Relaxation of the geometry

In many structures, it is possible to change the lengths of unstrained bonds in order to compensate for the stretching and compression required to make the 

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Using the path II, we may analyze a process when the multiplicity does not change but the external potential does, that is, the relaxation of the geometry would provoke the system going from one stationary state in the potential energy surface to another. Now, Equation 10.31 is reduced to... 

Another important point of distinction with E is that the three-body term is evaluated with all interactions computed in the precise geometry, internal as well as intermolecular, of the trimer. In contrast, E permits relaxation of the geometry of each entity, monomer, dimer, or trimer. The appropriate row of Table 5.24 reports these three-body terms for the 1 2 complexes, which are each reduced relative to This reduction is... 

The low-lying singlet excited state 2 A (tttt ) is responsible for the lowest-energy absorption and emission fluorescence bands (see O Table 14-2). Vertically, at the ground-state geometry, the transition energy is computed to be 3.98 eV and, upon relaxation of the geometry. 

It should be noted that no geometrical relaxation of the excited state geometry was considered in our calculations. Such relaxations may well occur to some degree and would then enhance the localization of the electronic excitation. However the relatively narrow spectral bandwidth suggests that the geometrical changes associated with excitation into the first excited singlet state are only minor. 

Figure 2-7. Origins of the increased O2 binding energy in IPNS when the protein is included in an ONIOM model. (A) A comparison of the optimized geometries from an active-site model (silver) and an ONIOM protein model (dark grey), show that the artificial structural relaxation of the active-site model is more pronounced for the reactant state than for the product state. (B) Contributions to O2 binding from the surrounding protein, evaluated only at the MM level (Adapted from Lundberg and Morokuma [26], Reprinted with permission. Copyright 2007 American Chemical Society.)...

Deviations from the Forster decay (Eq. 9.29) arise from the geometrical restrictions. In the case of spheres, the restricted space results in a crossover from a three-dimensional Forster-type behavior to a time-independent limit. In an infinite cylinder, the cylindrical geometry leads to a crossover from a three-dimensional to a one-dimensional behavior. In both cases, the geometrical restriction induces a slower relaxation of the donor. 

The initial removal of electrons (following the oxidation, p-doping process) leads to the formation of a positive charge localised in the polymer chain (radical cation), accompanied by a lattice distortion which is associated with a relaxation of the aromatic structural geometry of the polymer chain towards a quinoid form. This form extends over four pyrrolic rings ... 

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