Introduction to Force Fields

4
The Electrostatic Energy
The Coulomb interaction potential between two charged particles is
U el =
q A q B
4πε 0 r AB
, (7)
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where q A and q B are the charges on particles A and B and r AB is the distance between atoms A and B. The
attractive interaction between opposite charges in shown in Figure 5(a) and the repulsive interaction between like
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charges is shown in Figure 5(b).
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Electrostatic Energy
Electrostatic Energy
0 2 4 6 8 10
r AB (Å)
0 2 4 6 8 10
r AB (Å)
(a) (b)
Figure 5. Typical behavior of the electrostatic energy for (a) opposite charges and (b) like charges.
Determination of Force Field Parameters
The parameters that make up the force field generally are derived from experimental data. This can be done in many
different ways; thus, there are many different force fields available in the literature. Some have been constructed to
deal with small organic molecules, others have been generated to focus especially on biomolecules, and others are of
general utility.
Sample Force Field Parameters
Molecular mechanics (MM) calculations rely on force fields constructed from empirical data. The force field
parameters are obtained from experimental or quantum mechanical results. Shown in Tables 1 and 2 are some
example bond stretching and angle bending force field parameters. These parameters are from the MM3 force field.
Table 1. Example bond stretching parameters, MM3 force field
Bond type
r AB,eq
k s,AB
(Å)
(kJ mol –1 Å –2 )
Csp 3 –Csp 3 €
1.523
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1330
Csp 3 –Csp 2 1.497 1330
Csp 2 =Csp 2 1.337 2890
Csp 2 =O 1.208 3250
Csp 3 –Nsp 3 1.438 1540
Note that the stretching force constants for double bonds are in general larger than the stretching force constants for
single bonds.