Kohn-Sham orbitals, comparison

The discussion of the one-electron properties focused on the comparison of the Kohn-Sham orbital structure with the jellium-shell model. This was done by analyzing the... 

Since the Kohn-Sham orbitals, introduced and used in DFT, serve a different purpose than creating a reasonable single determinantal wave function P, chemists were seeking answers to the question what do the Kohn-Sham orbitals and eigenvalues mean as DFT moved into the spotUght of electronic structure theory. A simple answer was based on a comparison of orbitals of small molecules (H2O, N2, PdCl ) obtained from WFT (Hartree-Fock, EHT)... 

In spite of the absence of a typical chromophore, 1,2-dithiin is a bright reddish-orange color. Absorption maxima were found at 451 (2.75 eV), 279 (4.36 eV), and 248 nm (5.00 eV), and the colored band was assigned to a A excitation <1991JST(230)287>. The main reason for the colored absorption of 1,2-dithiin is the low HOMO-LUMO gap of the KS orbitals which amounts to only 3.6 eV (HOMO = highest occupied molecular orbital LUMO = lowest unoccupied molecular orbital KS = Kohn-Sham) <2000JMM177>. By comparison, saturated 1,2-dithiane is colorless (290 nm). 

This argument shows that the locality hypothesis fails for more than two electrons because the assumed Frechet derivative must be generalized to a Gateaux derivative, equivalent in the context of OEL equations to a linear operator that acts on orbital wave functions. The conclusion is that the use by Kohn and Sham of Schrodinger s operator t is variationally correct, but no equivalent Thomas-Fermi theory exists for more than two electrons. Empirical evidence (atomic shell structure, chemical binding) supports the Kohn-Sham choice of the nonlocal kinetic energy operator, in comparison with Thomas-Fermi theory [288]. A further implication is that if an explicit approximate local density functional Exc is postulated, as in the local-density approximation (LDA) [205], the resulting Kohn-Sham theory is variation-ally correct. Typically, for Exc = f exc(p)p d3r, the density functional derivative is a Frechet derivative, the local potential function vxc = exc + p dexc/dp. 

We review the Douglas-Kroll-Hess (DKH) approach to relativistic density functional calculations for molecular systems, also in comparison with other two-component approaches and four-component relativistic quantum chemistry methods. The scalar relativistic variant of the DKH method of solving the Dirac-Kohn-Sham problem is an efficient procedure for treating compounds of heavy elements including such complex systems as transition metal clusters, adsorption complexes, and solvated actinide compounds. This method allows routine ad-electron density functional calculations on heavy-element compounds and provides a reliable alternative to the popular approximate strategy based on relativistic effective core potentials. We discuss recent method development aimed at an efficient treatment of spin-orbit interaction in the DKH approach as well as calculations of g tensors. Comparison with results of four-component methods for small molecules reveals that, for many application problems, a two-component treatment of spin-orbit interaction can be competitive with these more precise procedures. 

The description of the photoionization process by means of a method based on the Density Functional Theory (DFT) is reviewed. The present approach is based on a basis set expansion in B-spline functions, which are particularly suited to deal with the boundary conditions of the continuum states. Both Kohn-Sham (KS) and its extension to the Time Dependent (TD-DFT) formalism are considered. The computational aspects of the method are described the implementations for atoms, for molecules in One Centre Expansion (OCE) and for molecules with the Linear Combination of Atomic Orbital (LCAO) scheme. The applications of the method are discussed, from atoms to large fullerenes, with comparison with available experimental data. 

However, as shown above, comparison with the orbital Schrodinger equations implies a sum rule ,e, = N/x. This sum rule requires all e = p, in violation of the exclusion principle for more than two electrons [7]. Thus it is incorrect to assume that the undetermined constants in ground-state theory can be set to the same value for different orbital energy levels. In contrast, Kohn and Sham [4] were correct in substituting t for 8T/bp in the KS-equations. There is no equivalent exact Thomas-Fermi theory. 

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