Calculating properties of chemical bonding

Calculated enthalpy and entropy correction terms for the three conformations of (SiClH2)2 (B3LYP/6- 

In quantum mechanics, the square of the wavefunction corresponds to the electron probability density, p, upon which we can construct ways to rationalize the concepts of chemical bonding. In this book, we shall discuss two related approaches to analyzing the topology of the electron density the electron localization function (ELF) and atoms in molecules (AIM). The latter is sometimes applied in the analysis of experimental data, as well as theoretical data, so we reserve discussion of this technique until Section 10.10. 

For a closed-shell wavefunction (that is, where every spin-a electron is paired with a spin-(3 electron), built from either Hartree-Fock or Kohn-Sham orbitals, the ELF as a function of position r can be written as 

Here Dh reflects the density of the homogenous electron gas, which is used as the reference point. The function is normalized between 0 and 1, and returns a high value within an electron pair region (a point where the Pauli repulsion is low) and a low value for the regions of space between electron pairs. Note that for the homogeneous electron-gas reference system the value of the ELF at all points is V2. A plot of the ELF is typically presented as an isosurface, which shows the extent of the function across the whole molecule at some set value of Tri(r). 

We can also calculate the energy of a particular bond, simply by adding up the optimization energies of the molecular fragments after we dissociate whichever bond we are interested in, and subtracting this from the energy obtained for the optimized structure. Take AEHe (3.111) as an example, formed by dimerization of AIH3 (Section 2.8.1). 

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