Split-charge Equilibration Research Articles

Dissipative split-charge formalism: Ohm's law, Nyquist noise, and non-contact friction.

The split-charge equilibration method is extended to describe dissipative charge transfer similarly as the Drude model, whereby the complex-valued frequency-dependent dielectric permittivities or conductivities of dielectrics and metals can be mimicked at non-zero frequencies. To demonstrate its feasibility, a resistor-capacitor circuit is simulated using an all-atom representation for the resistor and capacitor. The dynamics reproduce the expected charging process and Nyquist noise, the latter resulting from the thermal voltages acting on individual split charges. The method bears promise to model friction caused by the motion of charged particles past metallic or highly polarizable media.

Generalized Method for Charge-Transfer Equilibration in Reactive Molecular Dynamics.

Variable charge models (e.g., electronegativity equalization method (EEM), charge equilibration (QEq), electrostatic plus (ES+)) used in reactive molecular dynamics simulations often inherently impose a global charge transfer between atoms (approximating each system as an ideal metal). Consequently, most surface processes (e.g., adsorption, desorption, deposition, sputtering) are affected, potentially causing dubious dynamics. This issue has been addressed by certain split charge variants (i.e., split charge equilibration (SQE), redoxSQE) through a distance-dependent bond hardness, by the atomic charge ACKS2 and QTPIE models, which are based on the Kohn-Sham density functional theory, as well as by an electronegativity screening extension to the QEq model (approximating each system as an ideal insulator). In a brief review of the QEq and the QTPIE model, their applicability for studying surface interactions is assessed in this work. Following this evaluation, a revised generalization of the QEq and QTPIE models is proposed and formulated, called the charge-transfer equilibration model or in short the QTE model. This method is based on the equilibration of charge-transfer variables, which locally constrain the split charge transfer per unit time (i.e., due to overlapping orbitals) without any kind of bond hardness specification. Furthermore, a formalism relying solely on atomic charges is obtained by a respective transformation, employing an extended Lagrangian method. We moreover propose a mirror boundary condition and its implementation to accelerate surface investigations. The models proposed in this work facilitate reactive molecular dynamics simulations, which describe various materials and surface phenomena appropriately.

Optimized SQE atomic charges for peptides accessible via a web application

BackgroundPartial atomic charges find many applications in computational chemistry, chemoinformatics, bioinformatics, and nanoscience. Currently, frequently used methods for charge calculation are the Electronegativity Equalization Method (EEM), Charge Equilibration method (QEq), and Extended QEq (EQeq). They all are fast, even for large molecules, but require empirical parameters. However, even these advanced methods have limitations—e.g., their application for peptides, proteins, and other macromolecules is problematic. An empirical charge calculation method that is promising for peptides and other macromolecular systems is the Split-charge Equilibration method (SQE) and its extension SQE+q0. Unfortunately, only one parameter set is available for these methods, and their implementation is not easily accessible.ResultsIn this article, we present for the first time an optimized guided minimization method (optGM) for the fast parameterization of empirical charge calculation methods and compare it with the currently available guided minimization (GDMIN) method. Then, we introduce a further extension to SQE, SQE+qp, adapted for peptide datasets, and compare it with the common approaches EEM, QEq EQeq, SQE, and SQE+q0. Finally, we integrate SQE and SQE+qp into the web application Atomic Charge Calculator II (ACC II), including several parameter sets.ConclusionThe main contribution of the article is that it makes SQE methods with their parameters accessible to the users via the ACC II web application (https://acc2.ncbr.muni.cz) and also via a command-line application. Furthermore, our improvement, SQE+qp, provides an excellent solution for peptide datasets. Additionally, optGM provides comparable parameters to GDMIN in a markedly shorter time. Therefore, optGM allows us to perform parameterizations for charge calculation methods with more parameters (e.g., SQE and its extensions) using large datasets.Graphic

Improved general-purpose five-point model for water: TIP5P/2018.

A new five point potential for liquid water, TIP5P/2018, is presented along with the techniques used to derive its charges from ab initio per-molecule electrostatic potentials in the liquid phase using the split charge equilibration of Nistor et al. [J. Chem. Phys. 125, 094108 (2006)]. By taking the density and diffusion dependence on temperature as target properties, significant improvements to the behavior of isothermal compressibility were achieved along with improvements to other thermodynamic and rotational properties. While exhibiting a dipole moment close to ab initio values, TIP5P/2018 suffers from a too small quadrupole moment due to the charge assignment procedure and results in an overestimation of the dielectric constant.

A New Split Charge Equilibration Model and REPEAT Electrostatic Potential Fitted Charges for Periodic Frameworks with a Net Charge.

Periodic frameworks that possess a net charge, such as zeolites, are an important class of materials in wide use. For guest-host interactions to be simulated in these materials, partial atomic charges are often used. In this work, we investigate two methods for the generation of partial atomic charges in periodic systems having a net framework charge. We first examine the validity of generating REPEAT electrostatic potential fitted charges derived from periodic electronic structure calculations, where a constant background charge is added to neutralize the net charge on the framework. The constant background charge obviates the need to add neutralizing counterions, which may induce artifacts such as polarization in the infinite periodic system. The second method we explore is the split charge equilibration (SQE) method for the rapid generation of partial atomic charges. The original formulation of the SQE method cannot be applied to systems with a net charge. In this work, we reformulate the SQE method by transforming the split charges into an atomic charge basis that allows for non-neutral systems to be treated. The new SQE model, which we call SQEAB (for atomic basis), was validated with a series of tests using both charged and neutral metal organic frameworks and zeolites. It was shown that SQEAB gives equivalent results to those of the original SQE model for neutral systems. We then demonstrated that the SQEAB method is able to "capture" the chemical structure of a charged framework better than that of the charge equilibration model by comparing to REPEAT electrostatic potential fitted charges.

Split-Charge Equilibration Parameters for Generating Rapid Partial Atomic Charges in Metal–Organic Frameworks and Porous Polymer Networks for High-Throughput Screening

The split-charge equilibration (SQE) method was parametrized to reproduce the quantum mechanical, electrostatic potential (ESP) in an atomistically and topologically diverse training set of 559 metal–organic frameworks (MOFs) and 45 porous polymer networks (PPNs). The training set contained a total of 17 elements and 31 unique element–element bonds, 13 inorganic SBUs, 101 organic SBUs, and 30 functional groups. The split-charge equilibration MOF electrostatic-potential-optimized, or SQE-MEPO, method was validated against a set of 585 (520 MOFs and 65 PPNs) that were not part of the training set by comparing the derived ESP to the quantum mechanical ESP and comparing the computed CO2 uptakes and heats of adsorption at both low (0.15 bar) and high pressures (10 bar). For this large validation set, the SQE-MEPO ESP deviated from the QM ESP by 30% less than other parametrized charge determination methods with a mean absolute deviation (MAD) of 6.47 mHartree compared to the next closest method with a MAD of 9....

Assessment of split-charge equilibration model for development of polarizable force fields

Performance of split-charge equilibration model (SQE) for force field development was tested by computing static and response characteristics of water clusters. Results of the study show that SQE yields reliable results for the molecular electrostatic potential, dipole, and polarizability of clusters of increasing size. Intermolecular charge transfer needs to be considered for hydrogen bonded systems in order to accurately reproduce the dipole versus system size behavior. It was found that the model quantitatively mimics the IR intensities of intermolecular vibrational modes, but fails in the computation of the IR and Raman intensities of intramolecular vibrations. The response of charge distribution to perturbation by point charge is confidently modeled by SQE in the conditions corresponding to the linear-response regime.

Redox reactions with empirical potentials: Atomistic battery discharge simulations

Batteries are pivotal components in overcoming some of today's greatest technological challenges. Yet to date there is no self-consistent atomistic description of a complete battery. We take first steps toward modeling of a battery as a whole microscopically. Our focus lies on phenomena occurring at the electrode-electrolyte interface which are not easily studied with other methods. We use the redox split-charge equilibration (redoxSQE) method that assigns a discrete ionization state to each atom. Along with exchanging partial charges across bonds, atoms can swap integer charges. With redoxSQE we study the discharge behavior of a nano-battery, and demonstrate that this reproduces the generic properties of a macroscopic battery qualitatively. Examples are the dependence of the battery's capacity on temperature and discharge rate, as well as performance degradation upon recharge.

Towards time-dependent, non-equilibrium charge-transfer force fields

Force fields uniquely assign interatomic forces for a given set of atomic coordinates. The underlying assumption is that electrons are in their quantum-mechanical ground state or in thermal equilibrium. However, there is an abundance of cases where this is unjustified because the system is only locally in equilibrium. In particular, the fractional charges of atoms, clusters, or solids tend to not only depend on atomic positions but also on how the system reached its state. For example, the charge of an isolated solid -- and thus the forces between atoms in that solid -- usually depends on the counterbody with which it has last formed contact. Similarly, the charge of an atom, resulting from the dissociation of a molecule, can differ for different solvents in which the dissociation took place. In this paper we demonstrate that such charge-transfer history effects can be accounted for by assigning discrete oxidation states to atoms. With our method, an atom can donate an integer charge to another, nearby atom to change its oxidation state as in a redox reaction. In addition to integer charges, atoms can exchange "partial charges" which are determined with the split charge equilibration method.

Bond-order potentials with split-charge equilibration: Application to C-, H-, and O-containing systems

A method for extending charge transfer to bond-order potentials, known as the bond-order potential/split-charge equilibration (BOP/SQE) method [P. T. Mikulski, M. T. Knippenberg, and J. A. Harrison, J. Chem. Phys. 131, 241105 (2009)], is integrated into a new bond-order potential for interactions between oxygen, carbon, and hydrogen. This reactive potential utilizes the formalism of the adaptive intermolecular reactive empirical bond-order potential [S. J. Stuart, A. B. Tutein, and J. A. Harrison, J. Chem. Phys. 112, 6472 (2000)] with additional terms for oxygen and charge interactions. This implementation of the reactive potential is able to model chemical reactions where partial charges change in gas- and condensed-phase systems containing oxygen, carbon, and hydrogen. The BOP/SQE method prevents the unrestricted growth of charges, often observed in charge equilibration methods, without adding significant computational time, because it makes use of a quantity which is calculated as part of the underlying covalent portion of the potential, namely, the bond order. The implementation of this method with the qAIREBO potential is designed to provide a tool that can be used to model dynamics in a wide range of systems without significant computational cost. To demonstrate the usefulness and flexibility of this potential, heats of formation for isolated molecules, radial distribution functions of liquids, and energies of oxygenated diamond surfaces are calculated.

The chemical hardness of molecules and the band gap of solids within charge equilibration formalisms

This work finds that different charge equilibration methods lead to qualitatively different responses of molecules and solids to an excess charge. The investigated approaches are the regular charge equilibration (QE), the atom-atom-charge transfer (AACT), and the split-charge equilibration (SQE) method. In QE, the hardness of molecules and the band gap of solids approaches zero at large particle numbers, affirming the claim that QE induces metallic behavior. AACT suffers from producing negative values of the hardness; moreover valence and conduction bands of solids cross. In contrast to these methods, SQE can reproduce the generic behavior of dielectric molecules or solids. Moreover, first quantitative results for the NaCl molecule are promising. The results derived in this work may have beneficial implications for the modeling of redox reactions. They reveal that by introducing formal oxidation states into force field-based simulations it will become possible to simulate redox reactions including non-equilibrium contact electrification, voltage-driven charging of galvanic cells, and the formation of zwitterionic molecules.

Assessment of Atomic Charge Models for Gas-Phase Computations on Polypeptides.

The concept of the atomic charge is extensively used to model the electrostatic properties of proteins. Atomic charges are not only the basis for the electrostatic energy term in biomolecular force fields but are also derived from quantum mechanical computations on protein fragments to get more insight into their electronic structure. Unfortunately there are many atomic charge schemes which lead to significantly different results, and it is not trivial to determine which scheme is most suitable for biomolecular studies. Therefore, we present an extensive methodological benchmark using a selection of atomic charge schemes [Mulliken, natural, restrained electrostatic potential, Hirshfeld-I, electronegativity equalization method (EEM), and split-charge equilibration (SQE)] applied to two sets of penta-alanine conformers. Our analysis clearly shows that Hirshfeld-I charges offer the best compromise between transferability (robustness with respect to conformational changes) and the ability to reproduce electrostatic properties of the penta-alanine. The benchmark also considers two charge equilibration models (EEM and SQE), which both clearly fail to describe the locally charged moieties in the zwitterionic form of penta-alanine. This issue is analyzed in detail because charge equilibration models are computationally much more attractive than the Hirshfeld-I scheme. Based on the latter analysis, a straightforward extension of the SQE model is proposed, SQE+Q(0), that is suitable to describe biological systems bearing many locally charged functional groups.

Computation of Charge Distribution and Electrostatic Potential in Silicates with the Use of Chemical Potential Equalization Models

New parameters for the electronegativity equalization model (EEM) and the split-charge equilibration (SQE) model are calibrated for silicate materials, based on an extensive training set of representative isolated systems. In total, four calibrations are carried out, two for each model, either using iterative Hirshfeld (HI) charges or ESP grid data computed with density functional theory (DFT) as a reference. Both the static (ground state) reference quantities and their responses to uniform electric fields are included in the fitting procedure. The EEM model fails to describe the response data, whereas the SQE model quantitatively reproduces all of the training data. For the ESP-based parameters, we found that the reference ESP data are only useful at those grid points where the electron density is lower than 10–3 a.u. The density value correlates with a distance criterion used for selecting grid points in common ESP fitting schemes. All parameters are validated with DFT computations on an independent set...

The Significance of Parameters in Charge Equilibration Models.

Charge equilibration models such as the electronegativity equalization method (EEM) and the split charge equilibration (SQE) are extensively used in the literature for the efficient computation of accurate atomic charges in molecules. However, there is no consensus on a generic set of optimal parameters, even when one only considers parameters calibrated against atomic charges in organic molecules. In this work, the origin of the disagreement in the parameters is investigated by comparing and analyzing six sets of parameters based on two sets of molecules and three calibration procedures. The resulting statistical analysis clearly indicates that the conventional least-squares cost function based solely on atomic charges is in general ill-conditioned and not capable of fixing all parameters in a charge-equilibration model. Methodological guidelines are formulated to improve the stability of the parameters. Although in this case a simple interpretation of individual parameters is not possible, charge equilibration models remain of great practical use for the computation of atomic charges.

Merging bond-order potentials with charge equilibration

A method is presented for extending any bond-order potential (BOP) to include charge transfer between atoms through a modification of the split-charge equilibration (SQE) formalism. Variable limits on the maximum allowed charge transfer between atomic pairs are defined by mapping bond order to an amount of shared charge in each bond. Charge transfer is interpreted as an asymmetry in how the shared charge is distributed between the atoms of the bond. Charge equilibration (QE) assesses the asymmetry of the shared charge, while the BOP converts this asymmetry to the actual amount of charge transferred. When applied to large molecules, this BOP/SQE method does not exhibit the unrealistic growth of charges that is often associated with QE models.

The electronegativity equalization method and the split charge equilibration applied to organic systems: Parametrization, validation, and comparison

An extensive benchmark of the electronegativity equalization method (EEM) and the split charge equilibration (SQE) model on a very diverse set of organic molecules is presented. These models efficiently compute atomic partial charges and are used in the development of polarizable force fields. The predicted partial charges that depend on empirical parameters are calibrated to reproduce results from quantum mechanical calculations. Recently, SQE is presented as an extension of the EEM to obtain the correct size dependence of the molecular polarizability. In this work, 12 parametrization protocols are applied to each model and the optimal parameters are benchmarked systematically. The training data for the empirical parameters comprise of MP2/Aug-CC-pVDZ calculations on 500 organic molecules containing the elements H, C, N, O, F, S, Cl, and Br. These molecules have been selected by an ingenious and autonomous protocol from an initial set of almost 500,000 small organic molecules. It is clear that the SQE model outperforms the EEM in all benchmark assessments. When using Hirshfeld-I charges for the calibration, the SQE model optimally reproduces the molecular electrostatic potential from the ab initio calculations. Applications on chain molecules, i.e., alkanes, alkenes, and alpha alanine helices, confirm that the EEM gives rise to a divergent behavior for the polarizability, while the SQE model shows the correct trends. We conclude that the SQE model is an essential component of a polarizable force field, showing several advantages over the original EEM.

Dielectric properties of solids in the regular and split-charge equilibration formalisms

We investigate the generic dielectric properties of solids in the split-charge equilibration (SQE) formalism, which contains the regular charge equilibration (QE) method as a limiting case, but augments it with a bond hardness term. It is shown that QE always mimics ideal conductors, while any positive bond hardness used in SQE turns the solid into a dielectric. Crystals with simple cubic and rocksalt structure are considered explicitly. For these symmetries, we solve the continuum limit of the SQE formalism analytically. As a result, we provide simple analytical expressions for how dielectric constant and penetration depth of the electrostatic field depend on atomic hardness, bond hardness, and lattice constant. This mapping may prove useful not only for force field parametrization but also for solving dielectric responses on coarse-grained scales. Successful comparison of numerical data to analytical solutions is made, including those containing discretization corrections.

Origin and control of superlinear polarizability scaling in chemical potential equalization methods

Many common chemical potential equalization (muEq) methods are known to suffer from a superlinear scaling of the polarizability with increasing molecular size that interferes with model transferability and prevents the straightforward application of these methods to large, biochemically relevant molecules. In the present work, we systematically investigate the origins of this scaling and the mechanisms whereby some existing methods successfully temper the scaling. We demonstrate several types of topological charge constraints distinct from the usual single molecular charge constraint that can successfully achieve linear polarizability scaling in atomic charge based equilibration models. We find the use of recently employed charge conservation constraints tied to small molecular units to be an effective and practical approach for modulating the polarizability scaling in atomic muEq schemes. We also analyze the scaling behavior of several muEq schemes in the bond representation and derive closed-form expressions for the polarizability scaling in a linear atomic chain model; for a single molecular charge constraint these expressions demonstrate a cubic dependence of the polarizability on molecular size compared with linear scaling obtainable in the case of the atom-atom charge transfer (AACT) and split-charge equilibration (SQE) schemes. Application of our results to the trans N-alkane series reveals that in certain situations, the AACT and SQE schemes can become unstable due to an indefinite Hessian matrix. Consequently, we discuss sufficient criteria for ensuring stability within these schemes.

Split charge equilibration method with correct dissociation limits

Analytic reactive potentials rely on electronegativity equalization to describe how the electron distribution is affected as chemical reactions occur. However, such models predict fractional charges for neutral species with different electronegativities. To overcome this well-known dissociation problem, an approach taking advantage of the concept of split charges [R. A. Nistor, J. G. Polihronov, M. H. Muser, and N. J. Mosey, J. Chem. Phys. 125, 094108 (2006)] is put forward. A first implementation is presented. Starting from a previous model [P. Bultinck, W. Langenaeker, P. Lahorte, F. D. Proft, P. Geerlings, M. Waroquier, and J. P. Tollenaere, J. Phys. Chem. A 106, 7887 (2002)], a new contribution to the total energy is introduced in order to make up for the lack of suitable constraints on the charge density. Its effect is to restrain charge transfer between remote atoms. As a consequence, systems in gas phase naturally decompose into neutral fragments. This result is achieved using two empirical parameters in addition to atomic electronegativities and hardnesses.