Time charge distribution

The dependence of k on viscosity becomes even more puzzling when the time scale of motion along the reaction coordinate becomes comparable to that of solvent dipole reorientation around the changing charge distribution... 

We have found that display of nuclear trajectories and the simultaneous evolution of charge distributions to yield insightful details of complicated processes. Such descriptions also map more readily to the actual experimental conditions than do the more conventional time-independent scattering matrix descriptions. 

For large molecules, computation time becomes a consideration. Orbital-based techniques, such as Mulliken, Lowdin, and NBO, take a negligible amount of CPU time relative to the time required to obtain the wave function. Techniques based on the charge distribution, such as AIM and ESP, require a sig-nihcant amount of CPU time. The GAPT method, which was not mentioned above, requires a second derivative evaluation, which can be prohibitively expensive. 

Unfortunately, some authors use the same symbol p for a number density and for volume charge distributions the electron density is (—e) times the number density.) The number density is a constant in this simple model. 

When one places an electron into the donor molecule, the equilibrium fast polarization, which is purely electronic forms first. Being independent of the electron position, it is unimportant for the dynamics of electron transfer. Afterward the average slow polarization Pg, arises that corresponds to the initial (0 charge distribution (the electron in the donor). The interaction of the electron with this polarization stabilizes the electron state in the donor (with respect to that in the isolated donor molecule) (i.e., its energy level is lowered) (Fig. 34.1). At the same time, a given configuration of slow, inertial polarization destabilizes the electron state (vacant) in the acceptor (Fig. 34.1). Therefore, even for identical reactants, the electron energy levels in the donor and acceptor are different at the initial equilibrium value of slow polarization. 

In our opinion, the interesting photoresponses described by Dvorak et al. were incorrectly interpreted by the spurious definition of the photoinduced charge transfer impedance [157]. Formally, the impedance under illumination is determined by the AC admittance under constant illumination associated with a sinusoidal potential perturbation, i.e., under short-circuit conditions. From a simple phenomenological model, the dynamics of photoinduced charge transfer affect the charge distribution across the interface, thus according to the frequency of potential perturbation, the time constants associated with the various rate constants can be obtained [156,159-163]. It can be concluded from the magnitude of the photoeffects observed in the systems studied by Dvorak et al., that the impedance of the system is mostly determined by the time constant. 

These nuclei (and they form by far the majority of the NMR-active nuclei ) are subject to relaxation mechanisms which involve interactions with the quadrupole moment. The relaxation times Tj and T2 (T2 is a second relaxation variable called the spin-spin relaxation time) of such nuclei are very short, so that very broad NMR lines are normally observed. The relaxation times, and the linewidths, depend on the symmetry of the electronic environment. If the charge distribution is spherically symmetrical the lines are sharp, but if it is ellipsoidal they are broad. 

The electrons in a molecule s outer orbitals are relatively free to move. If we could compare snapshots of the molecule at two different instants in time then we would see slight differences in the charge distributions, reflecting the changing positions of the electrons in their orbitals. The ease with which the electrons can move with time depends on the molecule s polarizability, which itself measures how easily the electrons can move within their orbitals. 

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