Communication: Electronic structure of the solvated chloride anion from first principles molecular dynamics

Exploring the impact of ions on oxygen K-edge X-ray absorption spectroscopy in NaCl solution using the GW-Bethe-Salpeter-equation approach

X-ray absorption spectroscopy (XAS) is a powerful experimental tool to probe the local structure in materials with the core hole excitations. Here, the oxygen K-edge XAS spectra of the NaCl solution and pure water are computed by using a recently developed GW-Bethe-Salpeter equation approach, based on configurations modeled by path-integral molecular dynamics with the deep-learning technique. The neural network is trained on ab initio data obtained with strongly constrained and appropriately normed density functional theory. The observed changes in the XAS features of the NaCl solution, compared to those of pure water, are in good agreement between experimental and theoretical results. We provided detailed explanations for these spectral changes that occur when NaCl is solvated in pure water. Specifically, the presence of solvating ion pairs leads to localization of electron-hole excitons. Our theoretical XAS results support the theory that the effects of the solvating ions on the H-bond network are mainly confined within the first hydration shell of ions, however beyond the shell the arrangement of water molecules remains to be comparable to that observed in pure water.

Scaled charges for ions: An improvement but not the final word for modeling electrolytes in water

In this work, we discuss the use of scaled charges when developing force fields for NaCl in water. We shall develop force fields for Na⁺ and Cl^- using the following values for the scaled charge (in electron units): ±0.75, ±0.80, ±0.85, and ±0.92 along with the TIP4P/2005 model of water (for which previous force fields were proposed for q = ±0.85 and q = ±1). The properties considered in this work are densities, structural properties, transport properties, surface tension, freezing point depression, and maximum in density. All the developed models were able to describe quite well the experimental values of the densities. Structural properties were well described by models with charges equal to or larger than ±0.85, surface tension by the charge ±0.92, maximum in density by the charge ±0.85, and transport properties by the charge ±0.75. The use of a scaled charge of ±0.75 is able to reproduce with high accuracy the viscosities and diffusion coefficients of NaCl solutions for the first time. We have also considered the case of KCl in water, and the results obtained were fully consistent with those of NaCl. There is no value of the scaled charge able to reproduce all the properties considered in this work. Although certainly scaled charges are not the final word in the development of force fields for electrolytes in water, its use may have some practical advantages. Certain values of the scaled charge could be the best option when the interest is to describe certain experimental properties.

Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition-metal chemistry

Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d1 MOPs to be suitable for nearly eliminating all energetic delocalization error and static correlation error. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization error and static correlation error within a non-empirical framework.

Molecular DFT+U: A Transferable, Low-Cost Approach to Eliminate Delocalization Error

While density functional theory (DFT) is widely applied for its combination of cost and accuracy, corrections (e.g., DFT+U) that improve it are often needed to tackle correlated transition-metal chemistry. In principle, the functional form of DFT+U, consisting of a set of localized atomic orbitals (AOs) and a quadratic energy penalty for deviation from integer occupations of those AOs, enables the recovery of the exact conditions of piecewise linearity and the derivative discontinuity. Nevertheless, for practical transition-metal complexes, where both atomic states and ligand orbitals participate in bonding, standard DFT+U can fail to eliminate delocalization error (DE). Here, we show that by introducing an alternative valence-state (i.e., molecular orbital or MO) basis to the DFT+U approach, we recover exact conditions in cases for which standard DFT+U corrections have no error-reducing effect. This MO-based DFT+U also eliminates DE where standard AO-based DFT+U is already successful. We demonstrate the transferability of our approach on representative transition-metal complexes with a range of ligand field strengths, electron configurations (i.e., from Sc to Zn), and spin states.

Failure of molecular dynamics to provide appropriate structures for quantum mechanical description of the aqueous chloride ion charge-transfer-to-solvent ultraviolet spectrum

The lowest band in the charge-transfer-to-solvent ultraviolet absorption spectrum of aqueous chloride ion is studied by experiment and computation. Interestingly, the experiments indicate that at concentrations up to at least 0.25 M, where calculations indicate ion pairing to be significant, there is no notable effect of ionic strength on the spectrum. The experimental spectra are fitted to aid comparison with computations. Classical molecular dynamic simulations are carried out on dilute aqueous Cl-, Na+, and NaCl, producing radial distribution functions in reasonable agreement with experiment and, for NaCl, clear evidence of ion pairing. Clusters are extracted from the simulations for quantum mechanical excited state calculations. Accurate ab initio coupled-cluster benchmark calculations on a small number of representative clusters are carried out and used to identify and validate an efficient protocol based on time-dependent density functional theory. The latter is used to carry out quantum mechanical calculations on thousands of clusters. The resulting computed spectrum is in excellent agreement with experiment for the peak position, with little influence from ion pairing, but is in qualitative disagreement on the width, being only about half as wide. It is concluded that simulation by classical molecular dynamics fails to provide an adequate variety of structures to explain the experimental CTTS spectrum of aqueous Cl-.

Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory Based Ab Initio Molecular Dynamics. 1. Theory, Algorithm, and Performance

By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal density functional theory (DFT) and thereby furnish a more accurate and reliable description of the underlying electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we describe a linear-scaling approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions (MLWFs)) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems of interest at the hybrid DFT level. We focus our theoretical discussion on the integration of this approach into the framework of Car-Parrinello AIMD, and highlight the central role played by the MLWF-product potential (i.e., the solution of Poisson's equation for each corresponding MLWF-product density) in the evaluation of the EXX energy and wave function forces. We then provide a comprehensive description of the exx algorithm implemented in the open-source Quantum ESPRESSO program, which employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize the high-performance computing (HPC) resources available on current- and next-generation supercomputer architectures. This is followed by a critical assessment of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach when AIMD simulations of liquid water are performed in the canonical (NVT) ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT-based AIMD simulations of condensed-phase systems containing 500-1000 atoms (e.g., (H₂O)₂₅₆) with a wall time cost that is comparable to that of semilocal DFT. In doing so, exx takes us one step closer to routinely performing AIMD simulations of complex and large-scale condensed-phase systems for sufficiently long time scales at the hybrid DFT level of theory.

Aqueous solvation of the chloride ion revisited with density functional theory: impact of correlation and exchange approximations

Aqueous chloride is simulated using PBE-D3, PBE0-D3, and SCAN to investigate the impact of exchange and correlation approximations; we find the exact exchange fraction strongly impacts the energetics and polarizability of solvated chloride.

Quantum Chemical Methods for Modeling Covalent Modification of Biological Thiols

Targeted covalent inhibitor drugs require computational methods that go beyond simple molecular-mechanical force fields in order to model the chemical reactions that occur when they bind to their targets. Here, several semiempirical and density-functional theory (DFT) methods are assessed for their ability to describe the potential energy surface and reaction energies of the covalent modification of a thiol by an electrophile. Functionals such as PBE and B3LYP fail to predict a stable enolate intermediate. This is largely due to delocalization error, which spuriously stabilizes the prereaction complex, in which excess electron density is transferred from the thiolate to the electrophile. Functionals with a high-exact exchange component, range-separated DFT functionals, and variationally optimized exact exchange (i.e., the LC-B05minV functional) correct this issue to various degrees. The large gradient behavior of the exchange enhancement factor is also found to significantly affect the results, leading to the improved performance of PBE0. While ωB97X-D and M06-2X were reasonably accurate, no method provided quantitative accuracy for all three electrophiles, making this a very strenuous test of functional performance. Additionally, one drawback of M06-2X was that molecular dynamics (MD) simulations using this functional were only stable if a fine integration grid was used. The low-cost semiempirical methods, PM3, AM1, and PM7, provide a qualitatively correct description of the reaction mechanism, although the energetics is not quantitatively reliable. As a proof of concept, the potential of mean force for the addition of methylthiolate to methylvinyl ketone was calculated using quantum mechanical/molecular mechanical MD in an explicit polarizable aqueous solvent. © 2019 Wiley Periodicals, Inc.

Beyond Koopmans' theorem: electron binding energies in disordered materials

The topical review focuses on calculating ionization energies (IE), or electronic polarons in quasi-particle terminology, in large disordered systems, e.g. for a solute dissolved in a molecular solvent. The simplest estimate of the ionization energy is provided by one-electron energies in the Hartree-Fock theory, but the calculated quantities are not accurate. Density functional theory as many-body theory provides a principal opportunity for calculating one-electron energies including correlation and relaxation effects, i.e. the true energies of electronic polarons. We argue that such a principal possibility materializes within the concept of optimally tuned range-separated hybrid functionals (OT-RSH). We describe various schemes for optimal tuning. Importantly, the OT-RSH scheme is investigated for systems capped with dielectric continuum, providing a consistent picture on the QM/dielectric boundary. Finally, some limitations and open issues of the OT-RSH approach are addressed.

Predictive Simulations of Ionization Energies of Solvated Halide Ions with Relativistic Embedded Equation of Motion Coupled Cluster Theory

A subsystem approach for obtaining electron binding energies in the valence region is presented and applied to the case of halide ions (X^{-},X=F-At) in water. This approach is based on electronic structure calculations combining the relativistic equation-of-motion coupled cluster method for electron detachment and density functional theory via the frozen density embedding approach, using structures from classical molecular dynamics with polarizable force fields for discrete systems (in our study, droplets containing the anion and 50 water molecules). Our results indicate that one can accurately capture both the large solvent effect observed for the halides and the splitting of their ionization signals due to the increasingly large spin-orbit coupling of the p_{3/2}-p_{1/2} manifold across the series, at an affordable computational cost. Furthermore, owing to the quantum mechanical treatment of both solute and solvent electron binding energies of semiquantitative quality are also obtained for (bulk) water as by-products of the calculations for the halogens (in droplets).

The hydration structure of methylthiolate from QM/MM molecular dynamics

Thiols are widely present in biological systems, most notably as the side chain of cysteine amino acids in proteins. Thiols can be deprotonated to form a thiolate which affords a diverse range of enzymatic activity and modes for chemical modification of proteins. Parameters for modeling thiolates using molecular mechanical force fields have not yet been validated, in part due to the lack of structural data on thiolate solvation. Here, the CHARMM36 and Amber models for thiolates in aqueous solutions are assessed using free energy perturbation and hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations. The hydration structure of methylthiolate was calculated from 1 ns of QM/MM MD (PBE0-D3/def2-TZVP//TIP3P), which shows that the water-S^- distances are approximately 2 Å with a coordination number near 6. The CHARMM thiolate parameters predict a thiolate S radius close to the QM/MM value and predict a hydration Gibbs energy of -329.2 kJ/mol, close to the experimental value of -318 kJ/mol. The cysteine thiolate model in the Amber force field underestimates the thiolate radius by 0.2 Å and overestimates the thiolate hydration energy by 119 kJ/mol because it uses the same Lennard-Jones parameters for thiolates as for thiols. A recent Drude polarizable model for methylthiolate with optimized thiolate parameters also performs well. SAPT2+ [Symmetry Adapted Perturbation Theory (SAPT)] analysis indicates that exchange repulsion is larger for the methylthiolate, consistent with it having a more diffuse electron density distribution in comparison with the parent thiol. These data demonstrate that it is important to define distinct non-bonded parameters for the protonated/deprotonated states of amino acid side chains in molecular mechanical force fields.

First-Principles Simulations of Liquid Water Using a Dielectric-Dependent Hybrid Functional

We carried out first-principles simulations of liquid water under ambient conditions using a dielectric-dependent hybrid functional, where the fraction of exact exchange is set equal to the inverse of the high-frequency dielectric constant of the liquid. We found excellent agreement with experiment for the oxygen-oxygen partial correlation function at the experimental equilibrium density and 311 ± 3 K. Other structural and dynamical properties, such as the diffusion coefficient, molecular dipole moments, and vibrational spectra, are also in good agreement with experiment. Our results, together with previous findings on electronic properties of the liquid with the same functional, show that the dielectric-dependent hybrid functional accurately describes both the structural and electronic properties of liquid water.

Quadrupolar NMR Relaxation from ab Initio Molecular Dynamics: Improved Sampling and Cluster Models versus Periodic Calculations

Quadrupolar NMR relaxation rates are computed for ¹⁷O and ²H nuclei of liquid water, and of ²³Na⁺, and ³⁵Cl^- in aqueous solution via Kohn-Sham (KS) density functional theory ab initio molecular dynamics (aiMD) and subsequent KS electric field gradient (EFG) calculations along the trajectories. The calculated relaxation rates are within about a factor of 2 of experimental results and improved over previous aiMD simulations. The relaxation rates are assessed with regard to the lengths of the simulations as well as configurational sampling. The latter is found to be the more limiting factor in obtaining good statistical sampling and is improved by averaging over many equivalent nuclei of a system or over several independent trajectories. Further, full periodic plane-wave basis calculations of the EFGs are compared with molecular-cluster atomic-orbital basis calculations. The two methods deliver comparable results with nonhybrid functionals. With the molecular-cluster approach, a larger variety of electronic structure methods is available. For chloride, the EFG computations benefit from using a hybrid KS functional.

Performance of the AMOEBA Water Model in the Vicinity of QM Solutes: A Diagnosis Using Energy Decomposition Analysis

The importance of incorporating solvent polarization effects into the modeling of solvation processes has been well-recognized, and therefore a new generation of hybrid quantum mechanics/molecular mechanics (QM/MM) approaches that accounts for this effect is desirable. We present a fully self-consistent, mutually polarizable QM/MM scheme using the AMOEBA force field, in which the total energy of the system is variationally minimized with respect to both the QM electronic density and the MM induced dipoles. This QM/AMOEBA model is implemented through the Q-Chem/LibEFP code interface and then applied to the evaluation of solute-solvent interaction energies for various systems ranging from the water dimer to neutral and ionic solutes (NH₃, NH₄⁺, CN^-) surrounded by increasing numbers of water molecules (up to 100). In order to analyze the resulting interaction energies, we also utilize an energy decomposition analysis (EDA) scheme which identifies contributions from permanent electrostatics, polarization, and van der Waals (vdW) interaction for the interaction between the QM solute and the solvent molecules described by AMOEBA. This facilitates a component-wise comparison against full QM calculations where the corresponding energy components are obtained via a modified version of the absolutely localized molecular orbitals (ALMO)-EDA. The results show that the present QM/AMOEBA model can yield reasonable solute-solvent interaction energies for neutral and cationic species, while further scrutiny reveals that this accuracy highly relies on the delicate balance between insufficiently favorable permanent electrostatics and softened vdW interaction. For anionic solutes where the charge penetration effect becomes more pronounced, the QM/MM interface turns out to be unbalanced. These results are consistent with and further elucidate our findings in a previous study using a slightly different QM/AMOEBA model ( Dziedzic et al. J. Chem. Phys. 2016 , 145 , 124106 ). The implications of these results for further refinement of this model are also discussed.

Modelling heterogeneous interfaces for solar water splitting

The generation of hydrogen from water and sunlight offers a promising approach for producing scalable and sustainable carbon-free energy. The key of a successful solar-to-fuel technology is the design of efficient, long-lasting and low-cost photoelectrochemical cells, which are responsible for absorbing sunlight and driving water splitting reactions. To this end, a detailed understanding and control of heterogeneous interfaces between photoabsorbers, electrolytes and catalysts present in photoelectrochemical cells is essential. Here we review recent progress and open challenges in predicting physicochemical properties of heterogeneous interfaces for solar water splitting applications using first-principles-based approaches, and highlights the key role of these calculations in interpreting increasingly complex experiments.

Solvation structure of the halides from x-ray absorption spectroscopy

Three-dimensional models for the aqueous solvation structures of chloride, bromide, and iodide are reported. K-edge extended X-ray absorption fine structure (EXAFS) and Minuit X-ray absorption near edge (MXAN) analyses found well-defined single shell solvation spheres for bromide and iodide. However, dissolved chloride proved structurally distinct, with two solvation shells needed to explain its strikingly different X-ray absorption near edge structure (XANES) spectrum. Final solvation models were as follows: iodide, 8 water molecules at 3.60 ± 0.13 Å and bromide, 8 water molecules at 3.40 ± 0.14 Å, while chloride solvation included 7 water molecules at 3.15 ± 0.10 Å, and a second shell of 7 water molecules at 4.14 ± 0.30 Å. Each of the three derived solvation shells is approximately uniformly disposed about the halides, with no global asymmetry. Time-dependent density functional theory calculations simulating the chloride XANES spectra following from alternative solvation spheres revealed surprising sensitivity of the electronic state to 6-, 7-, or 8-coordination, implying a strongly bounded phase space for the correct structure during an MXAN fit. MXAN analysis further showed that the asymmetric solvation predicted from molecular dynamics simulations using halide polarization can play no significant part in bulk solvation. Classical molecular dynamics used to explore chloride solvation found a 7-water solvation shell at 3.12 (-0.04/+0.3) Å, supporting the experimental result. These experiments provide the first fully three-dimensional structures presenting to atomic resolution the aqueous solvation spheres of the larger halide ions.

Photoelectron Spectra of Aqueous Solutions from First Principles

We present a combined computational and experimental study of the photoelectron spectrum of a simple aqueous solution of NaCl. Measurements were conducted on microjets, and first-principles calculations were performed using hybrid functionals and many-body perturbation theory at the G0W0 level, starting with wave functions computed in ab initio molecular dynamics simulations. We show excellent agreement between theory and experiments for the positions of both the solute and solvent excitation energies on an absolute energy scale and for peak intensities. The best comparison was obtained using wave functions obtained with dielectric-dependent self-consistent and range-separated hybrid functionals. Our computational protocol opens the way to accurate, predictive calculations of the electronic properties of electrolytes, of interest to a variety of energy problems.

Density and Compressibility of Liquid Water and Ice from First-Principles Simulations with Hybrid Functionals

We determined the equilibrium density and compressibility of water and ice from first-principles molecular dynamics simulations using gradient-corrected (PBE) and hybrid (PBE0) functionals. Both functionals predicted the density of ice to be larger than that of water, by 15 (PBE) and 35% (PBE0). The PBE0 functional yielded a lower density of both ice and water with respect to PBE, leading to better agreement with experiment for ice but not for liquid water. Approximate inclusion of dispersion interactions on computed molecular-dynamics trajectories led to a substantial improvement of the PBE0 results for the density of liquid water, which, however, resulted to be slightly lower than that of ice.

Quantum mechanical study of solvent effects in a prototype SN2 reaction in solution: Cl- attack on CH3Cl

The nucleophilic attack of a chloride ion on methyl chloride is an important prototype SN2 reaction in organic chemistry that is known to be sensitive to the effects of the surrounding solvent. Herein, we develop a highly accurate Specific Reaction Parameter (SRP) model based on the Austin Model 1 Hamiltonian for chlorine to study the effects of solvation into an aqueous environment on the reaction mechanism. To accomplish this task, we apply high-level quantum mechanical calculations to study the reaction in the gas phase and combined quantum mechanical/molecular mechanical simulations with TIP3P and TIP4P-ew water models and the resulting free energy profiles are compared with those determined from simulations using other fast semi-empirical quantum models. Both gas phase and solution results with the SRP model agree very well with experiment and provide insight into the specific role of solvent on the reaction coordinate. Overall, the newly parameterized SRP Hamiltonian is able to reproduce both the gas phase and solution phase barriers, suggesting it is an accurate and robust model for simulations in the aqueous phase at greatly reduced computational cost relative to comparably accurate ab initio and density functional models.

Dissolution of NaCl nanocrystals: an ab initio molecular dynamics study

NaCl nanocrystal dissolution was investigated in atomistic detail revealing a difference in the solvation of two different ionic species.

Absolute redox potential of liquid water: a first-principles theory

The absolute redox potential of liquid water has been calculated by a first-principles method with good agreement with experimental data.

Ab initio studies of ionization potentials of hydrated hydroxide and hydronium

The ionization potential distributions of hydrated hydroxide and hydronium are computed with the many-body approach for electron excitations with configurations generated by ab initio molecular dynamics. The experimental features are well reproduced and found to be closely related to the molecular excitations. In the stable configurations, the ionization potential is mainly perturbed by solvent water molecules within the first solvation shell. On the other hand, electron excitation is delocalized on both proton receiving and donating complex during proton transfer, which shifts the excitation energies and broadens the spectra for both hydrated ions.