The electronic structure of some polyenes and aromatic molecules V-A comparison of molecular orbital and valence bond methods.
Authors: Wheland G. W. 
Published: December 2006

In the preceding papers of this series (Lennard-Jones, Turkevich and Penney 1937) it has been found that the molecular orbital and valence-bond methods lead to values for the lengths of links in polyenes and other molecules in satisfactory agreement with each other; in fact, it may be said that in most of the applications of these methods to problems of molecular structure the two methods are found to agree, in a roughly qualitative way, with each other and with experiment (Wheland 1934). Since the approximations involved in the two cases are of quite different natures, this fact suggests that both treatments are actually rather more reliable than might have been anticipated in view of the mathematical approximations necessary in both methods. It is, accordingly, of interest to examine in some detail the examples in which definite discrepancies do occur, in order that the factors responsible may be determined. In the present paper, this will be done for cyclobutadiene, C
4
H
4
. For purposes of comparison, a brief discussion of benzene will be given as well, in order that the differences between the two molecules may be brought out more clearly. In both the valence-bond and the molecular orbital treatments we shall introduce the usual simplification (Hückel 1931) of neglecting all the orbitals that are symmetrical with respect to reflexion in the plane of the molecule. These either belong to the
K
shells and so are not concerned in the binding or else merely contribute a constant additive term to the to ta l energy (in neither case does their neglect seriously affect the following discussion). The problem of C
4
H
4
reduces, accordingly, to one of four electrons, which are to be assigned to orbitals that are antisymmetric to such a reflexion. In the valence-bond treatment, one electron is assigned, with suitable spin, to each of the four atomic

p
z

orbitals (the molecule being assumed to lie in the
xy
plane), and these are then allowed to interact with each other in different ways. The binding is, accordingly, considered to be purely covalent. The subsequent calculation leads to the result that the ground state of the molecule is a singlet with energy
Q
+ 2
a
, whereas the lowest triplet state has the energy
Q. Q
is here the coulomb integral (
abcd | H | abcd
), and
a
is the single exchange integral between two adjacent

p
z

orbitals, (
abcd | H | bacd
) = (
abcd | H | acbd
) = (
abcd | H | abdc
) = (
abcd | H | dbca
), while
a, b, c
and
d
represent the

p
z

orbitals taken in order round the ring.* This result is based upon the assumption that all exchange integrals of the energy except
a
and all exchange integrals of unity can be neglected. If the molecule possessed one of the Kekulé-like structures its energy to the same approximation would be
Q+ a
. The difference between these two quantities is term ed the resonance energy and is equal simply to
a
. In order to obtain agreement with the observed resonance energies of a number of other hydrocarbons, it has been found necessary to set
a
equal to about — 1·5 e. volts (Pauling and Wheland 1933).