Transition structure relaxation methods

Fig. 13. The computational methods used for constructing a photochemical reaction path. The full path is computed by joining different MEPs, each one providing information on a specific part of the excited- or ground-state potential-energy surface. The IRD method is used to compute the steepest relaxation directions departing from the FC point (excited-state relaxation) or Cl (ground-state relaxation). The IRC method is used to compute the steepest-descent line defined by the computed IRDs. The CIO method is used to compute the lowest-energy conical intersection point directly. With TSO we indicate the standard transition structure optimization procedure.

Compared to the rigid polymer method, the average fluctuating polymer method improves the treatment of how polymer chains move during the penetrant diffusion process. Rather than remaining fixed in place, polymer chains execute harmonic vibrations about their equilibrium positions. Penetrant jumps are then coupled to elastic fluctuations of the polymer matrix and are independent of structural relaxation of the polymer chains [24,97]. After a penetrant jump completes, chains near the final sorption state will likely show slight elastic deviations as they swell to accommodate the penetrant molecule. Since no chain conformation relaxations are allowed, other polymer chains will essentially retain their initial conformation. The penetrant jump rate then depends only on the local, quasiharmonic fluctuations in the sorption state and the transition state [24,97]. 

The steepest descent reaction path (see Reaction Path Following) is usually calculated after the transition structure has been located. There are some approaches that calculate both in the same procedure. These methods start with an approximate reaction path represented by a series of structures interpolated between reactants and products. The path is successively improved by a series of relaxation steps. Elber and Karplus refined the path by minimizing the integral of the energy along the path under the constraint of equally spaced points ... 

Polymers are thus materials with peculiar physical properties which are controlled by their methods of synthesis and their internal structure. The first chapters (I to III) introduce the notions of configuration and conformation of polymers, their dimensionality, and how their multiple interactions contribute to their overall cohesion. The three next chapters are concerned with physical chemistry, namely the thermodynamics of polymer solutions (IV), the structures typical of polymer assemblies (V), and the experimental methods used to characterize the size, the shape and the structures of polymers (VI). Four chapters (VII to IX) then follow that elaborate on the methods of synthesis and modification of polymers, and the engineering of complex architectures (X). Chapters XI to XIII subsequently describe the thermal transitions and relaxations of polymers, their mechanical properties and their rheology. These thirteen chapters are rounded off by monographs (chapters XIV to XVI) of natural polymers and of some common monodimensional and tridimensional polymers. 

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