Modern Polymer Spect..

5.3 Amide Modes 249
to the nh initio force fields of a set of conformers of the model molecules for the
macromolecular system. In the case of the hydrocarbons, this consisted of the four
stable conformers of M-pentane and the ten stable conformers of n-hexane [26, 471.
At this stage, the non-bonded parameters are optimized under the standard MM
assumption that the intrinsic force constants (fl,) and intrinsic geometry parameters
(ql0) are the same for all conformers 1481. The relative (ah initio) conformer barriers
and energies are incorporated in optiniizing the V, and Q1. At this point, specific
forms of the conformation dependence of some fiJ can be determined and incorporated
in V.
Finally, since it is neither desirable nor necessary to include in I/ the huge number
off,,, most of which are very small and do not significantly affect the vibrational
frequencies, the set of force constants is systematically reduced based on a preassigned
limit on the frequency error [46]. In this process, the remaining fl, are
optimized, usually requiring minimal change, to compensate for the effects of the
force constants that were dropped.
There are a number of advantages to the SDFF approach to refining an MM
force field. By utilizing a complete (i.e., ab iizitio) spectroscopic force field scaled
to experimentally assigned bands, frequency agreement is assured at the start. This
not only incorporates highly accurate information about the minima in the potential
surface, but it avoids the possibility of biasing the non-bonded parameters to
compensate for an incomplete formulation of the fl, terms in V. In addition, since
the optimization is done in a nonredundant coordinate basis [49], the uniqueness of
the force field is assured; subsequent transformation to a redundant basis of choice
is always possible. Finally, since force fields for many different conformers are
involved in the optimization, there is a better chance of revealing the nature of
specific conformation dependences of the cross-terms.
The application of this procedure to an SDFF for the hydrocarbon chain has
given excellent results [47]. With a set of 50 force constant and geometry parameters
the observed frequencies of tt-pentane and ttr-hexane below 1500 c1n-l could be
reproduced with an rms error of N 11 cm-'. This force field has now been extended
to include branched saturated hydrocarbons [50]. An SDFF for the polypeptide
chain is now under development [51].
5.3 Amide Modes
Since the peptide group, -CONH-, is the most distinctive component of the backbone
of the polypeptide chain, it is not surprising that the normal modes of this
group, the so-called aniide modes, were first studied in the simplest representative
molecule, viz., NMA. It is useful to examine the nature of these modes in NMA and
in blocked dipeptides since they have served as important guideposts in the analysis
of polypeptide spectra in terms of structure.