Free valence number

F. 1-26. (a) ir-Bond order of the C-S bonds in the ground state, (fc) ir-Bond order of the C-S bonds in the first excited state, (c) Free-valence number of the intermediate diradicaf. (Most probable bicyclic intermediate resulting from the ring closure of the diradicai. 

Univalent radicals have the endings -enyl, -ynyl, -dienyl, -diynyl, etc. When necessary, the positions of the double and triple bonds are indicated by locants, with the carbon atom with the free valence numbered as 1. Examples ... 

Early studies of photocyclization reactivity using Coulson s Free Valence Numbers (Ff) were carried out by Scholz, Dietz and Miihlstadt and by Laarhoven et al. Relatively good reactivity predictions for several parallel cyclization paths were obtained taking the sums of excited state Free Valence numbers for the reacting C atom pair (S F ) as reactivity measure In this sense a threshold value of 2 F = 1 was assumed, 2F < 1 implying lack of reactivity (cf also Ref. ). 

The selectivity is caused by the electron distribution in the excited diarylethylene. Several reactivity parameters for the photocyclization have appeared to be valuable. The most simple one is the sum of the free valence numbers of the atoms r and s involved in the cyclization in the excited state (E F s) (Fr = /3 — IP, P = bond order)13). The following rules could be derived from a large number of photocyclization reactions 14) ... 

It is noted that in the synthesis of 52 the precursor 53 gave the product in good yield (70 %) (only small amounts of other photocyclization products were isolated), whereas the distyryl aromatic 51 did not yield the required product, in accordance with the relevant free valence numbers. 

In Table 27 the simple Hiickel indices, Nr (Dewar number), Fr (free valence number) and Lr (localization energy) are given, together with the Mulliken overlap population pr, calculated by the extended Hiickel method and using the geometry of hexahelicene as determined by X-ray analysis141) to account for the non-planarity. 

Equation (39) therefore remains unchanged since the term in a cancels. An exactly similar argument holds for nucleophilic substitution we therefore conclude that (1) the relative reactivities of different hydrocarbons, and the relative reactivities of different positions in the same hydrocarbon, should be the same for substitution by reagents of all kinds, and (2) there should be in each case a linear relation between log k and The first relationship holds qualitatively in all cases except where steric effects are involved thus naphthalene is more reactive than benzene to reagents of all three types (e.g. nitric acid, phenyl radicals, sodamide), and in each case the a-position in naphthalene is more reactive than the / the corresponding free valence numbers are ... 

The free valence number therefore provides a good guide to reactivity in alternant hydrocarbons unfortunately this approach cannot easily be extended to compounds of other types. It can be used only when the contribution to 6E due to changes in the qt is the same for different aromatic systems and this is so only if coulomb integrals a, are the same for all the atoms present. Equation (33) shows that this is not so for molecules containing heteroatoms the ionization potential Wt is different for different atoms. Equation (33) shows that non-alternant hydrocarbons such as azulene must also be excluded here the... 

The similarity between Eqs. (39) and (64) implies that there must be a relationship between free valence number and reactivity number. This is indeed the case, for it can be shown14 at once by first order perturbation theory that... 

We have already considered one criterion of this kind, the free valence number here we shall consider three other properties of molecules which have been used in similar connections. These are the charge density, self-polarizability, and frontier orbital density. All of these properties show correlations with reactivity, at least in certain ranges of compounds, but these correlations are due in each case to fortuitous correspondences between them and the quantities 6ED or 6E, —the same situation that arises in the case of free valence number. 

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... 

These free valence numbers in the S method run parallel to the self-polarizability from the M.O. description which has still to be discussed. A larger free valence therefore also means a smaller activation energy for (electrophilic) substitution and probably for radical substitution (p. 284). A high bond order runs parallel to a low bond localization energy of a tu electron pair in this bond and thus with a low activation energy for molecular addition and ozonization. 

This reaction is not limited to stilbene itself. Whether a diarylethylene may be cyclized, and if so, in which way, can be predicted from the sum = + of the free valence numbers F = calculated for... 

This reaction is not limited to stiibene itself. Whether a diarylethylene may be cyclized, and if so, in which way, can be predicted from the sum F = f + of the free valence numbers = V5 - calculated for the reacting positions g and oof the HOMO-LUMO excited reactant. Here, 2. is the sum of excited-state r-bond orders for all bonds p—g originating from atom g. Laarhoven (1983) derived the following rules ... 

X-ray crystallographic studies of the 1 1 molecular compound of 73 and TCNQ have been reported.1060 However, the synthesis of 73 apparently has not yet been published the synthetic procedure of Scheme 19 may have been used. Efforts to obtain 73 by double photocyclization of 290c failed,104 which is consistent with calculations of free valence numbers for the excited state of the atoms involved in the cyclization.106b 106d... 

Multiple electrocyclizations have been used for the synthesis of higher helicenes, and once again, the determination of the sum of the free valence numbers for the excited state may be used to optimize the synthesis. In compound 19, three phenanthrene moieties are linked by two ethylene... 

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