Modern Polymer Spect..

242 5 Vibrcitional Spcc.ii.o.scoyj~ of Po1jpt.ytitlt.s
number of valence-type off-diagonal terms are in effect included in the potential.
Such simple UBFFs can therefore be physically inaccurate, and as B result they
have had to be modified by the explicit inclusion of some additional F;,s [lo].
In the GVFF there is no inherent limit to the number of Fi,s that are included.
There is only the restraint that the number of Fs should not exceed the number or
observable frequencies; in fact, it should generally be much smaller so as to overdetermine
the force field. Since an independent set of coordinates can be chosen,
e.g.. local symmetry coordinates, and the redundancy conditions explicitly given.
there is no need to include linear terms in V, and Eq. (51) is the most general
representation of the force field. Our discussion will focus on applications of the
GVFF.
The refinement of an empirical force field for a niacroinolecule usually starts with
the vibrational analysis of a smaller model system of known structure followed by a
transfer of these force constants to the larger system, with possible subsequent force
constant adjustments. In the case of the polypeptides, the preferred model system
for the peptide group has been trans-N-methylacetamide (NMA), CH3CONHCHi.
Synthetic polypeptides of known structure such as P-sheet polyglycine (PG), R = H,
and a-helical and P-sheet poly(L-alanine) (PLA), R = CH3, have served as basic
examples of the polypeptide systems.
The force field refinement of the model system introduces important requirements
and constraints [5, 7, 81.
1. The types of F, to be included in V must be selected. In practice, this has been
based on prior experiences with the GVFF, but nevertheless the choices are, in
general, arbitrary.
2. A starting set of force constant values, from which are calculated a set of normal
coordinates, Pa, and normal frequencies, vx, needs to be chosen. These are
refined to observed data by a least-squares optimization procedure. We note that
a normal mode Q.* can be visualized in terms of the local, usually symmetry ($1,
coordinates since
S;=CL 1% p %
1
(5-7)
and the normal mode calculation provides the elements L,, of the eigenvector
matrix. Thus, for a given QLy the relative S, are given by the relative Lla. Visualization
in Cartesian coordinates is also possible. An analogous description is given
by another characteristic of the normal mode, namely the potential energy distribution
[PED). This consists of the relative contributions of each S, to the total
change in potential energy during QE, the fractional contribution of a particular
S, being given by
where I,, = 47c'c'v~. vu in cm-'. (Contributions from F,j elements are typically
small and ai-e usually neglected. However, they can be large and negative, which