Hybrid Monte Carlo

Tuckerman M, Berne B J, Martyna G J and Klein M L 1993 Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals J. Chem. Phys. 99 2796-808... 

The basic scheme of this algorithm is similar to cell-to-cell mapping techniques [14] but differs substantially In one important aspect If applied to larger problems, a direct cell-to-cell approach quickly leads to tremendous computational effort. Only a proper exploitation of the multi-level structure of the subdivision algorithm (also for the eigenvalue problem) may allow for application to molecules of real chemical interest. But even this more sophisticated approach suffers from combinatorial explosion already for moderate size molecules. In a next stage of development [19] this restriction will be circumvented using certain hybrid Monte-Carlo methods. 

Ch. Schiitte, A. Fischer, W. Huisinga, P. Deuflhard. A Hybrid Monte-Carlo Method for Essential Molecular Dynamics. Preprint, Preprint SC 98-04, Konrad Zuse Zentrum, Berlin (1998)... 

B. Mehlig, D. W. Heermann, and B. M. Forrest. Hybrid Monte Carlo method for condensed-matter systems. Phys. Rev. B, 45 679-685, 1992. 

In this case the shooting and shifting procedure may be viewed as a particular move in a Monte Carlo simulation similar to hybrid Monte Carlo [30]. 

This section is used to introduce the momentum-enhanced hybrid Monte Carlo (MEHMC) method that in principle converges to the canonical distribution. This ad hoc method uses averaged momenta to bias the initial choice of momenta at each step in a hybrid Monte Carlo (HMC) procedure. Because these average momenta are associated with essential degrees of freedom, conformation space is sampled effectively. The relationship of the method to other enhanced sampling algorithms is discussed. 

Hansmann, U.H.E. Okamoto, Y. Eisenmenger, F., Molecular dynamics, Langevin and hybrid Monte Carlo simulations in a multicanonical ensemble, Chem. Phys. Lett. 1996, 259, 321-330... 

Duane, S. Kennedy, A.D. Pendleton, B.J. Roweth, D., Hybrid Monte Carlo, Phys. 

Izaguirre, J.A. and Hampton, S.S., Shadow hybrid Monte Carlo an efficient propagator in phase space of macromolecules, J. Comput. Phys., 200, 581, 2004. 

Hampton, S.S. and Izaguirre, J.A., Improved sampling for biological molecules using shadow hybrid Monte Carlo, Comput. Sci.—ICCS 2004, Pt 2, Proceedings, 3037, 268, 2004. 

Kennedy, A.D., Pendleton, B. Acceptances and autocorrelations in hybrid Monte Carlo. Nucl. Phys. B (Proc. Suppl.) 1991, 20, 118-21. 

Mackenzie, P.B. An improved hybrid Monte Carlo method. Phys. Lett. B 1989, 226, 369-71. 

Akhmatskaya, E., Bou-Rabee, N., Reich, S. A comparison of generalized hybrid Monte Carlo methods with and without momentum flip. J. Comput. Phys. 2009, 228, 2256-65. 

Hence not only for numerical neutral gas diffusion models , but also for such hybrid Monte Carlo techniques internally consistent expressions for the i 0 1 integrals, for (/ = 0,1,2) must be computed. These fits should then, again, preferentially be given in terms of ln(Teff)-... 

The hybrid Monte Carlo method of Allancombined Monte Carlo and molecular dynamics steps within the same simulation. Allan et alP have discussed... 

M. E. Tuckerman, B. J. Berne, G. J. Martyna, and M. L. Klein, /. Chem. Phys., 99, 2796 (1993). Efficient Molecular Dynamics and Hybrid Monte Carlo Algorithms for Path Integrals. 

In summary, a promising new method, REPSWA, has been compared and contrasted to existing techniques. Due to its mathematical structure, REPSWA scales linear with system size and has been shown to perform well in model problems. It can easily be combined with parallel tempering and Hybrid Monte Carlo methods to form interesting and exciting novel sampling schemes. These will be described in future work. 

---