Computational Chemistry

color-coding it onto the van der Waals surface; the three possibilities are shown for
the water molecule in Fig.5.47. Color-coding (mapping) the ESP onto the surface
of the molecule enables one to see how an approaching reagent would perceive the
charge distribution. Showing the ESP as a surface residing in the region of space
where the net charge is negative gives a very useful picture of those parts of a
molecule where the electrostatic effect of the electrons wins out over that of the
nuclei; this is a particularly good way of seeing the presence of lone pairs, as
Fig.5.48, also, makes clear. Note that in Fig.5.47a and b(slice and depicting the
ESP itself as a surface) the lone pairs do not stick out like rabbit ears [ 323 ]. This is
because as electron density which can be ascribed to one orbital falls off, that due to
another increases: there is no “electron hole” between the two lone pairs (for the
same reason the electron density cross section through as–pdouble bond is
elliptical and through as–p–ptriple bond circular; see Section 4.3.2). Showing
the ESP as a surface made clear that the remarkable cycloalkane pyramidane [ 45 ]
has a lone pair, like the carbene CH 2 (Fig.5.48). Depicting the ESP by contour lines

H

H

N

H H

H

N

H

H

H

N H

H

H

H N H

H

N

H

H

H

N

H

–173.24023

–173.14119

without ZPE

(^0) relative energy, k J mol–1
–173.23317
–173.13486
16.5
ts 1 / 2 307 i C 1
ts 2 / 2 enant 192 i Cs
ts 1 / 2 enant 307 i C 1
hilltop 3^741288 iiCs
–173.24023
–173.14119
0
kJ mol–1
0
40
20
10
30
This N is planar; all the other species
here have pyramidal N
with ZPE
H
H
N
H
1 Cs H
H
N
H
1 Cs
–173.23681
–173.13811
8.0
2 C 1 2 enant C 1
–173.23317
–173.13486
16.5
–173.23578
–173.13740
9.9
–173.22571
–173.12906
31.8
Fig. 5.46 Cyclopropylamine conformations at the B3LYP/6–31G* level. Structure 1 is a hilltop
whose two imaginary frequencies indicate that it wants to undergo nitrogen pyramidalization and
rotation about the C–N bond to form the transition states (nomenclature:ts1/2 connects 1 and 2 ,
etc.) and, eventually, the minima. Each C 1 species has an enantiomer of the same energy
368 5 Ab initio Calculations