A new approach to local hardness.

The applicability of the local hardness as defined by the derivative of the chemical potential with respect to the electron density is undermined by an essential ambiguity arising from this definition. Further, the local quantity defined in this way does not integrate to the (global) hardness-in contrast with the local softness, which integrates to the softness. It has also been shown recently that with the conventional formulae, the largest values of local hardness do not necessarily correspond to the hardest regions of a molecule. Here, in an attempt to fix these drawbacks, we propose a new approach to define and evaluate the local hardness. We define a local chemical potential, utilizing the fact that the chemical potential emerges as the additive constant term in the number-conserving functional derivative of the energy density functional. Then, differentiation of this local chemical potential with respect to the number of electrons leads to a local hardness that integrates to the hardness, and possesses a favourable property; namely, within any given electron system, it is in a local inverse relation with the Fukui function, which is known to be a proper indicator of local softness in the case of soft systems. Numerical tests for a few selected molecules and a detailed analysis, comparing the new definition of local hardness with the previous ones, show promising results.

Effects of the substituents on the reactivity of carbonyl oxides. A theoretical study on the reaction of substituted carbonyl oxides with water.

The reactions between fifteen carbonyl oxides and water have been investigated with the aim of contributing to a better understanding of the effects of the substituents in the reactivity of carbonyl oxides. We have employed density functional theory and large scale ab initio methods (CCSD(T), CASSCF, and CASPT2), combined with transition state theory, to investigate the addition of water to carbonyl oxide and, for those carbonyl oxides having a methyl substituent in syn, the hydrogen transfer from the methyl group to the terminal oxygen of carbonyl oxide. In this case, the water acts as a catalyst and this reaction can contribute to the atmospheric formation of a hydroxyl radical. Carbonyl oxides with electron withdrawing substituents and zwitterionic character have low energy barriers and react fast, whereas carbonyl oxides with electron releasing substituents have high energy barriers and react slowly. The position of the substituents plays also an important role and carbonyl oxides having a hydrogen atom substituent in syn react faster than carbonyl oxides having a hydrogen atom substituent in anti. The differences in the reactivity of different substituted carbonyl oxides raise up to ten orders of magnitude and the branching ratios for the two different reactions investigated are also reported.

On the applicability of local softness and hardness.

Global hardness and softness and the associated hard/soft acid/base (HSAB) principle have been used to explain many experimental observed reactivity patterns and these concepts can be found in textbooks of general, inorganic, and organic chemistry. In addition, local versions of these reactivity indices and principles have been defined to describe the regioselectivity of systems. In a very recent article (Chem.-Eur. J. 2008, 14, 8652), the present authors have shown that the picture of these well-known descriptors is incomplete and that the understanding of these reactivity indices must be "reinterpreted". In fact, the local softness and hardness contain the same "potential information" and they should be interpreted as the "local abundance" or "concentration" of their corresponding global properties. In this contribution, we analyze the implications of this new point of view for the applicability of these well-known descriptors when comparing two sites in three situations: two sites within one molecule, two sites in two different, but noninteracting molecules, and two sites in two different, but interacting, molecules. The implications on the HSAB principle are highlighted, leading to the discussion of the role of the electrostatic interaction.

Role of vibrational anharmonicity in atmospheric radical hydrogen-bonded complexes.

Harmonic and anharmonic vibrational frequency calculations are reported for the most stable hydrogen bonded complexes formed between the hydroperoxyl radical and formic, acetic, nitric, and sulfuric acids which are of atmospheric interest. A comparison between the calculated IR spectra of the hydrogen bonded complexes with the corresponding separate monomers is also reported with the aim to facilitate a possible experimental identification of these complexes. The calculations have been carried out using the second-order vibrational perturbative treatment implemented by Barone applied to the PES obtained with the B3LYP functional using the 6-31+G(d,p) and 6-311+G(2d,2p) basis sets. Our calculations for the separate monomers predict vibrational frequencies with quite a good agreement with the experimental values. The anharmonic contribution results in differences of around 40 cm(-1) with respect to the harmonic values; although in some cases involving highly anharmonic modes, these differences can rise up to 300 and 450 cm(-1).

Initial Hardness Response and Hardness Profiles in the Study of Woodward-Hoffmann Rules for Electrocyclizations.

The fundamental principles of pericyclic reactions are governed by the Woodward-Hoffmann rules, which state that these reactions can only take place if the symmetries of the reactants' molecular orbitals and the products' molecular orbitals are the same. As such, these rules rely on the nodal structure of either the wave function or the frontier molecular orbitals, so it is unclear how these rules can be recovered in the density functional reactivity theory (or "conceptual DFT"), where the basic quantity is the strictly positive electron density. A third, nonsymmetry based approach to predict the outcome of pericyclic reactions is due to Zimmerman which uses the concept of the aromatic transition states: allowed reactions possess aromatic transition states, while forbidden reactions possess antiaromatic transition states. Based on our recent work on cycloadditions, we investigate the initial response of the chemical hardness, a central DFT based reactivity index, along the reaction profiles of a series of electrocyclizations. For a number of cases, we also compute complete initial reaction coordinate (IRC) paths and hardness profiles. We find that the hardness response is always higher for the allowed modes than for the forbidden modes. This suggests that the initial hardness response along the IRC is the key for casting the Woodward-Hoffmann rules into conceptual DFT.

Quantum similarity study of atoms: a bridge between hardness and similarity indices.

A hardness based similarity index for studying the quantum similarity for atoms is analyzed. The investigation of hardness and Fukui functions of atoms leads to the construction of a quantum similarity measure, which can be interpreted as a quantified comparison of chemical reactivity of atoms. Evaluation of the new measure reveals periodic tendencies throughout Mendeleev's table. Moreover on the diagonal the global hardness was recovered. Considering a corresponding quantum similarity index reveals that renormalization of the measure can mask periodic patterns. The hardness was calculated for atoms with nuclear charge 3

On the gas phase hydrogen bond complexes between formic acid and hydroperoxyl radical. A theoretical study.

We present a systematic study on the gas-phase hydrogen-bonded complexes formed between formic acid and hydroperoxyl radical, which has been carried out by using B3LYP and CCSD(T) theoretical approaches in connection with the 6-311+G(2df,2p) basis set. For all complexes we have employed the AIM theory by Bader and the NBO partition scheme by Weinhold to analyze the bonding features. We have found 17 stationary points, and 11 of them present a cyclic structure. Their computed stabilities vary from 0.3 to 11.3 kcal/mol, depending on several factors, such as involvement in the hydrogen bond interaction, the geometrical constraints, and the possible concurrence of further effects such as resonance-assisted hydrogen bonds or inductive effects. In addition, three stationary points correspond to transition structures involving a double proton-transfer process whose features are also analyzed.