Biomedical Engineering Reference
In-Depth Information
C
12
R
1
HB
−
C
10
R
1
HB
U
HB
=
(4.17)
Other authors take the view that hydrogen bonds are perfectly respectable chemical bonds
that should be treated just like any other bond. They are therefore given a force constant
and so on.
4.4.6 Coulomb Interactions
Many force fields take account of electronegativity differences between atoms and add
electrostatic terms. Atomic charges
Q
A
and
Q
B
are assigned to atoms A and B according to
the rules of the particular force field, and we write
1
4πε
0
Q
A
Q
B
R
AB
U
AB
=
4.5 Modelling the Solvent
I should remind you that the electrostatic expression above relates only to point charges
in free space. In the presence of a dielectric material (such as water), the force between
point charges is reduced by a factor ε
r
called the relative permittivity. Many force fields
were developed at a time when it was not feasible to include a solvent explicitly in such
calculations.
Various attempts were made to allow for the effect of a solvent; the most obvious thing to
do is to alter the relative permittivity even though no solvent molecules are actually taken
into account. There is no agreement between authors as to the correct value of ε
r
and values
ranging between 1 and 80 have been used for water. Some force fields take ε
r
proportional
to the distance between the point charges. I will explain some more up-to-date ways of
modelling the solvent in later chapters.
4.6 Time- and Money-Saving Tricks
All the contributions to the molecular potential energy
U
given above can be done on a
pocket calculator. The larger the molecular system, the larger the number of individual
contributions to
U
and the relationship between molecular size and computational effort
is roughly dependent on the square of the number of atoms. Over the years, people have
tried to reduce the computational time for a given problem by the use of various tricks of
the trade. Two such methods are as follows.
4.6.1 United Atoms
Some professional force fields use the so-called
united atom
approach. Here, we regard
(for example) a CH
3
group as a pseudo-atom, X, and develop parameters for a C(sp
2
)-X
stretch, and so on. It is customary to treat methyl, methylene and methane groups as united
atoms, especially when dealing with large biological systems.
