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

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Abstract
The optimum local-multiplicative exchange potential was found using as input the Hartree–Fock electron density, for the molecular systems: H 2 , LiH, HF, NH 3 , CH 4 , H 2 O , N 2 , CO, F 2 , C 2 H 2 and C 2 H 4 . 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 Hartree–Fock potential and those obtained with the local-multiplicative potential, both sets yielding the same electron density. As expected, the highest occupied molecular orbital (HOMO) energy was similar in both orbital sets. In contrast, the virtual orbital energies, and in particular the lowest unoccupied 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-multiplicative potential using the same large basis set goes to a bounded energy not equal to zero. The nonlocal Hartree–Fock potential generates a large gap between the HOMO and LUMO energies; this difference is equal to the negative of the HOMO energy at the complete basis set limit. Contrary to this behavior, the gap obtained with the local-multiplicative potential is a reasonable approximation to the lowest experimental vertical excitation energy. For some of the molecules tested, the ordering of the orbitals corresponding to the HF and local-multiplicative potential are different.