Orbital Dependent Improvements of the Density Functional Formalism with Applications to Atoms, Molecules and Crystalline Silicon
Abstract
Recently, it has been realized that significant improvements in the calculated electronic structure of single and multiatom systems may be realized by incorporating orbital dependent improvements into the energy density functional. These improvements correct for spurious electron selfinteraction terms which are present in all of the existing approximations of the densityfunctional. The numerical successes of this theory are illustrated using examples from atoms, diatomic molecules and crystalline silicon. A proper variational procedure for orbital dependent theories is introduced and applied to a variety of electronic systems. It is demonstrated that, in addition to the usual Schrodingerlike equations, "localization equations" need to be satisfied which ensure that the resulting Lagrange multiplier matrix is well defined. By following this variational procedure and extending the theory so that fractional electron occupancies may be incorporated into the total energy functional, it is demonstrated that canonical orbitals may be retained in orbital dependent theories. The corresponding eigenvalues lead to good approximations to the ionization energies. The virial theorem for orbital dependent theories is discussed and used to monitor the importance of the localization equations in minimizing the energy functional. An all electron variational procedure for the direct calculation of Wannier functions is introduced. This method is used to carry out selfconsistent field calculations on the silicon crystal in terms of local orbitals. These calculations are performed within the densityfunctional formalism with and without the selfinteraction correction.
 Publication:

Ph.D. Thesis
 Pub Date:
 1986
 Bibcode:
 1986PhDT........62P
 Keywords:

 SELF INTERACTION CORRECTION;
 WANNIER FUNCTIONS;
 Physics: Condensed Matter