Computational Chemistry

of saturation where relative energies are concerned; energies are discussed in the
next section. The insensitivity of geometries to basis sets beyond 6-31G is also
shown in Figs. 1 and 3 in reference [ 46 ], where with a wide selection of functionals
very similar errors resulted with the 6-31G, 6-31+G, and 6-31++G basis sets.

H N C

O

H

0.9720.964

0.963

1.3341.332

1.328

117.5117.7

117.7

H O

1.2911.297

1.300

1.2851.279

1.277

1.411

1.4121.408

1.523

1.5071.503

224

231

232

233

110.1

110.4110.5

1.3631.363

1.360

113.1113.5

113.6

118.6119.0

119.1

C C

O

1.5081.504

1.501

1.211

1.2061.204

120.5

120.1120.1

• 66.5


• 46.5


• 43.7
  –72

106.7106.7

106.6

1.0921.090

1.087

Cs

C Cs

1

0 B3LYP / 6-31G*

0 B3LYP / 6-311+G**

0 B3LYP / 6311++G(2df, 2p)

0 MP2 / 6-31G*

C

..

0

0

0

0

C C C

C2v C

(^1) D2d
Civ
Cs C
iv
126
127
128
140
–67.4
–58.6
–56.6
–87
0
0
0
0
25.4
19.6
13.6
25.7
–285
–287
–296
–288
1.0001.000
0.997
B3LYP / 6-31G*
B3LYP / 6-311+G
B3LYP / 6-311++G(2df, 2p)
1.1771.169
1.164
H
N C
N
54.754.5
54.5
70.871.7
1.1921.184 71.7
1.180
1.1941.193
1.190
1.3831.392
1.388
1.157
1.1491.146
H
1.0701.067
1.066
C
1.4861.489
1.486
1.5061.496
60.460.2 1.490
60.1
59.159.7
59.8
1.9791.990
1.985
C
C C
1.3931.390
1.385
1.4051.402
44.7 1.397
44.344.3
45.244.8
44.7
1.3071.304
1.300
116.8117.4
117.3
C N C
110.0
109.8109.9
1.094
1.0911.089
1.420
C 1.4231.419 1.1771.1701.165
3v
Cs
N C
C
1.0901.087
1.084
1.087
1.0841.081
1.784
1.8011.800
1.8331.844
1.846
1.199
1.1911.187
68.5
69.068.9 72.772.973.2
N C C
1.0941.092
1.089
1.160
1.1531.149
1.4611.457
C3v 1.455
0
0
0
0
164
162
164
173
–100
–100
–97.9
–120
Fig. 7.3 Comparison of geometries (A ̊and degrees) and relative energies (kJ mol"^1 ) from the
B3LYP functional using three basis sets (energies are also compared with those from MP2(fc)/6-
31G): 6-31G (53 basis functions for C 2 H 4 O, 32 for HCN, 51 for C 2 H 3 N, 53 for C 3 H 4 ). 6-311
+G (90 basis functions for C 2 H 4 O, 50 for HCN, 84 for C 2 H 3 N, 90 for C 3 H 4 ). 6-311++G(2df, 2p)
(142 basis functions for C 2 H 4 O, 78 for HCN, 132 for C 2 H 3 N, 142 for C 3 H 4 ). Energies are 0 K
energy (i.e. 0 K enthalpy differences) with ZPE correction; only for MP2 was the ZPE itself
corrected (multiplied by 0.9670 [ 77 ]), because for DFT methods the corrections appear to lie
between 0.96 and unity [ 77 ]. Where possible calculated barriers and reaction energies are
compared with experiment [ 70 ]. Calculations are by the author
476 7 Density Functional Calculations