Minimizing the impacts of the ammonia economy on the nitrogen cycle and climate.

Ammonia (NH3) is an attractive low-carbon fuel and hydrogen carrier. However, losses and inefficiencies across the value chain could result in reactive nitrogen emissions (NH3, NOx, and N2O), negatively impacting air quality, the environment, human health, and climate. A relatively robust ammonia economy (30 EJ/y) could perturb the global nitrogen cycle by up to 65 Mt/y with a 5% nitrogen loss rate, equivalent to 50% of the current global perturbation caused by fertilizers. Moreover, the emission rate of nitrous oxide (N2O), a potent greenhouse gas and ozone-depleting molecule, determines whether ammonia combustion has a greenhouse footprint comparable to renewable energy sources or higher than coal (100 to 1,400 gCO2e/kWh). The success of the ammonia economy hence hinges on adopting optimal practices and technologies that minimize reactive nitrogen emissions. We discuss how this constraint should be included in the ongoing broad engineering research to reduce environmental concerns and prevent the lock-in of high-leakage practices.

The technological and economic prospects for CO2 utilization and removal.

The capture and use of carbon dioxide to create valuable products might lower the net costs of reducing emissions or removing carbon dioxide from the atmosphere. Here we review ten pathways for the utilization of carbon dioxide. Pathways that involve chemicals, fuels and microalgae might reduce emissions of carbon dioxide but have limited potential for its removal, whereas pathways that involve construction materials can both utilize and remove carbon dioxide. Land-based pathways can increase agricultural output and remove carbon dioxide. Our assessment suggests that each pathway could scale to over 0.5 gigatonnes of carbon dioxide utilization annually. However, barriers to implementation remain substantial and resource constraints prevent the simultaneous deployment of all pathways.

Charting C-C coupling pathways in electrochemical CO2 reduction on Cu(111) using embedded correlated wavefunction theory.

The electrochemical CO2 reduction reaction (CO2RR) powered by excess zero-carbon-emission electricity to produce especially multicarbon (C2+) products could contribute to a carbon-neutral to carbon-negative economy. Foundational to the rational design of efficient, selective CO2RR electrocatalysts is mechanistic analysis of the best metal catalyst thus far identified, namely, copper (Cu), via quantum mechanical computations to complement experiments. Here, we apply embedded correlated wavefunction (ECW) theory, which regionally corrects the electron exchange-correlation error in density functional theory (DFT) approximations, to examine multiple C-C coupling steps involving adsorbed CO (*CO) and its hydrogenated derivatives on the most ubiquitous facet, Cu(111). We predict that two adsorbed hydrogenated CO species, either *COH or *CHO, are necessary precursors for C-C bond formation. The three kinetically feasible pathways involving these species yield all three possible products: *COH-CHO, *COH-*COH, and *OCH-*OCH. The most kinetically favorable path forms *COH-CHO. In contrast, standard DFT approximations arrive at qualitatively different conclusions, namely, that only *CO and *COH will prevail on the surface and their C-C coupling paths produce only *COH-*COH and *CO-*CO, with a preference for the first product. This work demonstrates the importance of applying qualitatively and quantitatively accurate quantum mechanical method to simulate electrochemistry in order ultimately to shed light on ways to enhance selectivity toward C2+ product formation via CO2RR electrocatalysts.

Strongly facet-dependent activity of iron-doped ß-nickel oxyhydroxide for the oxygen evolution reaction.

Iron (Fe)-doped ß-nickel oxyhydroxide (ß-NiOOH) is a highly active, noble-metal-free electrocatalyst for the oxygen evolution reaction (OER), with the latter being the bottleneck in electrochemical water splitting for sustainable hydrogen production. The mechanisms underlying how the Fe dopant modulates this host material's water electro-oxidation activity are still not entirely clear. Here, we combine hybrid density functional theory (DFT) and Hubbard-corrected DFT to investigate the OER activity of the most thermodynamically favorable (and therefore, expected to be the majority) crystallographic facets of ß-NiOOH, namely (0001) and (101̄0). By considering active sites involving both oxidation and reduction of the transition-metal active center during the redox cycle on these two different facets, we show that six-fold-lattice-coordinated Fe in ß-NiOOH is redox inactive towards both oxidation and reduction while five-fold-lattice-coordinated Fe in ß-NiOOH does exhibit redox activity. However, the determined redox activity of Fe (or lack of it) is not indicative of good (or bad) performance as a dopant on these two facets. Three of the four active sites investigated (oxo and hydroxo sites on (0001) and a hydrated site on (101̄0)) exhibit only a marginal (<0.1 V) decrease or increase in the thermodynamic overpotential upon doping with Fe. Only one of the redox-active sites investigated, the hydroxo site on (101̄0), exhibits a large attenuation in the thermodynamic overpotential upon doping (to ∼0.52 V from 0.86 V), although the doped overpotential is larger than that observed experimentally for Fe-doped NiOOH. Thus, although pure ß-NiOOH facets containing four-, five-, or six-fold lattice-coordinated Ni sites have roughly equal OER activities, yielding similar OER onset potentials (shown in A. Govind Rajan, J. M. P. Martirez and E. A. Carter, J. Am. Chem. Soc., 2020, 142, 3600-3612), only those facets containing four-fold lattice-coordinated Fe (e.g., as shown in J. M. P. Martirez and E. A. Carter, J. Am. Chem. Soc., 2019, 141, 693-705) would be active under analogous conditions for the Fe-doped material. It follows that, while undoped ß-NiOOH demonstrates a roughly facet-independent oxygen evolution activity, the activity of Fe-doped ß-NiOOH strongly depends on the crystallographic facet. Our study further motivates the investigation of strategies for the selective growth of facets with low iron coordination number to enhance the water splitting activity of Fe-doped ß-NiOOH.

Hot carrier multiplication in plasmonic photocatalysis.

Light-induced hot carriers derived from the surface plasmons of metal nanostructures have been shown to be highly promising agents for photocatalysis. While both nonthermal and thermalized hot carriers can potentially contribute to this process, their specific role in any given chemical reaction has generally not been identified. Here, we report the observation that the H2-D2 exchange reaction photocatalyzed by Cu nanoparticles is driven primarily by thermalized hot carriers. The external quantum yield shows an intriguing S-shaped intensity dependence and exceeds 100% for high light intensities, suggesting that hot carrier multiplication plays a role. A simplified model for the quantum yield of thermalized hot carriers reproduces the observed kinetic features of the reaction, validating our hypothesis of a thermalized hot carrier mechanism. A quantum mechanical study reveals that vibrational excitations of the surface Cu-H bond is the likely activation mechanism, further supporting the effectiveness of low-energy thermalized hot carriers in photocatalyzing this reaction.

Probing pH-Dependent Dehydration Dynamics of Mg and Ca Cations in Aqueous Solutions with Multi-Level Quantum Mechanics/Molecular Dynamics Simulations.

The dehydration of aqueous calcium and magnesium cations is the most fundamental process controlling their reactivity in chemical and biological phenomena, such as the formation of ionic solids or passing through ion channels. It holds particular relevance in light of recent advancements in the development of carbon capture techniques that rely on mineralization for long-term carbon storage. Specifically, dehydration of Ca2+ and Mg2+ is a key step in proposed carbon capture processes aiming to exploit the relatively high concentration of dissolved carbon dioxide in seawater via the formation of carbonate minerals from solvated Ca2+ and Mg2+ cations for sequestration and storage. Nevertheless, atomic-scale understanding of the dehydration of aqueous Ca2+ and Mg2+ cations remains limited. Here, we utilize rare event sampling via density functional theory molecular dynamics and embedded wavefunction theory calculations to elucidate the dehydration dynamics of aqueous Ca2+ and Mg2+. Emphasis is placed on the investigation of the effect pH has on the stability of the different coordination environments. Our results reveal significant differences in the dehydration dynamics of the two cations and provide insight into how they may be modulated by pH changes.

Solvent Dynamics Are Critical to Understanding Carbon Dioxide Dissolution and Hydration in Water.

Simulations of carbon dioxide (CO2) in water may aid in understanding the impact of its accumulation in aquatic environments and help advance technologies for carbon capture and utilization (via, e.g., mineralization). Quantum mechanical (QM) simulations based on static molecular models with polarizable continuum solvation poorly reproduce the energetics of CO2 hydration to form carbonic acid in water, independent of the level of QM theory employed. Only with density-functional-theory-based molecular dynamics and rare-event sampling, followed by energy corrections based on embedded correlated wavefunction theory (in conjunction with density functional embedding theory), can a close agreement between theory and experiment be achieved. Such multilevel simulations can serve as benchmarks for simpler, less costly models, giving insight into potential errors of the latter. The strong influence of sampling/averaging over dynamical solvent configurations on the energetics stems from the difference in polarity of both the transition state and product (both polar) versus the reactant (nonpolar). When a solute undergoes a change in polarity during reaction, affecting its interaction with the solvent, careful assessment of the energetic contribution of the solvent response to this change is critical. We show that static models (without structural sampling) that incorporate three explicit water molecules can yield far superior results than models with more explicit water molecules because fewer water molecules yield less configurational artifacts. Static models intelligently incorporating both explicit (molecules directly participating in the reaction) and implicit solvation, along with a proper QM theory, e.g., CCSD(T) for closed-shell systems, can close the accuracy gap between static and dynamic models.

Highly Selective Electrochemical Reduction of CO2 into Methane on Nanotwinned Cu.

The electrochemical carbon dioxide reduction reaction (CO2RR) is a promising route to close the carbon cycle by reducing CO2 into valuable fuels and chemicals. Electrocatalysts with high selectivity toward a single product are economically desirable yet challenging to achieve. Herein, we demonstrated a highly (111)-oriented Cu foil electrocatalyst with dense twin boundaries (TB) (tw-Cu) that showed a high Faradaic efficiency of 86.1 ± 5.3% toward CH4 at -1.2 ± 0.02 V vs the reversible hydrogen electrode. Theoretical studies suggested that tw-Cu can significantly lower the reduction barrier for the rate-determining hydrogenation of CO compared to planar Cu(111) under working conditions, which suppressed the competing C-C coupling, leading to the experimentally observed high CH4 selectivity.

Introducing the embedded random phase approximation: H2 dissociative adsorption on Cu(111) as an exemplar.

The random phase approximation (RPA) as a means of treating electron correlation recently has been shown to outperform standard density functional theory (DFT) approximations in a variety of cases. However, the computational cost of the RPA is substantially more than DFT, especially when aiming to study extended surfaces. Properly accounting for sufficient surface ensemble size, Brillouin zone sampling, and vacuum separation of periodic images in standard periodic-planewave-based DFT code raises the cost to achieve converged results. Here, we show that sub-system embedding schemes enable use of the RPA for modeling heterogeneous reactions at reduced computational cost. We explore two different embedded RPA (emb-RPA) approaches, periodic emb-RPA and cluster emb-RPA. We use the (experimentally and theoretically) well-studied H2 dissociative adsorption on Cu(111) as our exemplar, and first perform full periodic RPA calculations as a benchmark. The full RPA results match well the semi-empirical barrier fit to experimental observables and others derived from high-level computations, e.g., from recent embedded n-electron valence second order perturbation theory [Zhao et al., J. Chem. Theory Comput. 16(11), 7078-7088 (2020)] and quantum Monte Carlo [Doblhoff-Dier et al., J. Chem. Theory Comput. 13(7), 3208-3219 (2017)] simulations. Among the two emb-RPA approaches tested, the cluster emb-RPA accurately reproduces the energy profile (maximum error of 50 meV along the reaction pathway) while reducing the computational cost by approximately two orders of magnitude. We therefore expect that the embedded cluster approach will enable wider RPA implementation in heterogeneous catalysis.

First-Principles Insights into Plasmon-Induced Catalysis.

The size- and shape-controlled enhanced optical response of metal nanoparticles (NPs) is referred to as a localized surface plasmon resonance (LSPR). LSPRs result in amplified surface and interparticle electric fields, which then enhance light absorption of the molecules or other materials coupled to the metallic NPs and/or generate hot carriers within the NPs themselves. When mediated by metallic NPs, photocatalysis can take advantage of this unique optical phenomenon. This review highlights the contributions of quantum mechanical modeling in understanding and guiding current attempts to incorporate plasmonic excitations to improve the kinetics of heterogeneously catalyzed reactions. A range of first-principles quantum mechanics techniques has offered insights, from ground-state density functional theory (DFT) to excited-state theories such as multireference correlated wavefunction methods. Here we discuss the advantages and limitations of these methods in the context of accurately capturing plasmonic effects, with accompanying examples.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Optimal functionalization of a molecular electrocatalyst for hydride transfer.

Optimization of hydride transfer (HT) catalysts to enhance rates and selectivities of (photo)electroreduction reactions could be a crucial component of a sustainable chemical industry. Here, we analyze how ring functionalization of the adsorbed transient intermediate 2-pyridinide (2-PyH-*)-predicted to form in situ from pyridine (Py) in acidified water at a cathode surface and to be the key to selective CO2 photoelectroreduction on p-GaP-may enhance catalytic activity. Earlier studies revealed that 2-PyH-*'s instability results from a protonation side reaction producing adsorbed dihydropyridine (DHP*), which is relatively HT-inactive. Reducing the electron density on 2-PyH-* could limit this protonation, with the trade-off that it may become less active for HT from 2-PyH-*-R to CO2 We explore here how Py functionalization affects the electron distribution and in turn tunes the catalytic performance of 2-PyH-*. We indeed find that electron-withdrawing groups could enhance the stability of 2-PyH-* by reducing its electron density on the ring. Furthermore, we find that the change in the number of electrons on the substituting group of the hydride donor is a good descriptor for both the stability against protonation and the magnitude of the HT barrier. We predict that -CH2-CH2F is the best candidate substituent, as it significantly improves the stability of 2-PyH-* with only a small increase in HT barrier. -CH=CH2 and -CH2F also could be promising, although they require further investigation due to a larger HT-barrier increase.

Factors Governing Oxygen Vacancy Formation in Oxide Perovskites.

The control of oxygen vacancy (VO) formation is critical to advancing multiple metal-oxide-perovskite-based technologies. We report the construction of a compact linear model for the neutral VO formation energy in ABO3 perovskites that reproduces, with reasonable fidelity, Hubbard-U-corrected density functional theory calculations based on the state-of-the-art, strongly constrained and appropriately normed exchange-correlation functional. We obtain a mean absolute error of 0.45 eV for perovskites stable at 298 K, an accuracy that holds across a large, electronically diverse set of ABO3 perovskites. Our model considers perovskites containing alkaline-earth metals (Ca, Sr, and Ba) and lanthanides (La and Ce) on the A-site and 3d transition metals (Ti, V, Cr, Mn, Fe, Co, and Ni) on the B-site in six different crystal systems (cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, and monoclinic) common to perovskites. Physically intuitive metrics easily extracted from existing experimental thermochemical data or via inexpensive quantum mechanical calculations, including crystal bond dissociation energies and (solid phase) reduction potentials, are key components of the model. Beyond validation of the model against known experimental trends in materials used in solid oxide fuel cells, the model yields new candidate perovskites not contained in our training data set, such as (Bi,Y)(Fe,Co)O3, which we predict may have favorable thermochemical water-splitting properties. The confluence of sufficient accuracy, efficiency, and interpretability afforded by our model not only facilitates high-throughput computational screening for any application that requires the precise control of VO concentrations but also provides a clear picture of the dominant physics governing VO formation in metal-oxide perovskites.

Revisiting Understanding of Electrochemical CO2 Reduction on Cu(111): Competing Proton-Coupled Electron Transfer Reaction Mechanisms Revealed by Embedded Correlated Wavefunction Theory.

Copper (Cu) electrodes, as the most efficacious of CO2 reduction reaction (CO2RR) electrocatalysts, serve as prototypes for determining and validating reaction mechanisms associated with electrochemical CO2 reduction to hydrocarbons. As in situ electrochemical mechanism determination by experiments is still out of reach, such mechanistic analysis typically is conducted using density functional theory (DFT). The semilocal exchange-correlation (XC) approximations most often used to model such catalysis unfortunately engender a basic error: predicting the wrong adsorption site for CO (a key CO2RR intermediate) on the most ubiquitous facet of Cu, namely, Cu(111). This longstanding inconsistency casts lingering doubt on previous DFT predictions of the attendant CO2RR kinetics. Here, we apply embedded correlated wavefunction (ECW) theory, which corrects XC functional error, to study the CO2RR on Cu(111) via both surface hydride (*H) transfer and proton-coupled electron transfer (PCET). We predict that adsorbed CO (*CO) reduces almost equally to two intermediates, namely, hydroxymethylidyne (*COH) and formyl (*CHO) at -0.9 V vs the RHE. In contrast, semilocal DFT approximations predict a strong preference for *COH. With increasing applied potential, the dominance of *COH (formed via potential-independent surface *H transfer) diminishes, switching to the competitive formation of both *CHO and *COH (both formed via potential-dependent PCET). Our results also demonstrate the importance of including explicitly modeled solvent molecules in predicting electron-transfer barriers and reveal the pitfalls of overreliance on simple surface *H transfer models of reduction reactions.

Theoretical Insights into Heterogeneous (Photo)electrochemical CO2 Reduction.

Electrochemical and photoelectrochemical CO2 reduction technologies offer the promise of zero-carbon-emission renewable fuels needed for heavy-duty transportation. However, the inert nature of the CO2 molecule poses a fundamental challenge that must be overcome before efficient (photo)electrochemical CO2 reduction at scale will be achieved. Optimal catalysts exhibit enduring stability, fast kinetics, high selectivity, and low manufacturing cost. Identifying catalytic mechanisms of CO2 reduction in (photo)electrochemical systems could accelerate design of efficient catalysts. In recent decades, numerous theoretical studies have contributed to our understanding of CO2 reduction pathways and identifying rate-limiting steps. Although a significant body of work exists regarding homogeneous electrocatalysis for CO2 reduction, this review focuses specifically on the theory of heterogeneous (photo)electrochemical reduction. We first give an overview of the relevant thermodynamics and semiconductor physics. We then introduce important, widely used theoretical techniques and modeling approaches to catalysis. Recent progress in elucidating mechanisms of heterogeneous (photo)electrochemical CO2 reduction is discussed through the lens of two experimental systems: pyridine (Py)-catalyzed CO2 (photo)electrochemical reduction at p-GaP photoelectrodes and electrochemical CO2 reduction at Cu electrodes. We close by proposing strategies and principles for the future design of (photo)electrochemical catalysts to improve the selectivity and reaction kinetics of CO2 reduction.

Assessing cathode property prediction via exchange-correlation functionals with and without long-range dispersion corrections.

We benchmark calculated interlayer spacings, average topotactic voltages, thermodynamic stabilities, and band gaps in layered lithium transition-metal oxides (TMOs) and their de-lithiated counterparts, which are used in lithium-ion batteries as positive electrode materials, against available experimental data. Specifically, we examine the accuracy of properties calculated within density functional theory (DFT) using eight different treatments of electron exchange-correlation: the strongly constrained and appropriately normed (SCAN) and Perdew-Burke-Ernzerhof (PBE) density functionals, Hubbard-U-corrected SCAN and PBE (i.e., SCAN+U and PBE+U), and SCAN(+U) and PBE(+U) with added long-range dispersion (D) interactions (i.e., DFT(+U)+D). van der Waals interactions are included respectively via the revised Vydrov-Van Voorhis (rVV10) for SCAN(+U) and the DFT-D3 for PBE(+U). We find that SCAN-based functionals predict larger voltages due to an underestimation of stability of the MO2 systems, while also predicting smaller interlayer spacings compared to their PBE-based counterparts. Furthermore, adding dispersion corrections to PBE has a greater effect on voltage predictions and interlayer spacings than with SCAN, indicating that DFT-SCAN - despite being a ground-state theory - fortuitously captures some short and medium-range dispersion interactions better than PBE. While SCAN-based and PBE-based functionals yield qualitatively similar band gap predictions, there is no significant quantitative improvement of SCAN-based functionals over the corresponding PBE-based versions. Finally, we expect SCAN-based functionals to yield more accurate property predictions than the respective PBE-based functionals for most TMOs, given SCAN's stronger theoretical underpinning and better predictions of systematic trends in interlayer spacings, intercalation voltages, and band gaps obtained in this work.

Metal-to-Ligand Charge-Transfer Spectrum of a Ru-Bipyridine-Sensitized TiO2 Cluster from Embedded Multiconfigurational Excited-State Theory.

Understanding optical properties of the dye molecule in dye-sensitized solar cells (DSSCs) from first-principles quantum mechanics can contribute to improving the efficiency of such devices. While density functional theory (DFT) and time-dependent DFT have been pivotal in simulating optoelectronic properties of photoanodes used in DSSCs at the atomic scale, questions remain regarding DFT's adequacy and accuracy to furnish critical information needed to understand the various excited-state processes involved. Here, we simulate the absorption spectra of a dye-sensitized solar cell analogue, comprised of a Ru-bipyridine (Ru-bpy) dye molecule and a small TiO2 cluster via DFT and via an accurate embedded correlated wavefunction (CW) theory. We generated CW spectra for the adsorbed Ru-bpy dye via a recently introduced capped density functional embedding theory or capped-DFET (to generate the embedding potential that accounts for the interaction of the molecule and the TiO2 cluster). We then combined capped-DFET with the accurate but expensive multiconfigurational complete active space second-order perturbation theory (CASPT2)-embedded CASPT2. Because the CW theory is conducted on only a portion of the total system in the presence of an embedding potential that describes that portion's interaction with its environment, we efficiently obtain CW-quality predictions that reflect local properties of the entire system. Specifically, for example, with capped-DFET and embedded CW theory, we can simulate accurately a plethora of metal-to-ligand charge-transfer excited properties at a manageable computational cost. Here, we predict detailed electronic spectra within the visible region, featuring the lowest three singlet and triplet excited states, along with predictions of the singlets' lifetimes. We illustrated these results using a Jablonski diagram that show the relative energy position of the singlet and longer-lived triplet excited states and analyzed and proposed relaxation paths for the excited state corresponding to the most intense but short-lived absorption (interconversion, intersystem crossing, fluorescence, and phosphorescence) that may lead to longer-lived excited states necessary for efficient charge separation required to generate current in solar cells.

Facet-Independent Oxygen Evolution Activity of Pure ß-NiOOH: Different Chemistries Leading to Similar Overpotentials.

ß-Nickel oxyhydroxide (ß-NiOOH) is a promising electrocatalyst for the oxygen evolution reaction (OER), which is the more difficult half-reaction involved in water splitting. In this study, we revisit the OER activities of the two most abundant crystallographic facets of pristine ß-NiOOH, the (0001) and (1010) facets, which expose 6-fold-lattice-oxygen-coordinated and 5-fold-lattice-oxygen-coordinated Ni sites, respectively. To this end, we model various active sites on these two facets using hybrid density functional theory, which includes a fraction of the exact nonlocal Fock exchange in the electronic description of the system. By evaluating thermodynamic OER overpotentials, we show that the two active sites considered on each crystallographic facet demonstrate OER activities remarkably different from each other. However, the lowest OER overpotentials calculated for the two facets were found to be similar to each other and comparable to the overpotential for the 4-fold-lattice-oxygen-coordinated Ni site on the (1211) facet of ß-NiOOH previously examined in J. Am. Chem. Soc. 2019 , 141 , 1 , 693 - 705 . This finding shows that all of the low-index facets investigated so far could be responsible for the experimentally observed OER activity of pristine ß-NiOOH. However, the lowest overpotential active sites on these three crystallographic facets operate via different mechanisms, underscoring the importance of considering multiple OER pathways and intermediates on each crystallographic facet of a potential electrocatalyst. Specifically, our work demonstrates that consideration of previously overlooked active sites, transition-metal-ion oxidation states, reaction intermediates, and lattice-oxygen-stabilization are critical to reveal the lowest overpotential OER pathways on pristine ß-NiOOH.

Ionic Layering and Overcharging in Electrical Double Layers in a Poisson-Boltzmann Model.

Electrical double layers (EDLs) play a significant role in a broad range of physical phenomena related to colloidal stability, diffuse-charge dynamics, electrokinetics, and energy storage applications. Recently, it has been suggested that for large ion sizes or multivalent electrolytes, ions can arrange in a layered structure inside the EDLs. However, the widely used Poisson-Boltzmann models for EDLs are unable to capture the details of ion concentration oscillations and the effect of electrolyte valence on such oscillations. Here, by treating a pair of ions as hard spheres below the distance of closest approach and as point charges otherwise, we are able to predict ionic layering without any additional parameters or boundary conditions while still being compatible with the Poisson-Boltzmann framework. Depending on the combination of ion valence, size, and concentration, our model reveals a structured EDL with spatially oscillating ion concentrations. We report the dependence of critical ion concentration, i.e., the ion concentration above which the oscillations are observed, on the counter-ion valence and the ion size. More importantly, our model displays quantitative agreement with the results of computationally intensive models of the EDL. Finally, we analyze the nonequilibrium problem of EDL charging and demonstrate that ionic layering increases the total charge storage capacity and the charging timescale.

The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry.

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.