Modern Polymer Spect..

240 5 l i’hrrrtionnl Spectroscopy of Polypeptides
ing such force fields, which include empirical, ~ i h initio, and molecular mechanics
approaches. We then discuss applications to characterizing the aniide modes of
the peptide group. Finally, we describe some of the results that have been obtained
on characteristic polypeptide conformations, namely extended-chain and helical
structures.
5.2 Force Fields
The normal modes of a molecule are determined by its three-dimensional distribution
of atomic masses and its intra- and intermolecular force fields. The spectroscopic
validation of the structure and these interactions derives from a satisfactory
prediction of the frequencies and intensities of the observed IR and Raman bands,
with the proviso that the bands are appropriately assigned to the calculated eigenvectors.
Because of the complexity of the spectra this part of the process cannot be
treated lightly, since more than one band match-up may be possible. A number of
methods are available to verify band assignments [5] (isotopic substitution, dichroism,
etc.), but since these are usually limited in practice, the success of the normal
mode approach will ultimately depend on the reliability of the force fields. We
therefore devote part of this section to a discussion of the development of such
accurate force fields. This development has proceeded primarily through empirical
refinement of force constants but is relying increasingly on inputs from ab initio
calculations and will probably ultiinately be based on inolecular mechanics (MM)
energy functions.
The development of an empirical force field requires selecting a physical niodel
for the potential, choosing which terms are important, and optimizing the force
constant parameters by a least-squares fitting of calculated normal modes to
observed bands. (Since there have been summary [5] as well as detailed [6-8]
treatments of the methods for obtaining the frequencies (eigenvalues) and forms
(eigenvectors) of the normal inodes for a given force field, we will not repeat this
formalism here but will refer only to those aspects that are relevant to our discussion.)
It is useful to recall that while the computational challenge becomes quite
demanding for polypeptide structures lacking symmetry, such as globular proteins,
for those structures that have helical or translational symmetry, such as the helical
and extended-chain forms of synthetic polypeptides, the calculational problem is
much simplified. This is because the only modes that can exhibit IR or Raman
activity are those in which equivalent vibrations in each helix unit differ in phase by
0, &[ , or ?2