Computational Chemistry

For structure 1

X

bonds

EstretchðC$CÞ¼ 7 ) 1 ; 735 ð 1 : 538 $ 1 : 538 Þ^2 ¼ 0

Bond stretch contribution cf:structure withleq¼ 1 : 538

X

bonds

EstretchðC$HÞ¼ 18 ) 1934 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

Actually, nonbonding interactions are already included in the torsional term
(asgauche–butane interactions); we might have used an ethane-type torsional
function and accounted for CH 3 /CH 3 interactions entirely with nonbonded
terms. However, in comparing calculatedrelativeenergies the torsional term will
cancel out.

C C

3.974

3.120

C C

CH 3

CH 3

CH 3

CH 3

CH 3

H 3 C

H 3 C

H 3 C

H 3 C

H 3 C

H 3 C

3.931

3.065

stretch central C-C bond

CH 3

1.538 Å 1.600 Å

keeping bond angles and

other bond lengths constant

12

Fig. 3.8 Structures for a simple MM “by hand” calculation on the effect of changing the central
C–C length of (CH 3 ) 3 C–C(CH 3 ) 3 from 1.538 A ̊to 1.600 A ̊

58 3 Molecular Mechanics