Free valency index

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. 

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, ... 

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 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. 

Gutman, 1. (1978b) Topological formulas for free-valency index. Croat. Chem. Acta, 51, 29-33. 

The free-valence index is actually found to be of greatest importance in free-radical reactions. Early work by SwareRl° investigated the rate... 

JZ3 Tlie free-valence index F, for carbon atom r in a planar conjugated compound is defined as F) - Si / , where the sum is over the atoms bonded to atom r. fllie quantity... 

No. Atom Chaise Spin density Sum over Wiberg s coeff. Free valency index... 

Bond Orders, Free Valence Indexes, and Charge Distribytions... 

One possible approach to the study of chemical reactivity is to determine the degree that the atoms in a molecule are bonded to adjacent atoms relative to their theoretical maximum bonding power. If particular atoms are not much bonded compared to the maximum, we could say that they have considerable "free valence" and especially reactive positions. Coulson defines a free valence index, atom i as follows ... 

The usual way of reporting the results of MO calculations of free valence indexes, bond orders, and DE follows ... 

Clearly an electrophilic reagent would be expected to react at position 1 and nucleophilic reagents at positions 4 or 6. If free valence indexes are a reliable index of reactivity, either positions 3 or 4 should be most reactive toward neutral free radicals. These predictions are rather well in accord with experiment. 

Thus, we see that the free valence index of the ith position is meaningful when a radical reagent produces a perturbation of p.j as well when it is far away. 

The free valence indexes 3. are calculated by the following equation (cf. pp. 56-57) ... 

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