An Elementary Molecular Orbital Model

Consider the formation of two two-centre MOs obtained from two normalized nonorthogonal real AOs, Ai(r) on atom A and Xi(r) on atom B  

Optimization of the linear coefficients in this simple Hiickel scheme including overlap gives the 2x2 pseudosecular equation  

If ai = a2 = a, we have degeneracy of the atomic levels, and we obtain for orbital energies and MOs the following results  

If we assume a i to be the deepest level, using a Taylor expansion for the square root, we have  

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A simple rule for the occurrence of trans-h A distorted structures 2 at homopolar double bonds was derived from an elementary molecular orbital model treating a-jt mixing and a valence bond treatment . The relation between the singlet-triplet separation (A st) of the constituent ER2 and a +jt bond energy Ea+ was used as a criterion for determining the expected structure of R2E=ER2. The trans-b ai geometry 2 occurs when l/AEa+ < A sT < l/2Ea+n- The first part of the inequality determines the irawi-bending distortion of the double bond, while the second part determines the existence of a direct E=E link. 

An Elementary Molecular Orbital Model Bond Energies and Pauli Repulsions in Homonuclear Diatomics The Hydrogen Molecular Ion H2 (N=l)... 

For example, students develop an elementary understanding of bonding from the Lewis model. Then they refine it through the valence bond model and finally molecular orbital theory. Some exercises challenge students to refine models further—and to develop new ones. Students will see how current chemical knowledge is based on the authority—and the fallibility—of modern experimental techniques. 

There is no quantum-mechanical evidence for spatially directed bonds between the atoms in a molecule. Directed valency is an assumption, made in analogy with the classical definition of molecular frameworks, stabilized by rigid links between atoms. Attempts to rationalize the occurrence of these presumed covalent bonds resulted in the notion of orbital hybridization, probably the single most misleading concept of theoretical chemistry. As chemistry is traditionally introduced at the elementary level by medium of atomic orbitals, chemists are conditioned to equate molecular shape with orbital hybridization, and reluctant to consider alternative models. Here is another attempt to reconsider the issue in balanced perspective. 

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