Fukui Functions and Atomic Charges

The natural DFT quantity to use in probing site selectivity within a molecule is the Fukui function,/(r). The definition is 

The quantity/ is called the condensed Fukui function.It has a single value for each atom, k, in the molecule, and is not otherwise a function of position. The qkS are net charges on the atoms. In the last equation 4 is simply the square of the atom coefficient in the HOMO. It is also the frontier orbital density in FMO theory. It is the easiest to calculate, since we only need the wave function for the HOMO, which can often be found, at least roughly, from HMO theory. 

Equation (3.28) requires all the filled orbitals, followed by a Mulliken (or other) population analysis, for both the reactant molecule and its cation. It has the advanage that the charge, qk N), can also be useful. It will be recalled that only soft-soft interactions between two reactants are controlled by the Fukui function. That is, electron transfer, or covalency, is dominant. For hard-hard interactions, the charges on each atom dictate where reaction will occur. 

The function/ (r) requires a complete calculation, but it can be approximated from the HOMO, which is simpler. It gives more detailed information about the stereochemistry of the reaction path. For example, in a theoretical study of the reactions of HCHO with both electrophiles and nucleophiles, it was found that a base would approach the carbon atom from a direction perpendicular to the plane of the formaldehyde molecule.An acid such as H would attach itself to the oxygen atom, as a result of the net charge being more negative on that atom. 

An ab-initio calculation of the MOs of the NCS ion gives the wave function for the HOMO as  

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