Modern Polymer Spect..

244 5 Vibrational Spectroscopy oj Polypeptides
constants must be introduced. This is not a major problem since initial values, for
example for polypeptide side chains, are generally available. Second, the macromolecular
system generally experiences inter- as well as intramolecular interactions,
and these have to be incorporated into the force field. For polypeptides, these include
hydrogen bonds and non-bonded interactions. Third, since for polypeptides in
particular we are especially concerned with describing different molecular conformations,
attention has to be given to incorporating the conformation dependence
of the force constants. This is not easy to do in the fi-amework of an empirical force
field.
With respect to the intermolecular interactions, the hydrogen bonds can be
treated like the other internal coordinates, i.e., in term of bond stretching, angle
bending, and torsion force constants. However, since hydrogen bonds vary in their
geometry, we should ideally know how these force constants depend on the structure
of the bond. While preliminary studies have been done for the NH hydrogen
bond of the peptide group [13], there is at present no comprehensive description of
this relationship.
The itnportant non-bonded interactions are of two kinds, dispersion and transition
dipole moment interactions. The former correspond to the so-called van der
Waals forces and are generally given by a Lennard-Jones type of potential, viz.
where R,, is the distance between atoms i and j, the exponent of the repulsive term
is traditionally 12 (although 9 has been found to be more effective in some cases),
the exponent of the attractive term is for basic reasons 6, and A, and B, are respectively
the repulsive and attractive van der Waals parameters of atom i. Such
potentials have generally not been added to a GVFF for polypeptides since, in
distinction to polyethylene [ 141, they do not affect midrange and high frequencies
significantly. However, they probably are important in describing low-frequency
modes.
Transition dipole moment interactions between peptide groups can influence
higher frequency modes, as was shown by their effects on the splittings of amide I
and amide I1 modes of a-helix and P-sheet polypeptides [15, 161. Such transition
dipole coupling (TDC) arises from the potential energy of interaction, V&, between
transition moments, Aji, in different peptide groups, and is given by [17]
where LY4, is a geometrical factor given by
with E being the direction of the transition moment and YAB the distance between the