The Overlap Interaction

In the same year as that of the proposal of the frontier-electron theory, the theory of charge-transfer force was developed by Mulliken with regard to the molecular complex formation between an electron donor and an acceptor 47>. In this connection he proposed the "overlap and orientation principle 48> in which only the overlap interaction between the HO MO of the donor and the LU MO of the acceptor is considered. 

A majority of chemical reactions are liable to take place at the position and in the direction where the overlapping of HO and LU of the respective reactants is maximum in an electron-donating species, HO predominates in the overlapping interaction, whereas LU does so in an electron-accepting reactant in the reacting species which have SO MO s, these play the part of HO or LU, or both"... 

An alternate route to the electronic problem starts off at the HL limit and adds in the effect of the overlap interactions between the atomic orbitals (f and ( >2(= /9). Our treatment is adapted from that in reference 8. The complete set of singlet states of the problem are... 

Figure 1.2. Relationship showing computational biochemistry as an interdisciplinary subject. Biochemistry is represented by the overlap (interaction) between biology and chemistry. A further overlap (interaction) between biochemistry and computer science represents computational biochemistry.

Here, as in the discussion of simple molecules, we consider the two hybrids that make up the bond to be orthogonal, that is, = 0, so that there is no term in u, U2 in the denominator. We shall see in Appendix B that this is permissible since the two effects that nonorthogonality has can be absorbed in a redefinition of the covalent and polar energies and in a contribution to the overlap interaction between atoms, which is discussed in Chapter 7. Similarly, we have neglected the more complicated aspects of electron-electron interaction, treating it instead in terms of an average potential associated with each electron. The neglect of... 

A consideration of Fig. 7-1 indicates that the discrepancies must arise from an error in the overlap interaction in which the kinetic term and the term from Coulomb and exchange interaetions almost exactly cancel at the ob,served spacing. No minor modification of the bond energy could bring the minimum to the observed position, and a major modification would disrupt the agreement with... 

Two tilings liave developed since that calculation was made. First, the overlap interaction was evaluated and appears much too small to account for the angle (Cliapter 7), and second, the covalent and polar energies have been related to pseudopotentials (Chapter 18), suggesting that IT, is much less sensitive to distortions than one would guess from interatomic Coulomb interactions. Wc shall thercrorc not repeat the full analysis made by Pantelides and Harrison (1976) but extract only the parts that now seem most relevant. 

Their weak interatomic interaction is responsible for the condensation of the normal inert gases into solids. Atoms of normal inert gas are brought together until the repulsive terms in the overlap interaction prevent further contraction. The attraction favors a close-packed structure, and all of the normal inert gases form face-centered cubic lattices. These two contributions to the total interaction will remain almost the same in the ionic crystals, but with added Coulomb interactions, so it is desirable to understand all of these contributions with some care. 

The interatomic interaction for neon. The. solid line is the overlap interaction calculated by Gordon and Kim (1972). The dashed line is the Lennard-Joncs interaction with parameters determined by Bernardes (1958). 

Experimental Lennard-Jones parameters compared with estimates based upon the overlap interaction (Gordon and Kim, 1972). 

B. This is presumably the smallest electrostatic surface energy, which explains why the (100) surfaces arc the natural cleavage and growth planes. Seitz (1940, p. 97) discusses corrections due to the overlap interaction and indicates that they are surprisingly large. 

We turn next to the kinetic energy of the electrons. In Eq. (15-5) was given the kinetic energy for the uniform valencc-clcctron gas, and we might at first think that this could be directly added to the kinetic energy of the electrons in the cores. This would not be consistent with the way we calculated kinetic energy for the overlap interaction in Chapter 7, however, and would not be correct. In Appendix C we computed the kinetic energy locally in terms of the five-thirds power of the total electron density at each point. Let us write the valence density N and the core density N r)-, notice that [N + Thus, even in the free-... 

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