Ensemble solvent effects

The operators Fk(t) defined in Eq.(49) are taken as fluctuations based on the idea that at t=0 the initial values of the bath operators are uncertain. Ensemble averages over initial conditions allow for a definite specification of statistical properties. The statistical average of the stochastic forces Fk(t) is calculated over the solvent effective ensemble by taking the trace of the operator product pmFk (this is equivalent to sum over the diagonal matrix elements of this product), so that = Trace(pmFk) is identically zero (Fjk(t)=Fk(t) in this particular case). The non-zero correlation functions of the fluctuations are solvent statistical averages over products of operator forces,... 

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. 

An approach based on the sequential use of Monte Carlo simulation and Quantum Mechanics is suggested for the treatment of solvent effects with special attention to solvatochromic shifts. The basic idea is to treat the solute, the solvent and its interaction by quantum mechanics. This is a totally discrete model that avoids the use of a dielectric continuum. Statistical analysis is used to obtain uncorrelated structures. The radial distribution function is used to determine the solvation shells. Quantum mechanical calculations are then performed in supermolecular structures and the spectral shifts are obtained using ensemble average. Attention is also given to the case of specific hydrogen bond between the solute and solvent. 

Our Monte Carlo (MC) simulation uses the Metropolis sampling technique and periodic boundary conditions with image method in a cubic box(21). The NVT ensemble is favored when our interest is in solvent effects as in this paper. A total of 344 molecules are included in the simulation with one solute molecule and 343 solvent molecules. The volume of the cube is determined by the density of the solvent and in all cases used here the temperature is T = 298K. The molecules are rigid in the equilibrium structure and the intermolecular interaction is the Lennard-Jones potential plus the Coulombic term... 

It is interesting to mention that the statistical inefficiency is obtained only after performing the simulation and therefore it is of little practical use until the simulation is halted. However, for our applications in solvent effects it shows that within a given accuracy determined only by the total number of MC steps there is a great saving of the total calculation if only uncorrelated structures are used in the subsequent quantum mechanical calculations. For the case of the acetone-water calculations only 40 uncorrelated structures are used for the ensemble average of the calculated quantum mechanical results, instead of the total number of 32000. 

Photoinduced electron transfer is a subject characterised, particularly at the present time, by papers with a strongly theoretical content. Solvent relaxation and electron back transfer following photoinduced electron transfer in an ensemble of randomly distributed donors and acceptors, germinate recombination and spatial diffusion a comparison of theoretical models for forward and back electron transfer, rate of translational modes on dynamic solvent effects, forward and reverse transfer in nonadiabatic systems, and a theory of photoinduced twisting dynamics in polar solvents has been applied to the archetypal dimethylaminobenzonitrile in propanol at low temperatures have all been subjects of very detailed study. The last system cited provides an extended model for dual fluorescence in which the effect of the time dependence of the solvent response is taken into account. The mechanism photochemical initiation of reactions involving electron transfer, with particular reference to biological systems, has been discussed by Cusanovich. ... 

QM/EFP methods were applied to understand solvent effects and relaxation dynamics of the CT state of pNA in three different solvents water, dioxane, and cyclohexane [57], Specifically, pNA was described by the configuration interaction singles with perturbative doubles [C1S(D]] method [92] in 6-31-t-G basis, while solvent molecules were represented by the EFP fragments. For each system, pNA molecule was solvated by 64 solvent molecules. Configurational space of each system was sampled with EFP MD (in which pNA was also represented as an EFP fragment) with periodic boundary conditions, using NVT ensemble at 300 K. Snapshots from the... 

The effects of the environment, such as solvent effects. These may be modelled for example by a continuum model, by treating the solvent as an ensemble of classical particles (QM/MM methods), or by including them in the quantum... 

In this section, we briefly describe our hybrid approach for predicting conformations of biomolecules stabilized in solvent [15, 16, 17]. In this approach, the RISM theory is combined with the MC simulated annealing or one of the generalized-ensemble algorithms. Our approach falls into the third category, and both the biomolecule and the solvent are treated on the atomic level. The hybrid approach is implemented for two small peptides as the first step of the research. The solvent effects on the conformational stability of the peptides are discussed and the... 

Use only chemical protective clothing that has undergone appropriate material and construction performance testing. If the concentration of vapor exceeds the level necessary to produce effects through dermal exposure, then responders should wear a Level A protective ensemble. Reported permeation rates may be affected by solvents if solutions of agents have been released. 

The next step is to introduce temperature by averaging out the bath operators appearing in the time dependent terms of Eq.(51) [137] over an adequate ensemble. To this end, the partial trace (or sum of the diagonal elements) over the surrounding subsystem has to be taken. For the system in interaction, the effective Hamiltonian of the solvent Hmeff must be defined in such a way that the sum of HSeff+Hmeff leads to the... 

Before proceeding to discuss the effect of the solvent on the ligand-hgand correlation, we present here a simple probabilistic interpretation of AG. In the canonical ensemble the solvation Helmholtz energy is... 

QM/MM approaches where the solute is QM and the solvent MM are in principle useful for computing the effect of the slow reaction field (represented by the solute point charges) but require a polarizable solvent model if electronic equilibration to the excited state is to be included (Gao 1994). With an MM solvent shell, it is no more possible to compute differential dispersion effects directly than for a continuum model. An option is to make the first solvent shell QM too, but computational costs for MC or MD simulations quickly expand with such a model. Large QM simulations with explicit solvent have appeared using the fast semiempirical INDO/S model to evaluate solvatochromic effects, and the results have been promising (Coutinho, Canute, and Zemer 1997 Coutinho and Canute 2003). Such simulations offer the potential to model solvent broadening accurately, since they can compute absorptions for an ensemble of solvent configurations. 

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