Electronic Structure of Aqueous Sulfuric Acid from First-Principles Simulations with Hybrid Functionals

Speeding-up Hybrid Functional-Based Ab Initio Molecular Dynamics Using Multiple Time-stepping and Resonance-Free Thermostat

Ab initio molecular dynamics (AIMD) based on density functional theory (DFT) has become a workhorse for studying the structure, dynamics, and reactions in condensed matter systems. Currently, AIMD simulations are primarily carried out at the level of generalized gradient approximation (GGA), which is at the second rung of DFT functionals in terms of accuracy. Hybrid DFT functionals, which form the fourth rung in the accuracy ladder, are not commonly used in AIMD simulations as the computational cost involved is 100 times or higher. To facilitate AIMD simulations with hybrid functionals, we propose here an approach using multiple time stepping with adaptively compressed exchange operator and resonance-free thermostat, that could speed up the calculations by ∼30 times or more for systems with a few hundred of atoms. We demonstrate that by achieving this significant speed up and making the compute time of hybrid functional-based AIMD simulations at par with that of GGA functionals, we are able to study several complex condensed matter systems and model chemical reactions in solution with hybrid functionals that were earlier unthinkable to be performed.

First-principles redox energy estimates under the condition of satisfying the general form of Koopmans’ theorem: An atomistic study of aqueous iron

In this work, we explore the relative accuracy to which a hybrid functional, in the context of density functional theory, may predict redox properties under the constraint of satisfying the general form of Koopmans’ theorem. Taking aqueous iron as our model system within the framework of first-principles molecular dynamics, direct comparison between computed single-particle energies and experimental ionization data is assessed by both (1) tuning the degree of hybrid exchange, to satisfy the general form of Koopmans’ theorem, and (2) ensuring the application of finite-size corrections. These finite-size corrections are benchmarked through classical molecular dynamics calculations, extended to large atomic ensembles, for which good convergence is obtained in the large supercell limit. Our first-principles findings indicate that while precise quantitative agreement with experimental ionization data cannot always be attained for solvated systems, when satisfying the general form of Koopmans’ theorem via hybrid functionals, theoretically robust estimates of single-particle redox energies are most often arrived at by employing a total energy difference approach. That is, when seeking to employ a value of exact exchange that does not satisfy the general form of Koopmans’ theorem, but some other physical metric, the single-particle energy estimate that would most closely align with the general form of Koopmans’ theorem is obtained from a total energy difference approach. In this respect, these findings provide important guidance for the more general comparison of redox energies computed via hybrid functionals with experimental data.

Structure of Sulfuric Acid Solutions Using Pair Distribution Function Analysis

Solvation and mesoscale ordering of sulfuric acid and other strong acid solutions leads to suppressed freezing points and strong rheological changes with varying concentration. While the solid-state structures are well-understood, studies focused on the evolving solvation structure in the solution phase have probed a limited concentration range (∼1-6 M). This study applies a total scattering approach in both the wide-angle X-ray scattering (WAXS) and pair distribution function (PDF) regimes to elucidate the evolving solvation structure over its full range of acid concentration (0-18 M). The emergence of a prepeak in the WAXS regime at intermediate concentrations indicates a transition from noninteracting sulfate molecules in the dilute limit to sterically limited sulfates at concentrations near its deep eutectic point. Fits to the PDF data quantify this trend, showing a transition from octahedrally hydrated sulfates up to 6-7 M concentrations, followed by gradual dehydration, and eventually reaching a solution structure similar to that of water-in-salt electrolyte systems at high acid concentrations.

Improving the scaling and performance of multiple time stepping-based molecular dynamics with hybrid density functionals

Density functionals at the level of the generalized gradient approximation (GGA) and a plane-wave basis set are widely used today to perform ab initio molecular dynamics (AIMD) simulations. Going up in the ladder of accuracy of density functionals from GGA (second rung) to hybrid density functionals (fourth rung) is much desired pertaining to the accuracy of the latter in describing structure, dynamics, and energetics of molecular and condensed matter systems. On the other hand, hybrid density functional based AIMD simulations are about two orders of magnitude slower than GGA based AIMD for systems containing ~100 atoms using ~100 compute cores. Two methods, namely MTACE and s-MTACE, based on a multiple time step integrator and adaptively compressed exchange operator formalism are able to provide a speed-up of about 7-9 in performing hybrid density functional based AIMD. In this work, we report an implementation of these methods using a task-group based parallelization within the CPMD program package, with the intention to take advantage of the large number of compute cores available on modern high-performance computing platforms. We present here the boost in performance achieved through this algorithm. This work also identifies the computational bottleneck in the s-MTACE method and proposes a way to overcome it.

Concentration-Dependent Solvation Structure and Dynamics of Aqueous Sulfuric Acid Using Multinuclear NMR and DFT

Sulfuric acid is a ubiquitous compound for industrial processes, and aqueous sulfate solutions also play a critical role as electrolytes for many prominent battery chemistries. While the thermodynamic literature on it is quite well-developed, comprehensive studies of the solvation structure, particularly molecular-scale dynamical and transport properties, are less available. This study applies a multinuclear nuclear magnetic resonance (NMR) approach to the elucidation of the solvation structure and dynamics over wide temperature (-10 to 50 °C) and concentration (0-18 M) ranges, combining the ¹⁷O shift, line width, and T₁ relaxation measurements, ³³S shift and line width measurements, and ¹H pulsed-field gradient NMR measurements of proton self-diffusivity. In conjunction, these results indicate a crossover between two regimes of solvation structure and dynamics, occurring above the concentration associated with the deep eutectic point (∼4.5 M), with the high-concentration regime dominated by a strong water-sulfate correlation. This description was borne out in detail by the activation energy trends with increasing concentration derived from the relaxation of both the H₂O/H₃O⁺ and H₂SO₄/HSO₄^-/SO₄^{2- 17}O resonances and the ¹H self-diffusivity. However, the ¹⁷O chemical shift difference between the H₂O/H₃O⁺ and H₂SO₄/HSO₄^-/SO₄^2- resonances across the entire temperature range is nevertheless strikingly linear. A computational approach coupling molecular dynamics simulations and density functional theory NMR shift calculations to reproduce this trend is presented, which will be the subject of further development. This combination of multinuclear, dynamical NMR, and computational methods, and the results furnished by this study, will provide a platform for future studies on battery electrolytes where aqueous sulfate chemistry plays a central role in the solution structure.

Achieving an Order of Magnitude Speedup in Hybrid-Functional- and Plane-Wave-Based Ab Initio Molecular Dynamics: Applications to Proton-Transfer Reactions in Enzymes and in Solution

Ab initio molecular dynamics (MD) with hybrid density functionals and a plane wave basis is computationally expensive due to the high computational cost of exact exchange energy evaluation. Recently, we proposed a strategy to combine adaptively compressed exchange (ACE) operator formulation and a multiple time step integration scheme to reduce the computational cost significantly [J. Chem. Phys. 2019, 151, 151102 ]. However, it was found that the construction of the ACE operator, which has to be done at least once in every MD time step, is computationally expensive. In the present work, systematic improvements are introduced to further speed up by employing localized orbitals for the construction of the ACE operator. By this, we could achieve a computational speedup of an order of magnitude for a periodic system containing 32 water molecules. Benchmark calculations were carried out to show the accuracy and efficiency of the method in predicting the structural and dynamical properties of bulk water. To demonstrate the applicability, computationally intensive free-energy computations at the level of hybrid density functional theory were performed to investigate (a) methyl formate hydrolysis reaction in neutral aqueous media and (b) proton-transfer reaction within the active-site residues of the class C β-lactamase enzyme.

Efficient computation of free energy surfaces of chemical reactions using ab initio molecular dynamics with hybrid functionals and plane waves

Ab initio molecular dynamics (AIMD) simulations employing density functional theory (DFT) and plane waves are routinely carried out using density functionals at the level of generalized gradient approximation (GGA). AIMD simulations employing hybrid density functionals are of great interest as it offers a more accurate description of structural and dynamic properties than the GGA functionals. However, the computational cost for carrying out calculations using hybrid functionals and plane wave basis set is at least two orders of magnitude higher than that using GGA functionals. Recently, we proposed a strategy that combined the adaptively compressed exchange operator formulation and the multiple time step integration scheme to reduce the computational cost by an order of magnitude [J. Chem. Phys. 151, 151102 (2019)]. In this work, we demonstrate the application of this method to study chemical reactions, in particular, formamide hydrolysis in an alkaline aqueous medium. By actuating our implementation with the well-sliced metadynamics scheme, we can compute the two-dimensional free energy surface of this reaction at the level of hybrid-DFT. This work also investigates the accuracy of the PBE0 (hybrid) and the PBE (GGA) functionals in predicting the free energetics of this chemical reaction.

Large Presence of Carbonic Acid in CO2-Rich Aqueous Fluids under Earth's Mantle Conditions

The chemistry of carbon in aqueous fluids at extreme pressure and temperature conditions is of great importance to Earth's deep carbon cycle, which substantially affects the carbon budget at Earth's surface and global climate change. At ambient conditions, the concentration of carbonic acid in water is negligible; therefore, aqueous carbonic acid was simply ignored in previous geochemical models. However, by applying extensive ab initio molecular dynamics simulations at pressure and temperature conditions similar to those in Earth's upper mantle, we found that carbonic acid can be the most abundant carbon species in aqueous CO₂ solutions at ∼10 GPa and 1000 K. The mole percent of carbonic acid in total dissolved carbon species increases with increasing pressure along an isotherm, while its mole percent decreases with increasing temperature along an isobar. In CO₂-rich solutions, we found significant proton transfer between carbonic acid molecules and bicarbonate ions, which may enhance the conductivity of the solutions. The effects of pH buffering by carbonic acid may play an important role in water-rock interactions in Earth's interior. Our findings suggest that carbonic acid is an important carbon carrier in the deep carbon cycle.

Predicting vapor liquid equilibria using density functional theory: A case study of argon

Predicting vapor liquid equilibria (VLE) of molecules governed by weak van der Waals (vdW) interactions using the first principles approach is a significant challenge. Due to the poor scaling of the post Hartree-Fock wave function theory with system size/basis functions, the Kohn-Sham density functional theory (DFT) is preferred for systems with a large number of molecules. However, traditional DFT cannot adequately account for medium to long range correlations which are necessary for modeling vdW interactions. Recent developments in DFT such as dispersion corrected models and nonlocal van der Waals functionals have attempted to address this weakness with a varying degree of success. In this work, we predict the VLE of argon and assess the performance of several density functionals and the second order Møller-Plesset perturbation theory (MP2) by determining critical and structural properties via first principles Monte Carlo simulations. PBE-D3, BLYP-D3, and rVV10 functionals were used to compute vapor liquid coexistence curves, while PBE0-D3, M06-2X-D3, and MP2 were used for computing liquid density at a single state point. The performance of the PBE-D3 functional for VLE is superior to other functionals (BLYP-D3 and rVV10). At T = 85 K and P = 1 bar, MP2 performs well for the density and structural features of the first solvation shell in the liquid phase.

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.

The fate of carbon dioxide in water-rich fluids under extreme conditions

Investigating the fate of dissolved carbon dioxide under extreme conditions is critical to understanding the deep carbon cycle in Earth, a process that ultimately influences global climate change. We used first-principles molecular dynamics simulations to study carbonates and carbon dioxide dissolved in water at pressures (P) and temperatures (T) approximating the conditions of Earth's upper mantle. Contrary to popular geochemical models assuming that molecular CO₂(aq) is the major carbon species present in water under deep Earth conditions, we found that at 11 GPa and 1000 K, carbon exists almost entirely in the forms of solvated carbonate ([Formula: see text]) and bicarbonate ([Formula: see text]) ions and that even carbonic acid [H₂CO₃(aq)] is more abundant than CO₂(aq). Furthermore, our simulations revealed that ion pairing between Na⁺ and [Formula: see text]/[Formula: see text] is greatly affected by P-T conditions, decreasing with increasing pressure at 800 to 1000 K. Our results suggest that in Earth's upper mantle, water-rich geofluids transport a majority of carbon in the form of rapidly interconverting [Formula: see text] and [Formula: see text] ions, not solvated CO₂(aq) molecules.