MOLECULA R PHYSICS, 1998, VOL. 94, NO. 4, 727±733 Improving the eciency of the con®gurational-bias Monte Carlo algorithm By T. J. H. VLUGT 1 , M. G. MARTIN 2 , B. SMIT 1 , J. I. SIEPMANN 2 and R. KRISHNA 1 1 Department of Chemical Engineering, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands 2 Department of Chemistry, University of Minnesota, 207 Pleasant Street SE, Minneapolis, MN 55455-0431, USA ( Received 17 November 1997; revised version accepted 24 February 1998) Algorithms are presented to improve the eciency for the generation of trial orientations and for the calculation of the Rosenbluth weight in a con®gurational-bias Monte Carlo (CBMC) simulation. These algorithms were tested for NpT and NVT simulations of n-octane, 3-methyl- heptane, and 3,4-dimethylhexane at dierent temperatures and densities using a preliminary version of the TraPPE united-atom representation for the CH 3 , CH 2 and CH groups. It was found that for a system of 144 molecules these algorithms speed up the calculation three times for n-octane and almost four times for 3,4-dimethylhexane, resulting in a decreased dierence in simulation time between a branched molecule and a linear isomer. For larger systems the speedup is even greater. It is shown that the excluded volume of an atom is the dominant term for the selection of a trial orientation, which leads to an improved CBMC algorithm called dual cuto con®gurational-bias Monte Carlo (DC-CBMC). 1. Introduction Con®gurational-bias Monte Carlo (CBMC) [1±5] is an advanced simulation technique for complex mol- ecules. CBMC simulations are used frequently for the calculation of vapour±liquid equilibria of linear alkanes [6±8], branched alkanes [9±11], and for the simulation of adsorption of alkanes within porous structures [12±16]. These simulations are still computationally expensive. The architecture of the molecule has a large in¯uence on the simulation time and the acceptance probability for a CBMC move [9]. Therefore we have developed new algorithms which not only give an overall speedup, but also decrease the dierence in CPU time between a linear molecule and its branched isomers. To explain the improved algorithms, the basics of CBMC are summarized below. A more detailed discus- sion can be found in [4]. In the CBMC scheme it is convenient to split the total potential energy of a trial site into two parts. The ®rst part is the internal, bonded, intramolecular potential ( u internal ) which is used for the generation of trial orientations. The internal potential often has the form [17, 18] u internal = å u bend ( μ ) + å u tors ( u) , ( 1) u bend ( μ ) = 1 2 k μ[ μ- μ 0] 2 , ( 2) u tors ( u) = C 0 + C 1 cos ( u) + C 2 cos 2 ( u) + C 3 cos 3 ( u) , ( 3) where u bend ( μ ) is the bond-bending energy and u tors ( u ) is the torsion energy. The second part of the potential, the external potential ( u ext ), is used to bias the selection of a site from the set of trial sites. Note that this split into u internal and u ext is completely arbitrary and can be opti- mized for a particular application. For a new con®guration, a randomly chosen molecule is regrown segment by segment. If the entire molecule is being regrown than f trial sites for the ®rst bead are placed at random positions in the simulation box [19]. The Rosenbluth weight of this segment is w 1 ( n ) = å f j =1 exp ( - bu ext 1j ) , ( 4) where b = 1 / ( k B T ) , and one trial site is selected with probability P selecting 1i ( b i ) = exp ( - bu ext 1i ) w 1 ( n ) . ( 5) For the other segments l of the molecule, k trial orienta- tions b i are generated according to the Boltzmann weight of the internal potential of that segment: P generating li ( b i ) db = exp ( - bu internal li ) db ò exp ( - bu internal l ) db . ( 6) 0026±8976/98 $12 . 00 Ñ 1998 Taylor & Francis Ltd.