The implementation and optimization of fractional orbital occupations in density functional theory
Rabuck, Angela DeHart
Scuseria, Gustavo E.
Doctor of Philosophy thesis
The convergence of the Self Consistent Field (SCF) iteration process is one of the most commonly encountered problems in quantum chemistry calculations. Numerous cases are known in which calculations (both Hartree-Fock and Density Functional Theory), even when using extrapolation techniques, converge extremely slowly or do not converge at all. Many of these cases include molecules that contain transition metals. During my research, I developed two techniques that fractionally occupy orbitals around the Fermi energy during the SCF cycles. Both methods use fractionally occupied orbitals to aid in the iterative process, but the occupations at convergence are forced to be ones and zeros. I investigated how by using these fractionally occupied orbitals, convergence was improved for a number of difficult cases. There is also no significant overhead in the number of SCF cycles for molecules that easily converge with standard techniques. On the other hand, I also studied cases where the lowest energy solutions may be fractionally occupied. I implemented numerous methods to optimize the fractional orbital occupations in various Density Functional Theory methods. These methods, which included steepest descent and conjugate gradient techniques, are based on Janak's theorem. In general, the lowest energy solution is fractionally occupied if a solution containing an aufbau principle violation is lower in energy than a typical solution. In these cases, a fractionally occupied solution is indeed the lowest self-consistent field energy solution. New methods to optimize the fractional occupations based on optimizing a trigonometric or Fermi-Dirac based function of the orbital occupations are also discussed and compared.