Modern Polymer Spect..

248 5 Vibrational Spectroscopy qf Polypeptides
physically important contributions. The first iinplementation of this approach, viz.,
for linear saturated hydrocarbon chains [47], used a potential of the form
where the y,s are internal coordinates whose intrinsic (i.e., equilibrium) values are
ql0 and the flJ are the intrinsic MM quadratic (i.e., valence-type) force constants. At
this stage all possible cross-terms are included. The intrinsic torsion potential is
represented by a Fourier cosine series,
(5-13)
where V, is the barrier to a rotation of periodicity m associated with torsion angle
x. (In general, Vr,,. is a sum over terms in a Fourier series, but in the hydrocarbon
case only the V3 term was found to be necessary.) The non-bonded potential consists
of the dispersion term (an exponent of 9 was found to be more suitable for the
repulsive term) plus a coulomb teim that is usually represented by the interactions
between partial charges Qi and Q, on atoms i and j, i.e., in the case of the hydrocarbons
(5-14)
where K is the dielectric constant and EO the permittivity of free space. The summation
of Vf& is over all atom pairs 1,4 and higher. The Q1 can be fixed charges or they
can include charge fluxes, i.e., dQ1/dSJ [42]. (Inclusion of charge fluxes also permits
the calculation of TR intensities.)
The second element in the procedure is the choice of a spectroscopic force field,
i.e., a set of F,J. This could be an empirical force field, but since we wish to provide
as complete a description as possible at this stage, a scaled ab initio force field is the
one of choice. The scaling process also connects the force constants to experimental
frequencies and band assignments, and avoids the problems of having incorrect
eigeiivectors because of using inappropriate basis sets [26].
The most important part is the third element, viz., the ability to make a transformation
from the spectroscopic to the MM force field [46]. Since this transformation
is analytic, it preserves in the SDFF the frequency as well as structure
agreement of the scaled ah initio calculation. Although the transformation is initiated
by assuming a starting set of p:lt, parameters, these are subsequently optimized
in the refinement procedure [48]. In addition to providing the flJ, the transformation
procedure also gives the ql0 [46].
The fourth, and also important, element is the application of this transformation