Chemical Bonding I The Lewis Model

Of course, the Coulomb interaction appears in the Hamiltonian operator, H, and is often invoked for interpreting the chemical bond. However, the wave function, l7, must be antisymmetric, i.e., must satisfy the Pauli exclusion principle, and it is the only fact which explains the Lewis model of an electron pair. It is known that all the information is contained in the square of the wave function, 1I7 2, but it is in general much complicated to be analyzed as such because it depends on too many variables. However, there have been some attempts [3]. Lennard-Jones [4] proposed to look at a quantity which should keep the chemical significance and nevertheless reduce the dimensionality. This simpler quantity is the reduced second-order density matrix... 

The Lewis-type (L) contribution is considered the easy part of chemical wavefunction analysis, because it corresponds closely to the elementary Lewis structure model of freshman chemistry. Nevertheless, controversy often arises over the magnitude of steric or electrostatic effects that are associated with the Lewis model itself [i.e., distinct from the resonance-type effects contained in (NL)]. The NBO program offers useful tools for quantifying both steric and electrostatic interactions in terms of the space-filling (size and shape) and dielectric properties (charge, dipole moment, etc.) of the electron pair bonds and lone pairs that comprise the Lewis structure model. This chapter discusses the physical nature and numerical quantitation of these important chemical effects, which are often invoked in a hand-waving manner that reflects (and promotes) significant misconceptions. 

The basic idea of the Heitler-London model for the hydrogen molecule can be extended to chemical bonds between any two atoms. The orbital function (10.8) must be associated with the singlet spin function cro,o(l > 2) in order that the overall wavefunction be antisymmetric [cf. Eq (8.14)]. This is a quantum-mechanical realization of the concept of an electron-pair bond, first proposed by G. N. Lewis in 1916. It is also now explained why the electron spins must be paired, i.e., antiparallel. It is also permissible to combine an antisymmetric orbital function with a triplet spin function, but this will, in most cases, give a repulsive state, such as the one shown in red in Fig. 10.2. 

He, somewhat mischievously, made the following comment on the relationship between his molecular orbital analysis and the Lewis electron-pair model "Now I have a favourite argument that Lewis electron pair bonding is better described by a pair of electrons in a molecular orbital than by the Heitler-London bond. If the chemical bond has any polarity, it is necessary to add an ionic term, that is a Heitler-London plus an ionic term, to represent the bond. That is rather a messy description whereas the molecular orbital- this is not the spectroscopic but the chemical molecular orbital, the delocalized molecular orbital fits very nicely to the... 

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