FQ Model Research Articles

Parameterization of a Fluctuating Charge Model for Complexes Containing 3d Transition Metals.

Metalloproteins widely exist in biology, playing pivotal roles in diverse life processes. Meanwhile, molecular dynamics (MD) simulations based on classical force fields has emerged as an important tool in scientific research. Partial charges are critical parameters within classical force fields and usually derived from quantum mechanical (QM) calculations. However, QM calculations are often time-consuming and prone to basis set dependence. Alternatively, fluctuating charge (FQ) models offer another avenue for partial charge derivation, which has significant speed advantages and can be used for large-scale screening. Building upon our previous work, which introduced an FQ model for zinc-containing complexes, herein we extend this model to include additional 3d transition metals which are important to the life sciences, namely chromium, manganese, iron, cobalt, and nickel. Employing CM5 charges as target for parametrization, our FQ model accurately reproduces partial charges for 3d metal complexes featuring biologically relevant ligands. Furthermore, by using atomic charges derived by our FQ model, MD simulations have been performed. These charges showed excellent performance in simulating proteomic metal sites housing multiple metal ions, specifically, a metalloprotein containing an iron-sulfur cluster and another containing a dimanganese metal site, showcasing comparable performance to those of RESP charges. We anticipate that our study can accelerate the parametrization of atomic charges for metalloproteins featuring 3d transition metals, thereby facilitating simulations of relevant systems.

Nonzero spatial curvature in symmetric teleparallel cosmology

We consider the symmetric teleparallel fQ-gravity in Friedmann–Lemaître–Robertson–Walker cosmology with nonzero spatial curvature. For a nonlinear fQ model there exist always the limit of General Relativity with or without the cosmological constant term. The de Sitter solution is always provided by the theory and for the specific models fAQ≃Qαα−1,fBQ≃Q+f1Qαα−1 and fCQ≃Q+f1QlnQ it was found to be the unique attractor. Consequently small deviations from STGR can solve the flatness problem and lead to a de Sitter expansion without introduce a cosmological constant term. This result is different from that given by the power-law theories for the other two scalar of the trinity of General Relativity. What makes the nonlinear symmetric teleparallel theory to stand out are the new degree of freedom provided by the connection defined in the non-coincidence frame which describes the nonzero spatial curvature.

Electrical resistivity-Compressive strength predictions for normal strength concrete with waste steel slag as a coarse aggregate replacement using various analytical models

Concrete is a composite material that is highly used in construction fields. Steel slag (SS) is a molten liquidmelt of silicates and oxides, is a by-product of the steel-making process, and solidifies upon cooling. It is a complex solution of Silicates and Oxides. From an environmental standpoint and to save the environment and natural resources, steel slag recovery conserves natural resources and frees up space in landfills. Steel slag as waste materials has been used in concrete as a partial replacement with fine (sand) and coarse aggregate (gravel). A total of 338 data points were collected, analyzed, and modeled. The most effective factors affecting the compressive strength (CS) of concrete incorporated with steel slag replacement were considered during the modeling process. The cement content was ranged from 237.35 to 550 kg/m3, curing time 1–180 days, water/cement ratio ranged between 0.3 and 0.872, steel slag content varied between 0 – 1196 kg/m3, fine aggregate content ranged between 175.5 – 1285 kg/m3 and coarse aggregate content (natural aggregate) varied between 0 – 1253.75 kg/m3. Furthermore, 58 data were collected to analyze and model the effect of steel slag on the electrical resistivity (ER) of normal concrete. An Artificial Neural Network (ANN), a Multi Logistic Regression model (MLR), a Full Quadratic model (FQ), and an M5P-tree model were employed in this study to forecast the compressive strength of normal strength concrete (CS ranged between 10 and 55 MPa) with steel slag aggregate replacement, and Full quadratic model was applied to predict the ER of normal concrete (ER varied between 23.98 and 1440 Ω.m). Finally, the correlation between compressive strength and electrical resistivity was investigated through different models. Based on data from the literature, the steel slag content was increased the compressive strength and lowered the ER of concrete. According to statistical tool assessments such as objective function (OBJ), scatter index. Taylar diagram, the ANN model with the lowest root mean square error (RMSE) performed better than the other models in predicting the compressive strength. FQ model as a reliable mathematical model can be applied to forecast the ER of normal concrete due to the high coefficient of determination R2 is 0.91.

Linear response properties of solvated systems: a computational study.

We present a computational study of static and dynamic linear polarizabilities in solution. We use different theoretical approaches to describe solvent effects, ranging from quantum mechanics/molecular mechanics (QM/MM) to quantum embedding approaches. In particular, we consider non-polarizable and polarizable QM/MM methods, the latter based on the fluctuating charge (FQ) force field. In addition, we use a quantum embedding method defined in the context of multilevel Hartree-Fock (MLHF), where the system is divided into active and inactive regions, and combine it with a third layer described by means of the FQ model. The multiscale approaches are then used as reference wave functions for equation-of-motion coupled cluster (EOM-CC) response properties, allowing for the account of electron correlation. The developed models are applied to the calculation of linear response properties of two organic moieties-namely, para-nitroaniline and benzonitrile-in non-aqueous solvents-1,4-dioxane, acetonitrile, and tetrahydrofuran. The computed polarizabilities are then discussed in terms of the physico-chemical solute-solvent interactions described by each method (electrostatic, polarization and Pauli repulsion), and finally compared with the available experimental references.

Combining the Fluctuating Charge Method, Non-Periodic Boundary Conditions and Meta-Dynamics: Aqua Ions as case studies.

We present the current status of development of our code for performing Molecular Dynamics (MD) simulations exploiting a polarizable force field based on the Fluctuating Charge (FQ) method and non-Periodic Boundary Conditions (NPBC). Continuing on the path set in a previous work, we increased the capabilities of the code by implementing a number of new features, including: a non-iterative algorithm for rigid trigonal molecule simulations; two additional temperature coupling schemes; a meta-dynamics based approach for effective free energy evaluations. Although these are well known algorithms, each present in one or more widely used MD packages, they have now been tested, for the first time, in the context of the FQ model coupled with NPBC. As case studies, we considered three aqueous ions of increasing charge, namely Na+, Ca2+ and La3+, at infinite dilution. In particular, by exploiting a computational approach recently proposed by our group and based on the metadynamics technique, we focused on the important role played by solvent polarization on ionic hydration structures, also investigating the free energy landscapes of ion coordination and the water exchange rates. Such an approach, previously tested with standard non-polarizable models, was applied here to evaluate the effects of explicit polarization on water exchange barriers between different solvent coordination structures. Moreover, we have analyzed and discussed in some detail non-linear electrostatic effects arising from solvent polarization while going from a mono- to a di- and trivalent ion.

Development of a Fuzzy-Queue-Based Interval Linear Programming Model for Municipal Solid Waste Management

Abstract In this study, a fuzzy-queue-based interval linear programming (FQ-ILP) model was first developed through introducing FQ model into an ILP framework. The FQ-ILP model can not only address system uncertainties with complex presentations, but also reflect the influence of FQ in decision-making problems. Moreover, it can be used for analyzing various policy scenarios that are associated with different waiting costs, fuzzy waiting times, and different operation costs. The method has been applied to a typical case study area for long-term municipal solid waste management planning. Interval solutions associated with fuzzy arrival rate, fuzzy service rate, and different waiting costs have been generated. They can be further used for generating decision alternatives and thus help waste managers to identify desired policies under various environmental, economic, and fuzzy queuing problems. Compared with the conventional optimization methods, the developed FQ-ILP model can more actually reflect the complex...

Revisiting the hexane-water interface via molecular dynamics simulations using nonadditive alkane-water potentials

We present results addressing properties of a polarizable force field for hexane based on the fluctuating charge (FQ) formalism and developed in conjunction with the Chemistry at Harvard Molecular Mechanics (CHARMM) potential function. Properties of bulk neat hexane, its liquid-vapor interface, and its interface with a polarizable water model (TIP4P-FQ) are discussed. The FQ model is compared to a recently modified alkane model, C27r, also based on the CHARMM potential energy function. With respect to bulk properties, both models predict bulk density within 1%; the FQ model predicts the liquid vaporization enthalpy within 2%, while the C27r force field underestimates the property by roughly 20% (and in this sense reflects the quality of the C27r force field across the spectrum of linear and branched alkanes). The FQ hexane model realistically captures the dielectric properties of the bulk in terms of a dielectric constant of 1.94, in excellent agreement with experimental values in the range of 1.9-2.02. This behavior is also in conformity with a recent polarizable alkane model based on Drude oscillators. Furthermore, the bulk dielectric is essentially captured in the infinite frequency, or optical, dielectric contribution. The FQ model is in this respect a more realistic force field for modeling lipid bilayer interiors for which most current state-of-the-art force fields do not accurately capture the dielectric environment. The molecular polarizability of the FQ model is 11.79 A3, in good agreement with the range of experimental and ab initio values. In contrast to FQ models of polar solvents such as alcohols and water, there was no need to scale gas-phase polarizabilities in order to avoid polarization catastrophes in the pure bulk. In terms of the liquid-vapor and liquid-liquid interfaces, the FQ model displays a rich orientational structure of alkane and water in the respective interfacial systems, in general conforming with earlier simulation studies of such interfaces. The FQ force field shows a marked deviation in the interfacial dipole potentials computed from the charge densities averaged over simulation trajectories. At the liquid-vapor interface, the FQ model predicts a potential drop of -178.71 mV in contrast to the C27r estimate of -433.80 mV. For the hexane-water interface, the FQ force field predicts a dipole potential drop of -379.40 mV in contrast to the C27r value of -105.42 mV. Although the surface dipole potential predicted by the FQ model is roughly 3.5 times that predicted by the C27r potential, it is consistent with reported experimental potentials across solvated lipid bilayers in the range of 400-600 mV.

Structure, thermodynamics, and liquid-vapor equilibrium of ethanol from molecular-dynamics simulations using nonadditive interactions

We present a molecular-dynamics simulation study of the bulk and liquid-vapor interfacial properties of ethanol using a polarizable force field based on the fluctuating charge (FQ) formalism, as well as the nonpolarizable CHARMM22 force field. Both models are competitive with respect to the prediction of ambient liquid properties such as liquid density, enthalpy of vaporization, dielectric constant, and self-diffusion constants. The polarizable model predicts an average condensed-phase dipole moment of 2.2 D associated with an induced liquid-phase dipole moment of 0.6 D; though qualitatively in agreement with earlier nonadditive models as well as recent Car-Parinello calculations, the current FQ model underestimates the condensed-phase dipole moment. In terms of liquid structure, both models are in agreement with recent neutron-diffraction results of liquid ethanol structure, although the polarizable model predicts the hydroxyl-hydrogen-hydroxyl-hydrogen structure factor in closer agreement with the experimental data. In terms of interfacial properties, both models predict ambient surface tension to within 4% of the experimental value of 22.8 dyncm, while overestimating the surface excess entropy by almost a factor of 2. Both models display the characteristic preferential orientation of interfacial molecules. The polarizable model allows for a monotonic variation of the average molecular dipole moment from the bulk value to that of the vapor phase. Consequently, there is a dramatic difference in the surface potential predicted by the polarizable and nonpolarizable models. The polarizable model estimates a surface potential of -209+/-3 mV, while the nonpolarizable model yields a value of -944+/-10 mV. Finally, based on the vapor-liquid equilibrium simulation data from several temperatures, we estimate the critical properties of both models. As observed with other FQ models for associating fluids (such as water and methanol), and counter to what one would anticipate by modeling more physically the electrostatic response to local environment, the current FQ model underestimates the critical temperature and overestimates the critical density of ethanol; moreover, the FQ model is, in this respect, equivalent to the underlying fixed-charge model. These results further suggest the need to revisit polarizable models in terms of quantitative vapor-liquid equilibrium prediction.

CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model.

A fluctuating charge (FQ) force field is applied to molecular dynamics simulations for six small proteins in explicit polarizable solvent represented by the TIP4P-FQ potential. The proteins include 1FSV, 1ENH, 1PGB, 1VII, 1H8K, and 1CRN, representing both helical and beta-sheet secondary structural elements. Constant pressure and temperature (NPT) molecular dynamics simulations are performed on time scales of several nanoseconds, the longest simulations yet reported using explicitly polarizable all-atom empirical potentials (for both solvent and protein) in the condensed phase. In terms of structure, the FQ force field allows deviations from native structure up to 2.5 A (with a range of 1.0 to 2.5 A). This is commensurate to the performance of the CHARMM22 nonpolarizable model and other currently existing polarizable models. Importantly, secondary structural elements maintain native structure in general to within 1 A (both helix and beta-strands), again in good agreement with the nonpolarizable case. In qualitative agreement with QM/MM ab initio dynamics on crambin (Liu et al. Proteins 2001, 44, 484), there is a sequence dependence of average condensed phase atomic charge for all proteins, a dependence one would anticipate considering the differing chemical environments around individual atoms; this is a subtle quantum mechanical feature captured in the FQ model but absent in current state-of-the-art nonpolarizable models. Furthermore, there is a mutual polarization of solvent and protein in the condensed phase. Solvent dipole moment distributions within the first and second solvation shells around the protein display a shift towards higher dipole moments (increases on the order of 0.2-0.3 Debye) relative to the bulk; protein polarization is manifested via the enhanced condensed phase charges of typical polar atoms such as backbone carbonyl oxygens, amide nitrogens, and amide hydrogens. Finally, to enlarge the sample set of proteins, gas-phase minimizations and 1 ps constant temperature simulations are performed on various-sized proteins to compare to earlier work by Kaminsky et al. (J Comp Chem 2002, 23, 1515). The present work establishes the feasibility of applying a fully polarizable force field for protein simulations and demonstrates the approach employed in extending the CHARMM force field to include these effects.

CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations.

A first-generation fluctuating charge (FQ) force field to be ultimately applied for protein simulations is presented. The electrostatic model parameters, the atomic hardnesses, and electronegativities, are parameterized by fitting to DFT-based charge responses of small molecules perturbed by a dipolar probe mimicking a water dipole. The nonbonded parameters for atoms based on the CHARMM atom-typing scheme are determined via simultaneously optimizing vacuum water-solute geometries and energies (for a set of small organic molecules) and condensed phase properties (densities and vaporization enthalpies) for pure bulk liquids. Vacuum solute-water geometries, specifically hydrogen bond distances, are fit to 0.19 A r.m.s. error, while dimerization energies are fit to 0.98 kcal/mol r.m.s. error. Properties of the liquids studied include bulk liquid structure and polarization. The FQ model does indeed show a condensed phase effect in the shifting of molecular dipole moments to higher values relative to the gas phase. The FQ liquids also appear to be more strongly associated, in the case of hydrogen bonding liquids, due to the enhanced dipolar interactions as evidenced by shifts toward lower energies in pair energy distributions. We present results from a short simulation of NMA in bulk TIP4P-FQ water as a step towards simulating solvated peptide/protein systems. As expected, there is a nontrivial dipole moment enhancement of the NMA (although the quantitative accuracy is difficult to assess). Furthermore, the distribution of dipole moments of water molecules in the vicinity of the solutes is shifted towards larger values by 0.1-0.2 Debye in keeping with previously reported work.

Density and Temperature Dependences of Hydration Free Energy of Na+ and Cl- at Supercritical Conditions Predicted by ab Initio/Classical Free Energy Perturbation

The ab initio/classical free energy perturbation (ABC−FEP) method proposed previously by Wood et al. [J. Chem. Phys. 1999, 110, 1329] combines the free energy calculated from a classical simulation of an approximate model with the free energy of perturbing the approximate solute−solvent interactions to ab initio interaction energies. This method was used to calculate the hydration free energies of Na+ and Cl- at a variety of high-temperature state points (973 K with 0.0101, 0.0935, 0.2796 g/cm3 and 723 K with 0.0098, 0.0897, 0.5113 g/cm3). The classical simulations were done with an approximate model, previously derived by fitting ab initio results at 973 K and 0.535 g/cm3. These were followed by perturbation to a QM/MM model in which the interactions of Na+ with H2O and Cl- with H2O are calculated by an ab initio method, while the interactions of H2O with H2O are calculated by the fluctuating charge TIP4P−FQ model. The pairwise ion−water interaction energies are obtained at the MP2/6-311++G(3df,3pd) level and multibody interactions at the B3LYP/6-311++G(3df,3pd) level for Na+ and B3LYP/aug-cc-pVDZ level for Cl-. Estimates of the accuracy of the ab initio methods and of the sampling errors indicate that these results are more reliable than previous predictions and can be used as benchmarks to assess the accuracy of molecular dynamics simulations or empirically parametrized equations of state. Extrapolations using various semiempirical models were not very accurate at the state points studied. The model of Tanger and Pitzer, which interpolates between gas-phase mass spectroscopic results and high-density predictions, was very accurate. Born models failed at the low-density state points, while compressible continuum models were much better. Interpolation or extrapolation of the present results indicates that previous simulations of two different Lennard−Jones plus charge models have substantial errors at most state points. The approximate models used in the present work performed reasonably well at all state points, with differences from the ABC−FEP corrected results ranging from 0 to 22 kJ/mol.

Effects of charge transfer on a-SiO2 surface structure: A molecular dynamics study

The effects of charge transfer between atoms on an amorphous SiO2 surface were studied by comparing a model with fixed charge (FQ) and a model that takes into consideration charge transfer by the charge equilibration (QEq) method. The QEq surface has more oxygen atoms and denser structures compared to the FQ sample. We found, on the surface of the QEq sample, three-coordinated Si with an O–Si–O bond angle in the range of 109–115°. This structure is similar to that of the experimentally observed E′ center (≡Si⋅). We also found a structure similar to the nonbridging oxygen hole center (≡Si–O⋅), which has been observed experimentally on a silica glass surface. These structures were not observed in the FQ model. The results suggest that consideration of the charge transfer is essential to reproduce the defect structure of the silica glass surface.

Simulations of ice and liquid water over a range of temperatures using the fluctuating charge model

The temperature dependence of the thermodynamic and dynamical properties of liquid water using the polarizable fluctuating charge (FQ) model is presented. The properties of ice Ih, both for a perfect lattice with no thermal disorder and at a temperature of 273 K, are also presented. In contrast to nonpolarizable models, the FQ model has a density maximum of water near 277 K. For ice, the model has a dipole moment of the perfect lattice of 3.05 Debye, in good agreement with a recent induction model calculation. The simulations at 273 K and the correct density find that thermal motion decreases the average dipole moment to 2.96 D. The liquid state dipole moment is less than the ice value and decreases with temperature.

Adiabatic Nuclear and Electronic Sampling Monte Carlo Simulations in the Gibbs Ensemble: Application to Polarizable Force Fields for Water

The adiabatic nuclear and electronic sampling Monte Carlo algorithm (ANES-MC) is extended to simulations in the Gibbs ensemble. Whereas the maximum displacements used for translational, rotational, and volume trial moves can be adjusted to foster efficient sampling in the adiabatic limit, the transfer (swap) of particles always causes a major disturbance of the electronic structures of the two phases (supplying and receiving the particle). To reequilibrate the electronic structures requires additional sampling of the electronic degrees of freedom. A simple, distance-dependent criterion for the preferential selection of the electronic degrees of freedom, for which a move is to be attempted, is shown to improve the efficiency of the particle swap move. The ANES-MC algorithm is applied to the polarizable simple point charge-fluctuating charge (SPC−FQ) and transferable intermolecular potential 4 point-fluctuating charge (TIP4P−FQ) models proposed by Rick et al. (J. Chem. Phys. 1994, 101, 6141). For both models simulations were performed using the standard constraint on the neutrality of individual molecules. In addition, for the SPC−FQ model the use of a constraint on the neutrality of an entire phase was investigated, which allows for intermolecular charge transfer. Simulations in the Gibbs ensemble were performed to calculate the vapor−liquid coexistence curves from 323 to 523 K, whereas simulations in the grand canonical ensemble were performed for the near-critical region. Dielectric constants at different state points were calculated from canonical ensemble simulations. Neither the SPC−FQ nor the TIP4P−FQ force fields give a satisfactory description of the vapor−liquid equilibria. In particular, the critical temperature is greatly underestimated by both models. Although intermolecular charge transfer has only a very small influence on the internal energy and the radial distribution functions at ambient conditions and along the coexistence curve, it increases the dielectric constant by approximately 30%.

Fluctuating charge model for polyatomic ionic systems: A test case with diatomic anions

The fluctuating charge (FQ) model proposed by Rick et al. [(J. Chem. Phys. 101, 6141 (1994)] for molecular dynamics (MD) simulation of water is applied to a test case for polyatomic ionic systems. A system resembling alkali cyanide crystals, with two partial charges on the atomic sites of the polarizable anions, is considered. The need for charge fluctuation considerations in such a simple system is demonstrated by ab initio calculations of the partial charges in the cyanide ion with different orientations within a fixed octahedral environment of sodium ions. It is shown that the charge distributions in the crystal obtained with the FQ model are sensitive to changes in the environment in such a way that the anions become more polarizable as the lattice parameter increases. Conversely, the charge distributions shrink with increasing repulsive short-range interactions. Furthermore, a well-known polarization effect, that is, the reduction in the frequencies of longitudinal optic modes of the crystal, is also obtained with the FQ model.

Dynamical Fluctuating Charge Force Fields: The Aqueous Solvation of Amides

The fluctuating charge (FQ) force field, a polarizable potential model in which point charges on atomic sites fluctuate in response to the environment, is applied to the aqueous solvation of acetamide and trans- and cis-N-methylacetamide (NMA). Two parameters are assigned to each kind of atom, corresponding to an electronegativity and a hardness. The FQ model accurately reproduces both the gas-phase and aqueous-phase charge distributions of these molecules and is therefore effective in treating the influence of functional group substitutions, conformation changes, and solvent on the charge distribution. The FQ model does this in a way that is computationally efficient by propagating the charges in time using an extended Lagrangian method. Solvation free energy calculations are done using both an explicit (FQ) solvent and a dielectric continuum solvent. Both solvent models predict a negligible free energy difference between trans- and cis-NMA, in agreement with experimental estimates. The explicit solvent ...