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The semiempirical Atoms-in-a-Molecule (AIM) hardness matrix, 7 , is defined, using the usual finite difference formula, v,, = I, -A,, for the diagonal AIM hardness and the Ohno formula, r), = l / ( a 2 + R;)"*, for the off-diagonal AIM hardness. The Ohno formula is shown to exhibit the correct asymptotic behavior and satisfies the relevant stability criterion. The normal displacements in the AIM electron populations are examined for pyrmle and N-methyl pyrrole, and their relation to the polarization channels is briefly discussed. The new AIM hardness matrix is also tested by comparing the predicted global hardnesses with the corresponding experimental finite difference data for selected diatomics and triatomics. Finally implications of the hardness combination rules are examined and the corresponding softness combination rules are used to calculate the regional and global softnesses of selected molecules. We examine how the regional softnesses reflect known trends in selectivity of protonation of five membered heterocycles, and comment on the signs of the AIM fukui function and the Hard-Soft-Acids-and-Bases principle.

A different localization scheme for the elongation method is developed based on regional molecular orbitals. This scheme is more efficient and more accurate than the previous one especially for covalently bonded systems with strongly delocalized pi electrons. Ab initio test calculations have been performed on three model systems: water chains, polyglycine, and cationic cyanine chains. The dependence on the size of the starting clusters and the effect of the basis set are investigated. Our results are compared with conventional ab initio calculations and it is found in all cases that the error per added unit levels off to a satisfactorily small value as long as the starting cluster is sufficiently large.

We introduce a new tool (single exponential decay detector: SEDD) to extract information about bonding and localization in atoms, molecules, or molecular assemblies. The practical evaluation of SEDD does not require any explicit information about the orbitals. The only quantity needed is the electron density (calculated or experimental) and its derivatives up to the second order.

Interactions of the b-cyclodextrin (b-CD) ligand with Na ? , Cu ? , Mg 2? , Zn 2? , and Al 3? cations were investigated using density functional theory modeling. The objective of this study was to give insight into the mechanism of cation complexation. Two groups of conformers were found. The first group preserved the initial orientation of glucopyranose residues inside the b-CD ligand. The mutual orientation of glucopyranose residues was strongly affected by the cation in the second group of conformers. The system interaction energy was decomposed into electrostatic (ES), Pauli and orbital contributions using the Ziegler-Rauk energy partitioning scheme. The total electrostatic energy, i.e., the sum of ES energy and polarization energy, is the dominating term in the interaction energy. In vacuum, the complexes formed with Al 3? were found to be more stable than with di-and monocations. The vacuum stability sequence was changed in aqueous solution.

ABSTRACT:The elongation method uses the concept of locality and works in a regionally localized molecular orbital basis set. In this method the system is partitioned into several frozen fragments and an active one. If the coupling between a given frozen fragment and the active space is small enough, one can develop a cutoff scheme for effectively discarding the former in all further calculations. At the Hartree-Fock level many two-electron integrals are thereby eliminated, leading to a reduction in selfconsistent field computation time. In test calculations on four polyglycine conformers, with an appropriate default threshold for coupling, the cutoff error is very small and/ or comparable to that of a normal elongation calculation. On the other hand, the computation time for 20 residues is a factor of 5 less than that of a normal Hartree-Fock treatment and scales linearly (or even sublinearly) with the number of residues.

The reactions of methane and hydrofluoromethanes (CH4 - n F n , n = 0, 1, 2, or 3) with a hydroxyl radical have been investigated by a modified GAUSSIAN-2 (G2M) method. Reaction enthalpies have been compared to those obtained by original G2 and G2MP2 schemes. The average absolute error for the reaction enthalpies calculated with the G2M method was smaller than those calculated with the G2 and G2MP2 schemes. G2M reaction enthalpies were of chemical accuracy. Moreover, the G2M method and selected MP2 schemes (those with the smallest average errors in the calculations for the reaction enthalpies) were used to compute the classical barrier heights. According to the transition state theory, the reaction rates were computed in the temperature range of 280−420 K and then the activation energies were obtained by the least-squares fitting to the Arrhenius equation. The activation energies calculated by using G2M barrier heights showed the best agreement with the experimentally derived values. The influence of the fluorine substitution effect on the activation energy was correctly described only by G2M barrier heights.