Optimal charge and charge response determination through conformational space: global fitting scheme for representative charge and charge response kernel

We propose a global fitting scheme derived in the least-squares sense to estimate the optimal partial charge and charge response kernel (CRK), partial differential(Q(a))/partial differential(V(b)), with the data collected from conformational space sampling. We applied the global fitting method to the 1-butanol system and show the performance and accuracy of our global fitting procedure. In addition, we chose 1-pentanol as the test system for electronic structure change through conformational change and applied the global fitting method to it. From our study, it is indicated that intramolecular polarization can be influenced by intramolecular hydrogen bonding, and it is shown that our global fitting method can correspond to such a situation. Also, the global fitting procedure was tested on a large molecular system, 1-dodecanol. We show the results of the application of our fitting method for the system needed to sample large sets of data over a large conformational space. It is indicated that the nonlocality in intramolecular polarization in the alkyl chain sequence can be observed and that the large fluctuation of CRKs through nonbonded interactions such as intramolecular hydrogen bonding, as seen in the 1-pentanol case, can appear in common. The global fitting scheme we propose can be used for building molecular models considering polarization effects explicitly, even in the case of target systems that include many conformers.     

Probabilistic peak detection for first-order chromatographic data

We present a novel algorithm for probabilistic peak detection in first-order chromatographic data. Unlike conventional methods that deliver a binary answer pertaining to the expected presence or absence of a chromatographic peak, our method calculates the probability of a point being affected by such a peak. The algorithm makes use of chromatographic information (i.e. the expected width of a single peak and the standard deviation of baseline noise). As prior information of the existence of a peak in a chromatographic run, we make use of the statistical overlap theory. We formulate an exhaustive set of mutually exclusive hypotheses concerning presence or absence of different peak configurations. These models are evaluated by fitting a segment of chromatographic data by least-squares. The evaluation of these competing hypotheses can be performed as a Bayesian inferential task. We outline the potential advantages of adopting this approach for peak detection and provide several examples of both improved performance and increased flexibility afforded by our approach.     

Protein dynamics from NMR: the slowly relaxing local structure analysis compared with model-free analysis

(15)N-(1)H spin relaxation is a powerful method for deriving information on protein dynamics. The traditional method of data analysis is model-free (MF), where the global and local N-H motions are independent and the local geometry is simplified. The common MF analysis consists of fitting single-field data. The results are typically field-dependent, and multifield data cannot be fit with standard fitting schemes. Cases where known functional dynamics has not been detected by MF were identified by us and others. Recently we applied to spin relaxation in proteins the slowly relaxing local structure (SRLS) approach, which accounts rigorously for mode mixing and general features of local geometry. SRLS was shown to yield MF in appropriate asymptotic limits. We found that the experimental spectral density corresponds quite well to the SRLS spectral density. The MF formulas are often used outside of their validity ranges, allowing small data sets to be force-fitted with good statistics but inaccurate best-fit parameters. This paper focuses on the mechanism of force-fitting and its implications. It is shown that MF analysis force-fits the experimental data because mode mixing, the rhombic symmetry of the local ordering and general features of local geometry are not accounted for. Combined multifield multitemperature data analyzed with the MF approach may lead to the detection of incorrect phenomena, and conformational entropy derived from MF order parameters may be highly inaccurate. On the other hand, fitting to more appropriate models can yield consistent physically insightful information. This requires that the complexity of the theoretical spectral densities matches the integrity of the experimental data. As shown herein, the SRLS spectral densities comply with this requirement.     

A multidimensional approach to the analysis of chemical shift titration experiments in the frame of a multiple reaction scheme

We present a method for fitting curves acquired by chemical shift titration experiments, in the frame of a three‐step complexation mechanism. To that end, we have implemented a fitting procedure, based on a nonlinear least squares fitting method, that determines the best fitting curve using a “coarse grid search” approach and provides distributions for the different parameters of the complexation model that are compatible with the experimental precision. The resulting analysis protocol is first described and validated on a theoretical data set. We show its ability to converge to the true parameter values of the simulated reaction scheme and to evaluate complexation constants together with multidimensional uncertainties. Then, we apply this protocol to the study of the supramolecular interactions, in aqueous solution, between a lanthanide complex and three different model molecules, using NMR titration experiments. We show that within the uncertainty that can be evaluated from the parameter distributions generated during our analysis, the affinities between the lanthanide derivative and each model molecule can be discriminated, and we propose values for the corresponding thermodynamic constants. Copyright © 2013 John Wiley & Sons, Ltd.     

Stochastic approach to data analysis in fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) has emerged as a powerful technique for measuring low concentrations of fluorescent molecules and their diffusion constants. In FCS, the experimental data is conventionally fit using standard local search techniques, for example, the Marquardt-Levenberg (ML) algorithm. A prerequisite for these categories of algorithms is the sound knowledge of the behavior of fit parameters and in most cases good initial guesses for accurate fitting, otherwise leading to fitting artifacts. For known fit models and with user experience about the behavior of fit parameters, these local search algorithms work extremely well. However, for heterogeneous systems or where automated data analysis is a prerequisite, there is a need to apply a procedure, which treats FCS data fitting as a black box and generates reliable fit parameters with accuracy for the chosen model in hand. We present a computational approach to analyze FCS data by means of a stochastic algorithm for global search called PGSL, an acronym for Probabilistic Global Search Lausanne. This algorithm does not require any initial guesses and does the fitting in terms of searching for solutions by global sampling. It is flexible as well as computationally faster at the same time for multiparameter evaluations. We present the performance study of PGSL for two-component with triplet fits. The statistical study and the goodness of fit criterion for PGSL are also presented. The robustness of PGSL on noisy experimental data for parameter estimation is also verified. We further extend the scope of PGSL by a hybrid analysis wherein the output of PGSL is fed as initial guesses to ML. Reliability studies show that PGSL and the hybrid combination of both perform better than ML for various thresholds of the mean-squared error (MSE).     

Analysis of the genetic algorithm method of molecular conformation determination

Many important problems in chemistry require knowledge of the 3-D conformation of a molecule. A commonly used computational approach is to search for a variety of low-energy conformations. Here, we study the behavior of the genetic algorithm (GA) method as a global search technique for finding these low-energy conformations. Our test molecule is cyclic hexaglycine. The goal of this study is to determine how to best utilize GAs to find low-energy populations of conformations given a fixed amount of CPU time. Two measures are presented that help monitor the improvement in the GA populations and their loss of diversity. Different hybrid methods that combine coarse GA global search with local gradient minimization are evaluated. We present several specific recommendations about trade-offs when choosing GA parameters such as population size, number of generations, rate of interaction between subpopulations, and combinations of GA and gradient minimization. In particular, our results illustrate why approaches that emphasize convergence of the GA can actually decrease its effectiveness as a global conformation search method. © John Wiley & Sons, Inc.     

Anharmonic effect on unimolecular reactions with application to the photodissociation of ethylene

The importance of anharmonic effect on dissociation of molecular systems, especially clusters, has been noted. In this paper, we shall present a theoretical approach that can carry out the first principle calculations of anharmonic canonical and microcanonical rate constants of unimolecular reactions within the framework of transition state theory. In the canonical case, it is essential to calculate the partition function of anharmonic oscillators; for convenience, the Morse oscillator potential will be used for demonstration in this paper. In the microcanical case, which involves the calculation of the total number of states for the activated complex and the density of states for the reactant, we make use of the fact that both the total number of states and the density of states can be expressed in the inverse Laplace transformation of the partition functions and that the inverse Laplace transformation can in turn be carried out by using the saddle-point method. We shall also show that using the theoretical approach presented in this paper the total number of states and density of states can be determined from thermodynamic properties and the difference between the method used in this paper and the thermodynamic model used by Krems and Nordholm will be given. To demonstrate the application of our theoretical approach, we chose the photodissociation of ethylene at 157 and 193 nm as an example.     

Low temperature quantum rate coefficient of the H + CH+ reaction

In this paper we report the first theoretical study of the title reaction. A global, single-valued model of the ground-state potential energy surface has been obtained by fitting to an extensive set of high-level ab initio calculations. The surface is found to be attractive apart from linear geometries where energy barriers appear due to conical intersections. This model was then used to calculate the reactive reactant state selected cross sections for collision energies ranging from threshold up to 4000 cm(-1). These calculations were performed using our version of the Baer's approach of the RIOSA-NIP method which is based on the use of a negative imaginary potential. We find that the reaction probability is extremely oscillatory as a function of kinetic energy as it is a case for insertion reactions with a low exoergicity. The resulting reaction rate coefficient is found to first increase slowly as a function of temperature up to a broad maximum around 20 K and then to decrease slowly when temperature keeps increasing.     

Global optimization of parameters in the reactive force field ReaxFF for SiOH

We have used unbiased global optimization to fit a reactive force field to a given set of reference data. Specifically, we have employed genetic algorithms (GA) to fit ReaxFF to SiOH data, using an in‐house GA code that is parallelized across reference data items via the message‐passing interface (MPI). Details of GA tuning turn‐ed out to be far less important for global optimization efficiency than using suitable ranges within which the parameters are varied. To establish these ranges, either prior knowledge can be used or successive stages of GA optimizations, each building upon the best parameter vectors and ranges found in the previous stage. We have finally arrive‐ed at optimized force fields with smaller error measures than those published previously. Hence, this optimization approach will contribute to converting force‐field fitting from a specialist task to an everyday commodity, even for the more difficult case of reactive force fields. © 2013 Wiley Periodicals, Inc.     

Evaluation of protein 15N relaxation times by inverse Laplace transformation

Relaxation times (T1, T2, T1rho) are usually evaluated from exponential decay data by least-squares fitting methods. For this procedure, the integrals or amplitudes of signals must be determined, which can be laborious with large data sets. Moreover, the fitting requires a priori knowledge of the number of exponential components responsible for the decay. We have adapted inverse Laplace transformation (ILT) for the analysis of relaxation data. Exponential components are resolved with ILT to reciprocal space on their corresponding relaxation rate values. The ILT approach was applied to 3D linewidth-resolved 15N HSQC experiments to evaluate 15N T1 and T2 relaxation times of ubiquitin. The resulting spectrum is a true 3D spectrum, where the signals are separated by their 1H and 15N chemical shifts (HSQC correlations) and by their relaxation rate values (R1 or R2). From this spectrum, the relaxation times can be obtained directly with a simple peak-picking procedure.     

Capillary electrophoresis sequencing of small ssDNA molecules versus the Ogston regime: fitting data and interpreting parameters

We study the mobility of short ssDNA fragments (approximately 30-500 bases) separated by capillary electrophoresis in entangled polymer solutions. Although this corresponds to what is commonly called the Ogston regime, the corresponding sieving concept has never been defined properly nor tested quantitatively. We consider three formulas that have been suggested to fit data in this range of ssDNA sizes, and we discuss how their free parameters are related to actual physical parameters. We test these formulas with new data obtained in our laboratory using a commercial poly-N,N-dimethylacrylamide sieving matrix. Our results show that all three formulas provide decent fits. However, the traditional Ogston equation produces fitting parameters that appear to lack physical meaning. Surprisingly, all three approaches predict that the effective pore size and fiber radius are almost equal. This is the first step towards the development of a systematic approach to optimizing sequencing systems for this size range.     

Resolution of the identity atomic orbital Laplace transformed second order Møller-Plesset theory for nonconducting periodic systems

An improvement in performance of the atomic orbital Laplace transformed second-order M?ller-Plesset (AO-LT-MP2) method for periodic systems is reported using the resolution of identity (RI) technique. Transformation of the two-electron integrals constitutes the main computational bottleneck of the AO-LT-MP2 method. A substitution of regular four-center integrals by their three center counterparts in the RI approximation naturally reduces the computational cost of the integral transformation step. The RI divergence problem in the presence of periodic boundary conditions is solved in our implementation by restricting the fitting domain. Accuracy and computational efficiency of the RI-AO-LT-MP2 approach are assessed on a set of one-dimensional test systems: trans-polyacetylene and anti-transoid polymethineimine.     

Knowledge-based probabilistic representations of branching ratios in chemical networks: the case of dissociative recombinations

Experimental data about branching ratios for the products of dissociative recombination of polyatomic ions are presently the unique information source available to modelers of natural or laboratory chemical plasmas. Yet, because of limitations in the measurement techniques, data for many ions are incomplete. In particular, the repartition of hydrogen atoms among the fragments of hydrocarbons ions is often not available. A consequence is that proper implementation of dissociative recombination processes in chemical models is difficult, and many models ignore invaluable data. We propose a novel probabilistic approach based on Dirichlet-type distributions, enabling modelers to fully account for the available information. As an application, we consider the production rate of radicals through dissociative recombination in an ionospheric chemistry model of Titan, the largest moon of Saturn. We show how the complete scheme of dissociative recombination products derived with our method dramatically affects these rates in comparison with the simplistic H-loss mechanism implemented by default in all recent models.     

Examining the accuracy of ideal adsorbed solution theory without curve-fitting using transition matrix Monte Carlo simulations

Ideal adsorbed solution theory (IAST) is a well-known approach to predicting multicomponent adsorption isotherms in microporous materials from experimental or simulation data for single-component adsorption. A limitation in practical applications of IAST is that useful calculations often require extrapolation of fitted single-component isotherms beyond the range for which data are available. We introduce a molecular simulation approach in which the intrinsic accuracy of IAST can be examined in a context that avoids any need to perform curve fitting with single-component data. Our approach is based on using transition matrix Monte Carlo to define single-component adsorption isotherms for arbitrary bulk-phase pressures from a single simulation. We apply our approach to several light gas mixtures in silica zeolites and a carbon nanotube to examine the intrinsic accuracy of IAST for these model systems.     

Analytical resolution of the reaction rates of flavylium network by Laplace transform

A complete resolution of time evolution for all species of flavylium chemical reactions network in acidic to neutral media was obtained applying Laplace transform methods, Vieta’s formulae and the general partial fraction theorem. Analyses of particular systems under direct pH-jump, reverse pH-jump, stopped flow and flash photolysis experiments have been performed. The deduced formulas cover all possibilities of flavylium and anthocyanins compounds—with or without quinoidal base and with or without cis–trans isomerization barrier. The expressions for the observed rate constants in different type of experiments are quite similar. This allows creation of global procedure, based on fitting of one single set of expressions with data-set from different experiments. The mathematical approach allows easy and versatile programming.     

Direct Evaluation of Partial Molar Volumes of Binary Solutions of Dimethyl Sulfoxide with Ethyl Acrylate,Butyl Acrylate,Methyl Methacrylate and Styrene

The Tikhonov regularization is applied to convert specific molar volume data of binary solutions of dimethyl sulfoxide with a number of acrylates and with styrene into their second- and first-partial derivatives with respect to mole fraction under constant temperature and pressure. Generalized Cross Validation is used to guide the selection of the regularization parameter that keeps noise amplification under control. The resulting first derivative is then used to compute the partial molar volumes. These are compared against that obtained by the traditional method of least-squares fitting of excess molar volumes. Some of the advantages of the current approach and possible extension to other partial molar quantities are briefly discussed.     

The energy pump and the origin of the non-equilibrium flux of the dynamical systems and the networks

The global stability of dynamical systems and networks is still challenging to study. We developed a landscape and flux framework to explore the global stability. The potential landscape is directly linked to the steady state probability distribution of the non-equilibrium dynamical systems which can be used to study the global stability. The steady state probability flux together with the landscape gradient determines the dynamics of the system. The non-zero probability flux implies the breaking down of the detailed balance which is a quantitative signature of the systems being in non-equilibrium states. We investigated the dynamics of several systems from monostability to limit cycle and explored the microscopic origin of the probability flux. We discovered that the origin of the probability flux is due to the non-equilibrium conditions on the concentrations resulting energy input acting like non-equilibrium pump or battery to the system. Another interesting behavior we uncovered is that the probabilistic flux is closely related to the steady state deterministic chemical flux. For the monostable model of the kinetic cycle, the analytical expression of the probabilistic flux is directly related to the deterministic flux, and the later is directly generated by the chemical potential difference from the adenosine triphosphate (ATP) hydrolysis. For the limit cycle of the reversible Schnakenberg model, we also show that the probabilistic flux is correlated to the chemical driving force, as well as the deterministic effective flux. Furthermore, we study the phase coherence of the stochastic oscillation against the energy pump, and argue that larger non-equilibrium pump results faster flux and higher coherence. This leads to higher robustness of the biological oscillations. We also uncovered how fluctuations influence the coherence of the oscillations in two steps: (1) The mild fluctuations influence the coherence of the system mainly through the probability flux while maintaining the regular landscape topography. (2) The larger fluctuations lead to flat landscape and the complete loss of the stability of the whole system.     

Rigorous integral screening for electron correlation methods

We derive rigorous multipole-based integral estimates (MBIE) in order to account for the distance dependence occurring in atomic-orbital (AO) formulations of electron correlation theory, where our focus is on AO-MP2 theory within a Laplace scheme. We find for the exact transformed integral products an extremely early onset of a linear-scaling behavior and a very small number of significant products. To preselect the significant integral products we adapt our MBIE method as rigorous upper bound. In this way it is possible to exploit the favorable scaling behavior observed and to reduce the scaling of estimated products asymptotically to linear, without sacrificing accuracy or reliability. By separating Coulomb- and exchange-type contractions only half-transformed integrals need to be computed. Furthermore, our scheme of rigorously preselecting transformed integral products via MBIE seems to offer particularly interesting perspectives for a direct formation of half- or fully transformed integrals by using multipole expansions and auxiliary basis sets.     

Predicting mixture phase equilibria and critical behavior using the SAFT-VRX approach

The SAFT-VRX equation of state combines the SAFT-VR equation with a crossover function that smoothly transforms the classical equation into a nonanalytical form close to the critical point. By a combinination of the accuracy of the SAFT-VR approach away from the critical region with the asymptotic scaling behavior seen at the critical point of real fluids, the SAFT-VRX equation can accurately describe the global fluid phase diagram. In previous work, we demonstrated that the SAFT-VRX equation very accurately describes the pvT and phase behavior of both nonassociating and associating pure fluids, with a minimum of fitting to experimental data. Here, we present a generalized SAFT-VRX equation of state for binary mixtures that is found to accurately predict the vapor-liquid equilibrium and pvT behavior of the systems studied. In particular, we examine binary mixtures of n-alkanes and carbon dioxide + n-alkanes. The SAFT-VRX equation accurately describes not only the gas-liquid critical locus for these systems but also the vapor-liquid equilibrium phase diagrams and thermal properties in single-phase regions.     

High‐resolution peak analysis in TOF SIMS data

High mass resolution time‐of‐flight secondary ion mass spectrometry (TOF SIMS) can provide a wealth of chemical information about a sample, but the analysis of such data is complicated by detector dead‐time effects that lead to systematic shifts in peak shapes, positions, and intensities. We introduce a new maximum‐likelihood analysis that incorporates the detector behavior in the likelihood function, such that a parametric spectrum model can be fit directly to as‐measured data. In numerical testing, this approach is shown to be the most precise and lowest‐bias option when compared with both weighted and unweighted least‐squares fitting of data corrected for dead‐time effects. Unweighted least‐squares analysis is the next best, while weighted least‐squares suffers from significant bias when the number of pulses used is small. We also provide best‐case estimates of the achievable precision in fitting TOF SIMS peak positions and intensities and investigate the biases introduced by ignoring background intensity and by fitting to just the intense part of a peak. We apply the maximum‐likelihood method to fit two experimental data sets: a positive‐ion spectrum from a multilayer MoS₂ sample and a positive‐ion spectrum from a TiZrNi bulk metallic glass sample. The precision of extracted isotope masses and relative abundances obtained is close to the best‐case predictions from the numerical simulations despite the use of inexact peak shape functions and other approximations. Implications for instrument calibration, incorporation of prior information about the sample, and extension of this approach to the analysis of imaging data are also discussed.