Path free energy fluctuations

It is important to note that in this method, the dynamic fluctuations associated with the QM subsystem are assumed to be independent of the fluctuations from the MM subsystem. Also, in this method we assume that the contributions of the fluctuations of the QM subsystem to the total free energy are the same along the reaction coordinate. We have recently addressed these approximations by developing a novel reaction path potential method where the dynamics of the system are sampled by employing an analytical expression of the combined QM/MM PES along the MEP [40],... 

Our results show that the calculated potential energies for the TS obtained from the combined procedure are around 4 kcal/mol lower than the corresponding ones calculated with the CD method. In contrast, the calculated free energies of activation for all four paths differ by not more than 1.6 kcal/mol. These results show that the inclusion of the fluctuation of the MM environment dramatically improves the results of the calculations of enzymatic catalysis, even if the calculated PES is not highly accurate. In addition, the calculation of free energies for multiple paths using the QM/MM-FE method can serve as an alternative to more expensive sampling methods such as QM/MM-MFEP and QM/MM-MD. 

The elastic free energy AFe causes difficulty because of its sensitivity to the crystallization model assumed. To estimate AFe for lamellar morphology, consider first an important property of a network, amorphous or crystalline. Network crosslinks are considerably restricted in their fluctuations. Fluctuations of crosslinks several chains removed from a particular chain are therefore inconsequential for that chain. A chain in the interior of a path traced through several sequentially connected chains behaves as if the path ends are securely anchored at fixed positions ( 7). If Gj chain vectors make up the path, then... 

Additionally, non-Hamiltonian d5mamics can be used in applications/ methodologies such as Path-integral MD, replica-exchange methods, variable transformation techniques, free energy dynamics methods, and other new applications. Generating these alternative statistical ensembles from simulation requires the use of extended systems or extended phase space [9]. In these systems, the simulations do not only include the N coordinate and momentum vectors that are needed to describe a classical Ai-particle system, but they also include a set of additional control or extended variables that are used to drive the fluctuations required by the ensemble of interest. 

Each monomer is constrained to stay fairly close to the primitive path, but fluctuations driven by the thermal energy kT are allowed. Strand excursions in the quadratic potential are not likely to have free energies much more than kT above the minimum. Strand excursions that have free energy kT above the minimum at the primitive path define the width of the confining tube, called the tube diameter a (Fig. 7.10). In the classical affine -and phantom network models, the amplitude of the fluctuations of a... 

The fluctuational trajectory away from a stationary state to a given point in concentration space (x, y) may differ from the deterministic path from that point back to the stationary state, for systems without detailed balance. Of course, the free energy change must vanish for a closed loop in the space of A,B,X,Y) but need not vanish for a closed loop in the restricted space of (x,y). 

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