Fukui indexes

A DFT study of the reactivity of pyridine and the diazabenzenes towards electrophilic substitution, assuming frontier orbital control of the reactions, predicts their low reactivity as the HOMOs of these substrates are not n-orbitals.5 For pyridine-N-oxide, however, the HOMO is an aromatic orbital. DFT studies giving Fukui indices predict6 the preferred sites of electrophilic attack on pyrrole, furan, and thiophene and calculation of the local softness of the reactive sites rationalizes relative reactivities. 

Applications presented here include the computation of total hardness values of a selected number of atoms and molecules, orbital Fukui indices and orbital softness tensor (polarization) for test systems. In addition, the change of the hardness along the isomerization paths of HCN and 03H+ is reported. 

The orbital Fukui indices, defined through the eq. (16) can be also calculated from eq. 31 ... 

The relation between the orbital Fukui indices and the orbital softness, Sj = sjj, ... 

The performance of the method proposed above in the calculation of absolute hardness values of a set of neutral atoms and molecules is investigated. The Fukui indices and the polarization functions for the a-bonds of test molecules are also reported. Finally, the maximum hardness principle was checked by studying the "hardness profile" along the reaction path for the isomerization of HCN and 03H+ systems. 

Among the halide acids the o-bond Fukui function of HF is found to be the smallest. This correlates well with the anomalous behaviour of hydrofluoric acid with respect to the other acids of the series. In fact, HF is a weak acid, whereas the other are strong (e.g. with about the same strength in water solvent). The Fukui indices for HC1, HBr and HI fall almost in the same range. The polarization functions no indicates that o-bond of HF is the less polarizable (0.051 eV), while... 

Table 4. Fukui indices, polarizability functions, local ...

The Fukui function measures how sensitive a system s chemical potential is to an external perturbation at a particular point. In the approach ti.sed by us, the Fukui indices are approximated by the et uation ... 

The protonation process has been rationalized computing the orbital Fukui indices of neutral sulfine. 

An alternative indication can come, also in this case, from the computation of orbital Fukui indices of neutral aniline. We found a value of 0.19 and 0.06 eV for the orbitals mainly associated with nitrogen and para-carbon, respectively. So, the... 

Reactivity Fukui Indices for Heavy Atoms in Guanine Isomers... 

The Fukui Equations (4.16), (4.17), and (4.18) reactivity indices are considered a measure of the reactivity of the molecule (as nucleophil, electrophil, or radical) when the reaction center is the atom for which the indices have been calculated. The values of the Fukui indices, calculated for different atoms, allow the comparison of the atoms and the identification, as a rule, of the reaction center in different types of chemical reactions. The reactivity estimated in this way does not consider steric factors. Table 4.4 presents the values of the Fukui reactivity indices for the isomers of guanine that are analyzed here. The indices 1, Ie, and 1r do not reflect the deformation of the electron clouds of two molecules that are approaching in order to react 1 therefore they are called static. The reactivity indices that consider this factor also are called dynamic. Their calculation requires much more complicated formulas (Roothaan 1951) and involves the comparison of the energy of the molecular orbitals of the isolated molecules to the energy of the molecular orbitals of the supermolecule (i.e., the ensemble of the A and B molecules, situated at very short distances). 

Elumo- 2.00 Ehomo - 7.85 Elumo Ehomo 5.85 (Elumo EhomoV2 = 2.93 Fukui indices for N atoms in Fe-N bonds ... 

Elumo —3.84 EjjQjyjQ — —9.65 Elumo E omo — 5.81 (Elumo EjjomoV — 2.91 Fukui indices for O atom in Mn-O bond (carbonyl group) ... 

The chemical potential, chemical hardness and sofmess, and reactivity indices have been nsed by a number of workers to assess a priori the reactivity of chemical species from their intrinsic electronic properties. Perhaps one of the most successful and best known methods is the frontier orbital theory of Fukui [1,2]. Developed further by Parr and Yang [3], the method relates the reactivity of a molecule with respect to electrophilic or nucleophilic attack to the charge density arising from the highest occupied molecular orbital or lowest unoccupied molecular orbital, respectively. Parr and coworkers [4,5] were able to use these Fukui indices to deduce the hard and soft (Lewis) acids and bases principle from theoretical principles, providing one of the first applications of electronic structure theory to explain chemical reactivity. In essentially the same form, the Fukui functions (FFs) were used to predict the molecular chemical reactivity of a number of systems including Diels-Alder condensations [6,7], monosubstituted benzenes [8], as well as a number of model compounds [9,10]. Recent applications are too numerous to catalog here but include silylenes [11], pyridinium ions [12], and indoles [13]. 

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