Electron repulsion resonance

MO models with electron repulsion Resonance integral f)... 

The valence state ionization potential —the resonance integrals and the one-center electron repulsion integrals can be considered as basic parameters of the semiempirical method and can be adjusted to give optimal agreement. The core charges Z, indicate the number of 71 electrons the center M contributes to the n system, and the two-center electron repulsion integrals are obtained from an empirical relationship such as the Mataga-Nishimoto formula ... 

Resonance, as you saw in Organic I, occurs in many systems, and you need to be able to recognize when it s going to affect the outcome of a reaction. In general, resonance makes a species more stable by delocalizing the electrons. Delocalization, among other things, reduces electron-electron repulsion. 

The next step is to evaluate the coulomb and resonance integrals. Direct calculation of the latter requires specification of the Hamiltonian and hence explicit account of electron-repulsion terms, which is very difficult for these complex molecules. Accordingly, it is usual to make the earlier assumptions that is, either the resonance integral is directly proportional to the overlap integral or is related to it by a Wolfsberg-Helmholz formula... 

Tho author has repeatedly [6j pointed out that the valency conception of non-localized bonds (resonance among several valence-bond structures, many centre molecular orbitals) lias no reality and only arises from a neglect of electronic repulsions. It is noteworthy that on this basis the possibility of a contribution of structures IIIc and d (IVc %od d) to Ufa and b (IVa and b) and vice versa would not enter and, thus, this objection against the discussed interpretation of the hydrogen bond would be removed ... 

Quantum mechanics has made important contributions to the development of theoretical chemistry, e.g. the concept of quantum mechanical resonance in the interpretation of the perturbation in the excited states of polyelectronic systems, the concept of exchange in the formation of a covalent bond, the concept of non-localized bonds (though, in my view, unsatisfactory and only arising from a neglect of electronic repulsions), the concept of dispersion forces etc., but it is noteworthy that all these ideas owe their success and justification to their ability to account qualitatively for previously unexplained experimental facts rather than to their quantitative mathematical aspect. 

It is possible and probably very likely that both types of electronic effects are occurring in the acetal function. In other words, 2 could be more stable than 2 because 2 is stabilized relative to 2 by a partial electron transfer and 2 is destabilized relative to 2 by electronic repulsions. There is presently no experimental technique to differentiate between the two effects. At the present time, many chemists, including myself, prefer to consider the anomeric effect as a stabilizing rather than a destabilizing effect. The main reason is that the concept of stabilization of a system through electronic delocalization is a well established principle in organic chemistry. The resonance theory is indeed based on this principle. I believe that this concept rather than the dipole - dipole or electron pair - electron pair repulsions allows the organic chemist to rationalize his results better. 

Hubbard Hamiltonian An effective Hamiltonian, which includes on-site electron-electron repulsion and a resonance integral, and is used in VB to calculate states of molecular species with an average of one electron per site (atom), e.g., of polymers. 

The stability of the values of bond order is even more striking. In the described data set the values of the bond orders span the range from 0.929 to 0.992 with an average of 0.974 and standard deviation of 0.017. This corresponds to the precision of 1.7%. Of course the high stability is explained by the validity of the above limit, which in its turn is due to the fact that the difference between one- and two-center electron-electron repulsion integrals (Aym) at interatomic separations characteristic of chemical bonding is much smaller than the resonance interaction at the same distance. The most important reason for the stability (i.e. of transferability) of the bond orders is that they deviate from the ideally transferable value in the second order in two small parameters < and i. 

The resonance integrals (/ ) are calculated by the overlap integrals. The electron repulsion integral of type (rr rr) is approximately determined using the ionization potential [/p(r)] and the electron affinity [A(r)J of each core. 

The molecular and electronic structures of cyclic disulfide cation radicals of 1,2-dithietane 6 and 1,2-dithiete 7, and radical cations of 1,2-dithiolane 2 (2a-c represent stable conformations determined in terms of the symmetry restriction of Cs, Cz, and Czv), with emphasis on the nature of a two-center three-electron (Zc-ie) sulfur-sulfur bond have been examined by ab initio molecular orbital (MO) calculations <1997JMT(418)171>. Unrestricted Hartree-Fock (UHF)/ MIDI-4(d) computations showed that this bond in organodisulfide radical cation 2 is shorter in comparison to 1,2-dithiolane 2 and possesses partial Jt-bond character (structure A), as previously implied by electron spin resonance (ESR) spectroscopy <1982JA2318>, which correlates best with the form as the most favorable conformation of the cation radical 2. Contrary to the repulsive S-S interaction in the parent 1,2-dithiolane arising from the lone pairs of electrons, the hemi-7t-bond formed by one-electron oxidation should stabilize the five-membered ring of 2, or, for example, a similar cation radical of LA 3 which is involved in diverse biochemical reactions. 

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