Localizated states

FIGURE 46.41. Schematic illustration of ionic suppression of intergrain hopping. Compensation by cations of charge of acceptors removes the nearby localiz states on the polymer backbone that provide for holes easy hopping of electrons between grains. Reprinted from Ref. [235] > (2005) with permission from Elsevier. 

It could thus be stated that a pair description analogous to the Lewis picture is quite conveniently yielded by localized molecular orbitals. In other words, to the extent that the one-electron (orbital) method is in principle capable of faithful description of molecular electronic stmcture, the orbital analysis may provide a useful rationale of some molecular characteristics. Having generated LMOs, using any localizability criteria, the degree of spatial localization obtained may also be inquired. 

The (inertial) I-frame is an element of ordinary 3D (real) space it is origin localizable and can be rotated with respect to a second frame (e.g., Euler angles). Abstract quantum states are necessarily invariable to translations and rotations of such frames. Projected quantum states must be invariant to origin translations and I-frame rotations linear and angular momentum... 

A photon is left behind without specifying in which cavity it is this ensures presence but not localizability. The quantum state is then a linear superposition of states with one photon free ... 

There are significant differences between the UV-Vis and IR absorption spectra. IR spectra, even those of samples in condensed states, are generally characterized by a large number of well defined, sharp bands, with easily localizable positions. Therefore, IR spectra are useful for the fast, non-destructive identification of the chemical substances, and it is extremely unlikely that two substances that are chemically different to have, accidentally, identical IR spectra Instead, the quantitative determinations in the IR spectral range are more difficult because diffuse radiation in the IR spectrophotometers is greater than in the UV-Vis spectrophotometer, so the error sources affect the results of quantitative determinations more than in the UV or Vis range. 

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