Perturbation theory statistical

Jorgensen W L and J K Buckner 1987. Use of Statistical Perturbation Theory for Computing Solven Effects on Molecular Conformation. Butane in Water. Journal of Physical Chemistry 91 6083-6085. 

The statistical perturbation theory arising from the classical work of Zwanzig34 and its detailed implementation in a molecular dynamics program for computation of free energies is described in detail elsewhere.35 36 We give a very brief description of the method for the sake of completeness. The total Hamiltonian of a system may be written as the sum of the Hamiltonian (Ho) of the unperturbed system and the perturbation (Hi) ... 

To circumvent this problem avoiding such inefficient exploration of the configurational space, several methods have emerged. Two particularly useful approaches are the Umbrella Sampling and the Statistical Perturbation Theory. Both methods can be used either with Monte Carlo or with Molecular Dynamics simulations. 

The values AF0 m and AFi m have been calculated by using standard Statistical Perturbation Theory. Thus, equation (45) expresses the free energy difference between systems with mapping potentials Hj and Hj by... 

The combined QM/MM model can be used along with Statistical Perturbation Theory to carry out a Monte Carlo simulation of a chemical reaction in solution, with the advantage of allowing solute electronic structure relaxation in solution. Particularly, the combined AM1/TIP3P force field has recently been applied to simulate several chemical processes in solution. We will refer here briefly to the Claisen rearrangement and to the Menshutkin reaction. 

The Statistical Perturbation Theory should be applied allowing a complete sampling of the solute coordinates (and, if possible, of the solvent coordinates). This way no solvent equilibrium hypothesis would be introduced at all. 

An alternative for step 3 is now apparent through statistical perturbation theory. The approach follows from... 

The statistical perturbation theory arising from the classical work of... 

Jorgensen, W.L., Blake, J.F., Buckner, J.K. Free-energy of T1P4P water and the free-energies of hydration of CH4 and Q-from statistical perturbation theory. Chem. Phys. 1989,129(2), 193-200. 

W. L. Jorgensen, J. F. Blake, and J. K. Buckner, Chem. Phys., 129,193 (1989). Free Energy of TIP4P Water and the Free Energies of Hydration of CIT, and CP from Statistical Perturbation Theory. 

Statistical Perturbation Theory/Free Energy Perturbation... 

Jorgensen, W.L. and Buckner, J.K., Use of statistical perturbation theory for computing solvent effects on molecular conformation butane in water, J. Phys. Chem., 1987,91,6083-6085. 

Once the reaction or transformation path has been defined, two approaches have been taken to evaluating the free energy profile in solution, W(r ). The simpler one conceptually is to use statistical perturbation theory to "step along" the reaction coordinate and compute the free energy change at each step. The procedure follows from eq 1 which represents the free energy difference between points i and j along... 

Statistical perturbation theory has also recently been applied to this problem. The major advantage to this procedure is that the... 

Another fundamental class of molecular transformations features the complexation (association or dissociation) of two species. The potential of mean force needs to be determined as a function of the inter-species separation in this case. For two spherical atoms or ions a one-dimensional reaction coordinate is appropriate and W(r ) will reveal important information, e.g. on the existence of contact and solvent-separated ion pairs and on the intervening barriers. The treatment of non-spherical substrates can either involve some geometrical restrictions on the approach path or include appropriate orientational averaging with r as a characteristic distance such as the centers-of-mass separation. Since it will generally be desirable to cover substantial ranges of r, importance sampling or statistical perturbation theory can be used to obtain W(r ). 

Other work on complexation should be noted, especially the recent computations of relative binding affinities for substrates to enz3nnes in water.Statistical perturbation theory was used to compute the... 

Statistical perturbation theory was called to ccaipute the relative free energies of binding according to the thermoc namic cycle in Figure 1. Ihe difference, AG - AG2, is cbtained by computing aGq-aGq. This requires interconversions for the guests unbound and bound to the host in water. The perturbations are performed in small increments... 

TIP4P Water and the Free Energies of Hydration of CH4 and Cl from Statistical Perturbation Theory. 

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