Ensemble average conformation

Ensemble Average Conformation of Isolated Polymer Coils in Solid Blends... 

Due to the sensitivity of electronic excitation transport to the separation and orientation of chromophores, techniques which monitor the rate of excitation transport among chromophores on polymer chains are direct probes of the ensemble average conformation (S). It is straightforward to understand qualitatively the relationship between excitation transport dynamics and the size of an isolated polymer coil which is randomly tagged in low concentration with chromophores. An ensemble of tagged coils in a polymer blend will have some ensemble averaged root-mean-squared radius of gyration,... 

Hopfinger et al. [53, 54] have constructed 3D-QSAR models with the 4D-QSAR analysis formahsm. This formalism allows both conformational flexibility and freedom of alignment by ensemble averaging, i.e., the fourth dimension is the dimension of ensemble sampling. The 4D-QSAR analysis can be seen as the evolution of Molecular Shape Analysis [55, 56]. 

Due to the noncrystalline, nonequilibrium nature of polymers, a statistical mechanical description is rigorously most correct. Thus, simply hnding a minimum-energy conformation and computing properties is not generally suf-hcient. It is usually necessary to compute ensemble averages, even of molecular properties. The additional work needed on the part of both the researcher to set up the simulation and the computer to run the simulation must be considered. When possible, it is advisable to use group additivity or analytic estimation methods. 

The most serious problem with ensemble average approaches is that they introduce many more parameters into the calculation, making the parameter-to-observable ratio worse. The effective number of parameters has to be restrained. This can be achieved by using only a few confonners in the ensemble and by determining the optimum number of confonners by cross-validation [83]. A more indirect way of restraining the effective number of parameters is to restrict the conformational space that the molecule can search... 

In the case of being successful in calculating multiple conformations by using time- or ensemble-averaged MD restraints the solved molecular structures are presented as 3D models and can be deposited in an electronic structure database (17). Finally, it is recommended to provide an accurate explanation of the procedures used for the structure elucidation because the application of different methods (NMR, DG, MD, SA, Monte-Carlo calculations. X-ray crystallography) may result in varying conformational models which do not implicitly display the real state of a molecule. This aspect should be always kept in mind when dealing with structure determination methods. 

In order to calculate ensemble averages the explicit time-dependence of the exciton Hamiltonian is replaced by stochastic processes. If drastic changes of Jmn appear due to CC conformational transitions it is hard to apply this approach (Refs. [33] and [34] introduced a dichotomically fluctuating transfer coupling to cover such large conformational transitions). Instead, as it will be demonstrated here, it is more appropriate to directly generate the time-dependence of the exciton parameters Em and Jmn by MD simulations. Then, a microscopic account for solvent effects as well as a detailed description of solvent induced conformational transitions is possible. 

Thus, whereas ensemble-averaged time-resolved FRET measurements can yield P(R) in an indirect manner, SM FRET measurements can yield P(R) in a direct manner, but only if Tw is very short in comparison to the time scale of conformational dynamics. 

The foregoing relationship was utilized in conformational analysis of methyl 4-thio-a-maltoside in solution.153 The VC H values of 2.95 and 5.15 Hz measured151 for H-4 —C-4 —S—C-l—H-l differ from those predicted from Eq. 45 37c 4. h-i = 3.1 Hz and 37C-i,h-4 = 3.8 Hz for the conformation in the crystal154 as defined by H = 25.6° and PH = 3.6°. The observed VC H values were not reproduced by the calculated values for any of the stable conformations of methyl 4-thio-a-maltoside, but are in good agreement with the ensemble average (37c.h) values 2.67 and 5.24 Hz calculated for the compound in water solution, using PCILO-calculated potential surfaces. 

---