Lewis-inspired representation of dissociable water in clusters and Grotthuss chains

Adventures in interdisciplinary science: a half century at the nexus between chemistry, physics and biology

A look back over five decades of research.

Valence energy correction for electron reactive force field

Reactive force fields (ReaxFF) are a classical method to describe material properties based on a bond-order formalism, that allows bond dissociation and consequently investigations of reactive systems. Semiclassical treatment of electrons was introduced within ReaxFF simulations, better known as electron reactive force fields (eReaxFF), to explicitly treat electrons as spherical Gaussian waves. In the original version of eReaxFF, the electrons and electron-holes can lead to changes in both the bond energy and the Coulomb energy of the system. In the present study, the method was modified to allow an electron to modify the valence energy, therefore, permitting that the electron's presence modifies the three-body interactions, affecting the angle among three atoms. When a reaction path involving electron transfer is more sensitive to the geometric configuration of the molecules, corrections in the angular structure in the presence of electrons become more relevant; in this case, bond dissociation may not be enough to describe a reaction path. Consequently, the application of the extended eReaxFF method developed in this work should provide an improved description of a reaction path. As a first demonstration this semiclassical force field was parametrized for hydrogen and oxygen interactions, including water and water's ions. With the modified methodology both the overall accuracy of the force field but also the description of the angles within the molecules in presence of electrons could be improved.

Modeling Electronic Response Properties with an Explicit-Electron Machine Learning Potential

Explicit-electron force fields introduce electrons or electron pairs as semiclassical particles in force fields or empirical potentials, which are suitable for molecular dynamics simulations. Even though semiclassical electrons are a drastic simplification compared to a quantum-mechanical electronic wave function, they still retain a relatively detailed electronic model compared to conventional polarizable and reactive force fields. The ability of explicit-electron models to describe chemical reactions and electronic response properties has already been demonstrated, yet the description of short-range interactions for a broad range of chemical systems remains challenging. In this work, we present the electron machine learning potential (eMLP), a new explicit electron force field in which the short-range interactions are modeled with machine learning. The electron pair particles will be located at well-defined positions, derived from localized molecular orbitals or Wannier centers, naturally imposing the correct dielectric and piezoelectric behavior of the system. The eMLP is benchmarked on two newly constructed data sets: eQM7, an extension of the QM7 data set for small molecules, and a data set for the crystalline β-glycine. It is shown that the eMLP can predict dipole moments, polarizabilities, and IR-spectra of unseen molecules with high precision. Furthermore, a variety of response properties, for example, stiffness or piezoelectric constants, can be accurately reproduced.

Using C-DFT to develop an e-ReaxFF force field for acetophenone radical anion

Increased electricity usage over the past several decades has accelerated the need for efficient high-voltage power transmission with reliable insulating materials. Cross-linked polyethylene (XLPE) prepared via dicumyl peroxide (DCP) cross-linking has emerged as the insulator of choice for modern power cables. Although DCP cross-linking generates the desired XLPE product in high yield, other by-products are also produced. One such by-product, acetophenone, is particularly intriguing due to its aromaticity and positive electron affinity. In this work, constrained density functional theory (C-DFT) was utilized to develop an e-ReaxFF force field suitable for describing the acetophenone radical anion. Initial parameters were taken from the 2021 Akbarian e-ReaxFF force field, which was developed to describe XLPE chemistry. Then, C-DFT geometry optimizations were performed wherein an excess electron was constrained to each atom of acetophenone. The resulting C-DFT energy values for the various electronic positions were added to the e-ReaxFF training set. Next, an analogous set of structures was energy-minimized using e-ReaxFF, and equilibrium mixture compositions for the two methods were compared at multiple temperatures. Iterative fitting against C-DFT energy data was performed until satisfactory agreement was achieved. To test force field performance, molecular dynamics simulations were performed in e-ReaxFF and the resulting electronic distributions were qualitatively compared to unconstrained-DFT spin density data. By expanding our e-ReaxFF force field for XLPE, namely, adding the capability to describe acetophenone and its interactions with an excess electron, we move one step closer to a comprehensive molecular understanding of XLPE chemistry in a high-voltage power cable.

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.

A Review of Recent Developments in Molecular Dynamics Simulations of the Photoelectrochemical Water Splitting Process

In this review, we provide a short overview of the Molecular Dynamics (MD) method and how it can be used to model the water splitting process in photoelectrochemical hydrogen production. We cover classical non-reactive and reactive MD techniques as well as multiscale extensions combining classical MD with quantum chemical and continuum methods. Selected examples of MD investigations of various aqueous semiconductor interfaces with a special focus on TiO2 are discussed. Finally, we identify gaps in the current state-of-the-art where further developments will be needed for better utilization of MD techniques in the field of water splitting.

Morphological effect of side chain on H3O+ transfer inside polymer electrolyte membranes across polymeric chain via molecular dynamics simulation

Performance and durability of polymer electrolyte membrane are critical to fuel cell quality. As fuel cell vehicles become increasingly popular, membrane fundamentals must be understood in detail. Here, this study used molecular dynamic simulations to explore the morphological effects of perfluorosulfonic acid (PFSA)-based membranes on ionic conductivity. In particular, I developed an intuitive quantitative approach focusing principally on hydronium adsorbing to, and desorbing from, negatively charged sulfonate groups, while conventional ionic conductivity calculations featured the use of mean square displacements that included natural atomic vibrations. The results revealed that shorter side-chains caused more hydroniums to enter the conductive state, associated with higher ion conductivity. In addition, the hydronium path tracking showed that shorter side-chains allowed hydroniums to move among host groups, facilitating chain adsorption, in agreement with a mechanism suggested in earlier studies.

Exchange potentials for semi-classical electrons

Semi-classical electrons offer access to efficient and intuitive simulations of chemical reactions. As for any treatment of fermions, the greatest difficulty is in accounting for anti-symmetry effects. Semi-classical efforts to-date either reference Slater-determinants from ab initio treatments or adopt a heuristic approach inspired by density functional treatments. Here we revisit the problem with a combined approach. We conclude that semi-classical electrons need to reference a non-conventional wave function and find that (1) contrary to earlier suppositions, contributions from the electrostatic terms in the Hamiltonian are of similar magnitude to those from the kinetic terms and (2) the former point to a need to supplement pair potentials with 3-body potentials. The first result explains features of reported heuristic potentials, and the second provides a firm footing for extending the transferability of potentials across a wider range of elements and bonding scenarios.

Restrained Proton Indicator in Combined Quantum-Mechanics/Molecular-Mechanics Dynamics Simulations of Proton Transfer through a Carbon Nanotube

Recently, a collective variable "proton indicator" was purposed for tracking an excess proton solvated in bulk water in molecular dynamics simulations. In this work, we demonstrate the feasibility of utilizing the position of this proton indicator as a reaction coordinate to model an excess proton migrating through a hydrophobic carbon nanotube in combined quantum-mechanics/molecular-mechanics simulations. Our results indicate that applying a harmonic restraint to the proton indicator in the bulk solvent near the nanotube pore entrance leads to the recruitment of water molecules into the pore. This is consistent with an earlier study that employed a multistate empirical valence bond potential and a different representation (center of excess charge) of the proton. We attribute this water recruitment to the delocalized nature of the solvated proton, which prefers to be in high-dielectric bulk solvent. While water recruitment into the pore is considered an artifact in the present simulations (because of the artificially imposed restraint on the proton), if the proton were naturally restrained, it could assist in building water wires prior to proton transfer through the pore. The potential of mean force for a proton translocation through the water-filled pore was computed by umbrella sampling, where the bias potentials were applied to the proton indicator. The free energy curve and barrier heights agree reasonably with those in the literature. The results suggest that the proton indicator can be used as a reaction coordinate in simulations of proton transport in confined environments.

Chemistry with semi-classical electrons: reaction trajectories auto-generated by sub-atomistic force fields

For a century now, "Lewis dots" have been a mainstay of chemical thinking, teaching and communication. However, chemists have assumed that this semi-classical picture of electrons needs to be abandoned for quantitative work, and the recourse in computational simulations has been to the extremes of first principles treatments of electrons on the one hand and force fields that avoid explicit electrons on the other hand. Given both the successes and limitations of these highly divergent approaches, it seems worth considering whether the Lewis dot picture might be made quantitative after all. Here we review progress to that end, including variations that have been implemented and examples of applications, specifically the acid-base behavior of water, several organic reactions, and electron dynamics in silicon fracture. In each case, the semi-classical approach is highly efficient and generates reasonable and readily interpreted reaction trajectories in turnkey fashion (i.e., without any input about products). Avenues for further progress are also discussed.

Special Pairs Are Decisive in the Autoionization and Recombination of Water

Although water's chemical properties are no less important than its exceptional physical properties, its acid-base behavior is relatively poorly understood. In fact, the Grotthus trajectories for ion recombination predicted by density functional theory do not comport well with the almost 100-fold slower diffusive trajectories observed in time-resolved spectroscopy. And, in the reverse reaction, the barrier to autoionization is not well characterized. Here we develop a self-consistent picture of both processes based on the occurrence and role of ultrashort hydrogen bonds. The predicted populations of these special pairs in bulk water are consistent with the high frequency electrodynamics of water and its pressure dependence. The rate-limiting role of the special pairs manifests in autoionization as a two-stage barrier, first to form a contact ion pair and then to separate it by one water molecule. From this configuration, similar frequencies are observed for further separation vs recombination. The requirement of ultrashort hydrogen bonds for proton transfer in autoionization is consistent with the rise in K_w with increasing pressure and points to a role for density fluctuations in autoionization events. In neutralization, the manifestation of the role of special pairs is the prolonged diffusional process observed in time-resolved spectroscopy experiments. The requirement of special pairs as transition states for proton transfer is less obvious for neutralization in isolated water chains than in the bulk liquid only because an unbroken sequence of ultrashort H-bonds is more easily formed in a 1D H-bonded chain than in a 3D H-bonded network.

Magnetism and Bond Order in Diatomic Molecules Described by Semiclassical Electrons

The past decade has seen the first attempts at quantifying a semiclassical description of electrons in molecules. The challenge in this endeavor is to find potentials for electron interactions that adequately capture quantum effects. As has been the case for density functionals, the challenge is particularly great for the effects that follow from the requirement for wave function antisymmetry. Here we extend our empirical inquiry into effective potentials, from prior work on the monatomic atoms and ions of nonmetals, to diatomic molecules and ions formed by these elements. Newly adjusted and trained for the longer distances relevant to diatomics, pairwise potentials are able to fit the bond orders and magnetic properties of homonuclear species. These potentials are then found to do an excellent job of predicting the magnetism of heteronuclear species. In these molecules the predicted distribution of electrons also correctly reflects increasing ionic character with increasing difference in the electronegativities of the participating atoms. The distinctive features of the current potential are discussed, along with issues calling for further improvements.

Surface Propensities of the Self-Ions of Water

The surface charge of water, which is important in a wide range of chemical, biological, material, and environmental contexts, has been a subject of lengthy and heated debate. Recently, it has been shown that the highly efficient LEWIS force field, in which semiclassical, independently mobile valence electron pairs capture the amphiproticity, polarizability and H-bonding of water, provides an excellent description of the solvation and dynamics of hydroxide and hydronium in bulk water. Here we turn our attention to slabs, cylinders, and droplets. In extended simulations with 1000 molecules, we find that hydroxide consistently prefers the surface, hydronium consistently avoids the surface, and the two together form an electrical double layer until neutralization occurs. The behavior of hydroxide can largely be accounted for by the observation that hydroxide moving to the surface loses fewer hydrogen bonds than are gained by the water molecule that it displaces from the surface. At the same time, since the orientation of the hydroxide increases the ratio of dangling hydrogens to dangling lone pairs, the proton activity of the exposed surface may be increased, rather than decreased. Hydroxide also moves more rapidly in the surface than in the bulk, likely because the proton donating propensity of neighboring water molecules is focused on the one hydrogen that is not dangling from the surface.

Pointillist rendering of electron charge and spin density suffices to replicate trends in atomic properties

The monotonic and non-monotonic variations of atomic properties within and between the rows of the periodic table underlie our understanding of chemistry and accounting for these variations has been a signature strength of quantum mechanics (QM). However, the computational burden of QM motivates the development of more efficient means of describing electrons and reactivity. The recently developed LEWIS • model incorporates lessons learnt from QM into a force field that includes electrons as explicit pseudo-classical particles. Here, we extend LEWIS • across the 2 p and 3 p elements, and show that it is capable of reproducing both monotonic and non-monotonic variations of chemically important atomic properties in a cost-effective manner. An indicator of the strength of the construct is the ability of pairwise potentials trained on ionization energies and the order of spin configurations to predict atomic polarizabilities. In this manner, some insights of QM are uncoupled from its onerous computational burden.

Revised Parameters for the AMOEBA Polarizable Atomic Multipole Water Model

A set of improved parameters for the AMOEBA polarizable atomic multipole water model is developed. An automated procedure, ForceBalance, is used to adjust model parameters to enforce agreement with ab initio-derived results for water clusters and experimental data for a variety of liquid phase properties across a broad temperature range. The values reported here for the new AMOEBA14 water model represent a substantial improvement over the previous AMOEBA03 model. The AMOEBA14 model accurately predicts the temperature of maximum density and qualitatively matches the experimental density curve across temperatures from 249 to 373 K. Excellent agreement is observed for the AMOEBA14 model in comparison to experimental properties as a function of temperature, including the second virial coefficient, enthalpy of vaporization, isothermal compressibility, thermal expansion coefficient, and dielectric constant. The viscosity, self-diffusion constant, and surface tension are also well reproduced. In comparison to high-level ab initio results for clusters of 2-20 water molecules, the AMOEBA14 model yields results similar to AMOEBA03 and the direct polarization iAMOEBA models. With advances in computing power, calibration data, and optimization techniques, we recommend the use of the AMOEBA14 water model for future studies employing a polarizable water model.

Transferable pseudoclassical electrons for aufbau of atomic ions

Generalizing the LEWIS reactive force field from electron pairs to single electrons, we present LEWIS• in which explicit valence electrons interact with each other and with nuclear cores via pairwise interactions. The valence electrons are independently mobile particles, following classical equations of motion according to potentials modified from Coulombic as required to capture quantum characteristics. As proof of principle, the aufbau of atomic ions is described for diverse main group elements from the first three rows of the periodic table, using a single potential for interactions between electrons of like spin and another for electrons of unlike spin. The electrons of each spin are found to distribute themselves in a fashion akin to the major lobes of the hybrid atomic orbitals, suggesting a pointillist description of the electron density. The broader validity of the LEWIS• force field is illustrated by predicting the vibrational frequencies of diatomic and triatomic hydrogen species.

Specific Reaction Path Hamiltonian for Proton Transfer in Water: Reparameterized Semiempirical Models

The semiempirical MNDO-based AM1 and PM3 methods and the orthogonalization-corrected OM1, OM2, and OM3 models were reparameterized to improve their description of bulk water and of proton transfer in water. Reference data included the gas-phase geometries and energies of the water molecule, small water clusters, the hydronium ion, and small hydronium ion-water clusters, as well as the gas-phase potential energy surface for proton transfer between the two water molecules in a Zundel ion, all calculated at the MP2/aug-cc-pVTZ level of theory. Combined QM/MM molecular dynamics simulations were carried out for bulk water and for a proton solvated in water using large cluster models. Both the authentic and reparameterized semiempirical models were employed in the simulations. The reparameterization led to significantly better results in all cases. The new set of OM3 parameters gave the best overall results for the structural and dynamic properties of water and the hydrated proton, with a small but finite barrier of 0.1-0.2 kcal/mol in the potential of mean force for proton transfer, in agreement with ab initio path-integral molecular dynamics simulations. The reparameterized OM3 model is expected to be useful for efficient modeling of proton transfer in aqueous solution.

Lifetimes of excess protons in water using a dissociative water potential

Molecular dynamics simulations using a dissociative water potential were applied to study transport of excess protons in water and determine the applicability of this potential to describe such behavior. While originally developed for gas-phase molecules and bulk liquid water, the potential is transferrable to nanoconfinement and interface scenarios. Applied here, it shows proton behavior consistent with ab initio calculations and empirical models specifically designed to describe proton transport. Both Eigen and Zundel complexes are observed in the simulations showing the Eigen-Zundel-Eigen-type mechanism. In addition to reproducing the short-time rattling of the excess proton between the two oxygens of Zundel complexes, a picosecond-scale lifetime was also found. These longer-lived H3O(+) ions are caused by the rapid conversion of the local solvation structure around the transferring proton from a Zundel-like form to an Eigen-like form following the transfer, effectively severing the path along which the proton can rattle. The migration of H(+) over long times (>100 ps) deviates from the conventional short-time multiexponentially decaying lifetime autocorrelation model and follows the t(-3/2) power-law behavior. The potential function employed here matches many of the features of proton transport observed in ab initio molecular dynamics simulations as well as the highly developed empirical valence bond models, yet is computationally very efficient, enabling longer time and larger systems to be studied.

Proton defect solvation and dynamics in aqueous acid and base

Easy come, easy go: LEWIS, a new model of reactive and polarizable water that enables the simulation of a statistically reliable number of proton hopping events in aqueous acid and base at concentrations of practical interest, is used to evaluate proton transfer intermediates in aqueous acid and base (picture, left and right, respectively).

Natural polarizability and flexibility via explicit valency: the case of water

As the dominant physiological solvent, water drives the folding of biological macromolecules, influences conformational changes, determines the ionization states of surface groups, actively participates in catalytic events, and provides "wires" for long-range proton transfer. Elucidation of all these roles calls for atomistic simulations. However, currently available methods do not lend themselves to efficient simulation of proton transfer events, or even polarizability and flexibility. Here, we report that an explicit account of valency can provide a unified description for the polarizability, flexibility, and dissociability of water in one intuitive and efficient setting. We call this approach LEWIS, after the chemical theory that inspires the use of valence electron pairs. In this paper, we provide details of the method, the choice of the training set, and predictions for the neat ambient liquid, with emphasis on structure, dynamics, and polarization. LEWIS water provides a good description of bulk properties, and dipolar and quadrupolar responses.

Pairwise long-range compensation for strongly ionic systems

We propose a pairwise compensation method for long-range electrostatics, as an alternative to traditional infinite lattice sums. The approach represents the third generation in a series beginning with the shifted potential corresponding to counterions surrounding a cutoff sphere. That simple charge compensation scheme resulted in pairwise potentials that are continuous at the cutoff, but forces that are not. A second-generation approach modified both the potential and the force such that both are continuous at the cutoff. Here we introduce another layer of softening such that the derivative of the force is also continuous at the cutoff. In strongly ionic liquids, this extension removes structural artifacts associated with the earlier pairwise compensation schemes, and provides results that compare well with Ewald sums.