Modern Polymer Spect..

5.2 Force Fields 243
accounts for occasional unusually large contributions in a PED. In such a case,
the diagonal elements alone do not give a sufficiently complete description of the
norinal mode.)
3. Correct band assignments must be made in matching calculated to observed v,.
This is probably the most important part of the procedure, since acceptable frequency
agreement (usually 5-10 cm-' ) does not necessarily insure that correct
eigenvectors have been obtained. There are a number of properties that help
to judge the validity of band assignments: molecular symmetry, which specifies
the activity of a mode, and in appropriate situations predicts the IR dichroisni
(parallel, 11, or perpendicular, I, to the chain axis) and Raman polarization
characteristics of the bands; isotopic substitution, which identifies the general
nature of a mode, and by the reproduction of specific observed frequency shifts
substantiates the correctness of the eigenvectors; overtone and combination
bands, which should be consistent with the assignments of fundamentals; and
predicted band intensities, which are very sensitive to the eigenvectors. The
intensity agreement is particularly important since it provides a test of the
eigenvectors that is independent of the frequencies. For example, the IR
absorbance, A,, associated with normal mode Qa is given by [l 11
A, = 42.2547 (g) (5-4)
where dG/aQ, is the normal coordinate derivative of the dipole moment, viz., the
transition dipole moment (Dk' amup'l2), and A, is in km mol-'. Since from
Eq. (5-2)
= Li, (g)
(5-5)
Qu
we see that, through the eigenvector matrix, the IR intensities sample another
physical property of the molecule, namely the dipole derivatives, which arise
from the charge re-distributions during the vibrations. Such dipole derivatives
can also provide a measure of the coordinate contributions to the IR intensity of
a band through a dipole derivative distribution (DDD)[ 121. In addition, relative
intensities of different symmetry species of a mode can provide information on
structure. Thus, in a sample with a molecular chain axis aligned (say mechanically)
in a known direction, since the orientation of a specified dc/aQ, with
respect to the chain axis can be related mathematically to an experimentally
observed dichroic ratio, DR-A,( ll)/Av(L), a DR measurement can help to
establish the dG/L7Q, orientation and therefore provide a test of a structural
hypothesis.
The refinement of the macromolecular force field from that of the model system
follows concepts similar to those described above, with three important additions.
The first, and simplest, is that since the structures are different, new kinds of force