Computational Chemistry

The softness is thens¼1/(I"A)¼1/[(0.37840"("0.10999]¼2.048 h"^1
So the local softness of the two carbons as nucleophiles (softness toward electro-
philes) is

s"ðC^1 Þ¼ 0 : 538 ð 2 : 048 Þ¼ 1 : 102

and

s"ðC^2 Þ¼ 0 : 221 ð 2 : 048 Þ¼ 0 : 453

(Nguyen et al. report 1.096 and 0.460).
Since electron population is a pure number and global softness has the units of
reciprocal energy, local softness logically has these units too, but the practice is to
simply state that all these terms are in “atomic units”.
Now consider analogous calculations on the HNC C, but for local softness as an
electrophile(softness toward nucleophiles), usingfkþ. These calculations gave:

sþðHNCCÞ¼ 1 : 215

To predict which of the two alkyne carbons, C^1 or C^2 , HNC will preferentially
attack, one now invokes the “local hard-soft acid-base (HSAB) principle” (cf.
[ 157 ]), which says that interaction is favored between electrophile/nucleophile (or
radical/radical) of most nearly equal softness. The HNC carbon softness of 1.215 is
closer to the softness of C^1 (1.102) than that of C^2 (0.453) of the alkyne, so this
method predicts that in the reaction scheme above the HNC attacks C^1 in preference
to C^2 , i.e. that reaction should occur mainly by the zwitterion A. This kind of
analysis worked for –CH 3 and –NH 2 substituents on the alkyne, but not for –F.
The concepts of hardness, softness, and of frontier orbitals, with which latter the
Fukui function is closely connected, have been severely criticized [ 142 ], and cases
where frontier MO theory fails have been examined [ 159 ]. It is also true that in
some cases the results predicted using these methods can also be understood in
terms of more traditional chemical concepts. Thus in the alkyne-HNC reaction,
resonance theory leads one to suspect that the zwitterion A, with the positive charge
formally on the more substituted carbon, will be favored over B. Nevertheless, the
large amount of work which has been done using these ideas suggests that they offer
a useful approach to interpreting and predicting chemical reactivity. Even an
apparently unrelated property, or rather a set of properties, namely aromaticity,
has been subjected to analysis in terms of hardness [ 160 ]. As Parr and Yang
say, “This is perhaps an oversimplified view of chemical reactivity, but it is
useful” [ 161 ].
To cite some newer work on Fukui functions: it was claimed that if one accepts
negative values of the function (apparently previously shunned), one can under-
stand reactions in which oxidation of an entire molecule leads to reduction of a part
of it (removing electrons from alkynes can increase the electron density in the CC
bond) [ 162 ]; the Fukui functions concept has been extended beyond the “local

508 7 Density Functional Calculations