Determination of the intermolecular potential energy surface for (HCl)2 from vibration--rotation--tunneling spectra

An accurate and detailed semiempirical intermolecular potential energy surface for (HCl)2 has been determined by a direct nonlinear least-squares fit to 33 microwave, far-infrared and near-infrared spectroscopic quantities using the analytical potential model of Bunker et al. [J. Mol. Spectrosc. 146, 200 (l99l)] and a rigorous four-dimensional dynamical method (described in the accompanying paper). The global minimum (De= -692 cm-1) is located near the hydrogen-bonded L-shaped geometry (R=3.746 angstroms, theta1=9 degrees, theta2=89.8 degrees, and phi=180 degrees). The marked influence of anisotropic repulsive forces is evidenced in the radial dependence of the donor-acceptor interchange tunneling pathway. The minimum energy pathway in this low barrier (48 cm-1) process involves a contraction of 0.1 angstroms in the center of mass distance (R) at the C2h symmetry barrier position. The new surface is much more accurate than either the ab initio formulation of Bunker et al. or a previous semiempirical surface [J. Chem. Phys. 78, 6841 (1983)].     

Global optimization using bad derivatives: Derivative-free method for molecular energy minimization

A general method designed to isolate the global minimum of a multidimensional objective function with multiple minima is presented. The algorithm exploits an integral “coarse-graining” transformation of the objective function, U, into a smoothed function with few minima. When the coarse-graining is defined over a cubic neighborhood of length scale ϵ, the exact gradient of the smoothed function, 𝒰_ϵ, is a simple three-point finite difference of U. When ϵ is very large, the gradient of 𝒰_ϵ appears to be a “bad derivative” of U. Because the gradient of 𝒰_ϵ is a simple function of U, minimization on the smoothed surface requires no explicit calculation or differentiation of 𝒰_ϵ. The minimization method is “derivative-free” and may be applied to optimization problems involving functions that are not smooth or differentiable. Generalization to functions in high-dimensional space is straightforward. In the context of molecular conformational optimization, the method may be used to minimize the potential energy or, preferably, to maximize the Boltzmann probability function. The algorithm is applied to conformational optimization of a model potential, Lennard–Jones atomic clusters, and a tetrapeptide. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1445–1455, 1998     

Test of various theories forK-shell ionization by protons

Several theories for inner-shell ionization are tested by comparison with our recently published empirical reference cross-sections. The ECPSSR theory describes the data well except at low velocity where it becomes too high by as much as a factor 5. The recent RPWBA-BC calculation by Chen and Crasemann is excellent at intermediate velocity but only slightly better than ECPSSR at low velocity, since it uses the same Coulomb correction as ECPSSR, and even though it employs better wave functions. The recent SCA calculation by Hansteen et al. is the only one that describes the data within a few percent down to the lowest velocities available. The calculations by Ford et al. for Al are about 25% low. The comparatively simple formula by Montenegro and Sigaud describes the data about as well as ECPSSR, except at high velocities. Calculations by Aashamar, by Manson and by Ford et al. for Ne are about 10–20% low, but not far outside our estimated error. Our cross-sections agree well with the recent empirical fit due to Rosato but less with the fits due to Johansson et al. and Khan et al.     

A simple model for the Slater exchange potential and its performance for solids

A simple local model for the Slater exchange potential is determined by least square fit procedure from Hartree–Fock (HF) atomic data. Since the Slater potential is the exact exchange potential yielding HF electron density from Levy‐Perdew‐Sahni density functional formalism (Levy et al., Phys. Rev. A 1984, 30, 2745), the derived local potential is significantly more negative than the conventional local density approximation. On the set of 22 ionic, covalent and van der Waals solids including strongly correlated transition metal oxides, it has been demonstrated, that this simple model potential is capable of reproducing the band gaps nearly as good as popular meta GGA potentials in close agreement with experimental values.     

CF3CH3 --> HF + CF2CH2: a non-RRKM reaction?

The experimental shock tube data recently reported by Kiefer et al. [J. Phys. Chem. A 2004, 108, 2443-2450] for the title reaction at temperatures between 1600 and 2400 K have been compared to master equation simulations using three models: (a) standard RRKM theory, (b) RRKM theory modified by local random matrix theory, which introduces dynamical corrections arising from slow intramolecular vibrational energy randomization, and (c) an ad hoc empirical non-RRKM model. Only the third model provides a good fit of the Kiefer et al. unimolecular reaction rate data. In separate simulations, all three models accurately reproduce the experimental 300 K chemical activation data of Marcoux and Setser [J. Phys. Chem. 1978, 82, 97-108] when the energy transfer parameters are freely varied to fit the data. When experimental energy transfer parameters for a geometrical isomer (1,1,2-trifluoroethane) are used, the standard RRKM model fits the chemical activation data better than the other models, but if energy transfer in the 1,1,1-trifluoroethane is significantly reduced in comparison to the 1,1,2 isomer, then the empirical ad hoc non-RRKM model also gives a good fit. While the ad hoc empirical non-RRKM model can be made to fit the data, it is not based on theory, and we argue that it is physically unrealistic. We also show that the master equation simulations can mimic the Kiefer et al. vibrational relaxation data, which was the first shock tube observation of double-exponential relaxation. We conclude that, until more data on the trifluoroethanes become available, the current evidence is insufficient to decide with confidence whether non-RRKM effects are important in this reaction, or whether the Kiefer et al. data can be explained in some other way.     

Effect of surfactant on the swelling of polymeric nanoparticles: toward a generalized approach

Tauer et al. (Colloid Polym Sci 278:814–820, 2000) claim that the well-known Morton-Kaizerman-Altier (MKA) equation fails to describe experimental swelling data of polystyrene particles with toluene in the absence of free or adsorbed surfactant. They made modifications to the MKA equation to fit their own data; however, they were not able to fit the MKA data obtained in the presence of surfactant. In this work, based on the modified MKA equation, we propose a new approach to take into account the effect of surfactant on the swelling behavior of polymer latex particles such that with only one set of parameters, it is possible to fit the Tauer et al. data and to predict the MKA data. Comparisons of model against experimental data in presence and absence of surfactant are showed and discussed.     

The prediction of vapor-liquid equilibrium data from heat of mixing data for three non-ideal binary systems

The method of Hanks et al. was used with the heat of mixing data of McFall et al. for 1,3-butadiene + propylene, 1-butene + methyl tert.-butyl ether, and carbon disulfide + methanol to predict the vapor-liquid equilibrium behavior for these systems. The method involves curve-fitting an excess enthalpy model derived from an excess Gibbs energy model by means of the Gibbs-Helmholtz equation to the heat of mixing data, determining the adjustable parameters from this fit, and using the original excess Gibbs function equation to predict the vapor-liquid equilibrium behavior. The predicted vapor-liquid equilibrium values were compared with experimental values and good agreement was found.     

Correlation of Adsorption Equilibrium Data for Water Vapor on F-200 Activated Alumina

Single component adsorption equilibrium data for water vapor on commercially available activated alumina F-200 measured in a previous study (Serbezov, 2003) is correlated by two adsorption isotherm equations, both of which are based on the adsorption potential theory. The first equation is the well known Dubinin-Astakhov (D-A) equation. The second equation is obtained from a methodology proposed by Kotoh et al. (1993). It is referred to as a dual mechanism adsorption potential (DMAP) equation because it is a linear combination of two D-A terms with n = 1 where each term accounts for a specific mechanism of water retention. The D-A equation has two fitting parameters; the DMAP equation has three fitting parameters. The DMAP model provides a better fit for the adsorption data than the D-A model, while neither model describes the desorption data well. Analysis of the DMAP equation parameters shows that most of the water is retained by virtue of capillary condensation. In addition to fitting the experimental data, the heat of adsorption was calculated as function of the relative humidity and adsorbent loading. When capillary condensation is present, the heat of adsorption is only slightly higher than the latent heat of vaporization.     

On the efficiency of VBSCF algorithms,a comment on “An efficient algorithm for energy gradients and orbital optimization in valence bond theory”

We comment on the paper [Song et al., J. Comput. Chem. 2009, 30, 399]. and discuss the efficiency of the orbital optimization and gradient evaluation in the Valence Bond Self Consistent Field (VBSCF) method. We note that Song et al. neglect to properly reference Broer et al., who published an algorithm [Broer and Nieuwpoort, Theor. Chim. Acta 1988, 73, 405] to use a Fock matrix to compute a matrix element between two different determinants, which can be used for an orbital optimization. Further, Song et al. publish a misleading comparison with our VBSCF algorithm [Dijkstra and van Lenthe, J. Chem. Phys. 2000, 113, 2100; van Lenthe et al., Mol. Phys. 1991, 73, 1159] to enable them to favorably compare their algorithm with ours. We give detail timings in terms of different orbital types in the calculation and actual timings for the example cases. © 2012 Wiley Periodicals, Inc.     

Evaluation of laser induced breakdown spectroscopy for multielemental determination in soils under sewage sludge application

Laser induced breakdown spectroscopy (LIBS) is an atomic emission spectroscopy technique for simple, direct and clean analysis, with great application potential in environmental sustainability studies. In a single LIBS spectrum it is possible to obtain qualitative information on the sample composition. However, quantitative analysis requires a reliable model for analytical calibration. Multilayer perceptron (MLP), an artificial neural network, is a multivariate technique that is capable of learning to recognize features from examples. Therefore MLP can be used as a calibration model for analytical determinations. Accordingly, the present study proposes to evaluate the traditional linear fit and MLP models for LIBS calibration, in order to attain a quantitative multielemental method for contaminant determination in soil under sewage sludge application. Two sets of samples, both composed of two kinds of soils were used for calibration and validation, respectively. The analyte concentrations in these samples, used as reference, were determined by a reference analytical method using inductively coupled plasma optical emission spectrometry (ICP OES). The LIBS-MLP was compared to a LIBS-linear fit method. The values determined by LIBS-MLP showed lower prediction errors, correlation above 98% with values determined by ICP OES, higher accuracy and precision, lower limits of detection and great application potential in the analysis of different kinds of soils.     

A nested molecule-independent neural network approach for high-quality potential fits

It is shown that neural networks (NNs) are efficient and effective tools for fitting potential energy surfaces. For H2O, a simple NN approach works very well. To fit surfaces for HOOH and H2CO, we develop a nested neural network technique in which we first fit an approximate NN potential and then use another NN to fit the difference of the true potential and the approximate potential. The root-mean-square error (RMSE) of the H2O surface is 1 cm(-1). For the 6-D HOOH and H2CO surfaces, the nested approach does almost as well attaining a RMSE of 2 cm(-1). The quality of the NN surfaces is verified by calculating vibrational spectra. For all three molecules, most of the low-lying levels are within 1 cm(-1) of the exact results. On the basis of these results, we propose that the nested NN approach be considered a method of choice for both simple potentials, for which it is relatively easy to guess a good fitting function, and complicated (e.g., double well) potentials for which it is much harder to deduce an appropriate fitting function. The number of fitting parameters is only moderately larger for the 6-D than for the 3-D potentials, and for all three molecules, decreasing the desired RMSE increases only slightly the number of required fitting parameters (nodes). NN methods, and in particular the nested approach we propose, should be good universal potential fitting tools.     

The multiscale coarse-graining method. VIII. Multiresolution hierarchical basis functions and basis function selection in the construction of coarse-grained force fields

The multiscale coarse-graining (MS-CG) method is a method for determining the effective potential energy function for a coarse-grained (CG) model of a molecular system using data obtained from molecular dynamics simulation of the corresponding atomically detailed model. The coarse-grained potential obtained using the MS-CG method is a variational approximation for the exact many-body potential of mean force for the coarse-grained sites. Here we propose a new numerical algorithm with noise suppression capabilities and enhanced numerical stability for the solution of the MS-CG variational problem. The new method, which is a variant of the elastic net method [Friedman et al., Ann. Appl. Stat. 1, 302 (2007)], allows us to construct a large basis set, and for each value of a so-called "penalty parameter" the method automatically chooses a subset of the basis that is most important for representing the MS-CG potential. The size of the subset increases as the penalty parameter is decreased. The appropriate value to choose for the penalty parameter is the one that gives a basis set that is large enough to fit the data in the simulation data set without fitting the noise. This procedure provides regularization to mitigate potential numerical problems in the associated linear least squares calculation, and it provides a way to avoid fitting statistical error. We also develop new basis functions that are similar to multiresolution Haar functions and that have the differentiability properties that are appropriate for representing CG potentials. We demonstrate the feasibility of the combined use of the elastic net method and the multiresolution basis functions by performing a variational calculation of the CG potential for a relatively simple system. We develop a method to choose the appropriate value of the penalty parameter to give the optimal basis set. The combined effect of the new basis functions and the regularization provided by the elastic net method opens the possibility of using very large basis sets for complicated CG systems with many interaction potentials without encountering numerical problems in the variational calculation.     

Improved Kinetic Rate Constants for Nylon 6, Nylon 6,6, and Nylon 6/6,6 Copolymer

Nylon 6 and 6,6 literature data are collected over a wide range of water concentrations and temperatures (0 ≤ [W]₀ ≤ 40.8 wt%, 200 ≤ T ≤300 °C) and used to fit parameters in an updated batch reactor model. The resulting copolymerization model uses side reactions to account for the complex influence of water on kinetics and reaction equilibria. The proposed parameter estimates result in a significant improvement in the fit to the data, corresponding to a 73% reduction in the weighted‐least‐squares objective function compared to when the parameters of Arai et al. are used. Copolymerization simulations are conducted at industrially relevant conditions, shedding light on the complex influence of water and on the potential to include waste nylon 6 cyclic dimer in the feedstock. The model and parameter estimates will be helpful in future models of nylon 6/6,6 copolymerization in continuous reactor systems.     

POEM: Parameter Optimization using Ensemble Methods: application to target specific scoring functions

In computational biology processes such as docking, binding, and folding are often described by simplified, empirical models. These models are fitted to physical properties of the process by adjustable parameters. An appropriate choice of these parameters is crucial for the quality of the models. Locating the best choices for the parameters is often is a difficult task, depending on the complexity of the model. We describe a new method and program, POEM (Parameter Optimization using Ensemble Methods), for this task. In POEM we combine the DOE (Design Of Experiment) procedure with ensembles of different regression methods. We apply the method to the optimization of target specific scoring functions in molecular docking. The method consists of an iterative procedure that uses alternate evaluation and prediction steps. During each cycle of optimization we fit an approximate function to a defined loss function landscape and improve the quality of this fit from cycle to cycle by constantly augmenting our data set. As test applications we fitted the FlexX and Screenscore scoring functions to the kinase and ATPase protein classes. The results are promising: Starting from random parameters we are able to locate parameter sets which show superior performance compared to the original values. The POEM approach converges quickly and the approximated loss function landscapes are smooth, thus making the approach a suitable method for optimizations on rugged landscapes.     

Application of the CPA equation of state to reservoir fluids in presence of water and polar chemicals

The complex phase equilibrium between reservoir fluids and associating compounds like water, methanol and glycols has become more and more important as the increasing global energy demand pushes the oil industry to target reservoirs with extreme or complicated conditions, such as deep or offshore reservoirs. Conventional equation of state (EoS) with classical mixing rules cannot satisfactorily predict or even correlate the phase equilibrium of those systems. A promising model for such systems is the Cubic-Plus-Association (CPA) EoS, which has been successfully applied to well-defined systems containing associating compounds. In this work, a set of correlations was proposed to calculate the CPA model parameters for the narrow cuts in ill-defined C₇₊ fractions. The correlations were then combined with either the characterization method of Pedersen et al. or that of Whitson et al. to extend CPA to reservoir fluids in presence of water and polar chemical such as methanol and monoethylene glycol. With a minimum number of adjustable parameters from binary pairs, satisfactory results have been obtained for different types of phase equilibria in reservoir fluid systems and several relevant model multicomponent systems. In addition, modeling of mutual solubility between light hydrocarbons and water is also addressed.     

Modified Morse potential for unification of the pair interactions

We designed a novel model potential that unifies the pair interactions including the well known Morse and Lennard-Jones potentials. Using two parameters, the interactions at the minimum, short range, and long range of the new model potential can be controlled separately, so the potential is very flexible to fit various systems. It is found that for potentials with similar range with the Lennard-Jones potential at the minimum, due to the difference at the short and long ranges, the favorite structures can be very different, and some previously unknown magic numbers are located.     

Use of the Yukawa fluid as the reference system in perturbation theory

The Weeks-Chandler-Anderson (WCA) perturbation theory is studied utilising recent results for the Yukawa model fluid. Replacing the attractive tail of the Lennard-Jones potential with a Yukawa tail, where the Yukawa parameters are chosen using a least squares fit, it is shown that accurates field dstribution functions can be generated via the EXP approximation of the WCA optimized cluster theory. The comparative case and accuracy with which the correlation functions for the Yukawa fluid can be compared render this a very useful method for studying the equilibrium properties of simple liquids.     

Atomic multipoles: Electrostatic potential fit,local reference axis systems,and conformational dependence

Currently, all standard force fields for biomolecular simulations use point charges to model intermolecular electrostatic interactions. This is a fast and simple approach but has deficiencies when the electrostatic potential (ESP) is compared to that from ab initio methods. Here, we show how atomic multipoles can be rigorously implemented into common biomolecular force fields. For this, a comprehensive set of local reference axis systems is introduced, which represents a universal solution for treating atom‐centered multipoles for all small organic molecules and proteins. Furthermore, we introduce a new method for fitting atomic multipole moments to the quantum mechanically derived ESP. This methods yields a 50–90% error reduction compared to both point charges fit to the ESP and multipoles directly calculated from the ab initio electron density. It is shown that it is necessary to directly fit the multipole moments of conformational ensembles to the ESP. Ignoring the conformational dependence or averaging over parameters from different conformations dramatically deteriorates the results obtained with atomic multipole moments, rendering multipoles worse than partial charges. © 2012 Wiley Periodicals, Inc.     

Hybrid of Two Heuristic Optimizations with LSSVM to Predict Refractive Index as Asphaltene Stability Identifier

Asphaltene precipitation is a big challenge in the petroleum industry. This motivated us to develop a reliable model between refractive index and SARA fraction as a tool for the diagnosis of asphaltene stability. Least-square support vector machine (LSSVM), due to its several unique advantages, has been successfully verified as a predicting method in recent years. However, the success of LSSVMs depends on the adequate choice of the kernel and regularization parameters. We proposed the combination of two search algorithms to deal with the problem of support vector machine parameter selection. On this basis, we combined coupled simulated annealing (CSA) and the Nelder and Mead Simplex method to optimize the parameters. In this hybrid optimization, first, CSA finds suitable starting values and these are passed to the simplex method in order to tune the result. The LSSVM results are promising and accurate, and outperform both neural network and empirical models existing in literature.