Localized Bonds The Valence Bond Model

FIGURE 6.36 Two hydrogen atoms approach one another. The protons are separated by the distance Rab-(a) At large values of Rab each electron interacts only with the proton to which it is bound, (b) As the atoms approach closer, both electrons interact with both protons. The distance of electron 1 from nuclei A and B is given by / lA, / ib the distance of electron 2 from nuclei A and B is given by r2B, the distance between the electrons is given by 

The characteristics of most chemical bonds (bond length, bond energy, polarity, and so forth) do not differ significantly from molecule to molecule (see Section 3.7). If the bonding electrons are spread out over the entire molecule, as described by the LCAO model, then why should the properties of a bond be nearly independent of the nature of the rest of the molecule Would some other model be more suitable to describe chemical bonds  

The valence bond (VB) model grew out of the qualitative Tewis electron-pair model in which the chemical bond is described as a pair of electrons that is localized between two atoms. The VB model constructs a wave function for the bond by assuming that each atom arrives with at least one unpaired electron in an AO. The resulting wave function is a product of two one-electron wave functions, each describing an electron localized on one of the arriving atoms. The spins of the electrons must be paired to satisfy the Pauli exclusion principle. 

As the atoms begin to interact strongly, we cannot determine whether electron 1 arrived with proton A and electron 2 with proton B, or vice versa. (The electrons are indistinguishable.) Therefore, the wave function must allow for both possibilities  

Symmetry requires that Ci = C2 and Ci = -C2 are equally valid choices. We label these combinations gerade (g) and ungerade (u), respectively, to show how each behaves under inversion symmetry (see Sections 6.1 and 6.2). We must check both cases to determine whether they describe bond formation, using our familiar criteria of increased electron density between the nuclei and energy reduced below that of the separated atoms. 

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