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Center for Nonlinear Studies |
In the basic description of electronic systems, each electron is taken to be subject only to the average interaction with the other electrons, i.e. a mean field approximation. The many electron wave function is then constructed as a product of one-electron wavefunctions that are often referred to as ‘orbitals’. A variational optimization of an antisymmetrized product of orbitals gives Hartree-Fock (HF) theory which in some sense appears to be the optimal mean field theory. While molecular structure is quite well predicted by HF and the orbital energies can be used to estimate electronic excitations and photoelectron spectra, the total energy and, thereby, bond energy is not well predicted by HF. Kohn-Sham density functional theory (KS-DFT), which today is more widely used, is also a mean field theory based on orbitals but gives a better estimate of the total energy, while the orbital energies are inaccurate. HF and KS-DFT have several other shortcomings, for example an overemphasis on electron localization by the former and an overemphasis on delocalization by the latter. Is it possible to develop a mean field theory that gives accurate total energy as well as useful orbital energies and a proper balance between localized and delocalized states, thereby providing an optimal mean field theory, more accurate than either KS-DFT and HF? Since our intuition is based strongly on the concept of orbitals and the computational effort of higher level methods increases rapidly with the number of electrons, it seems worthwhile to seek such an optimal mean field theory. A promising approach appears to be the development of an energy functional that includes explicit orbital density dependence (ODD). Such a functional is not only dependent on the total electron density as in DFT, but rather is a functional of all the orbital densities separately. This expanded functional form makes it possible to avoid the self-interaction error inherent in KS-DFT while the computational effort still scales as the number of electrons cubed. Functionals formed by applying the Perdew-Zunger self-interaction correction to KS-DFT functionals are examples of ODD functionals. While they do not represent optimal mean field theory, they give encouraging results and could be used to guide the development of such a theory. Various results obtained recently using a fully variational implementation of PZ-SIC applied to gradient dependent KS-DFT functionals and complex valued orbitals will be given in this presentation and some suggestions for further work towards an optimal ODD functional discussed. The calculations presented include atomization energy of molecules, localized and delocalized charge states in a cation, dipole bound anion, Rydberg excited states of molecular clusters and electron holes in crystalline oxides.
Host: Angel E. Garcia