Computational Chemistry

species of interest to us; this avoids the problem of trying to do a geometry optimiza-
tion on a species that may not be a stationary point on the potential energy surface
(assuming that M is itself a stationary point – one will rarely be interested in
something that is not), a situation that arises particularly for some anions.
Charges and electron populations from calculations on SCN"and SCN.(and on
CH 3 CCH and CH 3 CCH.þ) are shown in Fig.7.11. The anion SCN"was optimized
and then the AIM (Section 5.5.4) electron population/charges were calculated (the
AIM calculations were done with G98 using the keywords AIM¼Charge). An AIM
calculation was then done on the radical at the anion geometry. The optimization
and both AIM calculations used the B3LYP/6-31þG method/basis; results for
other charges than AIM and other methods/basis sets are shown shortly.
The condensed Fukui functions may now be calculated (see Fig.7.11):

f"ðÞ¼S qðÞ"S;anion qðÞ¼S;neutral 16 : 142 " 15 : 488 ¼ 0 : 654

f"ðÞ¼C qðÞ"C;anion qðÞ¼C;neutral 5 : 430 " 5 : 428 ¼ 0 : 002

f"ðÞ¼N qðÞ"N;anion qðÞ¼N;neutral 8 : 431 " 8 : 087 ¼ 0 : 344

This indicates that in SCN"the order of nucleophilicity is S>N>>C (which
is what any chemist should expect). Sulfur is the softest atom here, and carbon
the hardest. The results of such a calculation vary somewhat with the method/basis
(e.g. HF/6-31G, MP2/6-31G, etc.), and especially with the way the charges/
electron populations are calculated. Here are thefk"functions from the use of

.

SCN SCN

.+

CH 3 C^2 C^1 CH^3 C^2 C^1 H

0.413 –0.031

5.587 6.031

–0.569

H

0.192

5.808 6.569

–0.142 0.570 –1.431

16.142 5.430 8.431

0.512 0.572 –1.087

15.488 5.428 8.087

AIM

charges

AIM

electron

populations

AIM

charges

AIM

electron

populations

ESP

charges

ESP

electron

populations

ESP

charges

ESP

electron

populations

Fig. 7.11 Charges on atoms and corresponding electron populations. For SCN"and SCN.AIM
(Section5.5.4) charges were used, and both species are at the optimized SCN"geometry. For
CH 3 CCH and CH 3 CCH.þelectrostatic potential charges (from Gaussian 98, keyword Pop¼MK)
were used, and both species are at the optimized CH 3 CCH geometry. The method/basis for optimi-
zation and charge calculation is B3LYP/6-31þG* for SCN"and SCN., and B3LYP/6-311G** for
CH 3 CCH and CH 3 CCH.þ

7.3 Applications of Density Functional Theory 505