Hybrid Monte Carlo: theoretical results and practical implications

Introduced by Duane and his co-workers in 1987, the hybrid Monte Carlo (HMC) proved itself to be both an efficient sampling device and an effective realization of a stochastic thermostat. The method combines the best features of two well established simulation techniques, molecular dynamics and Monte Carlo. Among its drawbacks are inability to reproduce dynamical properties of a system, and lack of efficiency in the simulation of very large systems. These have been recently overcome by introducing a partial momentum update, and by using importance sampling with respect to a shadow Hamiltonian. We highlight the ideas behind the HMC methods, while focusing on Generalized Shadow Hybrid Monte Carlo (GSHMC) methods first proposed in 2008 by Akhmatskaya and Reich. The GSHMC methods have been adapted to atomistic simulation, simulation of macromolecules and particle simulation. This required the development of three variants of the original GSHMC technique: (1) the standard GSHMC (a thermodynamically consistent implementation of constant-temperature molecular dynamics); (2) MTS-GSHMC (a multi-time stepping GSHMC) and (3) meso-GSHMC (a Metropolis corrected dissipative particle dynamics method). All the above methods provide efficient sampling, remove drawbacks of their predecessors and are, due to their flexibility, easily combined with other enhanced sampling techniques. In addition, the methods are suitable for massively parallel computing. We discuss possible implementation of these methods, as well as the range of applications expected to benefit most from their introduction. We describe computer implementation of GSHMC and MTSGSHMC techniques in two popular molecular simulation software packages, GROMACS and PROTOMOL, both designed for high performance computers. Performance of the GSHMC methods is analysed in some detail, and illustrated by the examples of three studies: simulations of a spider venom toxin in a membrane environment, dynamic modeling of multiphase polymer morphology development, and large-scale simulation of Serum TransferrinAluminium complexes.