Modern Polymer Spect..

3.4 Slzort- and Loiig-Range Vibrational Couyliiig in Molecules 97
According to King and Crawford [38], if li has to be insensitive to changes of the
molecular framework (ix., if the motion is to be localized) the sufficient conditions
are that the coupling terms in Eq. (3-32) be small, namely either
or
(3-33)
(3-34)
AGml z 0
AFm, E 0
(3-35)
(3-36)
It is interesting to note that the problem of dynamical localization versus collectivity
has never been a key issue in molecular spectroscopy and dynamics in the past
40 years as the molecules considered were of limited size, thus obviously implying
the existence of collective motions throughout the whole molecule. Moreover, most
of the molecules considered contained either only covalent CJ bonds or, if n bonds
existed, they were either isolated or with limited conjugation (e.g., aromatic molecules).
The recent explosive interest in highly conjugated polyene and polyaromatic
systems [40] has asked molecular dynamics to reconsider the problem of the extent
of conjugation (delocalization) of n: bonds aloiig the whole molecular chain 141, 421.
At the present stage of the spectroscopic studies for organic systems, a few
observations on Eqs. (3-32) to (3-36) must be made.
1. From the definition of the GR matrix (Eq. (3-15)) or, more directly, from the
analytical expressions of the GR matrix elements provided by Wilson et al. [3], it
transpires that the element (GR)~, connecting internal coordinates i and j may be
different from zero when they possess at least one atom in common. It follows
that atoms away from the functional group under study certainly will not affect
the group frequency; Eq. (3-35) holds, i.e., the G matrix favours localization.
2. For molecules made up exclusively by CJ bonds or containing also isolated and
noncoiijugated K bonds inductive effects are generally considered not to extend
at large distances, thus limiting the distances of the possible electronic effects
described by AFllli to a few bonds around the ftinctional group (hence to a few
internal coordinates). Equation (3-36) holds and again localization seems to be
favored when strong electronic delocalization over large distances is not likely to
occur within the molecule.
3. When intramolecular mechanical coupling is very large (i.e,, Eqs. (3-33) and (3-
34) do not hold) mechanical delocalization over a certain molecular domain
takes place and the concept of group frequency is lost. This generally happens
in the energy range between z 1500-400 cm-' where skeletal stretching and
bending motions are strongly coupled. In this case small mass, geometry. or
electronic perturbations may induce large changes in the spectrum, as indeed
observed experimentally.