Modern Polymer Spect..

5.2 Force Fields 245
centers of the moments. In terms of normal coordinate dipole derivatives,
A@ = (4.1058/~:’~) ~
(5-9)
sg
(3 P a
where v, is the unperturbed frequency. In view of Eq. (5-51, a calculation of Vlfcl will
require a summation over terms in 1 dcA/dSi I 1 ?yB/?5’, 1 . The force constant associated
with F’(/(/ is
in mdyn k’, and if we take the effect of TDC as a perturbation on va, the frequency
shift is given by
(5-1 1)
Early applications of this theory [18, 191 parametrized d@/dQ from observed band
splittings. Ah initio calculations of these dipole derivatives [20] showed that the
empirical TDC parameters were in agreement with nb initio as well as IR intensity
results [ 171, thus emphasizing that the TDC mechanism is an important intermolecular
interaction in polypeptides, particularly for modes with large d@/aQ such as
amide I and ainide 11.
The matter of the conformation dependence of the force field of a polypeptide
is one that has received little attention. We know that the differences in vibrational
frequencies of different conformers derive mainly from the differences in their threedimensional
structures, with force constant differences playing a secondary role.
Nevertheless, certain spectral features cannot be understood without taking into
account variations in force constants with conformation (a good example is the
tvans versus gnzrche angle-angle interaction force constant [213). Independent
empirical refinements of a-PLA and /I-PLA also demonstrate such force constant
differences [5]. The problem is how to express such variations in a general explicit
form in V. This is difficult to achieve simply from knowledge of independently refined
force fields of different conformers. We return to this question below in our
discussion of MM force fields.
Empirical force fields have been developed for NMA, for PG, and for CY-PLA and
/I-PLA. In the case of PLA, it has also been possible to refine an ‘approximate’ force
field in which the CH3 side chain is replaced by a point mass (of 15 amu) [22]. This
is useful in studying modes of the backbone chain that do not couple significantly
with side-chain modes.
5.2.2 Ab Iizitio Force Fields
Ab initio molecular orbital calculations, by giving the potential energy surface of
a molecule at its minimum energy conformations, provide a complete vibrational