Differential dynamic correlation

However, for larger molecules this approach might not be possible. The treatment of the differential dynamical correlation effects is for such cases not an easy task, which still awaits a satisfactory solution. 

The BOVB method is aimed at combining the qualities of interpretability and compactness of valence bond wave functions with a quantitative accuracy of the energetics. The fundamental feature of the method is the freedom of the orbitals to be different for each VB structure during the optimization process. In this manner, the orbitals respond to the instantaneous field of the individual VB structure rather than to an average field of all the structures. As such, the BOVB method accounts for the differential dynamic correlation that is associated with elementary processes like bond forming/breaking, while leaving the wave function compact. The use of strictly localized orbitals ensures a maximum correspondence between the wave function and the concept of Lewis structure, and makes the method suitable for calculation of diabatic states. 

Analogous to the PPP method for planar 7r-systems, semiempirical all-valence methods can be and were extended to include Cl, thus giving rise to a family of procedures based on the CNDO, INDO and NDDO variants of the zero-differential overlap (ZDO) approximation, many of which were applied also to the discussion of Cl effects in radical cations. Due to the parametric incorporation of dynamic correlation effects, such procedures often yield rather accurate predictions of excited-state energies and they continue to be the methods of choice for treating very large chromophores which are not amenable to ab initio calculations. 

The partial differential equations used to model the dynamic behavior of physicochemical processes often exhibit complicated, non-recurrent dynamic behavior. Simple simulation is often not capable of correlating and interpreting such results. We present two illustrative cases in which the computation of unstable, saddle-type solutions and their stable and unstable manifolds is critical to the understanding of the system dynamics. Implementation characteristics of algorithms that perform such computations are also discussed. 

The pair correlation function of the velocities and the pair correlation functions of some time derivatives of the velocity are sometimes taken into account.75 However, the validity of this description in the nonadiabaticity regions also has to be proved. The dynamic description or the description using the differentiable random process is more rigorous in this region.76... 

Structure-activity relationships are generally applied in the pharmaceutical sciences to drug molecules. The value of any structure-activity correlation is determined by the precision of the biological data. So it is with studies of the interaction of nonionic surfactants and biomembranes. Analysis of results is complicated by the difficulty in obtaining data in which one can discern small differences in the activity of closely related compounds, due to i) biological variability in tissues and animals, ii) potential differential metabolism of the surfactants in a homologous series (2), iii) kinetic and dynamic factors such as different rates of absorption of members of the surfactant homologous series (2) and iv) the typically biphasic concentration dependency of nonionic surfactant action (3 ). 

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