Metropolis criterion

This expression is most frequently satisfied using the Metropolis criterion... 

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For the purpose of minimization, if Fnew < Fcurr, the new solution is accepted and used to replace the old solution. If Fnew > Fcurr, the new solution is accepted only if the following Metropolis criterion is satisfied, i.e.,... 

Here p(i -> j) is the transition probability between two states i and j and P (i) is the population of state i at temperature n (in REMD assumed Boltzmann). If the Metropolis criterion is applied, the exchange probability is obtained as... 

A multicanonical MC simulation is performed, for instance, with the usual Metropolis criterion [118] The transition probability of state x with potential energy E to state x with potential energy E is given by... 

The transition probability of this replica-exchange process is given by the usual Metropolis criterion ... 

Fig. 2. Schematic of the Monte Carlo library design and redesign strategy (from Falcioni and Deem, 2000). (a) One Monte Carlo round with 10 samples an initial set of samples, modification of the samples, measurement of the new figures of merit, and the Metropolis criterion for acceptance or rejection of the new samples, (b) One parallel tempering round with five samples at and five samples at f>2- In parallel tempering, several Monte Carlo simulations are performed at different temperatures, with the additional possibility of sample exchange between the simulations at different temperatures.

Tildesley, 1990). Next, structural relaxation is performed based on MC trial moves of all the atoms in the supercell and acceptance or rejection of the generated configurations according to the Metropolis criterion. This hydrogenation of the a-Si layers results in a layered a-Si H/c-Si superstructure with structurally stable interfaces. The simulation cell is then cut in half and the periodic boundary conditions (PBCs) are removed in the direction normal to the plane of the a-Si H/c-Si interface. Additional c-Si atomic layers are placed at the appropriate interlayer distance at the bottom of the resulting simulation cell and are held fixed to simulate contact with an infinite rigid substrate. MC equilibration is used to distribute the hydrogen in the presence of the free surface. Finally, the surface is relaxed further by MD at the temperature of interest. 

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