Energy calculations for the 1εg+, 1Δg, and 3εg- electronic states of the oxygen molecule using a tangent spheres approach

J. W. Linnett has proposed in his book, The Electronic Structure of Molecules (l), an approach to molecular orbital theory which he calls the double-quartet approach. The double-quartet, or d-q approach in a molecule with a completed octet, states that electrons of each spin set assume, or try to assume a tetrahedral array around their \u27mother atom\u27. In the case of molecular oxygen, there are three d-q figures representing the molecule in its ground and 1∑+g , 2∆g, states. This representation is shown in Figure 1. Henry A. Bent, at the University of Minnesota, has proposed that the electrons in the d-q approach should be treated as a set of electron spheres(3); that is, treat the electron as a diffuse cloud that assumes a spherical shape due to energy considerations. The charge can be assumed to act from the center of the sphere in the energy calculations. The kinetic energy of such an electron sphere has been shown by Newmark (4) to be; Eq. 1 Kinetic Energy ≥ 9/(8r2) where r is the radius of the electron sphere. This means that the kinetic energy of an electron sphere drops off rapidly with an increase in radius. Due to the fact that the energy of the molecule tries to seek a minimum, the kinetic energy term will force the sphere to spread out and occupy as much space as possible. Consequently, it will run into another electron of its own spin set, and, by the Pauli Exclusion Principle will be halted there. Moreover, it will also be attracted to the nucleus, or, in this case, the o•6 ion. It will be halted at the o+6 ion also, since the inner (K) shell is filled and to overlap it would be a violation of the Pauli Exclusion Principle. Thus, the electron sphere will become tangent to the core electrons and any other electron in its own vicinity. It is worthwhile to note here that the introduction of the Pauli Exclusion Principle as a basic premise is essential to the tangent sphere model. The tangent sphere model was first treated such that the bonding electron spheres were smaller than the nonbonding electron spheres. This comes about because the attraction by the cores is greatest for these spheres, thus making them smaller. Later, it will be seen that the effect of using different size spheres is relatively small compared to that of using all the same size spheres for each spin set. Also, a great deal of difficulty in determining an energy expression will be avoided by the use of equal size spheres throughout each system