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Notes: The Hartree product is analyzed in the context of Kohn–Sham theory. The differential equations that emerge from this theory are solved with the optimized effective potential using the Krieger, Li, and Iafrate approximation, in order to get a local potential as required by the ordinary Kohn–Sham procedure. Because the diagonal terms of the exact exchange energy are included in Hartree theory, it is self-interaction free and the exchange potential has the proper asymptotic behavior. We have examined the impact of this correct asymptotic behavior on local and global properties using this simple model to approximate the exchange energy. Local quantities, such as the exchange potential and the average local electrostatic potential are used to examine whether the shell structure in an atom is revealed by this theory. Global quantities, such as the highest occupied orbital energy (related to the ionization potential) and the exchange energy are also calculated. These quantities are contrasted with those obtained from calculations with the local density approximation, the generalized gradient approximation, and the self-interaction correction approach proposed by Perdew and Zunger. We conclude that the main characteristics in an atomic system are preserved with the Hartree theory. In particular, the behavior of the exchange potential obtained in this theory is similar to those obtained within other Kohn–Sham approximations. © 2000 American Institute of Physics.

Notes: The Krieger, Li, and Iafrate approximation to the optimized effective potential including the self-interaction correction for density functional theory has been implemented in a molecular code, NWChem, that uses Gaussian functions to represent the Kohn and Sham spin–orbitals. The differences between the implementation of the self-interaction correction in codes where planewaves are used with an optimized effective potential are discussed. The importance of the localization of the spin–orbitals to maximize the exchange-correlation of the self-interaction correction is discussed. We carried out exchange-only calculations to compare the results obtained with these approximations, and those obtained with the local spin density approximation, the generalized gradient approximation and Hartree–Fock theory. Interesting results for the energy difference (GAP) between the highest occupied molecular orbital, HOMO, and the lowest unoccupied molecular orbital, LUMO, (spin–orbital energies of closed shell atoms and molecules) using the optimized effective potential and the self-interaction correction have been obtained. The effect of the diffuse character of the basis set on the HOMO and LUMO eigenvalues at the various levels is discussed. Total energies obtained with the optimized effective potential and the self-interaction correction show that the exchange energy with these approximations is overestimated and this will be an important topic for future work. © 2000 American Institute of Physics.

Notes: The self-interaction correction of Perdew and Zunger with the optimized effective potential using the Krieger–Li–Iafrate approximation is analyzed for atomic and molecular systems in the exchange-only context. Including the self-interaction correction (SIC) orbital by orbital shows that the appropriate asymptotic behavior of the exchange potential can be achieved if just the contribution of the highest occupied molecular orbital (HOMO) is considered. However, if a good description of the exchange potential in the valence region is required, and consequently a good description of the HOMO energy, then all electrons of the valence shell must be taken into account. In contrast, the lowest unoccupied molecular orbital (LUMO) is described adequately if just the HOMO SIC contribution is employed. In addition, if the lowest occupied orbital is also considered in the SIC approximation, there is an improvement in the description of the exchange potential in inner regions of an atom. When all electrons in an atom or in a molecule are considered in the SIC approximation, there exists a linear relationship between their occupied orbital energies and those obtained with the local density approximation (LDA). This indicates that the SIC and LDA occupied orbital energies are related by a shift. Furthermore, for a set of atoms or molecules there is a linear relationship between HOMO energies obtained with LDA and those obtained with the SIC approximation. Using both observations, the shift between the occupied orbital energies LDA and SIC is reported. We found that this shift (obtained for the occupied orbitals) cannot be applied to the virtual orbitals, in particular to the LUMO. However, we do find an additional linear relationship between LUMO energies obtained with LDA and those obtained with the SIC approximation. The difference between the LUMO and HOMO energy (GAP) obtained with the LDA and SIC approximations is compared with that obtained with an exact local-multiplicative exchange potential and all are compared with experimental vertical excitation energies. Whereas the LDA GAP underestimates the excitation energies, the GAP obtained with the SIC approximation and with an exact local-multiplicative exchange potential overestimates this quantity. From an analysis of the exchange energy for simple molecules, and with a similar approach to the modified Xα method, we found a linear relationship between the SIC and Hartree–Fock (HF) methods. We show numerically that the nondiagonal terms of the exact orbital representation of the exchange energy can be approximated by the SIC approach. © 2001 American Institute of Physics.

Notes: The optimum local-multiplicative exchange potential was found using as input the Hartree–Fock electron density, for the molecular systems: H2, LiH, HF, NH3, CH4, H2O, N2, CO, F2, 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 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. © 2000 American Institute of Physics.

Notes: We developed an in vitro tissue-culture model to analyze the process involved in mycobacterial spread through lung epithelial cell monolayers. A549 cells were infected with low numbers of viable Mycobacterium tuberculosis bacilli expressing the gfp gene. Subsequent addition of a soft agarose overlay prevented the dispersal of the bacilli from the initial points of attachment. By fluorescence microscopy the bacteria were observed to infect and grow within the primary target cells; this was followed by lysis of the infected cells and subsequent infection of adjacent cells. This process repeated itself until an area of clearing (plaque formation) was observed. The addition of amikacin after initial infection did not prevent intracellular growth; however, subsequent plaque formation was not observed. Plaque formation was also observed after infection with Mycobacterium bovis BCG bacilli, but the plaques were smaller than those formed after infection with M. tuberculosis. These observations reinforce the possibility that cell-to-cell spreading of M. tuberculosis bacilli, particularly early in the course of infection within lung macrophages, pneumocytes, and other cells, may be an important component in the infectious process.

Notes: The definition of local hardness is clarified within the Kohn-Sham formulation of the density functional theory. Exact equations for the local hardness of open- and closed-shell electronic systems are derived. It is found that the Kohn-Sham independent particle kinetic energy does not contribute to local hardness. The apparent contradiction with previous work of Parr et al. is cleared up when the local hardness definition is revised. © 1994 John Wiley & Sons, Inc.