Computational Chemistry

P

nonbond

Enonbondðanti$CH 3 =CH 3 Þþ

P

nonbond

Enonbondðgauche$CH 3 =CH 3 Þ

¼ 3 ) 4 : 7

3 : 85

3 : 931

 12

$

3 : 85

3 : 931

"# 6

þ 6 ) 4 : 7

3 : 85

3 : 065

 12

$

3 : 85

3 : 065

"# 6

¼ 3 )ð$ 0 : 487 Þþ 6 )ð 54 : 05 Þ¼$ 1 : 463 þ 324 : 3 ¼323 kJ mol$^1

nonbonding contribution cf:structure with noninteracting CH= 3 S

Etotal¼EstretchþEbendþEtorsion¼ 0 þ 0 þ 21 : 0 þ323 kJ mol$^1 ¼344 kJ mol$^1

For structure 2

X

bonds

EstretchðC$CÞ¼ 6 ) 1735 ð 1 : 538 $ 1 : 538 Þ^2 þ 1 ) 1 ; 735 ð 1 : 600 $ 1 : 538 Þ^2

¼ 0 þ 6 : 67 ¼ 6 :67 kJ mol$^1

Bond stretch contribution cf:structure withleq¼ 1 : 538

X

bonds

EstretchðC$HÞ¼ 18 ) 1 ; 934 ð 1 : 083 $ 1 : 083 Þ^2 ¼ 0

Bond stretch contribution cf:structure withleq¼ 1 : 083

X

angles

EbendðHCHÞ¼ 18 ) 0 : 093 ð 110 : 7 $ 110 : 7 Þ^2 ¼ 0

Bond bend contribution cf:structure withaeq¼ 110 : 70

X

angles

EbendðCCCÞ¼ 12 ) 0 : 110 ð 112 : 5 $ 112 : 5 Þ^2 ¼ 0

Bond bend contribution cf:structure withaeq¼ 112 : 50

X

dihedrals

EtorsionðCH 3 CCCH 3 Þ¼ 6 ) 3 : 5 ¼ 21 : 0

Torsional contribution cf:structure with no gauche$butane interactions

The stretching and bending terms for structure 2 are the same as for structure 1 ,
except for the contribution of the central C-C bond; strictly speaking, the torsional
term should be smaller, since the opposing C(CH 3 ) groups have been moved apart.

X

nonbond

Enonbondðanti$CH 3 /CH 3 Þþ

X

nonbond

Enonbondðgauche$CH 3 =CH 3 Þ

¼ 3 ) 4 : 7

3 : 85

3 : 974

 12

$

3 : 85

3 : 974

"# 6

þ 6 ) 4 : 7

3 : 85

3 : 120

 12

$

3 : 85

3 : 120

"# 6

¼ 3 )ð$ 0 : 673 Þþ 6 )ð 41 : 97 Þ¼$ 2 : 019 þ 251 : 8

¼250kJ mol$^1

nonbonding contribution cf:structure with noninteracting CH= 3 s

3.2 The Basic Principles of Molecular Mechanics 59