A configurational-bias approach for the simulation of inner sections of linear and cyclic molecules

A novel Monte Carlo technique, the rebridging configurational-bias (RCB) method, has been developed to rearrange inner sections of chain molecules having strong intramolecular interactions along the backbone. The ability of sampling inner chain segments is important for the simulation of systems with low concentration of chain ends, such as polymers and molecules with cyclic structures. In the RCB method, inner segments are removed and then regrown site-by-site in a configurational-bias fashion. However, a short preliminary simulation is carried out to calculate weighting functions based on histograms of the separation distance between pairs of sites along the chain; these functions are used to bias the trial positions of growing inner sites so as to promote efficient chain closure. A look-ahead search scheme is employed for the sampling of the last two sites to increase the overall acceptance rate of the reconstruction process. The validity and performance of the new algorithm were tested by studying linear alkane systems of various chain lengths. Fast conformational equilibration was observed, from the level of local bond orientations to the level of the chain end-to-end vector orientations. Cyclic alkanes containing from 8 to 100 carbon atoms were also studied by using the RCB method. Our results for the conformational properties of cyclooctane are generally consistent with previous molecular dynamics (MD) results and with experimental data. The vapor–liquid coexistence curve of cyclooctane was also mapped out by using the RCB method in conjunction with a histogram reweighting technique for the analysis of isothermal–isobaric simulations.

[1]  F. Allen,et al.  Symmetry‐modified conformational mapping and classification of the medium rings from crystallographic data. IV. Cyclooctane and related eight‐membered rings , 1996 .

[2]  S. Toxvaerd,et al.  Self‐diffusion in n‐alkane fluid models , 1991 .

[3]  Juan J. de Pablo,et al.  ON THE SIMULATION OF VAPOR-LIQUID EQUILIBRIA FOR ALKANES , 1998 .

[4]  Alan M. Ferrenberg,et al.  New Monte Carlo technique for studying phase transitions. , 1988, Physical review letters.

[5]  Jean-Paul Ryckaert,et al.  Molecular dynamics of liquid n-butane near its boiling point , 1975 .

[6]  U. Hansmann.  Parallel tempering algorithm for conformational studies of biological molecules , 1997, physics/9710041.

[7]  Søren Toxvaerd,et al.  Molecular dynamics calculation of the equation of state of alkanes , 1990 .

[8]  Philippe Ungerer,et al.  Optimization of the anisotropic united atoms intermolecular potential for n-alkanes , 2000 .

[9]  R. Bharadwaj,et al.  Conformational properties of cyclooctane: a molecular dynamics simulation study , 2000 .

[10]  D. Frenkel,et al.  Unexpected length dependence of the solubility of chain molecules , 1992 .

[11]  W. Rocha,et al.  Ab initio conformational analysis of cyclooctane molecule , 1998, J. Comput. Chem..

[12]  Travis D. Boone,et al.  End-bridging Monte Carlo: A fast algorithm for atomistic simulation of condensed phases of long polymer chains , 1999 .

[13]  William L. Jorgensen,et al.  Optimized intermolecular potential functions for liquid hydrocarbons , 1984 .

[14]  J. Pablo,et al.  Hyper-parallel tempering Monte Carlo: Application to the Lennard-Jones fluid and the restricted primitive model , 1999 .

[15]  J. Pablo,et al.  Comparison of histogram reweighting techniques for a flexible water model , 1998 .

[16]  D. Frenkel,et al.  Recoil growth algorithm for chain molecules with continuous interactions , 1999 .

[17]  K. Binder,et al.  Finite-size scaling for near-critical continuum fluids at constant pressure , 1996 .

[18]  A. Fuchs,et al.  Gibbs ensemble simulations of vapour—liquid phase equilibria of cyclic alkanes , 1999 .

[19]  Athanassios Z. Panagiotopoulos,et al.  A New Intermolecular Potential Model for the n-Alkane Homologous Series , 1999 .

[20]  A. W. Rosenbluth,et al.  MONTE CARLO CALCULATION OF THE AVERAGE EXTENSION OF MOLECULAR CHAINS , 1955 .

[21]  Athanassios Z. Panagiotopoulos,et al.  New intermolecular potential models for benzene and cyclohexane , 1999 .

[22]  Edward J. Maginn,et al.  A biased grand canonical Monte Carlo method for simulating adsorption using all-atom and branched united atom models , 1999 .

[23]  Alan M. Ferrenberg,et al.  Optimized Monte Carlo data analysis. , 1989, Physical Review Letters.

[24]  Michele Vendruscolo,et al.  Modified configurational bias Monte Carlo method for simulation of polymer systems , 1997 .

[25]  Richard L. Jaffe,et al.  Quantum Chemistry Study of Conformational Energies and Rotational Energy Barriers in n-Alkanes , 1996 .

[26]  Juan J. de Pablo,et al.  Extended continuum configurational bias Monte Carlo methods for simulation of flexible molecules , 1995 .

[27]  Juan J. de Pablo,et al.  Monte Carlo simulation of branched and crosslinked polymers , 1996 .

[28]  D. Cremer.  Calculation of puckered rings with analytical gradients , 1990 .

[29]  J. Ilja Siepmann,et al.  Self-Adapting Fixed-End-Point Configurational-Bias Monte Carlo Method for the Regrowth of Interior Segments of Chain Molecules with Strong Intramolecular Interactions , 2000 .

[30]  Juan J. de Pablo,et al.  Estimation of the chemical potential of chain molecules by simulation , 1992 .

[31]  K. Hukushima,et al.  Exchange Monte Carlo Method and Application to Spin Glass Simulations , 1995, cond-mat/9512035.

[32]  Alfred Uhlherr,et al.  Monte Carlo Conformational Sampling of the Internal Degrees of Freedom of Chain Molecules , 2000 .

[33]  Thomas A. Weber,et al.  Molecular dynamics simulation of polymers. I. Structure , 1979 .

[34]  D. Theodorou,et al.  A concerted rotation algorithm for atomistic Monte Carlo simulation of polymer melts and glasses , 1993 .

[35]  Walter H. Stockmayer,et al.  Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution , 1962 .

[36]  Hiromi Yamakawa,et al.  Modern Theory of Polymer Solutions , 1971 .

[37]  Berend Smit,et al.  Understanding Molecular Simulation , 2001 .

[38]  V. Basus,et al.  Detection of a crown family conformation in cyclooctane by proton and carbon-13 nuclear magnetic resonance , 1973 .

[39]  Manuel Laso,et al.  A critical evaluation of novel algorithms for the off-lattice Monte Carlo simulation of condensed polymer phases , 1994 .

[40]  H. Meirovitch.  Statistical properties of the scanning simulation method for polymer chains , 1988 .

[41]  Michael W. Deem,et al.  A configurational bias Monte Carlo method for linear and cyclic peptides , 1996, cond-mat/9709330.

[42]  M. Deem,et al.  Analytical rebridging Monte Carlo: Application to cis/trans isomerization in proline-containing, cyclic peptides , 1999, physics/9904057.