Modern Polymer Spect..

3.4 S11or.f- and Loizg-Rcrizye Vibrational Coupliiig in Molmrles 95
the software. Using Cartesian displacement coordinates, the identification of group
frequencies is not always straightforward and unambiguous. Moreover, the publication
of many drawings or of many tables of numbers becomes often graphical and
editorial problems.
In the past, in order to describe the normal modes much use has been made of the
so-called potential energy distribution (PEDI. Torkington [3 I] has first proposed
and Moriiio aiid Kuchitsu [32J have later generalized the concept of PED defined
as:
PED = APJF (3-28)
where J,,,, = Li, and J,,ml = 2LmlLll.
The advantage of PED is that it can be expressed either in internal or group
coordinates, thus allowing a more direct description of the main characteristic of
the nomal modes.
In simple words, PED provides quantitatively (generally PED is expressed as 'XI
contributions) the extent of involvement of one or several diagonal and off-diagonal
force constants in a given normal mode. The classical textbook case is that of the
well-known group frequency modes of a CH2 group. Using group coordinates (Eq.
3-20)), the modes commonly described as CH2 antisymmetric stretch (d-), CH2
symmetric stretch (d+), CH2 scissoring (a), wagging (w), twisting (t), and rocking
(P) can be easily identified with reference to the corresponding Fx group force
constants [27]. If the same motions were expressed in tenns of classical internal
coordinates of CCH bending the PED would indicate unselectively that in all the
four motions CCH bendings are involved without allowing any distinction of the
characteristic group modes. The same situation is found in the case of the characteristic
group modes of the -CH3 group which are recognized by their characteristic
frequencies of bending, umbrella (U), in-plane, and out-of-plane rocking.
A typical case, famous in organic vibrational spectroscopy, is represented by the
work on trans-planar n-alkanes by Schachtschneier and Snyder [33] aiid by Snyder
et a/. [34]; the latter has extended his study to branched paraffins [35], to a-alkanes
in the liquid phase [36] and to oligo and poly-ethers [37]. The use of PED has
allowed to distinguish clearly between band progressions and the evolution of the
normal modes by changing the phase-coupling (see later in this chapter).
3.4 Short- and Long-Range Vibrational Coupling in
Molecules
As in this chapter the aim is to understand tlie vibrations of large and highly disordered
and structurally irregular molecules, tlie basic problem to be faced is
whether and to what extent normal vibrations are able to probe the molecular
intrainolecular environment, i.e., whether normal vibrations are mostly localized or
extended over a large portion of the molecular system.