Background
We are interested in using Monte Carlo methods to compute thermodynamic properties of complex molecules. One particular application that we have been interested in is computing adsorption isotherms for large molecules in confined porous systems such as zeolites. The typical way in which this is done is through use of Grand Canonical Monte Carlo. This technique requires that molecules be thermally equilibrated and inserted into the pores of the system. For long chains, such moves are usually rejected, leading to inadequate sampling and incorrect results. This can be best appreciated by examining a picture of n-decane, and imagining how difficult it would be to generate random conformations that "thread" through the pores of the zeolite ZSM-5.
Fig 1: A snapshot of a gas phase n-decane molecule, and an adsorbed molecule. The adsorbed molecule was grown atom-by-atom using our fragment sampling configurational-bias MC method.
Fragment Sampling Method
The approach hinges upon the idea that any molecule may be decomposed into elementary fragments that are connected to the rest of the molecule via a single bond and dihedral angle. A large library of these fragments may be generated prior to a simulation. The probability density with which a given fragment occurs is known (i.e. they may be generated according to a canonical ensemble distribution using their hard degrees of freedom). During a molecule regrowth step, fragments are chosen from the library and added to the growing chain. A number of different conformations may be sampled by varying the connecting dihedral angle, with the actual one chosen according to an appropriate weighting function. A schematic of the method is shown in Fig. 2.
Fig. 2: Schematic of the fragment assembly process that comprises a configurational bias growth step.
The bias introduced is removed exactly in the acceptance rules
The key is that we know exactly what the attempt probabilities alpha are, since we kow the probability density of the fragment library. Complete details of the method may be found in:
M. D. Macedonia and E. J. Maginn, "A Biased Grand Canonical Monte Carlo Method for Simulating Adsorption Using All-Atom and Branched United Atom Models", Molecular Physics, 1999, 96, 1375-1390.
Applications of the method have appeared in several publications:
M. D. Macedonia and E. J. Maginn, "Pure and Binary Component Sorption Equilibria of Light Hydrocarbons in the Zeolite Silicalite from Grand Canonical Monte Carlo Simulations", Fluid Phase Equilibria, 1999, 158-160, 19-27.
M. D. Macedonia, D. D. Moore, E. J. Maginn, and M. M. Olken, "Adsorption Studies of Methane, Ethane, and Argon in the Zeolite Mordenite: Molecular Simulations and Experiments", Langmuir, 2000, 16, 3823-3834.
M. D. Macedonia and E. J. Maginn, "Impact of Confinement on Zeolite Cracking Selectivity via Monte Carlo Integration", AIChE Journal, 2000. 46, 2504-2517
Note that this method was also incorporated into the Cerius2 software package as "Flexisorb”.
Funding for this work was provided by the National Science Foundation through the CAREER award.