2 x 2 VB model

In the 2 X 2 VB model (Bernard et al., 1988. 1990b) the ground- and excited-state energies are given as... 

Figure4.4 c(2 x 2)A structure. Left panel structural model. Right top panel corresponding simulated STM image (VB = + 1.30V, / = 0.04nA). The protrusions correspond to oxygen couples, whereas the depressions are the hollow sites surrounded by O—H complexes. Right bottom panel simulated current profiles along [00 1] at decreasing (light blue to red) tip-surface distances. (Reprinted with permission from Ref. [18].)...

The VB model given by Heitler and London was the first description of covalent bonding that followed the formulation of quantum mechanics. If < (1) and (j>b(2) are the one-electron wavefunctions or orbitals localized on neighboring atoms labeled a and b (e.g., the Is-orbitals on the two hydrogen atoms labeled a and b in molecular hydrogen) and each is occupied by one electron (the numbers 1 and 2 represent the coordinates of the two electrons and stand for x, z, X2, 2 ... 

Figure 2.9. The qualitative behavior of the ground state energy of titanium oxide and nickel oxide calculated with a VB model that includes some ionic contribution (amount X). A pure valence bond wavefunction has = 0 and a molecular orbital state has A = 1. For titanium oxide the MO model predicts an energy closer to the real value than a VB calculation. For nickel oxide the valence bond model is more realistic.

The force field approach assumes that it is possible to describe the geometry of a molecule by a set of mechanical equivalents. Changes in bond length are, for example, represented by- a modified Hook s law V(r) = 0.5 x 1 x (r — r0)2 for a spring or bending of a bond angle is modelled by a bending potential VB = kB x (0 — 0O)2, where kB, ks, r0, and 0O are parameters that are dependent on the incorporated atom... 

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