This reaction involves electrophilic attack by HNC on the alkyne, to give a
zwitterion which reacts further. Can our concepts be used to predict which alkyne
atom, C^1 or C^2 (using the designations of [ 153 ]) will be attacked – will the products
be formed primarily through A or through B? Nguyen et al. approached this problem
by first showing that the reaction is indeed electrophilic attack of HNC (acting as an
electrophile) on the alkyne (acting as a nucleophile): the HOMO(alkyne)/LUMO
(HNC) interaction has a smaller energy gap than the HOMO(HNC)/LUMO(alkyne)
interaction. They then calculated thelocal softnessorcondensed softness parameters
(not quite the same as the condensed-to-atoms parameters of Eqs.7.42that we saw
above; see below) of C^1 and C^2 of the alkyne and the C of HNC. For C^1 and C^2 of the
alkyne the softness as a nucleophile, i.e. softness toward electrophiles, was calcu-
lated, with the aid offk", and for the HNC C softness as an electrophile, i.e. softness
toward nucleophiles, was calculated, with the aid offkþ.
Illustrating how the calculations for CH 3 CCH may be done:
- Optimize the structure of CH 3 CCH and calculate its atom charges (and energy).
- Use the optimized geometry of CH 3 CCH for a single-point (same geometry)
calculation of the charges (and energy) for CH 3 CCH.+.
Steps (1) and (2) enable calculation offk". - Use the optimized geometry of CH 3 CCH for a single-point calculation of the
energy of the anion CH 3 CCH."(This is a radical anion).
Steps (1), (2) and (3) enable us to calculate theglobal softness(the softness of
the molecule as a whole) of CH 3 CCH. This is done by calculating the vertical
ionization energy and electron affinity as energy differences, then calculating the
global softness as the reciprocal of global hardness. From Eq.7.35this iss¼1/(I"
E) ors¼2/(I"E), depending on whether we define hardness according to Eq.7.36
or7.37. Nguyen et al. uses¼1/(I"E), i.e. they take hardness as¼(I"E) rather
than ½(I"E). The local softness of any atom of interest may now be calculated by
multiplyingfk"for that atom bys. Let’s look at actual numbers. The CH 3 CCH
B3LYP/6-311G** basis set and electrostatic potential charges (with the Gaussian
keyword Pop¼MK) were used. These gave the charges (and thus electron popula-
tions) shown in Fig.7.11. From these populations,
f"C^1'(
¼qC^1 ;neutral'(
"qC^1 ;cation'(
¼ 6 : 569 " 6 : 031 ¼ 0 : 538
f"C^2'(
¼qC^2 ;neutral'(
"qC^2 ;cation'(
¼ 5 : 808 " 5 : 587 ¼ 0 : 221
The vertical ionization energy and vertical electron affinity are (here ZPEs have
not been taken into account, as they should nearly cancel; in any case the signifi-
cance of a calculated ZPE for the cation or anion at the geometry of the neutral is
questionable, since the two vertical species are not stationary points):
I¼EðÞ"cation EðÞ¼"neutral 116 : 31237 ""ðÞ¼ 116 : 69077 0 :37840 h
A¼EðÞ"neutral EðÞ¼"anion 116 : 69077 ""ðÞ¼" 116 : 58078 0 :10999 h7.3 Applications of Density Functional Theory 507