Coulomb integral, molecular

Most organic molecules are made up of the elements , H, N, and O, with lesser amounts of S, P, and X (Cl, Br, I). Molecular orbitals are built up by the interaction of the atomic orbitals of these elements held together at bonding separations. It is convenient at this point to adopt an energy scale derived from SHMO theory, in which the Coulomb integral a (=ac) is the reference point on the energy scale,... 

Most modern Hiickel programs will accept the molecular structure as the input. In older programs, the input requires the kind of atoms present in the molecule (characterized by their Coulomb integrals a) and the way in which they are connected (described by the resonance integrals. ). These are fed into the computer in the form of a secular determinant. Remember that the Coulomb and resonance integrals cannot be calculated (the mathematical expression of the Hiickel Hamiltonian being unknown) and must be treated as empirical parameters. 

In the simplest MO approximations, the 7l-electrons are assumed to move independently in MOs which are represented as linear combinations of atomic p orbitals. The distribution of the -electrons in each MO and their energies depend on the values of certain integrals. The Coulomb integrals (a) are characteristic of individual atomic p orbitals in a molecular environment and can be regarded as the effective electronegativity of that atom. The resonance integrals (P) are characteristic of bonds between pairs of p orbitals and are a measure of the strength of a localized 7l-bond. 

It is possible to derive instructive information concerning the general features of the electronic structure of a bond systems by making drastic assumptions on the value of the parameters a and fi. First, one obtains a bond orbital scheme if all resonance integrals between hybrids not involved in a chemical bond jure set equal to zero consequently, the delocalization effects can be treated by the standard perturbation theory of the molecular-orbital method second, if all the Coulomb integrals are... 

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