Valence 392 INDEX

The rroo valency index TV is a rneastire of reactivity, especially of free radicals... 

Draw bond order and free valency index diagrams for the butadienyl system. Write a counter into program MOBAS to detemiine how many iterations are executed in solving for the allyl system. The number is not the same for all computers or operating systems. Change the convergence criterion (statement 300) to several different values and determine the number of iterations for each. 

Free valences and localization energies have been calculated for a series of pyrazoles (neutral molecules and conjugate acids) for homolytic substitution. In all the compounds the site with the lowest localization energy has the Wghest free valence index. This parallel between the two indices of reactivity is maintained in pyrazole, 1-methylpyrazole and their conjugate acids, but not in 1-phenylpyrazole and its conjugate acid. For the three compounds examined experimentally, (32), (33) and (35) (Section 4.04.2.1.8(ii)), only the predictions for (33) are in agreement with the experimental results. 

Table 2.2 contains mean values of the Cu—Oz bond lengths ((<7Cu—())), copper valence index [11] (FCu) and partial charge (<2Cu), one-electron energies of the HOMO and LUMO ( HOmo> lumo) levels along with the bonding energy of Cu1 to the hosting cluster. 

From the comparison of the results, it can be inferred that copper ions exchanged in the ZSM-5 zeolites assumes a bidentate (sites 12 and II) or tridentate coordination (sites M5, Z6, and M7). These two groups differ also in the molecular properties (Table 2.2). The I-centers are characterized by lower values of the valence index and greater partial charges, QCu, in comparison to the M and Z centers, which is associated with the deeper laying HOMO and LUMO levels. In the M5, Z6, and M7 sites Cu1 ions exhibit more covalent character, and the frontier orbitals have less negative energies. As a result, the chemical hardness of the I-centers, located at the channel intersections, is smaller than those located on the walls of the ZSM-5 zeolite. 

The lability of thieno[3,4-6]thiophene (3) and other iso-annelated systems, such as benzo[c]thiophene and benzole] furan, may be due to the strain effect (Mills-Nixon effect see also Zwanenburg et alP and references therein) in the condensed five-membered ring. The stability of the iso-annelated dithienothiophenes 7—9 is noteworthy. Simple LCAO MO method calculations on benzo[c]thiophene indicate that its instability is due to low specific delocalization energy and high free valence index at position 1. 

Aromatic substitution reactions are often complicated and multistep processes. A correlation, however, in many cases can be found between the charged attacking species and the electron density distribution in the molecule attacked during electrophilic and nucleoph c substitution. No such correlation is expected in radical substitution where the attacking particles are neutral, rather a correlation between the reactivities of separate bonds and a free valency index of the bond order. This allows the prediction of the most reactive bonds. Such an approach has been used by researchers who applied quantum calculations to estimate the reactivities of the isomeric thienothiophenes and to compare them with thiophene or naphthalene. " Until recently quantum methods for studying reactivities of aromatics and heteroaromatics were developed mainly in the r-electron approximation (see, for example, Streitwieser and Zahradnik ). The M orbitals of a sulfur atom were shown not to contribute substantially to calculations of dipole moments, polarographic reduction potentials, spin-density distribution, ... 

The symbol 2% represents a simple second order simple index, whereas the symbol yf represents a first order valence index. 

In addition one can also speak of a free valence (index) or indice de liaison fibre of 0.07 for each corner of the benzene molecule since the para-para bond in the DEWAR-configurations is not a real bond but rather represents two free electrons (with opposite spins) at opposite corners. 

Both the bond character and the free valence index (but not the energy) depend in principle on the choice of the canonical configurations. In general, however, it is easy to make a proper choice on the basis of chemical intuition. In naphthalene the results for both quantities are as given below (see also Table 24 and p. 210). o.I0... 

We can also give a free valence number (quite different from the free valence index in V.B.) for atom i for this method of approximation (see also pp. 269 and 282) in the form Ii — C — 2 Pij, that is to say, by taking the sum of the bond i... 

Bond angles ground state TT-electron densities Free valence index... 

Compound pKh" Ionization potential (exp) (ev) Dipole moment (exp) (D) Free valence index... 

The valency index V, represents the valency of the ith atom as the sum of the valencies of its atomic orbitals [Armstrong et ai, 1973 Gopinathan and Jug, 1983a], Thus the valency V, of the /th atom is given by ... 

The free valence index was proposed as a measime of the residual valency of the ith atom in Ji-electron molecular orbitals [Coulson, 1946] it is defined as ... 

Gutman, I. (1978). Topological Formulas for Free-Valency Index. Croat.Chem.Acta, 51,29-33. 

The molecular valency index Vm has also been defined as... 

The first derivatives of the molecular valency index were also proposed as quantum descriptors [Balawender, Komorowski et al., 1998], where the left-hand-side derivative describes the effect of the electrophilic attack and the right-hand-side derivative measures reactivity toward a nucleophilic attack. This last one is also related to the aromatic character of a molecule, measured by the —> diamagnetic susceptibility exaltation. 

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