The role of the local-multiplicative Kohn-Sham potential on the description of occupied and unoccupied orbitals

The optimum local-multiplicative exchange potential was found using as inpu t the Hartree-Fock electron density, for the molecular systems: H-2, LiH, H F, NH3, CH4, H2O, N-2, CO, F-2, C2H2 and C2H4. The Zhao and Parr method was used to obtain the local-multiplicative potential where the kinetic energy is minimized using a constrained-search formulation of density functional theory. Two orbital sets were compared, those obtained with the nonlocal Ha rtree-Fock potential and those obtained with the local-multiplicative poten tial, both sets yielding the same electron density. As expected, the highes t occupied molecular orbital (HOMO) energy was similar in both orbital sets . In contrast, the virtual orbital energies, and in particular the lowest u noccupied molecular orbital (LUMO), exhibited considerable differences. The Hartree-Fock LUMO energy goes to zero in a complete basis set limit and to nearly zero with reasonably large basis sets (e.g., augmented triple zeta) with sufficient diffuse functions added. The LUMO provided by the local-mu ltiplicative potential using the same large basis set goes to a bounded ene rgy not equal to zero. The nonlocal Hartree-Fock potential generates a larg e gap between the HOMO and LUMO energies; this difference is equal to the n egative of the HOMO energy at the complete basis set limit. Contrary to thi s behavior, the gap obtained with the local-multiplicative potential is a r easonable approximation to the lowest experimental vertical excitation ener gy. For some of the molecules tested, the ordering of the orbitals correspo nding to the HF and local-multiplicative potential are different. (C) 2000 American Institute of Physics. [S0021-9606(00)30439-1].