correlation contributions, which is lost as soon as the exact Ex is used. On the other hand, the semiempirical orbital-dependent Colle-Salvetti functional [22] has been investigated [15]. Although the corresponding atomic correlation energies compare well [15] with the exact data extracted from experiment [23], the Colle-Salvetti correlation potential deviates substantially from the exact t)c = 8Ecl5n [24] in the case of closed subshell atoms [25]. 

The basic concepts of the one-electron Kohn-Sham theory have been presented and the structure, properties and approximations of the Kohn-Sham exchange-correlation potential have been overviewed. The discussion has been focused on the most recent developments in the theory, such as the construction of from the correlated densities, the methods to obtain total energy and energy differences from the potential, and the orbital dependent approximations to v. The recent achievements in analysis of the atomic shell and molecular bond midpoint structure of have been... 

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