Modern Polymer Spect..

246 5 Vibrationcil Spectroscopj.1 of Pol.vpeptides
force field, i.e., all diagonal and off-diagonal force constants [23]. Since the force
constants are given by the second derivatives of the potential in Cartesian, and
therefore non-redundant, coordinates, the force field is unique. Transformation is
then always possible into an internal or local symmetry coordinate basis. Dipole
and polarizability derivatives are also obtained from the ah iiiitio calculation, and
therefore IR and Ranian intensities can be predicted.
Aside from the previously mentioned problem of doing such calculations on very
large molecules, there are still some limitations at present in directly implementing
ab iriitio force field calculations on model systems. At the Hartree-Fock (HF)
level, force constants can be 10-30% too large because of basis set limitations and
the neglect of electron correlation. This necessitates the empirical scaling of force
constants so that calculated frequencies agree with observed. While systematic
scaling procedures have been developed [24], there is still variability in the number
and kind of scale factors that are used. In any case, a careful comparison of basis
sets in terms of their geometry and frequency predictions is still very important. For
example, the structure of NMA has non-planar symmetry at the HF/6-31G* level,
but it exhibits planar symmetry at the HF/6-31 +G* level, i.e., with the addition
of diffuse functions [25]; some well-assigned normal modes of malkanes cannot
be reproduced in the proper order at the scaled HF/6-31G* level but are correctly
calculated with a scaled HF/6-31G basis set [26]. With the inclusion of electron
correlation, for example by the Mdler-Plesset (MP) perturbation method, the force
constants are much closer to experiinentally compatible values, and such calculations,
though very computer-intensive as the molecule gets larger, can provide
usable force fields with minimal scaling.
Despite these problems, ab irzitio force fields provide an improved route to
avoiding the arbitrariness and incompleteness of empirical force fields. Although
such calculations on model systems do not translate into force fields for macromolecules,
they can provide important components of such force fields. For example:
an ab initio force field for glycine hydrogen bonded to two HzO molecules [27]
provided the necessary starting point for refining the carboxyl group part of the
empirical force field for glutathione [28]; an ah iiiitio force field for diethyl disulfide
[29] permitted detailed correlations to be made between SS and CS stretching frequencies
and the conformations of disulfide bridges in proteins [30, 311; an ab iiiitio
force field for ethanethiol, together with an empirical force field for the peptide
group, provided detailed structure-spectra correlations between CS and SH stretch
frequencies and the conformation of the cysteine side chains in proteins [32].
Ab iizitio force fields also demonstrate that force constants vary with conforination,
a factor that needs to be taken into account if we are to obtain an accurate
description of the normal modes associated with the many possible conformations
of the polypeptide chain. This is clearly illustrated by a study of the scaled ah irzitio
force fields of four iion-hydrogen-bonded conformers of the alanine dipeptide,
CH3CONHCaH(CPH3)CONHCH3 [33, 341. It was found that diagonal force constants
such as the torsion (t) change by very large amounts, and even the stretch (s)
and deformation (d) force constants are significantly dependent on the conforniation.
Off-diagonal force constants can also change significantly with conformation.
In principle this is not surprising since we must expect changes in electronic struc-