Stochastic approximation Monte Carlo algorithm for calculation of diagram of states of a single flexible-semiflexible copolymer chain

Abstract

We report in this paper on details and special aspects of using the stochastic approximation Monte Carlo (SAMC) algorithm for the calculation of the diagram of states of a single flexible-semiflexible copolymer chain. The SAMC algorithm is a quite recently suggested mathematical generalization of Wang-Landautype algorithms for very precise Monte Carlo estimates of the density of states function g(E) in computer simulations. It has been mathematically proven that the SAMC algorithm converges to the true g(E) function in the limit of infinite sampling, i.e. systematic errors are smaller than statistical errors. However, in practice one faces the reality that statistical errors become small enough only in the limit of the prohibitively large computation time, if one applies this algorithm in a straightforward way, as it is described. Therefore, one usually needs to apply additional technical tricks to accelerate the convergence to a reasonably good function g(E) sampling all most important conformations. In this paper we discuss all details of these inner workings to make the reader aware of real computational efforts, available accuracy, reachable limits, etc. We do this for the first realization of this algorithm for calculation of the two-dimensional density of states function g(Econtact, Estiffness) which depends on two contributions to the total energy—intermonomer contact energy and the intramolecular stiffness energy due to chain bending.