Essentials of Computational Chemistry

E rel (kcal mol −1 )
10
8
6
4
2
0
7 w O
5 O
4
6 1
2
3
ORBITAL LOCALIZATION 579
H
w
OCH3 C3H7 H
−4
−8
−12
−16
−20
0 60 120 180 240 300 360
wO(2)C(3)O(4)C(5) (°)
Figure D.2 The torsional potential for 2,4-dioxaheptane ( , left ordinate) exhibits a two-fold
periodicity suggesting a large influence from hyperconjugative effects. The sum of the NBO interaction
energies for the two O(4) lone pairs delocalizing into the C(3)–O(2) σ ∗ orbital(------,rightordinate)
shows the same periodicity, with an amplitude of about 11 kcal mol −1 . The smaller amplitude of the
full torsional potential reflects primarily the presence of other influences as well as the approximate
nature of the NBO analysis. See Cramer, Kelterer, and French 2001
deriving from hyperconjugation. Figure D.2 illustrates how the minima in the torsional potential
energy curve for 2,4-dioxaheptane are influenced by the changes in hyperconjugation
between the O(4) lone pairs and the C(3)–O(2) antibonding σ ∗ orbital as quantified by NBO
analysis (a similar analysis may be carried out for filled-orbital–filled-orbital repulsive interactions,
which are the electronic component of steric interactions). This approach is a nice
energetic complement to other analyses focusing on structural changes or changes in partial
atomic charges (cf. Figure 9.3) in the investigation of hyperconjugative effects. Nevertheless,
it must be stressed that the NBO procedure is only a conceptual model, since it is based on
orbitals, and limitations in its utility may be expected in cases where chemical species are
poorly represented as Lewis structures.
References
Cramer, C. J., Kelterer, A.-M., and French, A. D. 2001. J. Comput. Chem., 22, 1194.
Reed, A. E., Curtiss, L. A., and Weinhold, F. 1988. Chem. Rev., 88, 899.
E NBO (kcal mol −1 )