Bayesian error estimation in density-functional theory

Putting error bars on density functional theory

Predicting the error in density functional theory (DFT) calculations due to the choice of exchange-correlation (XC) functional is crucial to the success of DFT, but currently, there are limited options to estimate this a priori. This is particularly important for high-throughput screening of new materials. In this work, the structure and elastic properties of binary and ternary oxides are computed using four XC functionals: LDA, PBE-GGA, PBEsol, and vdW-DF with C09 exchange. To analyze the systemic errors inherent to each XC functional, we employed materials informatics methods to predict the expected errors. The predicted errors were also used to better the DFT-predicted lattice parameters. Our results emphasize the link between the computed errors and the electron density and hybridization errors of a functional. In essence, these results provide "error bars" for choosing a functional for the creation of high-accuracy, high-throughput datasets as well as avenues for the development of XC functionals with enhanced performance, thereby enabling the accelerated discovery and design of new materials.

SCINE-Software for chemical interaction networks

The software for chemical interaction networks (SCINE) project aims at pushing the frontier of quantum chemical calculations on molecular structures to a new level. While calculations on individual structures as well as on simple relations between them have become routine in chemistry, new developments have pushed the frontier in the field to high-throughput calculations. Chemical relations may be created by a search for specific molecular properties in a molecular design attempt, or they can be defined by a set of elementary reaction steps that form a chemical reaction network. The software modules of SCINE have been designed to facilitate such studies. The features of the modules are (i) general applicability of the applied methodologies ranging from electronic structure (no restriction to specific elements of the periodic table) to microkinetic modeling (with little restrictions on molecularity), full modularity so that SCINE modules can also be applied as stand-alone programs or be exchanged for external software packages that fulfill a similar purpose (to increase options for computational campaigns and to provide alternatives in case of tasks that are hard or impossible to accomplish with certain programs), (ii) high stability and autonomous operations so that control and steering by an operator are as easy as possible, and (iii) easy embedding into complex heterogeneous environments for molecular structures taken individually or in the context of a reaction network. A graphical user interface unites all modules and ensures interoperability. All components of the software have been made available as open source and free of charge.

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Highly loaded bimetallic iron-cobalt catalysts for hydrogen release from ammonia

Ammonia is a storage molecule for hydrogen, which can be released by catalytic decomposition. Inexpensive iron catalysts suffer from a low activity due to a too strong iron-nitrogen binding energy compared to more active metals such as ruthenium. Here, we show that this limitation can be overcome by combining iron with cobalt resulting in a Fe-Co bimetallic catalyst. Theoretical calculations confirm a lower metal-nitrogen binding energy for the bimetallic catalyst resulting in higher activity. Operando spectroscopy reveals that the role of cobalt in the bimetallic catalyst is to suppress the bulk-nitridation of iron and to stabilize this active state. Such catalysts are obtained from Mg(Fe,Co)2O4 spinel pre-catalysts with variable Fe:Co ratios by facile co-precipitation, calcination and reduction. The resulting Fe-Co/MgO catalysts, characterized by an extraordinary high metal loading reaching 74 wt.%, combine the advantages of a ruthenium-like electronic structure with a bulk catalyst-like microstructure typical for base metal catalysts.

Statistical Equivalence of Quantum Chemical Methods for Energy Distribution in Water Clusters

Methods of quantum chemistry are instrumental in understanding molecular structures and properties. However, the results demonstrate significant variability, which is difficult to predict and rationalize. The fundamental question is whether some molecular systems exhibit properties invariant with respect to the computational method. The idea explored here is that collective properties of statistical ensembles should be more robust than characteristics of individual molecules and their arbitrary sets. This effect is demonstrated for the complete set of hydrogen-bond topologies of the dodecahedral water cluster (H₂ O)₂₀ . Non-Gaussian energy distributions produced by various methods have the same functional form despite strong differences in mean values and standard deviations. The conclusion is tested on methods of different complexity and origin employing a number of criteria. A linear mapping between the energies produced by different methods is discussed. The significance of the results is in establishing a collective equivalence property of quantum chemical methods.

Redox-active ligands as a challenge for electronic structure methods

To improve the catalytic activity of 3d transition metal catalysts, redox-active ligands are a promising tool. These ligands influence the oxidation state of the metal center as well as the ground spin-state and make the experimental determination of both properties challenging. Therefore, first-principles calculations, in particular employing density functional theory with a proper choice of exchange-correlation (xc) functional, are crucial. Common xc functionals were tested on a simple class of metal complexes: homoleptic, octahedral tris(diimine) iron(II) complexes. The spin-state energy splittings for most of these complexes showed the expected linear dependence on the amount of exact exchange included in the xc functionals. Even though varying redox-activity affects the electronic structure of the complexes considerably, the sensitivity of the spin-state energetics to the exact exchange admixture is surprisingly small. For iron(II) complexes with highly redox-active ligands and for a broad range of ligands in the reduced tris(diimine) iron(I) complexes, self-consistent field convergence to local minima was observed, which differ from the global minimum in the redox state of the ligand. This may also result in convergence to a molecular structure that corresponds to an energetically higher-lying local minimum. One criterion to detect such behavior is a change in the sign of the slope for the dependence of the spin-state energy splittings on the amount of exact exchange. We discuss possible protocols for dealing with such artifacts in cases in which a large number of calculations makes checking by hand unfeasible.

Binding Energy and Diffusion Barrier of Formic Acid on Pd(111)

Velocity-resolved kinetics is used to measure the thermal rate of formic acid desorption from Pd(111) between 228 and 273 K for four isotopologues: HCOOH, HCOOD, DCOOH, DCOOD. Upon molecular adsorption, formic acid undergoes decomposition to CO₂ and H₂ and thermal desorption. To disentangle the contributions of individual processes, we implement a mass-balance-based calibration procedure from which the branching ratio between desorption and decomposition for formic acid is determined. From experimentally derived elementary desorption rate constants, we obtain the binding energy 639 ± 8 meV and the diffusion barrier 370 ± 130 meV using the detailed balance rate model (DBRM). The DBRM explains the observed kinetic isotope effects.

Modeling CoCu Nanoparticles Using Neural Network-Accelerated Monte Carlo Simulations

The correct description of catalytic reactions happening on bimetallic particles is not feasible without proper accounting of the segregation process. In this study, we tried to shed light on the structure of large CoCu particles, for which quite controversial results were published before. However, density functional theory (DFT) is challenging to be directly used for the systematic study of nanometer-sized particles. Therefore, we constructed a neural network-based potential and further applied it to the Monte Carlo simulations for the description of the segregation phenomenon. The resulting approach shows high efficiency and can be used in systems with thousands of atoms. The accuracy and transferability of the model to other sizes and compositions make this methodology useful for solving segregation problems.

Competition between reverse water gas shift reaction and methanol synthesis from CO2: influence of copper particle size

Converting CO₂ into value-added chemicals and fuels, such as methanol, is a promising approach to limit the environmental impact of human activities. Conventional methanol synthesis catalysts have shown limited efficiency and poor stability in a CO₂/H₂ mixture. To design improved catalysts, crucial for the effective utilization of CO₂, an in-depth understanding of the active sites and reaction mechanism is desired. The catalytic performance of a series of carbon-supported Cu catalysts, with Cu particle sizes in the range of 5 to 20 nm, was evaluated under industrially relevant temperature and pressure, i.e. 260 °C and 40 bar(g). The CO₂ hydrogenation reaction exhibited clear particle size effects up to 13 nm particles, with small nanoparticles having the lower activity, but higher methanol selectivity. MeOH and CO formation showed a different size-dependence. The TOF_CO increased from 1.9 × 10^-3 s^-1 to 9.4 × 10^-3 s^-1 with Cu size increasing from 5 nm to 20 nm, while the TOF_MeOH was size-independent (8.4 × 10^-4 s^-1 on average). The apparent activation energies for MeOH and CO formation were size-independent with values of 63 ± 7 kJ mol^-1 and 118 ± 6 kJ mol^-1, respectively. Hence the size dependence was ascribed to a decrease in the fraction of active sites suitable for CO formation with decreasing particle size. Theoretical models and DFT calculations showed that the origin of the particle size effect is most likely related to the differences in formate coverage for different Cu facets whose abundancy depends on particle size. Hence, the CO₂ hydrogenation reaction is intrinsically sensitive to the Cu particle size.

Adsorption and Absorption Energies of Hydrogen with Palladium

Thermal recombinative desorption rates of HD on Pd(111) and Pd(332) are reported from transient kinetic experiments performed between 523 and 1023 K. A detailed kinetic model accurately describes the competition between recombination of surface-adsorbed hydrogen and deuterium atoms and their diffusion into the bulk. By fitting the model to observed rates, we derive the dissociative adsorption energies (E _0, ads ^H₂ = 0.98 eV; E _0, ads ^D₂ = 1.00 eV; E _0, ads ^HD = 0.99 eV) as well as the classical dissociative binding energy ϵ_ads = 1.02 ± 0.03 eV, which provides a benchmark for electronic structure theory. In a similar way, we obtain the classical energy required to move an H or D atom from the surface to the bulk (ϵ_sb = 0.46 ± 0.01 eV) and the isotope specific energies, E _0, sb ^H = 0.41 eV and E _0, sb ^D = 0.43 eV. Detailed insights into the process of transient bulk diffusion are obtained from kinetic Monte Carlo simulations.

Pericyclic reaction benchmarks: hierarchical computations targeting CCSDT(Q)/CBS and analysis of DFT performance

Hierarchical, convergent ab initio benchmark computations were performed followed by a systematic analysis of DFT performance for five pericyclic reactions comprising Diels-Alder, 1,3-dipolar cycloaddition, electrocyclic rearrangement, sigmatropic rearrangement, and double group transfer prototypes. Focal point analyses (FPA) extrapolating to the ab initio limit were executed via explicit quantum chemical computations with electron correlation treatments through CCSDT(Q) and correlation-consistent Gaussian basis sets up to aug'-cc-pV5Z. Optimized geometric structures and vibrational frequencies of all stationary points were obtained at the CCSD(T)/cc-pVTZ level of theory. The FPA reaction barriers and energies exhibit convergence to within a few tenths of a kcal mol-1. The FPA benchmarks were used to evaluate the performance of 60 density functionals (eight dispersion-corrected), covering the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. The meta-hybrid M06-2X functional provided the best overall performance [mean absolute error (MAE) of 1.1 kcal mol-1] followed closely by the double-hybrids B2K-PLYP, mPW2K-PLYP, and revDSD-PBEP86 [MAE of 1.4-1.5 kcal mol-1]. The regularly used GGA functional BP86 gave a higher MAE of 5.8 kcal mol-1, but it qualitatively described the trends in reaction barriers and energies. Importantly, we established that accurate yet efficient meta-hybrid or double-hybrid DFT potential energy surfaces can be acquired based on geometries from the computationally efficient and robust BP86/DZP level.

Quantum effects in thermal reaction rates at metal surfaces

There is wide interest in developing accurate theories for predicting rates of chemical reactions that occur at metal surfaces, especially for applications in industrial catalysis. Conventional methods contain many approximations that lack experimental validation. In practice, there are few reactions where sufficiently accurate experimental data exist to even allow meaningful comparisons to theory. Here, we present experimentally derived thermal rate constants for hydrogen atom recombination on platinum single-crystal surfaces, which are accurate enough to test established theoretical approximations. A quantum rate model is also presented, making possible a direct evaluation of the accuracy of commonly used approximations to adsorbate entropy. We find that neglecting the wave nature of adsorbed hydrogen atoms and their electronic spin degeneracy leads to a 10× to 1000× overestimation of the rate constant for temperatures relevant to heterogeneous catalysis. These quantum effects are also found to be important for nanoparticle catalysts.

Data-driven and constrained optimization of semi-local exchange and nonlocal correlation functionals for materials and surface chemistry

Reliable predictions of surface chemical reaction energetics require an accurate description of both chemisorption and physisorption. Here, we present an empirical approach to simultaneously optimize semi-local exchange and nonlocal correlation of a density functional approximation to improve these energetics. A combination of reference data for solid bulk, surface, and gas-phase chemistry and physical exchange-correlation model constraints leads to the VCML-rVV10 exchange-correlation functional. Owing to the variety of training data, the applicability of VCML-rVV10 extends beyond surface chemistry simulations. It provides optimized gas phase reaction energetics and an accurate description of bulk lattice constants and elastic properties.

The long road to calibrated prediction uncertainty in computational chemistry

Uncertainty quantification (UQ) in computational chemistry (CC) is still in its infancy. Very few CC methods are designed to provide a confidence level on their predictions, and most users still rely improperly on the mean absolute error as an accuracy metric. The development of reliable UQ methods is essential, notably for CC to be used confidently in industrial processes. A review of the CC-UQ literature shows that there is no common standard procedure to report or validate prediction uncertainty. I consider here analysis tools using concepts (calibration and sharpness) developed in meteorology and machine learning for the validation of probabilistic forecasters. These tools are adapted to CC-UQ and applied to datasets of prediction uncertainties provided by composite methods, Bayesian ensembles methods, and machine learning and a posteriori statistical methods.

Autonomous Reaction Network Exploration in Homogeneous and Heterogeneous Catalysis

Autonomous computations that rely on automated reaction network elucidation algorithms may pave the way to make computational catalysis on a par with experimental research in the field. Several advantages of this approach are key to catalysis: (i) automation allows one to consider orders of magnitude more structures in a systematic and open-ended fashion than what would be accessible by manual inspection. Eventually, full resolution in terms of structural varieties and conformations as well as with respect to the type and number of potentially important elementary reaction steps (including decomposition reactions that determine turnover numbers) may be achieved. (ii) Fast electronic structure methods with uncertainty quantification warrant high efficiency and reliability in order to not only deliver results quickly, but also to allow for predictive work. (iii) A high degree of autonomy reduces the amount of manual human work, processing errors, and human bias. Although being inherently unbiased, it is still steerable with respect to specific regions of an emerging network and with respect to the addition of new reactant species. This allows for a high fidelity of the formalization of some catalytic process and for surprising in silico discoveries. In this work, we first review the state of the art in computational catalysis to embed autonomous explorations into the general field from which it draws its ingredients. We then elaborate on the specific conceptual issues that arise in the context of autonomous computational procedures, some of which we discuss at an example catalytic system.

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The online version contains supplementary material available at 10.1007/s11244-021-01543-9.

Closed-Loop Electrolyte Design for Lithium-Mediated Ammonia Synthesis

Novel methods for producing ammonia, a large-scale industrial chemical, are necessary for reducing the environmental impact of its production. Lithium-mediated electrochemical nitrogen reduction is one attractive alternative method for producing ammonia. In this work, we experimentally tested several classes of proton donors for activity in the lithium-mediated approach. From these data, an interpretable data-driven classification model is constructed to distinguish between active and inactive proton donors; solvatochromic Kamlet-Taft parameters emerged to be the key descriptors for predicting nitrogen reduction activity. A deep learning model is trained to predict these parameters using experimental data from the literature. The combination of the classification and deep learning models provides a predictive mapping from proton donor structure to activity for nitrogen reduction. We demonstrate that the two-model approach is superior to a purely mechanistic or a data-driven approach in accuracy and experimental data efficiency.

Role of Dihydride and Dihydrogen Complexes in Hydrogen Evolution Reaction on Single-Atom Catalysts

The hydrogen evolution reaction (HER) has a key role in electrochemical water splitting. Recently a lot of attention has been dedicated to HER from single atom catalysts (SACs). The activity of SACs in HER is usually rationalized or predicted using the original model proposed by Nørskov where the free energy of a H atom adsorbed on an extended metal surface M (formation of an MH intermediate) is used to explain the trends in the exchange current for HER. However, SACs differ substantially from metal surfaces and can be considered analogues of coordination compounds. In coordination chemistry, at variance with metal surfaces, stable dihydride or dihydrogen complexes (HMH) can form. We show that the same can occur on SACs and that the formation of stable HMH intermediates, in addition to the MH one, may change the kinetics of the process. Extending the original kinetic model to the case of two intermediates (MH and HMH), one obtains a three-dimensional volcano plot for the HER on SACs. DFT numerical simulations on 55 models demonstrate that the new kinetic model may lead to completely different conclusions about the activity of SACs in HER. The results are validated against selected experimental cases. The work provides an example of the important analogies between the chemistry of SACs and that of coordination compounds.

MCML: Combining physical constraints with experimental data for a multi-purpose meta-generalized gradient approximation

The predictive power of density functional theory for materials properties can be improved without increasing the overall computational complexity by extending the generalized gradient approximation (GGA) for electronic exchange and correlation to density functionals depending on the electronic kinetic energy density in addition to the charge density and its gradient, resulting in a meta-GGA. Here, we propose an empirical meta-GGA model that is based both on physical constraints and on experimental and quantum chemistry reference data. The resulting optimized meta-GGA MCML yields improved surface and gas phase reaction energetics without sacrificing the accuracy of bulk property predictions of existing meta-GGA approaches.

Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles

Virtual high-throughput screening (VHTS) with density functional theory (DFT) and machine-learning (ML)-acceleration is essential in rapid materials discovery. By necessity, efficient DFT-based workflows are carried out with a single density functional approximation (DFA). Nevertheless, properties evaluated with different DFAs can be expected to disagree for cases with challenging electronic structure (e.g., open-shell transition-metal complexes, TMCs) for which rapid screening is most needed and accurate benchmarks are often unavailable. To quantify the effect of DFA bias, we introduce an approach to rapidly obtain property predictions from 23 representative DFAs spanning multiple families, “rungs” (e.g., semi-local to double hybrid) and basis sets on over 2000 TMCs. Although computed property values (e.g., spin state splitting and frontier orbital gap) differ by DFA, high linear correlations persist across all DFAs. We train independent ML models for each DFA and observe convergent trends in feature importance, providing DFA-invariant, universal design rules. We devise a strategy to train artificial neural network (ANN) models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 187k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of computational lead compounds with literature-mined, experimental compounds over the typically employed single-DFA approach.

Machine learning (ML)-based feature analysis reveals universal design rules regardless of density functional choices. Using the consensus among multiple functionals, we identify robust lead complexes in ML-accelerated chemical discovery.

The Role of Oxygenic Groups and sp3 Carbon Hybridization in Activated Graphite Electrodes for Vanadium Redox Flow Batteries

Graphite felt is a widely used electrode material for vanadium redox flow batteries. Electrode activation leads to the functionalization of the graphite surface with epoxy, OH, C=O, and COOH oxygenic groups and changes the carbon surface morphology and electronic structure, thereby improving the electrode's electroactivity relative to the untreated graphite. In this study, density functional theory (DFT) calculations are conducted to evaluate functionalization's contribution towards the positive half-cell reaction of the vanadium redox flow battery. The DFT calculations show that oxygenic groups improve the graphite felt's affinity towards the VO²⁺ /VO₂ ⁺ redox couple in the following order: C=O>COOH>OH> basal plane. Projected density-of-states (PDOS) calculations show that these groups increase the electrode's sp³ hybridization in the same order, indicating that the increase in sp³ hybridization is responsible for the improved electroactivity, whereas the oxygenic groups' presence is responsible for this sp³ increment. These insights can aid the selection of activation processes and optimization of their parameters.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

The importance of exact exchange-A methodological investigation of NO reduction in heme-copper oxidases

Significant improvements of the density functional theory (DFT) methodology during the past few decades have made DFT calculations a powerful tool in studies of enzymatic reaction mechanisms. For metalloenzymes, however, there are still concerns about the reliability in the DFT-results. Therefore, a systematic study is performed where the fraction of exact exchange in a hybrid DFT functional is used as a parameter. By varying this parameter, a set of different but related functionals are obtained. The various functionals are applied to one of the reactions occurring in the enzyme family heme-copper oxidases, the reduction of nitric oxide (NO) to nitrous oxide (N₂O) and water. The results show that, even though certain parts of the calculated energetics exhibit large variations, the qualitative pictures of the reaction mechanisms are quite stable. Furthermore, it is found that the functional with 15% exact exchange (B3LYP^*) gives the best agreement with experimental data for the particular reactions studied. An important aspect of the procedure used is that the computational results are carefully combined with a few more general experimental data to obtain a complete description of the entire catalytic cycle of the reactions studied.

Uncertainty quantification in classical molecular dynamics

Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach has begun to advance from being a computer-based means of rationalizing experimental observations to producing apparently credible predictions for a number of real-world applications within industrial sectors such as advanced materials and drug discovery. However, key aspects concerning the reproducibility of the method have not kept pace with the speed of its uptake in the scientific community. Here, we present a discussion of uncertainty quantification for molecular dynamics simulation designed to endow the method with better error estimates that will enable it to be used to report actionable results. The approach adopted is a standard one in the field of uncertainty quantification, namely using ensemble methods, in which a sufficiently large number of replicas are run concurrently, from which reliable statistics can be extracted. Indeed, because molecular dynamics is intrinsically chaotic, the need to use ensemble methods is fundamental and holds regardless of the duration of the simulations performed. We discuss the approach and illustrate it in a range of applications from materials science to ligand-protein binding free energy estimation. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (E_b, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate E_b can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol^-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for E_b for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH₄. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of E_b for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate E_b for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O₂, H₂O, NH₃, CO₂, and CH₃OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.

Addressing the uncertainty of DFT-determined hydrogenation mechanisms over coinage metal surfaces

Density functional theory (DFT) has been considered as a powerful tool for the identification of reaction mechanisms. However, it is still unclear whether the error of DFT calculations would lead to mis-identification of mechanisms. Here, taking the hydrogenation of acetylene and 1,3-butadiene as model reactions and employing a well-trained Bayesian error estimation functional with van der Waals correlation (BEEF-vdW), we try to estimate the error of DFT calculation results statistically, and therefore predict the reliability of the hydrogenation mechanisms identified. With an ensemble of 2000 functionals obtained around the BEEF-vdW functional as well as a descriptor developed to represent the possibility of different mechanisms, we found that the non-Horiuti-Polanyi mechanism is preferred on Ag(211) and Au(211), while the Horiuti-Polanyi mechanism is dominant on Cu(211). We further discovered that the descriptor is linearly correlated with the adsorption energies of reaction intermediates during acetylene and butadiene hydrogenation, and the hydrogenation of strongly adsorbed species are more likely to follow the Horiuti-Polanyi mechanism. We found the probability of following the non-HP mechanism obeys the order Cu(211) < Au(211) < Ag(211). Our work gives a more comprehensive explanation for the mechanisms of coinage metal catalyzed hydrogenation reactions, and also provides more theoretical insights into the development of new high-performance catalysts for selective hydrogenation reactions.

Influence of Electronic Structure Modeling and Junction Structure on First-Principles Chiral Induced Spin Selectivity

We have carried out a comprehensive study of the influence of electronic structure modeling and junction structure description on the first-principles calculation of the spin polarization in molecular junctions caused by the chiral induced spin selectivity (CISS) effect. We explore the limits and the sensitivity to modeling decisions of a Landauer/Green's function/two-component density functional theory approach to CISS. We find that although the CISS effect is entirely attributed in the literature to molecular spin filtering, spin-orbit coupling being partially inherited from the metal electrodes plays an important role in our calculations on ideal carbon helices, even though this effect cannot explain the experimental conductance results. Its magnitude depends considerably on the shape, size, and material of the metal clusters modeling the electrodes. Also, a pronounced dependence on the specific description of exchange interaction and spin-orbit coupling is manifest in our approach. This is important because the interplay between exchange effects and spin-orbit coupling may play an important role in the description of the junction magnetic response. Our calculations are relevant for the whole field of spin-polarized electron transport and electron transfer, because there is still an open discussion in the literature about the detailed underlying mechanism and the magnitude of physical parameters that need to be included to achieve a consistent description of the CISS effect: seemingly good quantitative agreement between simulation and the experiment can be caused by error compensation, because spin polarization as contained in a Landauer/Green's function/two-component density functional theory approach depends strongly on computational and structural parameters.

Probabilistic performance estimators for computational chemistry methods: Systematic improvement probability and ranking probability matrix. I. Theory

The comparison of benchmark error sets is an essential tool for the evaluation of theories in computational chemistry. The standard ranking of methods by their mean unsigned error is unsatisfactory for several reasons linked to the non-normality of the error distributions and the presence of underlying trends. Complementary statistics have recently been proposed to palliate such deficiencies, such as quantiles of the absolute error distribution or the mean prediction uncertainty. We introduce here a new score, the systematic improvement probability, based on the direct system-wise comparison of absolute errors. Independent of the chosen scoring rule, the uncertainty of the statistics due to the incompleteness of the benchmark datasets is also generally overlooked. However, this uncertainty is essential to appreciate the robustness of rankings. In the present article, we develop two indicators based on robust statistics to address this problem: P_inv, the inversion probability between two values of a statistic, and P_r, the ranking probability matrix. We demonstrate also the essential contribution of the correlations between error sets in these scores comparisons.

Towards theoretical spectroscopy with error bars: systematic quantification of the structural sensitivity of calculated spectra

Molecular spectra calculated with quantum-chemical methods are subject to a number of uncertainties (e.g., errors introduced by the computational methodology) that hamper the direct comparison of experiment and computation. Judging these uncertainties is crucial for drawing reliable conclusions from the interplay of experimental and theoretical spectroscopy, but largely relies on subjective judgment. Here, we explore the application of methods from uncertainty quantification to theoretical spectroscopy, with the ultimate goal of providing systematic error bars for calculated spectra. As a first target, we consider distortions of the underlying molecular structure as one important source of uncertainty. We show that by performing a principal component analysis, the most influential collective distortions can be identified, which allows for the construction of surrogate models that are amenable to a statistical analysis of the propagation of uncertainties in the molecular structure to uncertainties in the calculated spectrum. This is applied to the calculation of X-ray emission spectra of iron carbonyl complexes, of the electronic excitation spectrum of a coumarin dye, and of the infrared spectrum of alanine. We show that with our approach it becomes possible to obtain error bars for calculated spectra that account for uncertainties in the molecular structure. This is an important first step towards systematically quantifying other relevant sources of uncertainty in theoretical spectroscopy.

Uncertainty quantification is applied in theoretical spectroscopy to obtain error bars accounting for the structural sensitivity of calculated spectra.

A comparative test of different density functionals for calculations of NH3-SCR over Cu-Chabazite

A general challenge in density functional theory calculations is to simultaneously account for different types of bonds. One such example is reactions in zeolites where both van der Waals and chemical bonds should be described accurately. Here, we use different exchange-correlation functionals to explore O₂ dissociation over pairs of Cu(NH₃)₂⁺ complexes in Cu-Chabazite. This is an important part of selective catalytic reduction of NO_x using NH₃ as a reducing agent. The investigated functionals are PBE, PBE+U, PBE+D, PBE+U+D, PBE-cx, BEEF and HSE06+D. We find that the potential energy landscape for O₂ activation and dissociation depends critically on the choice of functional. However, the van der Waals contributions are similarly described by the functionals accounting for this interaction. The discrepancies in the potential energy surface are instead related to different descriptions of the Cu-O chemical bond. By investigating the electronic, structural and energetic properties of reference systems including bulk copper oxides and (Cu₂O₂)²⁺ enzymatic crystals, we find that the PBE+U approach together with van der Waals corrections provides a reasonable simultaneous accuracy of the different bonds in the systems.

Designing in the Face of Uncertainty: Exploiting Electronic Structure and Machine Learning Models for Discovery in Inorganic Chemistry

Recent transformative advances in computing power and algorithms have made computational chemistry central to the discovery and design of new molecules and materials. First-principles simulations are increasingly accurate and applicable to large systems with the speed needed for high-throughput computational screening. Despite these strides, the combinatorial challenges associated with the vastness of chemical space mean that more than just fast and accurate computational tools are needed for accelerated chemical discovery. In transition-metal chemistry and catalysis, unique challenges arise. The variable spin, oxidation state, and coordination environments favored by elements with well-localized d or f electrons provide great opportunity for tailoring properties in catalytic or functional (e.g., magnetic) materials but also add layers of uncertainty to any design strategy. We outline five key mandates for realizing computationally driven accelerated discovery in inorganic chemistry: (i) fully automated simulation of new compounds, (ii) knowledge of prediction sensitivity or accuracy, (iii) faster-than-fast property prediction methods, (iv) maps for rapid chemical space traversal, and (v) a means to reveal design rules on the kilocompound scale. Through case studies in open-shell transition-metal chemistry, we describe how advances in methodology and software in each of these areas bring about new chemical insights. We conclude with our outlook on the next steps in this process toward realizing fully autonomous discovery in inorganic chemistry using computational chemistry.

Bayesian machine learning for quantum molecular dynamics

This article discusses applications of Bayesian machine learning for quantum molecular dynamics.

Breaking the scaling relationship via thermally stable Pt/Cu single atom alloys for catalytic dehydrogenation

Noble-metal alloys are widely used as heterogeneous catalysts. However, due to the existence of scaling properties of adsorption energies on transition metal surfaces, the enhancement of catalytic activity is frequently accompanied by side reactions leading to a reduction in selectivity for the target product. Herein, we describe an approach to breaking the scaling relationship for propane dehydrogenation, an industrially important reaction, by assembling single atom alloys (SAAs), to achieve simultaneous enhancement of propylene selectivity and propane conversion. We synthesize γ-alumina-supported platinum/copper SAA catalysts by incipient wetness co-impregnation method with a high copper to platinum ratio. Single platinum atoms dispersed on copper nanoparticles dramatically enhance the desorption of surface-bounded propylene and prohibit its further dehydrogenation, resulting in high propylene selectivity (~90%). Unlike previous reported SAA applications at low temperatures (<400 °C), Pt/Cu SAA shows excellent stability of more than 120 h of operation under atmospheric pressure at 520 °C.

Enhancing the catalytic activity of noble-metal alloys is frequently accompanied by side reactions. Here, the authors describe an approach to break the scaling relationship for propane dehydrogenation, by assembling single atom alloys, to achieve simultaneous enhancement of propylene selectivity and propane conversion.

Polarizable Drude Model with s-Type Gaussian or Slater Charge Density for General Molecular Mechanics Force Fields

Gas-phase electric properties of molecules can be computed routinely using wave function methods or density functional theory (DFT). However, these methods remain computationally expensive for high-throughput screening of the vast chemical space of virtual compounds. Therefore, empirical force fields are a more practical choice in many cases, particularly since force field methods allow one to routinely predict the physicochemical properties in the condensed phases. This work presents Drude polarizable models, to increase the physical realism in empirical force fields, where the core particle is treated as a point charge and the Drude particle is treated either as a 1 s-Gaussian or a ns-Slater ( n = 1, 2, 3) charge density. Systematic parametrization to large high-quality quantum chemistry data obtained from the open access Alexandria Library ( https://doi.org/10.5281/zenodo.1004711 ) ensures the transferability of these parameters. The dipole moments and isotropic polarizabilities of the isolated molecules predicted by the proposed Drude models are in agreement with experiment with accuracy similar to DFT calculations at the B3LYP/aug-cc-pVTZ level of theory. The results show that the inclusion of explicit polarization into the models reduces the root-mean-square deviation with respect to DFT calculations of the predicted dipole moments of 152 dimers and clusters by more than 50%. Finally, we show that the accuracy of the electrostatic interaction energy of the water dimers can be improved systematically by the introduction of polarizable smeared charges as a model for charge penetration.