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David A Kofke

Publications and source records attributed to David A Kofke.

17 recordsLinked to original sources
PubMed2005

Phase-space overlap measures. II. Design and implementation of staging methods for free-energy calculations.

We consider staged free-energy calculation methods in the context of phase-space overlap relations, and argue that the selection of work-based methods should be guided by consideration of the phase-space overlap of the systems of interest. Stages should always be constructed such that work is performed only into a system that has a phase-space subset relation with the starting system. Thus multiple stages are required if the systems of interest are not such that one forms a phase-space subset with the other. Three two-stage methods are possible, termed umbrella sampling, overlap sampling, and funnel sampling. The last is appropriate for cases in which the subset relation holds, but only in the extreme, meaning that one system's important phase space constitutes a very small portion of the others. Umbrella sampling is most suitable for nonoverlap systems, and overlap sampling is appropriate for systems exhibiting partial phase-space overlap. We review recently introduced metrics that characterize phase-space overlap, showing that the performance of the single- and two-stage methods is consistent with the phase-space picture. We also demonstrate that a recently introduced bias-detection measure is effective in identifying inaccuracy in single- and multistage calculations. The examples used are the chemical-potential calculation for a Lennard-Jones liquid at moderate and at high densities, the same for model water at ambient conditions, and a process of charging a neutral ion in water.

Journal Article↗
PubMed2005

Phase-space overlap measures. I. Fail-safe bias detection in free energies calculated by molecular simulation.

We consider ways to quantify the overlap of the parts of phase space important to two systems, labeled A and B. Of interest is how much of the A-important phase space lies in that important to B, and how much of B lies in A. Two measures are proposed. The first considers four total-energy distributions, formed from all combinations made by tabulating either the A-system or the B-system energy when sampling either the A or B system. Measures for A in B and B in A are given by two overlap integrals defined on pairs of these distributions. The second measure is based on information theory, and defines two relative entropies which are conveniently expressed in terms of the dissipated work for free-energy perturbation (FEP) calculations in the A-->B and B-->A directions, respectively. Phase-space overlap is an important consideration in the performance of free-energy calculations. To demonstrate this connection, we examine bias in FEP calculations applied to a system of independent particles in a harmonic potential. Systems are selected to represent a range of overlap situations, including extreme subset, subset, partial overlap, and nonoverlap. The magnitude and symmetry of the bias (A-->B vs B-->A) are shown to correlate well with the overlap, and consequently with the overlap measures. The relative entropies are used to scale the amount of sampling to obtain a universal bias curve. This result leads to develop a simple heuristic that can be applied to determine whether a work-based free-energy measurement is free of bias. The heuristic is based in part on the measured free energy, but we argue that it is fail-safe inasmuch as any bias in the measurement will not promote a false indication of accuracy.

Algorithms↗
PubMed2005

Rosenbluth-sampled nonequilibrium work method for calculation of free energies in molecular simulation.

We present methods that introduce concepts from Rosenbluth sampling [M. N. Rosenbluth and A. W. Rosenbluth, J. Chem. Phys. 23, 356 (1955)] into the Jarzynski nonequilibrium work (NEW) free-energy calculation technique [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)]. The proposed hybrid modifies the way steps are taken in the NEW process. With it, each step is selected from a range of alternatives, with bias given to steps that contribute the least work. The definition of the work average is modified to account for the bias. We introduce two variants of this method, lambda-bias sampling and configuration-bias sampling, respectively; a combined lambda- and configuration-bias method is also considered. By reducing the likelihood that large nonequilibrated work values enter the ensemble average, the Rosenbluth sampling aids in remedying problems of inaccuracy of the calculation. We demonstrate the performance of the proposed methods through a model system of N independent harmonic oscillators. This model captures the difficulties involved in calculating free energies in real systems while retaining many tractable features that are helpful to the study. We examine four variants of this model that differ qualitatively in the nature of their phase-space overlap. Results indicate that the lambda-bias sampling method is most useful for systems with entropic sampling barriers, while the configuration-bias methods are best for systems with energetic sampling barriers. The Rosenbluth-sampling schemes yield much more accurate results than the unbiased nonequilibrium work method. Typically the accuracy can be improved by about an order of magnitude for a given amount of sampling; this improvement translates into two or more orders of magnitude less sampling required to obtain a given level of accuracy, owing to the generally slow convergence of the NEW calculation when the inaccuracy is large.

Algorithms↗
PubMed2005

Molecular simulation study of the effect of pressure on the vapor-liquid interface of the square-well fluid.

We examine a model system to study the effect of pressure on the surface tension of a vapor-liquid interface. The system is a two-component mixture of spheres interacting with the square-well (A-A) and hard-sphere (B-B) potentials and with unlike (A-B) interactions ranging (for different cases) from hard sphere to strongly attractive square well. The bulk-phase and interfacial properties are measured by molecular dynamics simulation for coexisting vapor-liquid phases for various mixture compositions, pressures, and temperatures. The variation of the surface tension with pressure compares well to values given by surface-excess formulas derived from thermodynamic considerations. We find that surface tension increases with pressure only for the case of an inert solute (hard-sphere A-B interactions) and that the presence of A-B attractions strongly promotes a decrease of surface tension with pressure. An examination of density and composition profiles is made to explain these effects in terms of surface-adsorption arguments.

Journal Article↗
PubMed2005

Evaluation of bridge-function diagrams via Mayer-sampling Monte Carlo simulation.

We report coefficients of the h-bond expansion of the bridge function of the hard-sphere system up to order rho(4) (where rho is the density in units of the hard-sphere diameter), which in the highest-order term includes 88 cluster diagrams with bonds representing the total correlation function h(r). Calculations are performed using the recently introduced Mayer-sampling method for evaluation of cluster integrals, and an iterative scheme is applied in which the h(r) used in the cluster integrals is determined by solution of the Ornstein-Zernike equation with a closure given by the calculated clusters. Calculations are performed for reduced densities from 0.1 to 0.9 in increments of 0.1. Comparison with molecular simulation data shows that the convergence is very slow for the density expansion of the bridge function calculated this way.

Journal Article↗
PubMed2005

Trimer based polarization as a multibody molecular model. Application to hydrogen fluoride.

A molecular modeling approach is introduced as a way to treat multibody (more than two molecules) contributions to the intermolecular potential. There are two key features to the method. First, it employs polarizable electrostatics on the molecules, but converges the charges and fields for only three molecules at a time, taken separately for all trimers (three molecules falling within a cutoff distance) in the system. This feature introduces significant computational savings when applied in Monte Carlo simulation (in comparison to a full N-body polarization treatment), as movement of a single molecule does not require re-converging of the polarization of all molecules, and it achieves this without approximations that cause the value of the energy to depend on the history of the simulation. Second, the approach defines the polarization energy in excess of the pairwise contribution, meaning that the trimer energy has subtracted from it the sum of the energies obtained by converging the polarization of each molecule pair in the trimer. This feature is advantageous because it removes the need (often found in polarizable models) to stiffen inappropriately the repulsive part of the pair potential. The polarization contribution is thus a purely three-body potential. The approach is applied to model hydrogen fluoride, which in experiments exhibits unusual properties that have proven difficult to capture well by molecular models. The new HF model is shown to be much more successful than previous modeling efforts in obtaining agreement with a broad range of experimental data (volumetric properties, heat effects, molecular structure, and vapor-liquid equilibria).

Journal Article↗
PubMed2004

Asymmetric bias in free-energy perturbation measurements using two Hamiltonian-based models.

We present two model systems that are suitable for the study of bias in free-energy perturbation (FEP) calculations which are performed in molecular simulations. The models exhibit the asymmetry that is sometimes seen in these calculations, in which the magnitude of the bias is greater when the calculation is performed in one direction ( A-->B , sampling system A and perturbing into system B ) versus the other (B-->A) . Both models are formulated as a system of N independent particles, each sampling a space in the presence of a one-body field that is different for the A and B systems. In one model the field is a harmonic potential. The other model is discrete, such that each particle can be at one of two points (or states) of different energy. The neglected-tail bias model is applied to each system to estimate the average bias as a function of the amount of FEP sampling, and numerical calculations are performed to show that the bias model is effective. We show that the bias is significantly smaller when sampling is performed on the system having a broader work distribution (we designate this direction "insertion") compared to the bias for FEP calculations that sample the system with a narrower distribution ("deletion").

Journal Article↗
PubMed2004

Molecular simulation study of effect of molecular association on vapor-liquid interfacial properties.

Vapor-liquid interfacial properties of square-well associating fluids are studied via transition-matrix Monte Carlo simulation. Results for one-site and two-site association models are presented. Coexistence properties, surface tension, cluster distribution, density profile, and orientation profile are presented. Molecular association affects the interfacial properties and cluster fractions more than it affects the bulk densities. We observe that the surface tension exhibits a maximum with respect to association strength. This behavior is in agreement with the recent study of Peery and Evans for one site system using a square-gradient approach.

Chemistry, Physical↗
PubMed2004

Model for small-sample bias of free-energy calculations applied to Gaussian-distributed nonequilibrium work measurements.

We present a model for the bias of free-energy differences when determined using the nonequilibrium work (NEW) formalism due to Jarzynski. Input to the model is the distribution of work values underlying the NEW calculation, and the bias is estimated by assuming that all of the inaccuracy is incurred by failure to sample work values beyond a specific point in the tail of the distribution. The model is formulated considering both small- and large-sample NEW calculations. It is then applied to the study of bias for cases in which the work distribution is Gaussian. The model is shown to give an excellent description of the bias in situations where the bias is a more significant source of error than the sample variance. A scaling law is presented and it is shown that the bias as a function of sampling can be reduced to a single universal curve, approximately valid for all Gaussian work distributions. This result is used to formulate a simple criterion that can be applied to test if a NEW calculation is effectively free of bias. The criterion is shown to be effective even though it uses the measured (and perhaps biased) free energy as an input.

Chemistry, Physical↗
PubMed2004

Mayer sampling: calculation of cluster integrals using free-energy perturbation methods.

Free-energy simulation methods are applied toward the calculation of cluster integrals that appear in diagrammatic methods of statistical mechanics. In this approach, Monte Carlo sampling is performed on a number of molecules equal to the order of the integral, and configurations are weighted according to the absolute value of the integrand. An umbrella-sampling average yields the value of the cluster integral in reference to a known integral. Virial coefficients, up to the sixth for the Lennard-Jones model and the fifth for the SPCE model of water, are calculated as a demonstration.

Journal Article↗
PubMed2004

Using overlap and funnel sampling to obtain accurate free energies from nonequilibrium work measurements.

Two concepts are presented for accurate nonequilibrium work free-energy measurements, realized both in molecular simulation and experiment. First, the need for an intermediate important to both the reference and the target systems (overlap) is indicated. Second, the use of a soft path from each end point to the intermediate (funnel) is demonstrated. Schemes implementing these concepts dramatically improve efficiency and accuracy of free energy calculations, as shown by calculation of the free energy of ion charging in water, and the free energy change in mutation of an adenosine molecule.

Adenosine↗
PubMed2004

Improving the efficiency and reliability of free energy perturbation calculations using overlap sampling methods.

A challenge in free energy calculation for complex molecular systems by computer simulation is to obtain a reliable estimate within feasible computational time. In this study, we suggest an answer to this challenge by exploring a simple method, overlap sampling (OS), for producing reliable free-energy results in an efficient way. The formalism of the OS method is based on ensuring sampling of important overlapping phase space during perturbation calculations. This technique samples both forward and reverse free energy perturbation (FEP) to improve the free-energy calculation. It considers the asymmetry of the FEP calculation and features an ability to optimize both the precision and the accuracy of the measurement without affecting the simulation process itself. The OS method is tested at two optimization levels: no optimization (simple OS), and full optimization (equivalent to Bennett's method), and compared to conventional FEP techniques, including the widely used direct FEP averaging method, on three alchemical mutation systems: (a) an anion transformation in water solution, (b) mutation between methanol and ethane, and (c) alchemical change of an adenosine molecule. It is consistently shown that the reliability of free-energy estimates can be greatly improved using the OS techniques at both optimization levels, while the performance of Bennett's method is particularly striking. In addition, the efficiency of a calculation can be significantly improved because the method is able to (a) converge to the right answer quickly, and (b) work for large perturbations. The basic two-stage OS method can be extended to admit additional stages, if needed. We suggest that the OS method can be used as a general perturbation technique for computing free energy differences in molecular simulations.

Journal Article↗
PubMed2003

Variational formula for the free energy based on incomplete sampling in a molecular simulation.

Finite sampling in free-energy perturbation (FEP) calculations by molecular simulation leads to reproducible systematic errors, with sign shown to depend (in a known way) only on which system governs sampling in the simulation. Thus the result of a FEP calculation can be used as a bound on the true free energy. This inequality is of a wholly different nature from established forms such as the Gibbs-Bogoliubov inequality or the second law, in that its origins relate to the performance of a molecular simulation. If one can identify a suitable reference system having a free energy known as a function of some defining parameter, variational schemes based on the finite-sampling inequalities can be implemented. This idea is demonstrated through calculation of the free energy of a hard-sphere solid by perturbing from harmonic references and of a hard-sphere fluid by perturbing from infinitely polydisperse references. The tightness of the bounds increases with the amount of sampling in the simulation and correlates with the entropy difference between the target and reference systems. The bounds are tightest near the point where the entropy difference is least.

Journal Article↗
PubMed2002

Self-referential method for calculation of the free energy of crystals by Monte Carlo simulation.

We propose a Monte Carlo simulation method for the evaluation of free energies in crystalline systems. In principle, the method involves evaluating the free-energy difference between systems of N molecules and 2N molecules. This difference, coupled with the assumption that the free energy is extensive and thus proportional to N, provides sufficient information to obtain the absolute free energy of the crystal. The approach to doubling the system size does not involve insertion or removal of molecules in the system. Instead, the configurations of the molecules are expressed in terms of the normal-mode coordinates of a harmonic lattice. By decoupling certain of these coordinates from the molecule configurations, we obtain a transformation that in effect yields the system-size doubling. The method is examined via application to a system of hard rods in one dimension. This simple model is considered principally because of the availability of an analytic solution for its free energy, which permits accurate testing of the performance and correctness of the proposed method. In using the hard-rod model we also avoid other complications related to treatment of the temperature, and application of normal-mode coordinate decoupling in higher dimensions. The proposed method is shown to be able to provide good results for the free-energy calculation, but further development will be needed before it can be considered practical for general-purpose use.

Journal Article↗