Dynamic correlation model

For (Li, Cs)Cl, the internal mobilities have been calculated from Eqs. (27) and (28), and are given in Table 8. The SEVs were calculated from the same MD runs and are plotted against the calculated internal mobilities in Fig. 17 with excellent correlation between these calculated quantities. The good correlation of the SEV with the calculated and experimental internal mobilities suggests that relatively short-range cation-anion interaction plays a role in internal mobilities and the separating motion of pairs, that is dissociation, is related to the internal mobilities. In other words, the result of the SEV supports the dynamic dissociation model. 

The electronic structure method used to provide the energies and gradients of the states is crucial in photochemistry and photophysics. Ab initio electronic structure methods have been used for many years. Treating closed shell systems in their ground state is a problem that, in many cases, can now be solved routinely by chemists using standardized methods and computer packages. In order to obtain quantitative results, electron correlation (also referred to as dynamical correlation) should be included in the model and there are many methods available for doing this based on either variational or perturbation principles [41],... 

A great deal more could be said about models - to understand behavior like strong correlation, Coulomb blockade, and actual line shapes, it is necessary to use a number of empirical parameters, and a quite sophisticated form of density functional theory that deals with both static and dynamic correlation at a high level. Often this can be done only within a very simple representation of the electrons - something like the Hubbard model [51-53], which is very common in this situation. 

Unfortunately, the dynamic correlation energy is not constant for a given molecule but may vary considerably between different electronic states. Thus, any procedure geared towards quantitative accuracy in predicting excited-state energies must in some way account for these variations. The most economical way to achieve this is to introduce a number of parameters into the model. By scaling those to a set of experimental data... 

In ab initio methods (which, by definiton, should not contain empirical parameters), the dynamic correlation energy must be recovered by a true extension of the (single configuration or small Cl) model. This can be done by using a very large basis of configurations, but there are more economical methods based on many-body perturbation theory which allow one to circumvent the expensive (and often impracticable) large variational Cl calculation. Due to their importance in calculations of polyene radical ion excited states, these will be briefly described in Section 4. 

Luckily, this impasse was removed through the recent introduction of the CASPT2 model, which combines a powerful procedure for treating cases of strong non-dynamic correlation (CASSCF) with a very economical one for treating dynamic correlation296. As will be shown below, the CASPT2 method works very well for polyene radical cations. 

The time dependence of the dynamic correlation function q t) was investigated numerically on the Ising EA model by Ogielski [131], An empirical formula for the decay of q t) was proposed as a combination of a power law at short times and a stretched exponential at long times... 

Lockman JW, Paul NM, Parquette JR. The role of dynamically correlated conformational equilibria in the folding of macromolecular structures. A model for the design of folded dendrimers. Prog Polym Sci 2005 30 423-452. 

We have also seen that the said complementarity of the CC and Cl approaches can be exploited in a reversed order, namely that we can rely on the MR GISD results and adjust them for their lack of dynamical correlation via the Davidson-like corrections that are based on the CC theory, as proposed by Meissner et al. [10,72-74]. We have seen that, at least for the studied DZP H4 model, either variant leads to excellent results. 

The dynamic RIS model developed for investigating local chain dynamics is further improved and applied to POE. A set of eigenvalues characterizes the dynamic behaviour of a given segment of N motional bonds, with v isomeric states available to each bond. The rates of transitions between isomeric states are assumed to be inversely proportional to solvent viscosity. Predictions are in satisfactory agreement with the isotropic correlation times and spin-lattice relaxation times from 13C and 1H NMR experiments for POE. 

So far we have not been able to treat chains with bond correlations in more than one dimension. The introduction of more detailed or realistic models of local conformational processes, such as those of Reneker34 or of Schatzki,35 has, therefore, not been feasible. We may remark that the theory of dielectric relaxation by Work and Fujita,36 which applies Glauber s methods25 to delayed (dynamic) correlations between chain dipoles, is also in essence a one-dimensional affair. 

Proton transfer and non-dynamical correlation energy in model molecular... 

This suggests that to first order the effect of disorder induced localization can be introduced into a reduced model for DNA by sampling the couplings from a normal distribution about the average B-DNA coupling. However, this may introduce too severe of an approximation when it comes to dynamics and transport related properties that may be sensitive to dynamical correlations amongst the coupling terms. 

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