Computational Chemistry

and so

s¼ 2 $^1 =^6 ðRAþRBÞ¼ 0 : 89 ðRAþRBÞ (3.7)

Thusscan be calculated fromrminor estimated from the van der Waals radii.

SettingE¼0, we find that for this point on the curver¼s,

i.e: s¼rðE¼ 0 Þ (3.8)

If we setr¼rmin¼ 21 =^6 s(from Eq.3.6) in Eq.3.5, we find

Eðr¼rminÞ¼ð$ 1 = 4 Þknb

i.e.

knb¼$ 4 Eðr¼rminÞ (3.9)

Soknbcan be calculated from the depth of the energy minimum.
In deciding to use equations of the form (3.2), (3.3), (3.4)(3.5) we have decided
on a particular MM forcefield. There are many alternative forcefields. For example,

.

.RA RB

r

AB

0

energy

r

rmin = (RA + RB)

Emin

Fig. 3.6 Variation of the
energy of a molecule with
separation of nonbonded
atoms or groups. Atoms/
groups A and B may be in the
same molecule (as indicated
here) or the interaction may
be intermolecular. The
minimum energy occurs at
van der Waals contact. For
small nonpolar atoms or
groups the minimum energy
point represents a drop of a
few kJ mol$^1 (Emin¼$1.2 kJ
mol$^1 for CH 4 /CH 4 ), but
short distances can make
nonbonded interactions
destabilize a molecule by
many kJ mol$^1

52 3 Molecular Mechanics