Efficient path sampling on multiple reaction channels

Due to the time scale problem, rare events are not accessible by straight forward molecular dynamics. The presence of multiple reaction channels complicates the problem even further. The feasibility of the standard free energy based methods relies strongly on the success in finding a proper reaction coordinate. This can be very difficult task in high-dimensional complex systems and even more if several distinct reaction channels exist. Moreover, even if a proper reaction coordinate can be found, ergodic sampling will be a challenge. In this article, we discuss the recent advancements of path sampling methods to tackle this problem. We argue why the path sampling methods, via the transition interface sampling technique, is less sensitive to the choice of reaction coordinate. Moreover, we review a new algorithm, parallel path swapping, that can dramatically improve the ergodic sampling of trajectories for the multiple reaction channel systems.Comment: 7 pages, 4 figures. Article submitted for the proceedings of the Conference on Computational Physics, Brussels 200

Efficiency analysis of reaction rate calculation methods using analytical models I: The 2D sharp barrier

We analyze the efficiency of different methods for the calculation of reaction rates in the case of two simple analytical benchmark systems. Two classes of methods are considered: the first are based on the free energy calculation along a reaction coordinate and the calculation of the transmission coefficient, the second on the sampling of dynamical pathways. We give scaling rules for how this efficiency depends on barrier height and width, and we hand out simple optimization rules for the method-specific parameters. We show that the path sampling methods, using the transition interface sampling technique, become exceedingly more efficient than the others when the reaction coordinate is not the optimal one.Comment: 22 pages, 5 figure

Ab Initio Molecular Dynamics Study of Aqueous Solvation of Ethanol and Ethylene

The structure and dynamics of aqueous solvation of ethanol and ethylene are studied by DFT-based Car-Parrinello molecular dynamics. We did not find an enhancement of the structure of the hydrogen bonded network of hydrating water molecules. Both ethanol and ethylene can easily be accommodated in the hydrogen-bonded network of water molecules without altering its structure. This is supports the conclusion from recent neutron diffraction experiments that there is no hydrophobic hydration around small hydrophobic groups. Analysis of the electronic charge distribution using Wannier functions shows that the dipole moment of ethanol increases from 1.8 D to 3.1 D upon solvation, while the apolar ethylene molecule attains an average dipole moment of 0.5 D. For ethylene, we identified configurations with $\pi$-H bonded water molecules, that have rare four-fold hydrogen-bonded water coordination, yielding instantaneous dipole moments of ethylene of up to 1 D. The results provide valuable information for the improvement of empirical force fields, and point out that for an accurate description of the aqueous solvation of ethanol, and even of the apolar ethylene, polarizable force fields are required.Comment: 15 pages, 10 figures, 4 tables, revtex4, submitted to J. Chem. Phy

Reaction rate calculation by parallel path swapping

The efficiency of path sampling simulations can be improved considerably using the approach of path swapping. For this purpose, we have devised a new algorithmic procedure based on the transition interface sampling technique. In the same spirit of parallel tempering, paths between different ensembles are swapped, but the role of temperature is here played by the interface position. We have tested the method on the denaturation transition of DNA using the Peyrard-Bishop-Dauxois model. We find that the new algorithm gives a reduction of the computational cost by a factor 20.Comment: 5 pages, 3 figure

Rate constants for diffusive processes by partial path sampling

We introduce a path sampling method for the computation of rate constants for systems with a highly diffusive character. Based on the recently developed algorithm of transition interface sampling (TIS) this procedure increases the efficiency by sampling only parts of complete transition trajectories confined within a certain region. The algorithm assumes the loss of memory for highly diffusive progression along the reaction coordinate. We compare the new technique to the TIS method for a simple diatomic system and show that the computation time of the new method scales linearly, instead of quadraticaly, with the length of the diffusive barrier. The validity of the memory loss assumption is also discussed.Comment: 12 pages, including 8 figures, RevTeX

A Novel Path Sampling Method for the Calculation of Rate Constants

We derive a novel efficient scheme to measure the rate constant of transitions between stable states separated by high free energy barriers in a complex environment within the framework of transition path sampling. The method is based on directly and simultaneously measuring the fluxes through many phase space interfaces and increases the efficiency with at least a factor of two with respect to existing transition path sampling rate constant algorithms. The new algorithm is illustrated on the isomerization of a diatomic molecule immersed in a simple fluid.Comment: 14 pages, including 13 figures, RevTeX

Aubry transition studied by direct evaluation of the modulation functions of infinite incommensurate systems

Incommensurate structures can be described by the Frenkel Kontorova model. Aubry has shown that, at a critical value K_c of the coupling of the harmonic chain to an incommensurate periodic potential, the system displays the analyticity breaking transition between a sliding and pinned state. The ground state equations coincide with the standard map in non-linear dynamics, with smooth or chaotic orbits below and above K_c respectively. For the standard map, Greene and MacKay have calculated the value K_c=.971635. Conversely, evaluations based on the analyticity breaking of the modulation function have been performed for high commensurate approximants. Here we show how the modulation function of the infinite system can be calculated without using approximants but by Taylor expansions of increasing order. This approach leads to a value K_c'=.97978, implying the existence of a golden invariant circle up to K_c' > K_c.Comment: 7 pages, 5 figures, file 'epl.cls' necessary for compilation provided; Revised version, accepted for publication in Europhysics Letter

The dynamics of the DNA denaturation transition

The dynamics of the DNA denaturation is studied using the Peyrard-Bishop-Dauxois model. The denaturation rate of double stranded polymers decreases exponentially as function of length below the denaturation temperature. Above Tc, the rate shows a minimum, but then increases as function of length. We also examine the influence of sequence and solvent friction. Molecules having the same number of weak and strong base-pairs can have significantly different opening rates depending on the order of base-pairs.Comment: 6 pages, 6 figures, to be published in Europhysics Letter

Can one predict DNA Transcription Start Sites by studying bubbles?

It has been speculated that bubble formation of several base-pairs due to thermal fluctuations is indicatory for biological active sites. Recent evidence, based on experiments and molecular dynamics (MD) simulations using the Peyrard-Bishop-Dauxois model, seems to point in this direction. However, sufficiently large bubbles appear only seldom which makes an accurate calculation difficult even for minimal models. In this letter, we introduce a new method that is orders of magnitude faster than MD. Using this method we show that the present evidence is unsubstantiated.Comment: 4 pages, 3 figures, accepted for publication in physical review letter

Prospects of Transition Interface Sampling simulations for the theoretical study of zeolite synthesis

The transition interface sampling (TIS) technique allows to overcome large free energy barriers within reasonable simulation time, which is impossible for straightforward molecular dynamics. Still, the method does not impose an artificial driving force, but it surmounts the timescale problem by an importance sampling of true dynamical pathways. Recently, it was shown that the efficiency of TIS to calculate reaction rates is less sensitive to the choice of reaction coordinate than those of the standard free energy based techniques. This could be an important advantage in complex systems for which a good reaction coordinate is usually very difficult to find. We explain the principles of this method and discuss some of the promising applications related to zeolite formation.Comment: 9 pages, accepted for publication in Phys. Chem. Chem. Phys. for the special issue of the CECAM workshop: Computational aspects of building blocks, nucleation, and synthesis of porous materials Aug. 29 2006 to Aug. 31 200