Biomedical Engineering Reference
In-Depth Information
or written explicitly in terms of the contributions discussed above
2
k
AB
R
AB
−
R
e,AB
2
2
k
ABC
θ
ABC
−
θ
e,ABC
2
1
1
U
=
+
bonds
bends
U
0
2
k
2 sin
2
ψ
e
cos ψ
e
)
2
+
(1
−
cos (
n
(χ
−
χ
0
)))
+
(cos ψ
−
(4.19)
dihedrals
out-of -plane
C
1
AB
R
1
AB
−
C
AB
R
AB
1
4πε
0
Q
A
Q
B
R
AB
+
+
nonbonded
charges
4.7.1 Variations on a Theme
There are a number of variants of this expression in the literature. Some force fields contain
mixed terms like
k
2
(
R
−
R
e
)(θ
−
θ
e
)
which couple together the bond stretching modes with angle bending. Others use more
complicated expressions for the individual bending and stretching terms. Some force fields
allow interactions between lone pairs, which are often referred to as nonatomic interaction
centres. In addition, there are specialist force fields that are appropriate for restricted ranges
of compounds such as ions, liquid metals and salts.
Force fields are determined by one of two routes. First of all, in an ideal world, one might
calibrate their parameters against accurate quantum mechanical calculations on clusters of
small molecules. The alternative is to calibrate against experimental data such as crystal
structure, infrared absorption, X-ray measurements and liquid properties such as density,
enthalpy of vaporization, Gibbs energies of solvation and the like. To date, almost all
modern force fields have been obtained by the latter approach.
The choice of a particular force field for a given application should depend on the type
of system for which the force field was designed. For example, some force fields have been
calibrated against the solution properties of amino acids. These are obviously the ones to
choose when it comes to modelling proteins in solution.
Finally, Imust emphasize the importance of the
atom type
(i.e. the chemical environment).
The chemical environment of an atom can be distinguished by
•
its hybridization
•
its formal atomic charge
•
its nearest neighbours.
For example, one well-known force field distinguishes five types of oxygen atom:
1. A carbonyl oxygen
2. A hydroxyl oxygen
3. A carboxylic or phosphate oxygen
4. An ester or ether oxygen
5. An oxygen in water.
The interactions are calculated according to atom type, not the 'raw' elements.
