Computational Chemistry

below zero in one case and a little above in the other is of no particular significance;
see Bachrach’s discussion of the gas and solution phase SN2 reaction and in
particular his Tables 5.1 and 5.2 [ 40 ]. The formation of the ion-dipole complex in

Cl C

H

H

H

Cl– Cl–

r = rC – Cl – rT<0

C Cl

H

HH

r = rC–Cl – rT = 0

TS

C

H

H H

rT

Cl Cl

TS

rT = 2.373 Å

r = 0

E = – 2.10 kJ mol–1

Cl– Cl–

CH3Cl / Cl– complex

E = –39.0 kJ mol–^1

CH3Cl /Cl– complex

E = – 39.0 kJ mol–1

100

50

r = rC–Cl – rT

r = rC–Cl – rT<0

–5 –4 –3 –2 –1^012345

E (kJ mol–1)

relative to E at rC – Cl = 25 Å, r = 22.627 Å

complex complex

C

H

HH

1.856

Cl

r = 0.827

3.200

rT =

2.373

C

H

HH

1.856

Cl

r = 0.827

3.200

rT =

2.373

Fig. 8.3 Profile for the SN2 reaction Cl"+ CH 3 Cl in the gas phase. Calculations by the author
using B3LYP/6-31+G* in the gas phase, with Spartan [ 31 ]. Note thatris the distance of the Cl"
from the transition state bond length (2.373 A ̊), not the Cl"/C distance; thusrmeasures the
“deviation” from the transition state and becomes zero at the transition state. This makes the graph
symmetrical about the energy axis, as it should be presented for this identity reaction. The zero of
energy is taken asrC–Cl¼25 A ̊,r¼22.627 A ̊. Note the two complexes, which are absent from the
water phase calculation of Fig. 8.2

Table 8.2 Some of the data used to construct Fig.8.3. Variation of energy with Cl-/C distance for
the SN2 reaction Cl"+ CH 3 Cl in the gas phase. Calculations by the author using B3LYP/6-31+G*
in the gas phase, and Spartan [ 31 ]. Therof the x-axis in Fig.8.2isrC–Cl"r(transition state)¼
rC–Cl"2.373. Hartrees were converted to kJ mol"^1 by multiplying by 2,626
rC–ClA ̊ rA ̊ Gas phase E Relative E
Hartrees kJ mol"^1
25 22.627 "960.38646 0
5 2.627 "960.394 "19.8
4 1.627 "960.39801 "30.3
3 0.627 "960.40063 "37.2
2.5 0.127 "960.38983 "8.85
2.373 transition state 0 "960.38726 "2.1

530 8 Some “Special” Topics