Computational Chemistry

2. PBE [ 72 ] (a nonempirical GGA functional; Section7.2.3.4c).


3. TPSS [ 73 ] ( a nonempirical meta-GGA functional; Section7.2.3.4d).

In our classification (7.2.3.4a–g) PBE is on rung three and TPSS is on rung four
(these are rungs two and three if LDA and LSDA are collapsed into rung one).

H O O

H

O

CNC NCC

CCC

Cs

Cs

C3v

C3v

D2d

1.094

1.095

1.0971.091

110.0

110.1

109.7109.4

1.4201.414

1.4261.426

1.177

1.1781.187

1.189

1.160

1.1601.170

1.180

1.461

1.4521.465

1.462

1.0941.095

1.0971.093

–100

–97.5

–98.3

–120

1.3071.304

1.313

1.313

116.8

116.8

116.8117.2

–285

–248

–276

–288

25.4

46.8

21.3

25.7

0

0

0

0

0.972

0.9690.979

0.974

1.363

1.3531.372

1.334 1.369

1.3311.341

1.337

117.5

117.5

117.5117.7

110.1110.4

109.7

110.3

B3LYP

M06

MP2

0 B3LYP

0 M06

0 TPSS

0 MP2

1.508

1.4981.514

1.503

1.211

1.206

1.2201.223

1.092

1.094

1.0951.091

106.7

106.5106.6

107.2 –66.5

–68.1

–69.1

–72

C 1

C 1

1.2911.271

1.3031.293

1.2851.280

1.2981.295

1.411

1.4071.415

1.406

1.521

1.502

1.5291.521

113.1

112.8

112.8114.0

118.6118.9

224 118.4118.4

217

205

233

Cs

C

N C

1.833

1.7851.819

1.858

1.7841.726

1.7881.753

1.1991.201

1.210

1.206

1.0901.094

1.093

1.088

1.0871.090

1.090

1.085

68.567.4

69.0

65.9

72.772.6

71.875.3

1.4861.475

1.4891.482

59.1

59.058.9

59.1

60.460.5

60.6

60.4

1.506

1.4971.515

1.502

C

C C

.. 1.3931.379

1.413

1.389

1.9791.966

1.978

2.014

90.1

90.389.5

92.2

45.245.2

45.0

44.744.6 44.2

45.643.6

1.4051.394

1.398

1.406 C

C C

C2v

TPSS

120.5

120.7120.6

120.3

C HNC

iv

0

0

0

0

1.0001.002

1.0051.003

1.177

1.177

1.1851.187

126

129

123

140

1.192

1.1911.203

1.196

1.3831.393

1.372

1.409

1.194

1.178

1.2011.177

54.753.6

55.152.9

70.872.0

69.6

72.8

H

N C

Cs

C N C H

iv

–67.4

–58.8

–70.9

–87

1.1571.157

1.166

1.177

1.070

1.072

1.0731.069

0

0

0

0

164

164

154

173

Fig. 7.2 Calculated geometries (A ̊and degrees) and energies (kJ mol"^1 ) for four reactions (most
H’s are omitted, for clarity). The purpose of the Figure is to compare among themselves DFT
(B3LYP, M06, TPSS) and MP2 geometries and relative energies; the basis set is 6-31G*. 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

472 7 Density Functional Calculations