Other molecules and quantitative m.o. theory

3 Other molecules and quantitative m.o. theory The ethane molecule, CiHg 

Depending on the relative orientation of the two methyl groups, the total electronic energy is different. This means that rotation about the carbon-carbon axis is not free , but involves an energy barrier. The maximum occurs for the eclipsed conformation. For a simple m.o. treatment of the barrier to internal rotation in the ethane molecule, see ref. 80. 

Whenever the molecule does not have sufficient symmetry, the determination of the atomic coefficients in the expressions of the various m.o.s 

The exact wavefunction leads to the minimum energy and the more an approximate wavefunction approaches the exact one the closer the corresponding expectation value becomes to the true energy (for a recent application of the variation principle to the particle in a box problem, see ref. 81). 

Therefore, the m.o.s obtained (as linear combinations of a.o.s) which enable an approximate wavefunction to be constructed (a Slater determinant for a closed-shell system) must lead to the minimum energy attainable for the basis set of atomic orbitals used, within the constraints of the method being apphed. The larger the basis set, that is, the more flexible the wave-function, the lower the calculated energy and, by implication, the better the wavefunction. Thus, m.o.s based on an infinite set of a.o.s would lead to the best wavefunction (within the eventual constraints of the hamiltonian used). 

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The band picture of metals developed by physicists accounts very well for conduction and other electric and magnetic properties. The valence bond description of the bonds in metals related to the concepts of chemistry explains much better than the former theory such properties as lattice energies and bond distances. Today, however, the V.B. picture does not lend itself well to a priori quantitative calculations of these properties and it seems doubtful to what extent a bond in solid lithium with a bond order of o. 11 (with respect to the bond order one in a gas molecule) has any fundamental meaning. There is no doubt, however, that in less typical metals and compounds Pauling s theory is valuable as a counterpart to the band picture, just as the V.B. and the M.O. methods are both of great importance for the description of the constitution of organic molecules. 

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