Computational Chemistry

Table 5.13

Energy differences (kJ mol

#^1

) of some isomers, calculated at modest ab initio levels; plu

s at the G3(MP2) level, and from experiment. The energies

used were 298 K gas-phase enthalpies, thus the differences are differences in standard heats of formation, i.e.

DD

H

Yf298

. The higher-energy molecule is shown first,

e.g. fulvene lies above benzene in energy. In parentheses, for each of the four levels the enthalpies of the two molecules are given, and their differen

ces (

D

), in

hartrees; hartrees were converted to kJ mol

#^1

by multiplying by 2,626; for each of the experimental differences, the two heats of formation are shown

Isomer pair

HF/3–21G(*)

HF/6–31G

MP2/6–31G*

G3(MP2)

Experiment

Fulvene

>

benzene

>

165.1

150.0

151.4

132.1

141.5

a

(#

229.24281

>

(#

230.53328

>

(#

231.29393

>

(#

231.77396

>

(224–82.5)

#

229.30570

#

230.59042

#

231.35158

#

231.82428

[^229

/^230

]

D

¼

0.06289)

D

¼

0.05714)

D

¼

0.05765)

D

¼

0.05032)

Cyclopropane

>

propene>

61.9

36.0

22.3

38.4

33.1

(#

116.30975

>

(#

116.96743

>

(#

117.36047

>

(#

117.65305

>

(53.1–20.1)

#

116.33333

#

116.98113

#

117.36895

#

117.66768

[^231

/^231

]

D

¼

0.02358)

D

¼

0.01370)

D

¼

0.00848)

D

¼

0.01463)

Dimethyl ether

>

ethanol

O

Me

Me

>

CH

CH 3

OH 2

25.6

29.4

35.8

50.4

50.7

(#

153.12245

>

(#

153.97345

>

(#

154.41606

>

(#

154.76644

>

(#

184.1–

#

153.13221

#

153.98465

#

154.42971

#

154.78565

(#

234.8)

D

¼

0.00976)

D

¼

0.01120)

D

¼

0.01365)

D

¼

0.01921)

[^232

/^233

]

Methylcyclopentane

>

cyclohexane

>

16.5

19.5

16.7

17.3

18.6

(#

232.72152

>

(#

234.01184

>

(#

234.80454

>

(#

235.38913

>

(#

106.0–

#

232.72781

#

234.01925

#

234.81090

#

235.39570

(#

124.6)

D

¼

0.00629)

D

¼

0.00741)

D

¼

0.00636)

D

¼

0.00657)

[^230

/^234

]

aIf the heat of formation of fulvene is really 214 kJ mol

#^1

[^229

], then the enthalpy difference is 214

#

82.5

¼

131.5, essentially the same as the G2(MP2) value

5.5 Applications of the Ab initio Method 331