1972 Articles

Efficient Computer Simulation of Polymer Conformation. I. Geometric Properties of the Hard-Sphere Model

Stellman, Steven D.; Gans, Paul J.

A system of efficient computer programs has been developed for simulating the conformations of macromolecules. The conformation of an individual polymer is defined as a point in conformation space, whose mutually orthogonal axes represent the successive dihedral angles of the backbone chain. The statistical-mechanical average of any property is obtained as the usual configuration integral over this space. A Monte Carlo method for estimating averages is used because of the impossibility of direct numerical integration. Monte Carlo corresponds to the execution of a Markoffian random walk of a representative point through the conformation space. Unlike many previous Monte Carlo studies of polymers, which sample conformation space indiscriminately, importance sampling increases efficiency because selection of new polymers is biased to reflect their Boltzmann probabilities in the canonical ensemble, leading to reduction of sampling variance and hence to greater accuracy! in given computing time. The simulation is illustrated in detail. Overall running time is proportional to n^(5/4), where n is the chain length. Results are presented for a hard-sphere linear polymer of n atoms, with free dihedral rotation, with n = 20-298. The fraction of polymers accepted in the importance sampling scheme, fA, is fit to a Fisher-Sykes attrition relation, giving an effective attrition constant of zero. fA is itself an upper bound to the partition function, Q, relative to the unrestricted walk. The mean-squared end-to-end distance and radius of gyration exhibit the expected exponential dependence, but with exponent for the radius of gyration significantly greater than that of the end-to-end distance. The 90% confidence limits calculated for both exponents did not include either 6/5 or 4/3, the lattice and zero-order perturbation values, respectively. A self-correcting scheme for generating coordinates free of roundoff error is given in an Appendix.