Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Resonance integral Coulomb integrals

In the Pariser-Parr-Pople scheme, the so-called zero differential overlap approximation is used, and the u-electron system is treated as a nonpolarizable core. The interelectronic repulsions are explicitly taken into account in the total Hamiltonian. Resonance integrals, core integrals, and electronic repulsion integrals are given empirically, and Coulomb penetration integrals are neglected. ... [Pg.45]

Uickel and McLachlan calculations of spin densities with resonance and Coulomb integral perturbations. Isotopically enriched (90% C). [Pg.404]

One convention (Dickson. 1968) for oxygen heterocycles sets the coulomb integral at z 2f) and the resonance integral at Eor the oxirane moiety,... [Pg.199]

Hi2 is the resonance integral, usually symbolized by p. In a homonuclear diatomic molecule Hi I = H22 = a, which is known as the Coulomb integral, and the secular determinant becomes... [Pg.228]

For unsubstituted aromatic hydrocarbons all the carbon atoms are assigned the same Coulomb integral (a) and all C—C bonds are assigned the same resonance Integral (/3). [Pg.5]

The CNDO method has been modified by substitution of semiempirical Coulomb integrals similar to those used in the Pariser-Parr-Pople method, and by the introduction of a new empirical parameter to differentiate resonance integrals between a orbitals and tt orbitals. The CNDO method with this change in parameterization is extended to the calculation of electronic spectra and applied to the isoelectronic compounds benzene, pyridine, pyri-dazine, pyrimidine and pyrazine. The results obtained were refined by a limited Cl calculation, and compared with the best available experimental data. It was found that the agreement was quite satisfactory for both the n TT and n tt singlet transitions. The relative energies of the tt and the lone pair orbitals in pyridine and the diazines are compared and an explanation proposed for the observed orders. Also, the nature of the lone pairs in these compounds is discussed. [Pg.150]

Here q represents the coulomb energy of an electron occupying a definite p]h orbital in unsubstituted benzene its value has been estimated to be about —2.7 v. e. = —60 kcal./mole.5 /3 is a resonance integral between adjacent orbitals its value has been estimated to be about —0.85 v. e. = — 20 kcal./mole.6 Sk is a constant, the purpose of which is to allow for the different electron affinities of the different atoms. For Sk > 0, the... [Pg.196]

It is seen that J represents the Coulomb interaction of an electron in a Is orbital on nucleus A with nucleus B. K may be called a resonance or exchange integral, since both functions uu and Uub occur in it. [Pg.211]

The Coulomb repulsion integrals are evaluated using the Mataga-Nishimoto formula The resonance integral is assumed to be of exponential form p=Be , the value of exponent a being taken as 1.7 A... [Pg.24]

Here the operator af creates (and the operator a, removes) an electron at site i the nn denotes near-neighbors only, and /i,y = J drr/),/l(j)j denotes a Coulomb integral if i = j and a resonance integral otherwise. The second quantization form of this equation clearly requires a basis set. It is a model for the behavior of benzene - not a terribly accurate one, but one that helps us understand many things about its spectroscopy, its stability, its binding patterns, and other physical and chemical properties. [Pg.10]

The charges and bond orders thus indicate the response of the system to infinitesimal changes of its coulomb and resonance integrals, respectively. [Pg.78]

Fukui et al. (1957a) also derived a further important relationship connecting the free valence and the localization energy L. In this case the changes imposed were not in coulomb integrals, but in the two resonance integrals and j8, j connecting the atom position r under attack... [Pg.111]

The coulomb integral associated with is a and the resonance integral between % and r is jS. The secular determinant defining the augmented system takes the form... [Pg.113]

Here Zg is the number of tt electrons provided by atom is essentially an ionization potential for an electron extracted from in the presence of the part of the framework associated with atom r alone (a somewhat hypothetical quantity), is a framework resonance integral, and is the coulomb interaction between electrons in orbitals < >, and <(>,. The essential parameters, in the semi-empirical form of the theory, are cug, and and from their definition these quantities are expected to be characteristic of atom r or bond r—s, not of the particular molecule in which they occur (for a discussion see McWeeny, 1964). In the SCF calculation, solution of (95) leads to MO s from which charges and bond orders are calculated using (97) these are used in setting up a revised Hamiltonian according to (98) and (99) and this is put back into (95) which is solved again to get new MO s, the process being continued until self-consistency is achieved. It is now clear that prediction of the variation of the self-consistent E with respect to the parameters is a matter of considerable difficulty. [Pg.132]

Analogous theoretical calculations on conjugated systems involving heteroatoms are more difficult, because more numerous assumptions about the unknown Coulomb integrals and resonance integrals are needed. Conclusions about the relative basicity of two conjugated sites obtained from such calculations are therefore necessarily more tentative. [Pg.289]


See other pages where Resonance integral Coulomb integrals is mentioned: [Pg.16]    [Pg.11]    [Pg.120]    [Pg.180]    [Pg.229]    [Pg.267]    [Pg.5]    [Pg.173]    [Pg.32]    [Pg.194]    [Pg.68]    [Pg.187]    [Pg.213]    [Pg.8]    [Pg.24]    [Pg.383]    [Pg.26]    [Pg.40]    [Pg.171]    [Pg.357]    [Pg.176]    [Pg.5]    [Pg.5]    [Pg.7]    [Pg.8]    [Pg.8]    [Pg.9]    [Pg.9]    [Pg.88]    [Pg.95]    [Pg.127]    [Pg.127]    [Pg.3]   
See also in sourсe #XX -- [ Pg.118 ]




SEARCH



Coulomb integral

Coulombic integral

Integration, resonances

Resonance integrals

© 2024 chempedia.info