Shifted-force method

In the shifted force method, both the potential and the force are smoothed out to zero at a certain cutoff distance Rq... 

Just as in the shifted-force method, the taper method replaces a strict cutoff radius by a cutoff region in which the interactions are smoothly tapered to zero. This is done by multiplying the Coulomb potential from r = Ator = B... 

Finally, it should be noted that both the shifted-force method and the tapered method can be made more computer efficient by the construction of lookup tables for the potentials and their derivatives. 

Each simulation extended to about 15000 time-steps after a pre-equilibration of approximately the same length. Ewald summation in tabulated form was used for the Coulomb interactions, and the shifted-force method (e.g., Allen and Tildesley 1987) was used for the non-Coulomb parts of the BJH potential. All technical details of the simulations are described in detail elsewhere (Kalinichev and Heinzinger 1992, 1995 Kalinichev 1993). 

This means that when the Zn++ and Cu+"1" have reached equilibrium, the concentiation of Zn++ is io87 times that of Cu++ It is evident therefore that in the ordinary precipitation of metallic coppei from solution by metallic zinc, the solution will have become, to all intents and purposes, pure zinc sulphate, the copper bemg quantitatively precipitated The equilibrium point in this case is so far shifted over to one side that it would be utterly hopeless to attempt to determine K directly by analysis This is a striking illustration of the usefulness of the electromotive force method... 

Melander and Saunders (1980) have given a comprehensive description of the development of methods of computer calculations of isotope effects on the kinetics of chemical reactions. Such techniques, originally proposed by Wolfsberg and Stem (1964), Shiner (1975), Buddenbaum and Shiner (1977), and Schowen (1977), marry the methods ofEyring s absolute rate (activated complex) theory with detailed modeling of molecular vibrational properties. Input parameters are a mix of spectroscopically determined or quantum mechanically calculated force constants and/or force constant shifts. The method has resulted in informative and detailed molecular description of the molecular changes that occur as the system proceeds from reactant to product along the reaction coordinate. As a result, kinetic isotope effect studies now constitute one of the most important methods employed in the development of detailed... 

The small changes to the force and potential energy, resulting from the change to a shifted force potential function, provide improved accuracy eind stcibility in computer simulations, with negligible changes to structure and time correlation functions, at short to moderate times, calculated from the usual truncated potential. Corrections to calculated thermodynamic properties to account for modifications to the potential can be calculated by a perturbation method similar to that used for the long tail corrections. This matter will be discussed in detail in a separate paper. 

There are quite a number of ways to effectively change the equation in an SCF calculation. These include switching computation methods, using level shifting, and using forced convergence methods. 

The Ziegler and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

The driving force for the temperature-dependent spin crossover (SCO) is the entropy difference between the HS and the LS isomers which arises mainly from a shift of the vibrational frequencies when passing from the HS to the LS state [97-99]. This frequency shift has been studied by IR- and Raman-spectroscopy and recently also by NIS [23, 39, 87]. The NIS method is isotope ( Fe) selective and, therefore, its focus is on iron-ligand bond-stretching vibrations which exhibit the most prominent contribution to the frequency shift upon SCO [87]. 

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