Multicanonical sampling

The multicanonical simulation method [94-96] is the most consequent realization of the ideas developed in the context of microcanonical statistical analysis. This method 

Monte Carlo and chain growth methods for molecular simulations 

The fundamental idea is to deform the Boltzmann energy distribution pcan (E T) a g E)e in such a way that the notoriously difficult sampling of the tails of this distribution is increased and - particularly useful - the sampling rates of the entropically strongly suppressed energetic coexistence regimes in first-order-like transitions and of lowest-energy conformations are improved. 

The simplest approach is to modify the canonical Boltzmann probability by multiplying it by an artificial weight function W X T), 

The general idea is to develop an iterative method for the determination of the weight 

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Flattening the Energy Distribution Multicanonical Sampling and Related Methods... 

Figure 5. Results from a multicanonical simulation of the 3D Lennard-Jones fluid at a point on the coexistence curve. The figure shows both the multicanonical sampling distribution PAP) (symbol o) and the corresponding estimate of the equilibrium distribution Ro(p) with p = N/V the number density (symbol ). The inset shows the value of the equilibrium distribution in the...

A more robust (though computationally more intensive) alternative to GDI is provided by a synthesis of extended (multicanonical) sampling and histogram reweighting techniques. The method is bootstrapped by an ES measurement of the full canonical distribution of a suitable order parameter, at some point on the coexistence curve [identified by the equal areas criterion specified in Eq. (10)]. 

The WL procedure can be applied to any chosen macrovariable, M. But while a good estimate G(E) is sufficient to allow multicanonical sampling in E [and a definitive one is enough to determine Z(p), Eq. (A10)], the M-density of states does not itself deliver the desired analogues we need, instead, the joint density of states G(E, M) which determines the restricted, single-phase partition functions through... 

Since multicanonical sampling effectively works at infinite canonical temperature, we use (4,153) to express the partition sum that then coincides with the total number of all possible conformations as... 

Table 8.2 Minimal energies and temperatures of the maximum specific heats as obtained by multicanonical sampling for the six heteropolymers 20.1-20.6 listed in [ ]. The global maximum ofthe respective...

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