Computational Chemistry

In this connection another nice example (E. Lewars, unpublished) is provided by
cyclopropylamine (Fig.5.46). At the B3LYP/6–31G* level (a density functional
method,Chapter 7), apart from enantiomers five stationary points were found: two
minima, two transition states, and one hilltop. The structure 3 is a hilltop whose two
imaginary frequencies indicate that it wants to undergo nitrogen pyramidalization and
rotation about the C–N bond to form other conformations. Removing the stricture of a
planar nitrogen without further disturbing the structure, and optimizing, yields the
relative minimum 2. Rotating the planar N around the C–N bond to the alternative Cs
structure and optimizing gives the global minimum 1. The transition states were
found by allowing the transition state algorithm to operate on input structures lying
between the two relevant minima. The experimental gas-phase structure of cyclo-
propylamine, from electron diffraction, corresponds to 1 [ 322 ].

5.5.6.2 Electrostatic Potential

Electrostatic potential (ESP), the net electrostatic potential energy (roughly, the
charge) due to nuclei and electrons was mentioned inSection 5.5.4in connection
with calculation of atom charges. The ESP can be displayed (visualized) (a) with
contour lines as a slice through the molecule, by (b) as a surface itself, or by (c)

1

2

3 3 ¢

4 4 ¢

1'

energy

C2v

Cs C

s

D 2 D 2

D3d D3d

Fig. 5.45 One might have guessed that the chair cyclohexane conformations 1 and 10 are
connected by a boat-shaped intermediate 2. However, this C2vstructure shows an imaginary
frequency: it is a transition state which wants to twist toward 3 (arrows) or 30 (arrows in opposite
directions, not shown), which are the actual intermediates (no imaginary frequencies) between
1 and 10. The chair conformation reaches the twist via a half-chair 4

5.5 Applications of the Ab initio Method 367