Computational Chemistry

CH 3 NC to CH 3 CN

Transition state 0 K relative E¼ 173 Product 0 K relative E¼# 120

Ea¼DH{þRT¼DH{þ2.48¼174.0

O

107.2

107.2, sic

120.3120.3, sic

1.082

1.090

1.504

1.503

1.188

1.223

Cs

–153.22222 + 0.04951

= –153.17271, rel. E = 236 kJ

• 153.22564 + 0.04983
  = – 153.17581, rel. E = 233 kJ mol–1

–153.34454 + 0.05474

= –153.28980, rel. E = –71.6 kJ

• 153.34692 + 0.05507
  = –153.29185, rel. E = –71.7, sic kJ mol–1

–93.12310 + 0.01557

• 93.12554 + 0.01520
  = – 93.11034, rel. E = 0 kJ mol–1

–93.06713 + 0.01061

= –93.05652, rel. E = 134 kJ

• 93.06747 + 0.01063
  = – 93.05684, rel. E = 140 kJ mol–1

–93.15452 + 0.01643

= –93.13809, rel. E = -80.3 kJ

• 93.15894 + 0.01540
  = – 93.14354, rel. E = – 87.2 kJ mol–1

–132.22339 + 0.04191

= –132.18148, rel. E = 168 kJ

• 132.22493 + 0.04236

–132.29008 + 0.04450

–132.29289 + 0.04463

–132.33371 + 0.04466

= –132.28905, rel. E = –114 kJ

• 132.33825 + 0.04445

579i

C

C C

1.386

1.406

96.1

92.2

41.8

43.6

1.380

1.389

2.057

2.014

42.144.2

C

C 1.478 C

1.482

1.4961.502

59.2

59.1

60.460.4 CCC

D2d

1.296

1.313

–116.12337 + 0.05303

= –116.07034, rel. E = 0 kJ mol–1

• 116.12370 + 0.05321
  = – 116.07049, rel. E = 0 kJ mol–1

–116.11229 + 0.05246

= –116.05983, rel. E = 27.6 kJ

• 116.11330 + 0.05260
  = –116.06070, rel. E = 25.7 kJ mol–1
  (rel. E = 70.3 kJ mol–1)

O

H

Cs

117.7117.5

110.7

110.3

1.318

1.337

1.3471.369

0.9490.974HF geom

MP2 geom

N C

1.135

1.180

1.468

1.463

H O

C 1

112.6114.0 1.420

1.406 119.2118.4

1.252

1.295

1.2931.234

1.519

1.521

2574 i HF freq

2345i MP2 freq

1227 i

1310i

H N C

1.0020.9851.1541.187

Civ

C3v

C2v

C3v

Cs Civ

Cs

C 1

H

N

1.455

1.409

1.155

1.177

50.8

53.0

77.5

72.8

N C H

1.1331.177 1.0591.069

N C

1.422

1.426

1.153

1.189

NC

C

64.2

65.9 75.875.3

1.174

1.206

1.8581.896 1.742

1.753

468 i

444i

–116.23306 + 0.05430

= –116.17876, rel. E = –285 kJ

• 116.23413 + 0.05393
  = –116.18020, rel. E = – 288 kJ mol–1

HF optimization

–153.31831 + 0.05578

= –153.26253, rel. E = 0 kJ mol–1

• 153.32005 + 0.05546
  = – 153.26459, rel. E = 0 kJ mol–1

MP2 single point on HF geom

MP2 optimization

C

548 i

(rel. E = 0 kJ mol–1) (rel. E = 294 kJ mol–1) (rel. E = –73.8 kJ mol–1)

(rel. E = 0 kJ mol–1) (rel. E = 153 kJ mol–1) (rel. E = –50.4 kJ mol–1)

(rel. E = 0 kJ mol–1) (rel. E = 184 kJ mol–1) (rel. E = –86.7 kJ mol–1)

= – 132.18257, rel. E = 173 kJ mol–1 =^ – 132.29380, rel. E =^ – 120 kJ mol–1

= –132.24558, rel. E = 0 kJ mol–1

= – 132.24826, rel. E = 0 kJ mol–1

= –93.10753, rel. E = 0 kJ mol–1

(rel. E = 0 kJ mol–1) (rel. E = –243 kJ mol–1)

Fig. 5.21 Calculated geometries and energies for four reactions (most H’s are omitted, for
clarity). The purpose of the figure is the compare the single-point energies with energies from
optimization at a higher level. Geometries are HF/6–31G and MP2/6–31G. Energies are MP2/
6–31G//HF/6–31G (i.e. single-point) with HF ZPE, MP2/6–31G//MP2//6–31G with MP2/
6–31G ZPE, and (only relative energies shown,in parentheses) HF/6–31G//HF/6–31G* with
HF ZPE. Ab initioE(hartrees)þZPE (hartrees)¼corrected ab initioE; relativeE(strictly
speaking, 0 K enthalpy differences):Edifference in hartrees' 2626 ¼kJ mol#^1 ). The ZPEs
shown are the ab initio ZPEs multiplied by 0.9135 (HF) or 0.967 (MP2) [ 80 ]. For a discussion of
experimental measurements on these reactions, see [ 92 ]; available experimental activation and
reaction energies (kJ mol#^1 ) are shown here. Calculations here are by the author

268 5 Ab initio Calculations