Monte Carlo free energy calculations using electronic structure methods

The molecular mechanics-based importance sampling function (MMBIF) algorithm [R. Iftimie, D. Salahub, D. Wei, and J. Schofield, J. Chem. Phys. 113, 4852 (2000)] is extended to incorporate semiempirical electronic structure methods in the secondary Markov chain, creating a fully quantum mechanical Monte Carlo sampling method for simulations of reactive chemical systems which, unlike the MMBIF algorithm, does not require the generation of a system-specific force field. The algorithm is applied to calculating the potential of mean force for the isomerization reaction of HCN using thermodynamic integration. Constraints are implemented in the sampling using a modification of the SHAKE algorithm, including that of a fixed, arbitrary reaction coordinate. Simulation results show that sampling efficiency with the semiempirical secondary potential is often comparable in quality to force fields constructed using the methods suggested in the original MMBIF work. The semiempirical based importance sampling method presented here is a useful alternative to MMBIF sampling as it can be applied to systems for which no suitable MM force field can be constructed.     

Calculation of rotational partition functions by an efficient Monte Carlo importance sampling technique

The evaluation of the classical rotational partition function represented by a configuration integral over all external and internal rotational degrees of freedom of nonrigid chain polyatomic molecules is described. The method of Pitzer and Gwinn is used to correct the classical partition function for quantum mechanical effects at low temperatures. The internal rotor hindrance and all coupling arising from the external and internal rotational degrees of freedom are explicitly taken into account. Importance sampling Monte Carlo based on the adaptive VEGAS algorithm to perform multidimensional integration is implemented within the TINKER program package. A multidimensional potential energy hypersurface is calculated with the MM3(2000) molecular mechanics force field. Numerical tests are performed on a number of small n-alkanes (from ethane to octane), for which the absolute entropies calculated at three different temperatures are compared both with the experimental values and with the previous theoretical results. The application of a more efficient importance sampling technique developed here results in a substantial reduction of statistical errors in the evaluation of the configuration integral for a given number of Monte Carlo steps. Error estimates for the calculated entropies are given, and possible sources of systematic errors, and their importance for a reliable prediction of the absolute entropy, are discussed.     

Importance sampling for quantum Monte Carlo in manifolds: addressing the time scale problem in simulations of molecular aggregates

Several importance sampling strategies are developed and tested for stereographic projection diffusion Monte Carlo in manifolds. We test a family of one parameter trial wavefunctions for variational Monte Carlo in stereographically projected manifolds which can be used to produce importance sampling. We use the double well potential in one dimensional Euclidean space to study systematically sampling issues for diffusion Monte Carlo. We find that diffusion Monte Carlo with importance sampling in manifolds is orders of magnitude more efficient compared to unguided diffusion Monte Carlo. Additionally, diffusion Monte Carlo with importance sampling in manifolds can overcome problems with nonconfining potentials and can suppress quasiergodicity effectively. We obtain the ground state energy and the wavefunction for the Stokmayer trimer.     

Ground-state properties of LiH by reptation quantum Monte Carlo methods

We apply reptation quantum Monte Carlo to calculate one- and two-electron properties for ground-state LiH, including all tensor components for static polarizabilities and hyperpolarizabilities to fourth-order in the field. The importance sampling is performed with a large (QZ4P) STO basis set single determinant, directly obtained from commercial software, without incurring the overhead of optimizing many-parameter Jastrow-type functions of the inter-electronic and internuclear distances. We present formulas for the electrical response properties free from the finite-field approximation, which can be problematic for the purposes of stochastic estimation. The α, γ, A and C polarizability values are reasonably consistent with recent determinations reported in the literature, where they exist. A sum rule is obeyed for components of the B tensor, but B(zz,zz) as well as β(zzz) differ from what was reported in the literature.     

Adaptive importance sampling Monte Carlo simulation of rare transition events

We develop a general theoretical framework for the recently proposed importance sampling method for enhancing the efficiency of rare-event simulations [W. Cai, M. H. Kalos, M. de Koning, and V. V. Bulatov, Phys. Rev. E 66, 046703 (2002)], and discuss practical aspects of its application. We define the success/fail ensemble of all possible successful and failed transition paths of any duration and demonstrate that in this formulation the rare-event problem can be interpreted as a "hit-or-miss" Monte Carlo quadrature calculation of a path integral. The fact that the integrand contributes significantly only for a very tiny fraction of all possible paths then naturally leads to a "standard" importance sampling approach to Monte Carlo (MC) quadrature and the existence of an optimal importance function. In addition to showing that the approach is general and expected to be applicable beyond the realm of Markovian path simulations, for which the method was originally proposed, the formulation reveals a conceptual analogy with the variational MC (VMC) method. The search for the optimal importance function in the former is analogous to finding the ground-state wave function in the latter. In two model problems we discuss practical aspects of finding a suitable approximation for the optimal importance function. For this purpose we follow the strategy that is typically adopted in VMC calculations: the selection of a trial functional form for the optimal importance function, followed by the optimization of its adjustable parameters. The latter is accomplished by means of an adaptive optimization procedure based on a combination of steepest-descent and genetic algorithms.     

Development of sampling approaches for the determination of the presence of genetically modified organisms at the field level

In order to comply with the European Union regulatory threshold for the adventitious presence of genetically modified organisms (GMOs) in food and feed, it is important to trace GMOs from the field. Appropriate sampling methods are needed to accurately predict the presence of GMOs at the field level. A 2-year field experiment with two maize varieties differing in kernel colour was conducted in Slovenia. Based on the results of data mining analyses and modelling, it was concluded that spatial relations between the donor and receptor field were the most important factors influencing the distribution of outcrossing rate (OCR) in the field. The approach for estimation fitting function parameters in the receptor (non-GM) field at two distances from the donor (GM) field (10 and 25 m) for estimation of the OCR (GMO content) in the whole receptor field was developed. Different sampling schemes were tested; a systematic random scheme in rows was proposed to be applied for sampling at the two distances for the estimation of fitting function parameters for determination of OCR. The sampling approach had already been validated with some other OCR data and was practically applied in the 2009 harvest in Poland. The developed approach can be used for determination of the GMO presence at the field level and for making appropriate labelling decisions. The importance of this approach lies in its possibility to also address other threshold levels beside the currently prescribed labelling threshold of 0.9% for food and feed.     

Searching for globally optimal functional forms for interatomic potentials using genetic programming with parallel tempering

Molecular dynamics and other molecular simulation methods rely on a potential energy function, based only on the relative coordinates of the atomic nuclei. Such a function, called a force field, approximately represents the electronic structure interactions of a condensed matter system. Developing such approximate functions and fitting their parameters remains an arduous, time-consuming process, relying on expert physical intuition. To address this problem, a functional programming methodology was developed that may enable automated discovery of entirely new force-field functional forms, while simultaneously fitting parameter values. The method uses a combination of genetic programming, Metropolis Monte Carlo importance sampling and parallel tempering, to efficiently search a large space of candidate functional forms and parameters. The methodology was tested using a nontrivial problem with a well-defined globally optimal solution: a small set of atomic configurations was generated and the energy of each configuration was calculated using the Lennard-Jones pair potential. Starting with a population of random functions, our fully automated, massively parallel implementation of the method reproducibly discovered the original Lennard-Jones pair potential by searching for several hours on 100 processors, sampling only a minuscule portion of the total search space. This result indicates that, with further improvement, the method may be suitable for unsupervised development of more accurate force fields with completely new functional forms.     

On the use of Bennett's acceptance ratio method in multi-canonical-type simulations

A common strategy for mapping coexistence curves is to employ multi-canonical (MUCA) sampling to simulate along a macrostate path connecting two phases. Central to this approach is the task of accurately calculating the importance weights used in the MUCA procedure, which are needed for both effective sampling and accurate determination of phase boundaries. The purpose of this study is to develop a strategy for determining the importance weights that is built upon Bennett's optimized acceptance ratio method. This approach is shown to be closely related to transition matrix schemes, and is used to compute the vapor-liquid equilibrium of a Lennard-Jones fluid and the liquid-liquid equilibrium of a n-hexane/n-perfluorohexane mixture. For the Lennard-Jones system, the importance weights as a function of the number of particles "N" (at fixed temperature and volume) are obtained by using Bennett's method to estimate free energy differences between N and N+1 particle systems over the desired range of N values. In this application, the method is found to perform slightly better than a related transition matrix scheme. For the n-hexane/n-perfluorohexane liquid mixture, the method is designed to obtain weights as a function of composition (for fixed temperature, pressure, and total number of particles); in this case, the method is found to outperform the Gibbs ensemble approach.     

Soil sampling uncertainty on arable fields estimated from reference sampling and a collaborative trial

On three fields of arable land of (3–6)×10⁴ m², simple reference sampling was performed by taking up to 195 soil increments from each field applying a systematic sampling strategy. From the analytical data reference values for 15 elements were established, which should represent the average analyte mass fraction of the areas. A “point selection standard deviation” was estimated, from which a prediction of the sampling uncertainty was calculated for the application of a standard sampling protocol (X-path across the field, totally 20 increments for a composite sample). Predicted mass fractions and associated uncertainties are compared with the results of a collaborative trial of 18 experienced samplers, who had applied the standard sampling protocol on these fields. In some cases, bias between reference and collaborative values is found. Most of these biases can be explained by analyte heterogeneity across the area, in particular on one field, which was found to be highly heterogeneous for most nutrient elements. The sampling uncertainties estimated from the reference sampling were often somewhat smaller compared to those from the collaborative trial. It is suspected that the influence of sample preparation and the variation due to sampler were responsible for these differences. For the applied sampling protocol, the uncertainty contribution from sampling generally is in the same range as the uncertainty contribution from analysis. From these findings, some conclusions were drawn, especially about the consequences for a sampling protocol, if in routine sampling a demanded “certainty of trueness” for the measurement result should be met.     

Applications of polydimethylsiloxane in analytical chemistry: A review

Silicones have innumerable applications in many areas of life. Polydimethylsiloxane (PDMS), which belongs to the class of silicones, has been extensively used in the field of analytical chemistry owing to its favourable physicochemical properties. The use of PDMS in analytical chemistry gained importance with its application as a stationary phase in gas chromatographic separations. Since then it has been used in many sample preparation techniques such as solid phase microextraction (SPME), stir bar sorptive extraction (SBSE), thin-film extraction, permeation passive sampling, etc. Further, it is gaining importance in the manufacturing of lab-on-a-chip devices, which have revolutionized bio-analysis. Applications of devices containing PDMS and used in the field of analytical chemistry are reviewed in this paper.     

Derivation of class II force fields. I. Methodology and quantum force field for the alkyl functional group and alkane molecules

A new method for deriving force fields for molecular simulations has been developed. It is based on the derivation and parameterization of analytic representations of the ab initio potential energy surfaces. The general method is presented here and used to derive a quantum mechanical force field (QMFF) for alkanes. It is based on sampling the energy surfaces of 16 representative alkane species. For hydrocarbons, this force field contains 66 force constants and reference values. These were fit to 128,376 quantum mechanical energies and energy derivatives describing the energy surface. The detailed form of the analytic force field expression and the values of all resulting parameters are given. A series of computations is then performed to test the ability of this force field to reproduce the features of the ab initio energy surface in terms of energies as well as the first and second derivatives of the energies with respect to molecular deformations. The fit is shown to be good, with rms energy deviations of less than 7% for all molecules. Also, although only two atom types are employed, the force field accounts for the properties of both highly strained species, such as cyclopropane and methylcyclopropanes, as well as unstrained systems. The information contained in the quantum energy surface indicates that it is significantly anharmonic and that important intramolecular coupling interactions exist between internals. The representation of the nature of these interactions, not present in diagonal, quadratic force fields (Class I force fields), is shown to be important in accounting accurately for molecular energy surfaces. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each 4.2 to 18.2%. This fourfold increase in the second derivative error dramatically demonstrates the importance of bond anharmonicity in the ab initio potential energy surface. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each of the interaction terms of the potential energy function has also been assessed. Bond anharmonicity, angle anharmonicity, and bond/angle, bond/torsion, and angle/angle/ torsion cross-term interactions result in the most significant overall improvement in distorted structure energies and energy derivatives. The implications of each energy term for the development of advanced force fields is discussed. Finally, it is shown that the techniques introduced here for exploring the quantum energy surface can be used to determine the extent of transferability and range of validity of the force field. The latter is of crucial importance in meeting the objective of deriving a force field for use in molecular mechanics and dynamics calculations of a wide range of molecules often containing functional groups in novel environments. © 1994 by John Wiley & Sons, Inc.     

On the Influence of Elastic Modes on the N.M.R. Lineshapes of Polymer Liquid Crystals

We have studied the influence of thermally excited orientational fluctuations on the N.M.R. lineshape of a nematic monodomain. The influence is characterized by a static order parameter S_stat whose theoretical expression in terms of viscoelastic parameters is derived. This model is applied to the proton N.M.R. spectrum of a thermotropic main chain polymer. The values of S_stat are deduced from the study of the changes of the N.M.R. lineshape as a function of the angle between the static magnetic field and the nematic director. Good agreement is obtained with theoretical values calculated using estimated values of the Leslie viscosity coefficients and the Frank elastic constants. The importance of an accurate knowledge of S_stat for a number of problems is stressed.     

Calculation of free energy through successive umbrella sampling

We consider an implementation of umbrella sampling in which the pertinent range of states is subdivided into small windows that are sampled consecutively and linked together. This allows us to simulate without a weight function or to extrapolate the results to the neighboring window in order to estimate a weight function. Additionally, we present a detailed error analysis in which we demonstrate that the error in umbrella sampling is controlled and, in the absence of sampling difficulties, independent of the window sizes. In this case, the efficiency of our implementation is comparable to a multicanonical simulation with a very good weight function, which in our scheme does not need to be known ahead of time. The analysis also allows us to detect sampling difficulties such as correlations between adjacent windows and provides a test of equilibration. We exemplify the scheme by simulating the liquid-vapor coexistence in a Lennard-Jones system.     

Kerr Effect of Xanthan/DTAB Aqueous Solutions

The Kerr effect of the Xanthan (charged polyelectrolyte; 113 ppm)/DTAB (surfactant) mixture in aqueous solution was studied. The static Kerr constant (B) and mean relaxation times (τ) values as a function of surfactant concentration (C_DTAB ) were determined. The observed birefringence (Δn) is not a linear function of the electric applied field (E ²). For small E values Δn grows with E ² and at a certain field value the birefringence tends to saturate. The addition of small quantities of DTAB lowers B values with respect to the Kerr constant of Xanthan (113 ppm) aqueous solution. The relaxation time of the mixtures is linearly dependent on the applied field and it decreases when DTAB concentration increases. The importance of the equivalent point is signalled. It is supposed that the initial rigidity of the polyelectrolite decreases because of the surfactant addition. Conductivity (σ) values as a function of surfactant concentration are presented.     

Sampling of water, soil and sediment to trace organic pollutants at a river-basin scale

Sampling is considered a crucial step in the analysis of organic compounds in the environment. This review describes field sampling techniques and provides detailed step-by-step procedures for collection and preservation of all major environmental matrices (water, sediment and soil) integrated as part of the river-basin water cycle. Attention is given to the prerequisites for obtaining reliable samples, and the practical issues of sample collection (planning, field sampling, sampling strategies and equipment and data quality assessment) are considered. Considering the heterogeneity of environmental matrices, special considerations for each matrix are given to solve typical problems and to find the most appropriate solutions to ensure the quality of the sample. The procedures described in the next sections are commonly used protocols that reflect true field conditions and current state-of-the-art techniques used in the sampling of organic compounds. The aim is to signify the importance of sampling to the overall analytical procedure. Finally, quality control issues to be considered in environmental sampling are given.     

Genetic algorithms for protein conformation sampling and optimization in a discrete backbone dihedral angle space

We have investigated protein conformation sampling and optimization based on the genetic algorithm and discrete main chain dihedral state model. An efficient approach combining the genetic algorithm with local minimization and with a niche technique based on the sharing function is proposed. Using two different types of potential energy functions, a Go-type potential function and a knowledge-based pairwise potential energy function, and a test set containing small proteins of varying sizes and secondary structure compositions, we demonstrated the importance of local minimization and population diversity in protein conformation optimization with genetic algorithms. Some general properties of the sampled conformations such as their native-likeness and the influences of including side-chains are discussed.     

Accelerating quantum mechanical/molecular mechanical sampling using pure molecular mechanical potential as an importance function: the case of effective fragment potential

Acceleration of sampling from a quantum mechanical/effective fragment mechanical (QM/EFP) potential is explored with effective fragment potential (EFP) as an importance function. EFP, generated on the fly, is found to be an excellent choice for an importance function for a QM/EFP potential. This technique is used to find nine stationary points of a blocked amino acid with twelve waters in a semi-automated way.     

Tri-peptide reference structures for the calculation of relative solvent accessible surface area in protein amino acid residues

Relative amino acid residue solvent accessibility values allow the quantitative comparison of atomic solvent-accessible surface areas in different residue types and physical environments in proteins and in protein structural alignments. Geometry-optimised tri-peptide structures in extended solvent-exposed reference conformations have been obtained for 43 amino acid residue types at a high level of quantum chemical theory. Significant increases in side-chain solvent accessibility, offset by reductions in main-chain atom solvent exposure, were observed for standard residue types in partially geometry-optimised structures when compared to non-minimised models built from identical sets of proper dihedral angles abstracted from the literature. Optimisation of proper dihedral angles led most notably to marked increases of up to 54% in proline main-chain atom solvent accessibility compared to literature values. Similar effects were observed for fully-optimised tri-peptides in implicit solvent. The relief of internal strain energy was associated with systematic variation in N, C^α and C^β atom solvent accessibility across all standard residue types. The results underline the importance of optimisation of ‘hard’ degrees of freedom (bond lengths and valence bond angles) and improper dihedral angle values from force field or other context-independent reference values, and impact on the use of standardised fixed internal co-ordinate geometry in sampling approaches to the determination of absolute values of protein amino acid residue solvent accessibility. Quantum chemical methods provide a useful and accurate alternative to molecular mechanics methods to perform energy minimisation of peptides containing non-standard (chemically modified) amino acid residues frequently present in experimental protein structure data sets, for which force field parameters may not be available. Reference tri-peptide atomic co-ordinate sets including hydrogen atoms are made freely available.     

Field sampling demonstration of portable thermal desorption collection and analysis instrumentation

The HAPSITE® (Hazardous Air Pollutants on Site) is a portable gas chromatography-mass spectrometry (GC–MS) unit designed to aid air sampling technicians by identifying and quantifying volatile organic compounds from occupational and environmental sampling. The main goal of the present study was to extend prior laboratory-based work with the portable HAPSITE® ER (extended range model) thermal desorption (TD) capability to real-world field samples from both indoor and outdoor environments using different types of active and passive sampling mechanisms. Understanding the performance of the HAPSITE® ER in a realistic field setting will allow air quality sampling technicians to make improved decisions related to sampling and analysis methods in the field. An important finding was that certain charcoal-based TD sorbents were contraindicated for the HAPSITE® ER because of a substantial hydrocarbon bleed which degraded system performance. A novel time series TD sampler (Logistically Enabled Sampling System-Portable [LESS-P]) was validated using Tenax TA TD tubes against standard active sampling across multiple field sampling sites, and the qualitative analytical trends and compound identities were similar between LESS-P replicates analysed via benchtop GC–MS and HAPSITE® ER. Once validated, the LESS-P was used to determine the reference concentrations for passive sampling calculations. The results confirmed the passive sampling methodology within the benchtop system, but highlighted some systemic sensitivity limitations that must be addressed in order for the HAPSITE® to be accurately applied to passive sampling. We propose that the LESS-P time-series sampler may help to alleviate the requirement for sampling technicians to be on-site during active sampling, allowing for automated sampling throughout the duration of a sampling event.     

Three-dimensional square water in the presence of an external electric field

In this work we study a tridimensional statistical model for the hydrogen-bond (HB) network formed in liquid water in the presence of an external electric field. This model is analogous to the so-called square water, whose ground state gives a good estimate for the residual entropy of the ice. In our case, each water molecule occupies one site of a cubic lattice, and no hole is allowed. The hydrogen atoms of water molecules are disposed at the lines connecting nearest-neighbor sites, in a way that each water can be found in 15 different states. We say that there is a hydrogen bond between two neighboring molecules when only one hydrogen is in the line connecting both molecules. Through Monte Carlo simulations with Metropolis and entropic sampling algorithms, and by exact calculations for small lattices, we determined the dependence of the number of molecules aligned to the field and the number of hydrogen bonds per molecule as a function of temperature and the intensity of the external field. The results for both approaches showed that, different of the two-dimensional case, there is no maximum in the number of HBs as a function of the electric field. However, we observed nonmonotonic behaviors as a function of the temperature of the quantities of interest. We also found the dependence of the entropy on the external electric field at very low temperatures. In this case, the entropy vanishes for the value of the external field for which the contributions to the total energy coming from the HBs and the field become the same.