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PyDFT-QMMM is a Python-based package for performing hybrid quantum mechanics/molecular mechanics (QM/MM) simulations at the density functional level of theory. The program is designed to treat short-range and long-range interactions through user-specified combinations of electrostatic and mechanical embedding procedures within periodic simulation domains, providing necessary interfaces to external quantum chemistry and molecular dynamics software. To enable direct embedding of long-range electrostatics in periodic systems, we have derived and implemented force terms for our previously described QM/MM/PME approach [Pederson and McDaniel, J. Chem. Phys. 156, 174105 (2022)]. Communication with external software packages Psi4 and OpenMM is facilitated through Python application programming interfaces (APIs). The core library contains basic utilities for running QM/MM molecular dynamics simulations, and plug-in entry-points are provided for users to implement custom energy/force calculation and integration routines, within an extensible architecture. The user interacts with PyDFT-QMMM primarily through its Python API, allowing for complex workflow development with Python scripting, for example, interfacing with PLUMED for free energy simulations. We provide benchmarks of forces and energy conservation for the QM/MM/PME and alternative QM/MM electrostatic embedding approaches. We further demonstrate a simple example use case for water solute in a water solvent system, for which radial distribution functions are computed from 100 ps QM/MM simulations; in this example, we highlight how the solvation structure is sensitive to different basis-set choices due to under- or over-polarization of the QM water molecule's electron density. [ABSTRACT FROM AUTHOR]

Redox potentials depend on the nature of the solvent/electrolyte through the solvation energies of the ionic solute species. For concentrated electrolytes, ion solvation may deviate significantly from the Born model predictions due to ion pairing and correlation effects. Recently, Ghorai and Matyushov [J. Phys. Chem. B 124, 3754–3769 (2020)] predicted, on the basis of linear response theory, an anomalous trend in the solvation energies of room temperature ionic liquids, with deviations of hundreds of kJ/mol from the Born model for certain size solutes/ions. In this work, we computationally evaluate ionic solvation energies in the prototypical ionic liquid, 1-butyl-3-methylimidazolium tetrafluoroborate (BMIM/BF4), to further explore this behavior and benchmark several of the approximations utilized in the solvation energy predictions. For comparison, we additionally compute solvation energies within acetonitrile and molten NaCl salt to illustrate the limiting behavior of purely dipolar and ionic solvents. We find that the overscreening effect, which results from the inherent charge oscillations of the ionic liquid, is substantially reduced in magnitude due to screening from the dipoles of the molecular ions. Therefore, for the molten NaCl salt, for which the ions do not have permanent dipoles, modulation of ionic solvation energies from the overscreening effect is most significant. The conclusion is that ionic liquids do indeed exhibit unique solvation behavior due to peak(s) in the electrical susceptibility caused by the ion shell structure; redox potential shifts for BMIM/BF4 are of more modest order ∼0.1 V, but may be larger for other ionic liquids that approach molten salt behavior. [ABSTRACT FROM AUTHOR]

In this work, we propose and validate a generalization of the Helmholtz model that can account for both "bell-shaped" and "camel-shaped" differential capacitance profiles of concentrated electrolytes, the latter being characteristic of ionic liquids. The generalization is based on introducing voltage dependence of both the dielectric constant "ϵr(V)" and thickness "L(V)" of the inner Helmholtz layer, as validated by molecular dynamics (MD) simulations. We utilize MD simulations to study the capacitance profiles of three different electrochemical interfaces: (1) graphite/[BMIm+][ BF 4 − ] ionic liquid interface; (2) Au(100)/[BMIm+][ BF 4 − ] ionic liquid interface; (3) Au(100)/1M [Na+][Cl−] aqueous interface. We compute the voltage dependence of ϵr(V) and L(V) and demonstrate that the generalized Helmholtz model qualitatively describes both camel-shaped and bell-shaped differential capacitance profiles of ionic liquids and concentrated aqueous electrolytes (in lieu of specific ion adsorption). In particular, the camel-shaped capacitance profile that is characteristic of ionic liquid electrolytes arises simply from combination of the voltage-dependent trends of ϵr(V) and L(V). Furthermore, explicit analysis of the inner layer charge density for both concentrated aqueous and ionic liquid double layers reveal similarities, with these charge distributions typically exhibiting a dipolar region closest to the electrode followed by a monopolar peak at larger distances. It is appealing that a generalized Helmholtz model can provide a unified description of the inner layer structure and capacitance profile for seemingly disparate aqueous and ionic liquid electrolytes. [ABSTRACT FROM AUTHOR]

In silico property prediction based on density functional theory (DFT) is increasingly performed for crystalline materials. Whether quantitative agreement with experiment can be achieved with current methods is often an unresolved question, and may require detailed examination of physical effects such as electron correlation, reciprocal space sampling, phonon anharmonicity, and nuclear quantum effects (NQE), among others. In this work, we attempt first-principles equation of state prediction for the crystalline materials ScF3 and CaZrF6, which are known to exhibit negative thermal expansion (NTE) over a broad temperature range. We develop neural network (NN) potentials for both ScF3 and CaZrF6 trained to extensive DFT data, and conduct direct molecular dynamics prediction of the equation(s) of state over a broad temperature/pressure range. The NN potentials serve as surrogates of the DFT Hamiltonian with enhanced computational efficiency allowing for simulations with larger supercells and inclusion of NQE utilizing path integral approaches. The conclusion of the study is mixed: while some equation of state behavior is predicted in semiquantitative agreement with experiment, the pressure-induced softening phenomenon observed for ScF3 is not captured in our simulations. We show that NQE have a moderate effect on NTE at low temperature but does not significantly contribute to equation of state predictions at increasing temperature. Overall, while the NN potentials are valuable for property prediction of these NTE (and related) materials, we infer that a higher level of electron correlation, beyond the generalized gradient approximation density functional employed here, is necessary for achieving quantitative agreement with experiment. [ABSTRACT FROM AUTHOR]

Structural excitations that enable interbasin (IB) barrier crossings on a potential energy landscape are thought to play a facilitating role in the relaxation of liquids. Here, we show that the population of these excitations exhibits the same density scaling observed for α relaxation in propylene carbonate, even though they are heavily influenced by intramolecular modes. We also find that IB crossing modes exhibit a Gr u ̈ neisen parameter (γG) that is approximately equivalent to the density scaling parameter γTS. These observations suggest that the well-documented relationship between γG and γTS may be a direct result of the pressure dependence of the frequency of unstable (relaxation) modes associated with IB motion. [ABSTRACT FROM AUTHOR]

We present a density functional theory (DFT)-based, quantum mechanics/molecular mechanics (QM/MM) implementation with long-range electrostatic embedding achieved by direct real-space integration of the particle-mesh Ewald (PME) computed electrostatic potential. The key transformation is the interpolation of the electrostatic potential from the PME grid to the DFT quadrature grid from which integrals are easily evaluated utilizing standard DFT machinery. We provide benchmarks of the numerical accuracy with choice of grid size and real-space corrections and demonstrate that good convergence is achieved while introducing nominal computational overhead. Furthermore, the approach requires only small modification to existing software packages as is demonstrated with our implementation in the OpenMM and Psi4 software. After presenting convergence benchmarks, we evaluate the importance of long-range electrostatic embedding in three solute/solvent systems modeled with QM/MM. Water and 1-butyl-3-methylimidazolium tetrafluoroborate (BMIM/BF4) ionic liquid were considered as "simple" and "complex" solvents, respectively, with water and p-phenylenediamine (PPD) solute molecules treated at the QM level of theory. While electrostatic embedding with standard real-space truncation may introduce negligible errors for simple systems such as water solute in water solvent, errors become more significant when QM/MM is applied to complex solvents such as ionic liquids. An extreme example is the electrostatic embedding energy for oxidized PPD in BMIM/BF4 for which real-space truncation produces severe errors even at 2–3 nm cutoff distances. This latter example illustrates that utilization of QM/MM to compute redox potentials within concentrated electrolytes/ionic media requires carefully chosen long-range electrostatic embedding algorithms with our presented algorithm providing a general and robust approach. [ABSTRACT FROM AUTHOR]

Reactive molecular dynamics simulations enable a detailed understanding of solvent effects on chemical reaction mechanisms and reaction rates. While classical molecular dynamics using reactive force fields allows significantly longer simulation time scales and larger system sizes compared with ab initio molecular dynamics, constructing reactive force fields is a difficult and complex task. In this work, we describe a general approach following the empirical valence bond framework for constructing ab initio reactive force fields for condensed phase simulations by combining physics-based methods with neural networks (PB/NNs). The physics-based terms ensure the correct asymptotic behavior of electrostatic, polarization, and dispersion interactions and are compatible with existing solvent force fields. NNs are utilized for a versatile description of short-range orbital interactions within the transition state region and accurate rendering of vibrational motion of the reacting complex. We demonstrate our methodology for a simple deprotonation reaction of the 1-ethyl-3-methylimidazolium cation with acetate to form 1-ethyl-3-methylimidazol-2-ylidene and acetic acid. Our PB/NN force field exhibits ∼1 kJ mol−1 mean absolute error accuracy within the transition state region for the gas-phase complex. To characterize the solvent modulation of the reaction profile, we compute potentials of mean force for the gas-phase reaction as well as the reaction within a four-ion cluster and benchmark against ab initio molecular dynamics simulations. We find that the surrounding ionic environment significantly destabilizes the formation of the carbene product, and we show that this effect is accurately captured by the reactive force field. By construction, the PB/NN potential may be directly employed for simulations of other solvents/chemical environments without additional parameterization. [ABSTRACT FROM AUTHOR]

Reactive molecular dynamics simulations enable a detailed understanding of solvent effects on chemical reaction mechanisms and reaction rates. While classical molecular dynamics using reactive force fields allows significantly longer simulation time scales and larger system sizes compared with ab initio molecular dynamics, constructing reactive force fields is a difficult and complex task. In this work, we describe a general approach following the empirical valence bond framework for constructing ab initio reactive force fields for condensed phase simulations by combining physics-based methods with neural networks (PB/NNs). The physics-based terms ensure the correct asymptotic behavior of electrostatic, polarization, and dispersion interactions and are compatible with existing solvent force fields. NNs are utilized for a versatile description of short-range orbital interactions within the transition state region and accurate rendering of vibrational motion of the reacting complex. We demonstrate our methodology for a simple deprotonation reaction of the 1-ethyl-3-methylimidazolium cation with acetate to form 1-ethyl-3-methylimidazol-2-ylidene and acetic acid. Our PB/NN force field exhibits ∼1 kJ mol−1 mean absolute error accuracy within the transition state region for the gas-phase complex. To characterize the solvent modulation of the reaction profile, we compute potentials of mean force for the gas-phase reaction as well as the reaction within a four-ion cluster and benchmark against ab initio molecular dynamics simulations. We find that the surrounding ionic environment significantly destabilizes the formation of the carbene product, and we show that this effect is accurately captured by the reactive force field. By construction, the PB/NN potential may be directly employed for simulations of other solvents/chemical environments without additional parameterization. [ABSTRACT FROM AUTHOR]

Erratum: "Physics-based, neural network force fields for reactive molecular dynamics: Investigation of carbene formation from [EMIM+][OAc-]" [J. Chem. Phys. We have recomputed the PMFs with AIMD, utilizing a consistent collective variable definition of Eq. (1). This was done using the plumed/ASE interface with a CP2K calculator.[[2], [5]] Corrected PMFs that employ the collective variable of Eq. (1) for all calculations are shown in the corrected Fig. [Extracted from the article]

Ionic liquids are widely used as electrolytes in electronic devices in which they are subject to nanoconfinement within nanopores or nanofilms. Because the intrinsic width of an electrical double layer is on the order of several nanometers, nanoconfinement is expected to fundamentally alter the double layer properties. Furthermore, in confined systems, a large portion of the ions are interfacial, e.g., at the electrode interface, leading to significant deviations of electrostatic screening and ion dynamics as compared to bulk properties. In this work, we systematically investigate the interference between electrical double layers for nanoconfined ionic liquids and the resulting influence on the structure, dynamics, and screening behavior. We perform molecular dynamics simulations for the ionic liquids [ B M I m + ] [ B F 4 − ] and [ B M I m + ] [ P F 6 − ] confined between two flat electrodes at systematic separation distances between 1.5 nm and 4.5 nm for both conducting and insulating boundary conditions. We find that while ion dynamics is expectedly slower than in the bulk (by ∼2 orders of magnitude), there is an unexpected non-linear trend with the confinement length that leads to a local maximum in dynamic rates at ∼3.5–4.5 nm confinement. We show that this nonlinear trend is due to the ion correlation that arises from the interference between opposite double layers. We further evaluate confinement effects on the ion structure and capacitance and investigate the influence of electronic polarization of the ionic liquid on the resulting properties. This systematic evaluation of the connection between electrostatic screening and structure and dynamics of ionic liquids in confined systems is important for the fundamental understanding of electrochemical supercapacitors. [ABSTRACT FROM AUTHOR]

The diffusion of protons in self-assembled systems is potentially important for the design of efficient proton exchange membranes. In this work, we study proton dynamics in a low-water content, lamellar phase of a sodium-carboxylate gemini surfactant/water system using computer simulations. The hopping of protons via the Grotthuss mechanism is explicitly allowed through the multi-state empirical valence bond method. We find that the hydronium ion is trapped on the hydrophobic side of the surfactant-water interface, and proton diffusion then proceeds by hopping between surface sites. The importance of hydrophobic traps is surprising because one would expect the hydronium ions to be trapped at the charged headgroups. The physics illustrated in this system should be relevant to the proton dynamics in other amphiphilic membrane systems, whenever there exist exposed hydrophobic surface regions. [ABSTRACT FROM AUTHOR]

We present a multi-scale, hierarchical, approach for developing lattice models to estimate adsorption in nano-porous sorbents, derived on the basis of underlying atomistic potentials. This approach is a generalization of earlier work in zeolites (where the specific adsorption sites are easily definable) to encompass both specific as well as diffuse adsorption; the latter often dominates in the case of nano-porous metal-organic frameworks (MOFs). In conjunction with appropriately coarse grained guest-guest interactions, we demonstrate that our lattice approach offers semi-quantitative to quantitative agreement as compared to fully atomistic simulation from the low pressure regime through saturation. However, it also yields orders-of-magnitude acceleration versus the latter, thus enabling high-throughput screenings of both non-polar and polar adsorbates with high efficiency. We also show how our lattice model can be extended to facilitate rapid, qualitative screening of transport properties via appropriate calibration. Although our example applications focus on CO2 adsorption in MOFs, this approach is readily generalizable to various nano-porous materials (MOFs, zeolites...) and guest adsorbates (CO2, H2, hydrocarbons). [ABSTRACT FROM AUTHOR]

Water in nanoconfinement is ubiquitous in biological systems and membrane materials, with altered properties that significantly influence the surrounding system. In this work, we show how ionic liquid (IL)/water mixtures can be tuned to create water environments that resemble nanoconfined systems. We utilize molecular dynamics simulations employing ab initio force fields to extensively characterize the water structure within five different IL/water mixtures: [BMIM +][BF4−], [BMIM+][PF6−], [BMIM+][OTf−], [BMIM+][NO3−] and [BMIM+] [TFSI−] ILs at varying water fraction. We characterize water clustering, hydrogen bonding, water orientation, pairwise correlation functions and percolation networks as a function of water content and IL type. The nature of the water nanostructure is significantly tuned by changing the hydrophobicity of the IL and sensitively depends on water content. In hydrophobic ILs such as [BMIM+][PF6-], significant water clustering leads to dynamic formation of water pockets that can appear similar to those formed within reverse micelles. Furthermore, rotational relaxation times of water molecules in supersaturated hydrophobic IL/water mixtures indicate the close-connection with nanoconfined systems, as they are quantitatively similar to water relaxation in previously characterized lyotropic liquid crystals. We expect that this physical insight will lead to better design principles for incorporation of ILs into membrane materials to tune water nanostructure. [ABSTRACT FROM AUTHOR]