Kohn-Sham potentials comparison

Fig. 6.4 Calculated potential energy curves of At2 in terms of the inter-atomic distance Kohn-Sham potential energy curves of pure GGA and LC-GGA functionals (left) and of dispersion-corrected functionals (right). For comparison, the curve of the CCSD(T) method (see Sect. 3.5) is also illustrated. The 6-311- -- -G(3df, 3pd) basis functions are used. See Tsuneda and Sato (2009)...

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. 

Simple self-interaction corrected approximations have been shown to provide viable alternative to accurate polarizability calculations of long-chain polymers within DFT." The schemes have been applied to (H2) chains with n = 2-6 in comparison with HF, conventional DFT, and high-level electron correlation schemes. SIC functionals have been shown to exhibit a field counteracting term in the response part of the XC potential as a result of which the calculated polarizabilities are much improved in comparison to normal LDA and GGA functionals. In a related investigation, it has been demonstrated that a self-interaction correction implemented rigorously within Kohn-Sham theory via the optimized effective potential... 

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