Mobile bond order

Compounds Method Net charges Mobile bond orders ... 

Adams and Slack compared the electron densities and mobile bond orders of the parent molecule (21) with those of thiazole (22) and P50 idme (23). Overlap was neglected in these simplified calculations,... 

A typical example is given in the case of aromatic substitutions. The sum of the mobile bond orders of the bonds between the reaction center... 

The studies in this field are based on Coulson s well-known finding116 that there is a correlation between bond length and mobile bond order. 

An MO study of triplet coumarin has indicated that the mobile bond order for the 3,4-double bond decreases significantly on excitation (73MI22201). Furthermore, the electron density at C-3 is decreased but is increased at C-4 and hence an explanation of the orientational specificity of the photoaddition of coumarin to 1,1-diethoxyethylene is available (equation 1) (66TL1419). The reactivity of the 3- and 4-positions of triplet coumarin is also substantiated by the high spin-densities calculated for these positions (70JPC4234). 

Instead of the bond character of the V.B. method we have in this case the mobile bond order or double bond order defined by Coulson41 as p= - mcmicmj t ie bond between the atoms i andj again summed over all electrons in the occupied levels m. The double bond order runs from o for the pure single bond to 1 for a pure double bond. For benzene we find 0.667. We obtain with a factor 2 on account of the occupation of each level by two electrons (p. 277) ... 

Fig. 1.it-Electron densities and mobile bond orders for indoxazene.60 Density values in parentheses are taken from Berthier and Del Re.61... 

Recently, 7r electron densities and mobile bond orders have been calculated for the indoxazene system, both by the simple Hiickel method,80 and by a modified scheme of Berthier and Del Re.61 The values are given in the accompanying formula (Fig. 1) for comparison. 

Htickel molecular orbital calculations have been performed for anthranil the n electron densities and mobile bond orders of Del Re80 and Berthier and Del Re81 are given in Fig. 2. 

Ham, N.S. (1958a). Mobile Bond Orders in the Resonance and Molecular Orbital Theories. J.Chem.Phys.,29,1229-1231. 

Ruedenberg, K. (1958). Theorem on the Mobile Bond Orders of Alternant Conjugated Systems. J.Chem.Phys., 29,1232-1233. 

Ham, N.S. and Ruedenberg, K. (1958b) Mobile bond orders in conjugated systems. /. Chim. Phys., 29, 1215-1229. 

The number of electrons in the system is dEJdfi n/2, while a measure of the mobile bond order is ( ln)cEJc VC/2. This value is close to the accurate one, 0.79, for the graphene sheet with a coordination number 3. 

The relative energies of the lowest 18 molecular orbitals are illustrated in Fig. 14. These are only approximate since configurational interaction has been ignored. The electron densities and mobile bond orders are shown in Fig. 15, assuming different coulombic integrals for the carbon and nitro-... 

Fig. 15. Mobile bond orders and electron density in phthalocyanine. A single bond has a mobile bond order of zero, and a double bond has a mobile bond order of one.

The skeletal configuration of polyphenyl molecules, that is, biphenyl, para-terphenyl, pora-quaterphenyl, and me/a-terphenyl, and the numbering of atoms in those molecules are shown in Fig. 1. In our previous papers we calculated the mobile bond orders and discussed the related phenomena for... 

To calculate the Hamiltonian matrix elements shown in (5) and (16), the above-mentioned molecular integrals and the constant a are put into the equations. As a first trial input, mobile bond orders are estimated from the Hiickel approximation. ... 

The inner-shell electrons and the a electrons were supposed to have their energies and distribution governed solely by the atomic orbitals or pair of orbitals in which they move. All effects depending on conjugation of the mobile ti electrons such as resonance energies and variation in bond order were ascribed to the ji electrons. Such a mobile bond order between atoms r und s was formulated as ... 

This approach has been put on a quantitative basis by Coulson through p j, the "mobile bond order" between adjacent atoms i and j. This is defined by the equation... 

Calculate the mobile bond orders for bicvclobuta-diene. (A check on the answers is available in Appendix I.)... 

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