Computational Chemistry

The Nonbonded Interactions Term This represents the change in potential
energy with distance apart of atoms A and B that are not directly bonded (as in
A–B) and are not bonded to a common atom (as in A–X–B); these atoms, separated
by at least two atoms (A–X–Y–B) or even in different molecules, are said to be
nonbonded (with respect to each other). Note that the A-B case is accounted for by
the bond stretching termEstretch, and the A–X–B term by the angle bending term
Ebend, but the nonbonded termEnonbondis, for the A–X–Y–B case, superimposed
upon the torsional termEtorsion: we can think ofEtorsionas representing some factor
inherent to resistance to rotation about a (usually single) bond X–Y (MM does not
attempt to explain the theoretical, electronic basis of this or any other effect), while
for certain atoms attached to X and Y there may also be nonbonded interactions.

A

B C

D

AD

B C

A 60°

D

B C

A

B C

D

dihedral angle = 0° dihedral angle = 60°

rotate C-D bond

about the B-C bond

Fig. 3.3Dihedral angles (torsional angles) affect molecular geometries and energies. The energy
is a periodic (cosine or combination of cosine functions) function of the dihedral angle; see e.g.
Figs.3.4and3.5

H

C C

H

H

H

H

H

HCCH dihedral, degrees

energy

kJ mol–1

(^060120180)
10
12 kJ mol–1
D3h D3d D3h D3d
Fig. 3.4Variation of the energy of ethane with dihedral angle. Thecurvecan be represented as a
cosine function
50 3 Molecular Mechanics