Computational Chemistry

of ethane with stretching of the C/C bond, as calculated by the ab initio STO-3G
method. The equilibrium bond length has been taken as the STO-3G length:

leqðC$CÞ¼ 1 : 538 Å (3.10)

The slope of the graph is

kstretch(C$C) = 1,735 kJ mol$^1 Å

$ 2

(3.11)

Similarly, the CH bond of methane was stretched using ab initio STO-3G
calculations; the results are

leq 0 ðC$H) = 1: 083 Å (3.12)

kstretch(C$H)1.934 kJ mol$^1 Å$^2 (3.13)

Parameterizing the Angle Bending Term From Eq.3.3, a plot ofEbendagainst
(a–aeq)^2 should be linear with a slope ofkbend. From STO-3G calculations on
bending the H–C–C angle in ethane we get (cf. Table3.1and Fig.3.7)

aeqðHCCÞ¼ 110 : 7  (3.14)

kbendðHCCÞ¼ 0 :093 kJ mol$^1 deg$^2 (3.15)

(l – leq)^2 , Å^2

0

Estretch, kJ mol–1

0.001 0.002 0.003 0.004

1

2

3

4

5

6

7

Fig. 3.7 Energyvs.the square of the extension of the C–C bond in CH 3 –CH 3. The data in
Table3.1were used

54 3 Molecular Mechanics