Targeted free energy perturbation

A generalization of the free energy perturbation identity is derived, and a computational strategy based on this result is presented. A simple example illustrates the efficiency gains that can be achieved with this method.Comment: 8 pages + 1 color figur

Multicanonical Multigrid Monte Carlo

To further improve the performance of Monte Carlo simulations of first-order phase transitions we propose to combine the multicanonical approach with multigrid techniques. We report tests of this proposition for the $d$-dimensional $\Phi^4$ field theory in two different situations. First, we study quantum tunneling for $d = 1$ in the continuum limit, and second, we investigate first-order phase transitions for $d = 2$ in the infinite volume limit. Compared with standard multicanonical simulations we obtain improvement factors of several resp. of about one order of magnitude.Comment: 12 pages LaTex, 1 PS figure appended. FU-Berlin preprint FUB-HEP 9/9

Model of a fluid at small and large length scales and the hydrophobic effect

We present a statistical field theory to describe large length scale effects induced by solutes in a cold and otherwise placid liquid. The theory divides space into a cubic grid of cells. The side length of each cell is of the order of the bulk correlation length of the bulk liquid. Large length scale states of the cells are specified with an Ising variable. Finer length scale effects are described with a Gaussian field, with mean and variance affected by both the large length scale field and by the constraints imposed by solutes. In the absence of solutes and corresponding constraints, integration over the Gaussian field yields an effective lattice gas Hamiltonian for the large length scale field. In the presence of solutes, the integration adds additional terms to this Hamiltonian. We identify these terms analytically. They can provoke large length scale effects, such as the formation of interfaces and depletion layers. We apply our theory to compute the reversible work to form a bubble in liquid water, as a function of the bubble radius. Comparison with molecular simulation results for the same function indicates that the theory is reasonably accurate. Importantly, simulating the large length scale field involves binary arithmetic only. It thus provides a computationally convenient scheme to incorporate explicit solvent dynamics and structure in simulation studies of large molecular assemblies

Multi-Overlap Simulations for Transitions between Reference Configurations

We introduce a new procedure to construct weight factors, which flatten the probability density of the overlap with respect to some pre-defined reference configuration. This allows one to overcome free energy barriers in the overlap variable. Subsequently, we generalize the approach to deal with the overlaps with respect to two reference configurations so that transitions between them are induced. We illustrate our approach by simulations of the brainpeptide Met-enkephalin with the ECEPP/2 energy function using the global-energy-minimum and the second lowest-energy states as reference configurations. The free energy is obtained as functions of the dihedral and the root-mean-square distances from these two configurations. The latter allows one to identify the transition state and to estimate its associated free energy barrier.Comment: 12 pages, (RevTeX), 14 figures, Phys. Rev. E, submitte

Spin glass overlap barriers in three and four dimensions

For the Edwards-Anderson Ising spin-glass model in three and four dimensions (3d and 4d) we have performed high statistics Monte Carlo calculations of those free-energy barriers $F^q_B$ which are visible in the probability density $P_J(q)$ of the Parisi overlap parameter $q$. The calculations rely on the recently introduced multi-overlap algorithm. In both dimensions, within the limits of lattice sizes investigated, these barriers are found to be non-self-averaging and the same is true for the autocorrelation times of our algorithm. Further, we present evidence that barriers hidden in $q$ dominate the canonical autocorrelation times.Comment: 20 pages, Latex, 12 Postscript figures, revised version to appear in Phys. Rev.

Phase Behavior of Bent-Core Molecules

Recently, a new class of smectic liquid crystal phases (SmCP phases) characterized by the spontaneous formation of macroscopic chiral domains from achiral bent-core molecules has been discovered. We have carried out Monte Carlo simulations of a minimal hard spherocylinder dimer model to investigate the role of excluded volume interations in determining the phase behavior of bent-core materials and to probe the molecular origins of polar and chiral symmetry breaking. We present the phase diagram as a function of pressure or density and dimer opening angle $\psi$. With decreasing $\psi$, a transition from a nonpolar to a polar smectic phase is observed near $\psi = 167^{\circ}$, and the nematic phase becomes thermodynamically unstable for $\psi < 135^{\circ}$. No chiral smectic or biaxial nematic phases were found.Comment: 4 pages Revtex, 3 eps figures (included

Lattice-switch Monte Carlo

We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate configuration of the other by `switching' one set of lattice vectors for the other, while keeping the displacements with respect to the lattice sites constant. The sampling of the displacement configurations is biased, multicanonically, to favor paths leading to `gateway' arrangements for which the Monte Carlo switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. We explore and exploit the method in the context of extensive studies of systems of hard spheres. We show that the efficiency of the method is controlled by the extent to which the switch conserves correlated microstructure. We also show how, microscopically, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the differences between the free energies of the two close packed structures (fcc and hcp) in both the constant density and the constant pressure ensembles.Comment: 34 pages, 9 figures, RevTeX. To appear in Phys. Rev.

Constraint methods for determining pathways and free energy of activated processes

Activated processes from chemical reactions up to conformational transitions of large biomolecules are hampered by barriers which are overcome only by the input of some free energy of activation. Hence, the characteristic and rate-determining barrier regions are not sufficiently sampled by usual simulation techniques. Constraints on a reaction coordinate r have turned out to be a suitable means to explore difficult pathways without changing potential function, energy or temperature. For a dense sequence of values of r, the corresponding sequence of simulations provides a pathway for the process. As only one coordinate among thousands is fixed during each simulation, the pathway essentially reflects the system's internal dynamics. From mean forces the free energy profile can be calculated to obtain reaction rates and insight in the reaction mechanism. In the last decade, theoretical tools and computing capacity have been developed to a degree where simulations give impressive qualitative insight in the processes at quantitative agreement with experiments. Here, we give an introduction to reaction pathways and coordinates, and develop the theory of free energy as the potential of mean force. We clarify the connection between mean force and constraint force which is the central quantity evaluated, and discuss the mass metric tensor correction. Well-behaved coordinates without tensor correction are considered. We discuss the theoretical background and practical implementation on the example of the reaction coordinate of targeted molecular dynamics simulation. Finally, we compare applications of constraint methods and other techniques developed for the same purpose, and discuss the limits of the approach

Adsorption of mono- and multivalent cat- and anions on DNA molecules

Adsorption of monovalent and multivalent cat- and anions on a deoxyribose nucleic acid (DNA) molecule from a salt solution is investigated by computer simulation. The ions are modelled as charged hard spheres, the DNA molecule as a point charge pattern following the double-helical phosphate strands. The geometrical shape of the DNA molecules is modelled on different levels ranging from a simple cylindrical shape to structured models which include the major and minor grooves between the phosphate strands. The densities of the ions adsorbed on the phosphate strands, in the major and in the minor grooves are calculated. First, we find that the adsorption pattern on the DNA surface depends strongly on its geometrical shape: counterions adsorb preferentially along the phosphate strands for a cylindrical model shape, but in the minor groove for a geometrically structured model. Second, we find that an addition of monovalent salt ions results in an increase of the charge density in the minor groove while the total charge density of ions adsorbed in the major groove stays unchanged. The adsorbed ion densities are highly structured along the minor groove while they are almost smeared along the major groove. Furthermore, for a fixed amount of added salt, the major groove cationic charge is independent on the counterion valency. For increasing salt concentration the major groove is neutralized while the total charge adsorbed in the minor groove is constant. DNA overcharging is detected for multivalent salt. Simulations for a larger ion radii, which mimic the effect of the ion hydration, indicate an increased adsorbtion of cations in the major groove.Comment: 34 pages with 14 figure