ORBITAL HARDNESS MATRIX AND FUKUI INDEXES, THEIR DIRECT SELF-CONSISTENT-FIELD CALCULATIONS, AND A DERIVATION OF LOCALIZED KOHN-SHAM ORBITALS

Formulas governing fixed orbital hardnesses and their relation to the hardness kernel are derived. It is shown how the orbital hardness matr ix and its inverse matrix, the orbital softness matrix, may thus be di rectly calculated, and then the total chemical hardness, softness, and electronegativity of a molecular species. These quantities are calcul ated for the molecule HCN, using Dirac exchange and von Barth-Hedin co rrelation in the local density form of Kohn-Sham theory. The result co mplies with the frontier orbital theory. As quantitative indicators of orbital reactivity, the frontier orbital softness and Fukui indices g enerally have larger values than inner electron orbitals. The relation of orbital hardness matrix elements to the two-electron orbital integ rals in a typical molecular orbital calculation is discussed, and it i s demonstrated that diagonalization of the orbital hardness matrix lea ds to orbitals more localized than conventional Kohn-Sham orbitals. (C ) 1997 American Institute of Physics.