Embedded correlated wavefunction schemes: theory and applications

Strategies to Obtain Reliable Energy Landscapes from Embedded Multireference Correlated Wavefunction Methods for Surface Reactions

Embedded correlated wavefunction (ECW) theory is a powerful tool for studying ground- and excited-state reaction mechanisms and associated energetics in heterogeneous catalysis. Several factors are important to obtaining reliable ECW energies, critically the construction of consistent active spaces (ASs) along reaction pathways when using a multireference correlated wavefunction (CW) method that relies on a subset of orbital spaces in the configuration interaction expansion to account for static electron correlation, e.g., complete AS self-consistent field theory, in addition to the adequate partitioning of the system into a cluster and environment, as well as the choice of a suitable basis set and number of states included in excited-state simulations. Here, we conducted a series of systematic studies to develop best-practice guidelines for ground- and excited-state ECW theory simulations, utilizing the decomposition of NH3 on Pd(111) as an example. We determine that ECW theory results are relatively insensitive to cluster size, the aug-cc-pVDZ basis set provides an adequate compromise between computational complexity and accuracy, and that a fixed-clean-surface approximation holds well for the derivation of the embedding potential. Additionally, we demonstrate that a merging approach, which involves generating ASs from the molecular fragments at each configuration, is preferable to a creeping approach, which utilizes ASs from adjacent structures as an initial guess, for the generation of consistent potential energy curves involving open-d-shell metal surfaces, and, finally, we show that it is essential to include bands of excited states in their entirety when simulating excited-state reaction pathways.

Emerging Atomistic Modeling Methods for Heterogeneous Electrocatalysis

Heterogeneous electrocatalysis lies at the center of various technologies that could help enable a sustainable future. However, its complexity makes it challenging to accurately and efficiently model at an atomic level. Here, we review emerging atomistic methods to simulate the electrocatalytic interface with special attention devoted to the components/effects that have been challenging to model, such as solvation, electrolyte ions, electrode potential, reaction kinetics, and pH. Additionally, we review relevant computational spectroscopy methods. Then, we showcase several examples of applying these methods to understand and design catalysts relevant to green hydrogen. We also offer experimental views on how to bridge the gap between theory and experiments. Finally, we provide some perspectives on opportunities to advance the field.

Coupled-cluster treatment of complex open-shell systems: the case of single-molecule magnets

We investigate the reliability of two cost-effective coupled-cluster methods for computing spin-state energetics and spin-related properties of a set of open-shell transition-metal complexes. Specifically, we employ the second-order approximate coupled-cluster singles and doubles (CC2) method and projection-based embedding that combines equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) with density functional theory (DFT). The performance of CC2 and EOM-CCSD-in-DFT is assessed against EOM-CCSD. The chosen test set includes two hexaaqua transition-metal complexes containing Fe(II) and Fe(III), and a large Co(II)-based single-molecule magnet with a non-aufbau ground state. We find that CC2 describes the excited states more accurately, reproducing EOM-CCSD excitation energies within 0.05 eV. However, EOM-CCSD-in-DFT excels in describing transition orbital angular momenta and spin-orbit couplings. Moreover, for the Co(II) molecular magnet, using EOM-CCSD-in-DFT eigenstates and spin-orbit couplings, we compute spin-reversal energy barriers, as well as temperature-dependent and field-dependent magnetizations and magnetic susceptibilities that closely match experimental values within spectroscopic accuracy. These results underscore the efficiency of CC2 in computing state energies of multi-configurational, open-shell systems and highlight the utility of the more cost-efficient EOM-CCSD-in-DFT for computing spin-orbit couplings and magnetic properties of complex and large molecular magnets.

Core Binding Energy Calculations: A Scalable Approach with the Quantum Embedding-Based Equation-of-Motion Coupled-Cluster Method

We investigated the use of density matrix embedding theory to facilitate the computation of core ionization energies (IPs) of large molecules at the equation-of-motion coupled-cluster singles doubles with perturbative triples (EOM-CCSD*) level in combination with the core-valence separation (CVS) approximation. The unembedded IP-CVS-EOM-CCSD* method with a triple-ζ basis set produced ionization energies within 1 eV of experiment with a standard deviation of ∼0.2 eV for the core65 data set. The embedded variant contributed very little systematic error relative to the unembedded method, with a mean unsigned error of 0.07 eV and a standard deviation of ∼0.1 eV, in exchange for accelerating the calculations by many orders of magnitude. By employing embedded EOM-CC methods, we computed the core ionization energies of the uracil hexamer, doped fullerene, and chlorophyll molecule, utilizing up to ∼4000 basis functions within 1 eV from experimental values. Such calculations are not currently possible with the unembedded EOM-CC method.

A Vision for the Future of Multiscale Modeling

The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.

Open-boundary cluster model with a parameter-free complex absorbing potential

In quantum chemical calculations of heterogeneous structures in solids, e.g., when an impurity is located on the surface, the conventional cluster model is insufficient to describe the electronic structure of substrates due to its finite size. The open-boundary cluster model (OCM) overcomes this problem by performing cluster calculations under the outgoing-wave boundary condition. In this method, a complex absorbing potential (CAP) is used to impose the boundary condition, but the CAP used in the previous studies required parameter optimization based on the complex variational principle. This study proposes and applies a parameter-free CAP to OCM calculations. This approach makes it possible to uniquely determine the band-specific CAP based on the surface Green's function theory. Using this CAP, we conducted OCM calculations of the tight-binding model of a one-dimensional semi-infinite chain, and we found that the calculated density of states agreed with the exact one. Surface states of the Newns-Anderson-Grimley model were also computed using the CAP, and the projected density of states on the adsorbed atom was successfully reproduced.

Characterizing the Mechanisms of Ca and Mg Carbonate Ion-Pair Formation with Multi-Level Molecular Dynamics/Quantum Mechanics Simulations

The carbonate minerals of Ca and Mg are abundant throughout the lithosphere and have recently garnered significant research interest as possible long-term carbon sinks in the sequestration of atmospheric carbon dioxide. Nonetheless, an understanding of the atomic-level processes comprising their mineralization remains limited. Here, we characterize and contrast the mechanisms of contact ion-pair formation in aqueous Ca and Mg carbonate systems, which represents the most fundamental step leading to the formation of their mineral solids. Utilizing multilevel embedded correlated wavefunction-based ab initio molecular dynamics/quantum mechanics simulations, we characterize not only the dynamics of these processes but also factors arising from the electronic structure of the involved species, revealing further details of the fundamentally different mechanisms for the interconversion between the contact ion-pairs and solvent-shared ion-pairs of Ca versus Mg carbonate.

Constructing Mixed Density Functionals for Describing Dissociative Chemisorption on Metal Surfaces: Basic Principles

The production of a majority of chemicals involves heterogeneous catalysis at some stage, and the rates of many heterogeneously catalyzed processes are governed by transition states for dissociative chemisorption on metals. Accurate values of barrier heights for dissociative chemisorption on metals are therefore important to benchmarking electronic structure theory in general and density functionals in particular. Such accurate barriers can be obtained using the semiempirical specific reaction parameter (SRP) approach to density functional theory. However, this approach has thus far been rather ad hoc in its choice of the generic expression of the SRP functional to be used, and there is a need for better heuristic approaches to determining the mixing parameters contained in such expressions. Here we address these two issues. We investigate the ability of several mixed, parametrized density functional expressions combining exchange at the generalized gradient approximation (GGA) level with either GGA or nonlocal correlation to reproduce barrier heights for dissociative chemisorption on metal surfaces. For this, seven expressions of such mixed density functionals are tested on a database consisting of results for 16 systems taken from a recently published slightly larger database called SBH17. Three expressions are derived that exhibit high tunability and use correlation functionals that are either of the PBE GGA form or of one of two limiting nonlocal forms also describing the attractive van der Waals interaction in an approximate way. We also find that, for mixed density functionals incorporating GGA correlation, the optimum fraction of repulsive RPBE GGA exchange obtained with a specific GGA density functional is correlated with the charge-transfer parameter, which is equal to the difference in the work function of the metal surface and the electron affinity of the molecule. However, the correlation is generally not large and not large enough to obtain accurate guesses of the mixing parameter for the systems considered, suggesting that it does not give rise to a very effective search strategy.

Molecules in Environments: Toward Systematic Quantum Embedding of Electrons and Drude Oscillators

We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational Ansatz for the correlated ground state of the fully interacting molecule-environment system. This wave function is optimized via the variational Monte Carlo method and the ground state energy is subsequently estimated through the diffusion Monte Carlo method. The proposed scheme allows an explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the molecule and the environment. We study solvation energies and excitation energies of benzene derivatives, obtaining excellent agreement with explicit ab initio calculations and experiments.

Many-Body Methods for Surface Chemistry Come of Age: Achieving Consensus with Experiments

The adsorption energy of a molecule onto the surface of a material underpins a wide array of applications, spanning heterogeneous catalysis, gas storage, and many more. It is the key quantity where experimental measurements and theoretical calculations meet, with agreement being necessary for reliable predictions of chemical reaction rates and mechanisms. The prototypical molecule-surface system is CO adsorbed on MgO, but despite intense scrutiny from theory and experiment, there is still no consensus on its adsorption energy. In particular, the large cost of accurate many-body methods makes reaching converged theoretical estimates difficult, generating a wide range of values. In this work, we address this challenge, leveraging the latest advances in diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] to obtain accurate predictions for CO on MgO. These reliable theoretical estimates allow us to evaluate the inconsistencies in published temperature-programed desorption experiments, revealing that they arise from variations in employed pre-exponential factors. Utilizing this insight, we derive new experimental estimates of the (electronic) adsorption energy with a (more) precise pre-exponential factor. As a culmination of all of this effort, we are able to reach a consensus between multiple theoretical calculations and multiple experiments for the first time. In addition, we show that our recently developed cluster-based CCSD(T) approach provides a low-cost route toward achieving accurate adsorption energies. This sets the stage for affordable and reliable theoretical predictions of chemical reactions on surfaces to guide the realization of new catalysts and gas storage materials.

A Perspective on Sustainable Computational Chemistry Software Development and Integration

The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.

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.

Optical Properties of Neutral F Centers in Bulk MgO with Density Matrix Embedding

The optical spectra of neutral oxygen vacancies (F0 centers) in the bulk MgO lattice are investigated using density matrix embedding theory. The impurity Hamiltonian is solved with the complete active space self-consistent field and second-order n-electron valence state perturbation theory (NEVPT2-DMET) multireference methods. To estimate defect-localized vertical excitation energies at the nonembedding and thermodynamic limits, a double extrapolation scheme is employed. The extrapolated NEVPT2-DMET vertical excitation energy value of 5.24 eV agrees well with the experimental absorption maxima at 5.03 eV, whereas the excitation energy value of 2.89 eV at the relaxed triplet defect-localized state geometry overestimates the experimental emission at 2.4 eV by only nearly 0.5 eV, indicating the involvement of the triplet-singlet decay pathway.

Toward a Rigorous Theoretical Description of Photocatalysis Using Realistic Models

This Perspective aims at providing a road map to computational heterogeneous photocatalysis highlighting the knowledge needed to boost the design of efficient photocatalysts. A plausible computational framework is suggested focusing on static and dynamic properties of the relevant excited states as well of the involved chemistry for the reactions of interest. This road map calls for explicitly exploring the nature of the charge carriers, the excited-state potential energy surface, and its time evolution. Excited-state descriptors are introduced to locate and characterize the electrons and holes generated upon excitation. Nonadiabatic molecular dynamics simulations are proposed as a convenient tool to describe the time evolution of the photogenerated species and their propagation through the crystalline structure of photoactive material, ultimately providing information about the charge carrier lifetime. Finally, it is claimed that a detailed understanding of the mechanisms of heterogeneously photocatalyzed reactions demands the analysis of the excited-state potential energy surface.

Bootstrap Embedding on a Quantum Computer

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match─at little additional computational cost─full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.

Accurate descriptions of molecule-surface interactions in electrocatalytic CO2 reduction on the copper surfaces

Copper-based catalysts play a pivotal role in many industrial processes and hold a great promise for electrocatalytic CO₂ reduction reaction into valuable chemicals and fuels. Towards the rational design of catalysts, the growing demand on theoretical study is seriously at odds with the low accuracy of the most widely used functionals of generalized gradient approximation. Here, we present results using a hybrid scheme that combines the doubly hybrid XYG3 functional and the periodic generalized gradient approximation, whose accuracy is validated against an experimental set on copper surfaces. A near chemical accuracy is established for this set, which, in turn, leads to a substantial improvement for the calculated equilibrium and onset potentials as against the experimental values for CO₂ reduction to CO on Cu(111) and Cu(100) electrodes. We anticipate that the easy use of the hybrid scheme will boost the predictive power for accurate descriptions of molecule-surface interactions in heterogeneous catalysis.

On the accuracy of orbital based multi-level approaches for closed-shell transition metal chemistry

In this work, we investigate the accuracy of the local molecular orbital molecular orbital (LMOMO) scheme and projection-based wave function-in-density functional theory (WF-in-DFT) embedding for the prediction of reaction energies and barriers of typical reactions involving transition metals. To analyze the dependence of the accuracy on the system partitioning, we apply a manual orbital selection for LMOMO as well as the so-called direct orbital selection (DOS) for both approaches. We benchmark these methods on 30 closed shell reactions involving 16 different transition metals. This allows us to devise guidelines for the manual selection as well as settings for the DOS that provide accurate results within an error of 2 kcal mol^-1 compared to local coupled cluster. To reach this accuracy, on average 55% of the occupied orbitals have to be correlated with coupled cluster for the current test set. Furthermore, we find that LMOMO gives more reliable relative energies for small embedded regions than WF-in-DFT embedding.

A variational formulation of the Harris functional as a correction to approximate Kohn-Sham density functional theory

Accurate descriptions of intermolecular interactions are of great importance in simulations of molecular liquids. We present an electronic structure method that combines the accuracy of the Harris functional approach with the computational efficiency of approximately linear-scaling density functional theory (DFT). The non-variational nature of the Harris functional has been addressed by constructing a Lagrangian energy functional, which restores the variational condition by imposing stationarity with respect to the reference density. The associated linear response equations may be treated with linear-scaling efficiency in an atomic orbital based scheme. Key ingredients to describe the structural and dynamical properties of molecular systems are the forces acting on the atoms and the stress tensor. These first-order derivatives of the Harris Lagrangian have been derived and implemented in consistence with the energy correction. The proposed method allows for simulations with accuracies close to the Kohn-Sham DFT reference. Embedded in the CP2K program package, the method is designed to enable ab initio molecular dynamics simulations of molecular solutions for system sizes of several thousand atoms. Available subsystem DFT methods may be used to provide the reference density required for the energy correction at near linear-scaling efficiency. As an example of production applications, we applied the method to molecular dynamics simulations of the binary mixtures cyclohexane-methanol and toluene-methanol, performed within the isobaric-isothermal ensemble, to investigate the hydrogen bonding network in these non-ideal mixtures.

Characterization of excited states in time-dependent density functional theory using localized molecular orbitals

Localized molecular orbitals are often used for the analysis of chemical bonds, but they can also serve to efficiently and comprehensibly compute linear response properties. While conventional canonical molecular orbitals provide an adequate basis for the treatment of excited states, a chemically meaningful identification of the different excited-state processes is difficult within such a delocalized orbital basis. In this work, starting from an initial set of supermolecular canonical molecular orbitals, we provide a simple one-step top-down embedding procedure for generating a set of orbitals, which are localized in terms of the supermolecule but delocalized over each subsystem composing the supermolecule. Using an orbital partitioning scheme based on such sets of localized orbitals, we further present a procedure for the construction of local excitations and charge-transfer states within the linear response framework of time-dependent density functional theory (TDDFT). This procedure provides direct access to approximate diabatic excitation energies and, under the Tamm-Dancoff approximation, also their corresponding electronic couplings-quantities that are of primary importance in modeling energy transfer processes in complex biological systems. Our approach is compared with a recently developed diabatization procedure based on subsystem TDDFT using projection operators, which leads to a similar set of working equations. Although both of these methods differ in the general localization strategies adopted and the type of basis functions (Slaters vs Gaussians) employed, an overall decent agreement is obtained.

Quantum computing in pharma: A multilayer embedding approach for near future applications

Quantum computers are special purpose machines that are expected to be particularly useful in simulating strongly correlated chemical systems. The quantum computer excels at treating a moderate number of orbitals within an active space in a fully quantum mechanical manner. We present a quantum phase estimation calculation on F₂ in a (2,2) active space on Rigetti's Aspen-11 QPU. While this is a promising start, it also underlines the need for carefully selecting the orbital spaces treated by the quantum computer. In this work, a scheme for selecting such an active space automatically is described and simulated results obtained using both the quantum phase estimation (QPE) and variational quantum eigensolver (VQE) algorithms are presented and combined with a subtractive method to enable accurate description of the environment. The active occupied space is selected from orbitals localized on the chemically relevant fragment of the molecule, while the corresponding virtual space is chosen based on the magnitude of interactions with the occupied space calculated from perturbation theory. This protocol is then applied to two chemical systems of pharmaceutical relevance: the enzyme [Fe] hydrogenase and the photosenzitizer temoporfin. While the sizes of the active spaces currently amenable to a quantum computational treatment are not enough to demonstrate quantum advantage, the procedure outlined here is applicable to any active space size, including those that are outside the reach of classical computation.

Active Spaces and Non-Orthogonal Configuration Interaction Approaches for Investigating Molecules on Metal Surfaces

We test a set of multiconfigurational wavefunction approaches for calculating the ground state electron population for a two-site Anderson model representing a molecule on a metal surface. In particular, we compare (i) a Hartree Fock like wavefunction where frontier orbitals are allowed to be nonorthogonal versus (ii) a fully non-orthogonal configuration interaction wavefunction based on constrained Hartree-Fock states. We test both the strong and weak metal-molecule hybridization (Γ) limits as well as the strong and weak electron-electron repulsion (U) limits. We obtain accurate results as compared with exact numerical renormalization group theory, recovering charge transfer states where appropriate. The current framework should open a path to run molecular non-adiabatic dynamics on metal surfaces.

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.

Earth-abundant photocatalyst for H 2 generation from NH 3 with light-emitting diode illumination

Catalysts based on platinum group metals have been a major focus of the chemical industry for decades. We show that plasmonic photocatalysis can transform a thermally unreactive, earth-abundant transition metal into a catalytically active site under illumination. Fe active sites in a Cu-Fe antenna-reactor complex achieve efficiencies very similar to Ru for the photocatalytic decomposition of ammonia under ultrafast pulsed illumination. When illuminated with light-emitting diodes rather than lasers, the photocatalytic efficiencies remain comparable, even when the scale of reaction increases by nearly three orders of magnitude. This result demonstrates the potential for highly efficient, electrically driven production of hydrogen from an ammonia carrier with earth-abundant transition metals.

Electrochemical Hydrogenation of CO on Cu(100): Insights from Accurate Multiconfigurational Wavefunction Methods

Copper (Cu) remains the most efficacious electrocatalyst for electrochemical CO₂ reduction (CO₂R). Its activity and selectivity are highly facet-dependent. We recently examined the commonly proposed rate-limiting CO hydrogenation step on Cu(111) via embedded correlated wavefunction (ECW) theory and demonstrated that only this higher-level theory yields predictions consistent with potential-dependent experimental kinetics. Here, to understand the differing activities of Cu(111) and Cu(100) in catalyzing CO₂R, we explore CO hydrogenation on Cu(100) using ECW theory. We predict that the preferred pathway involves the reduction of adsorbed CO (*CO) to *COH via proton-coupled electron transfer (PCET) at working potentials, although *CHO also may form with a kinetically accessible but higher barrier. In contrast, our earlier work on Cu(111) concluded that *COH and *CHO formation via PCET are equally feasible. This work illustrates one possible origin of the facet dependence of CO₂R mechanisms and products on Cu electrodes and sheds light on how the selectivity of CO₂R electrocatalysts can be controlled by the surface morphology.

Charting C–C coupling pathways in electrochemical CO 2 reduction on Cu(111) using embedded correlated wavefunction theory

The electrochemical CO 2 reduction reaction (CO 2 RR) powered by excess zero-carbon-emission electricity to produce especially multicarbon (C 2+ ) products could contribute to a carbon-neutral to carbon-negative economy. Foundational to the rational design of efficient, selective CO 2 RR 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 C 2+ product formation via CO 2 RR electrocatalysts.

Plasmonic Photocatalysis with Chemically and Spatially Specific Antenna-Dual Reactor Complexes

Plasmonic antenna-reactor photocatalysts have been shown to convert light efficiently to chemical energy. Virtually all chemical reactions mediated by such complexes to date, however, have involved relatively simple reactions that require only a single type of reaction site. Here, we investigate a planar Al nanodisk antenna with two chemically distinct and spatially separated active sites in the form of Pd and Fe nanodisks, fabricated in 90° and 180° trimer configurations. The photocatalytic reactions H₂ + D₂ → 2HD and NH₃ + D₂ → NH₂D + HD were both investigated on these nanostructured complexes. While the H₂-D₂ exchange reaction showed an additive behavior for the linear (180°) nanodisk complex, the NH₃ + D₂ reaction shows a clear synergistic effect of the position of the reactor nanodisks relative to the central Al nanodisk antenna. This study shows that light-driven chemical reactions can be performed with both chemical and spatial control of the specific reaction steps, demonstrating precisely designed antennas with multiple reactors for tailored control of chemical reactions of increasing complexity.

Cluster-in-Molecule Method Combined with the Domain-Based Local Pair Natural Orbital Approach for Electron Correlation Calculations of Periodic Systems

The cluster-in-molecule (CIM) method was extended to systems with periodic boundary conditions (PBCs) in a previous work (PBC-CIM) [J. Chem. Theory Comput.2019, 15, 2933], which is able to compute the electronic structures of periodic systems at second-order Møller-Plesset perturbation theory (MP2) and coupled cluster singles and doubles (CCSD) levels. However, the high computational costs of CCSD with respect to the size of clusters limit the usage of PBC-CIM to crystals with small or medium unit cells. In this work, we further develop the PBC-CIM method by employing the domain-based local pair natural orbital (DLPNO) methods for the electron correlation calculations of clusters to reduce the computational costs. The combined approach allows CCSD with perturbative triples, denoted as CCSD(T), to be computationally available for accurate descriptions of periodic systems. The distant-pair correction is also implemented to improve the accuracy of PBC-CIM. As in the molecular cases, the distant pair correction significantly improves the accuracy of various PBC-CIM methods with few additional costs. The PBC-CIM-DLPNO-CCSD(T) approach has been applied to investigate the optimized lattice parameter of the cubic LiCl crystal and two adsorption problems (CO on the NaCl(100) surface and H₂O on the h-BN surface). The results show that the CIM-DLPNO-CCSD(T) method offers accurate and efficient descriptions for the studied systems. Another application to the cohesive energy of the acetic acid crystal reveals that large basis sets are necessary for reliable calculations on the cohesive energies of molecular crystals.

Quantum embedding theories to simulate condensed systems on quantum computers

Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties that are more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate-scale quantum computers using embedding theories, and we give examples for a specific class of materials, that is, solid materials hosting spin defects. These are promising systems to build future quantum technologies, such as quantum computers, quantum sensors and quantum communication devices. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Simulating core electron binding energies of halogenated species adsorbed on ice surfaces and in solution via relativistic quantum embedding calculations

In this work, we investigate the effects of the environment on the X-ray photoelectron spectra of hydrogen chloride and chloride ions adsorbed on ice surfaces, as well as of chloride ions in water droplets. In our approach, we combine a density functional theory (DFT) description of the ice surface with that of halogen species using the recently developed relativistic core-valence separation equation of motion coupled cluster (CVS-EOM-IP-CCSD) via the frozen density embedding formalism (FDE), to determine the K and L_1,2,3 edges of chlorine. Our calculations, which incorporate temperature effects through snapshots from classical molecular dynamics simulations, are shown to reproduce experimental trends in the change of the core binding energies of Cl^- upon moving from a liquid (water droplets) to an interfacial (ice quasi-liquid layer) environment. Our simulations yield water valence band binding energies in good agreement with experiment, which vary little between the droplets and the ice surface. For halide core binding energies there is an overall trend for overestimating experimental values, though good agreement between theory and experiment is found for Cl^- in water droplets and on ice. For HCl on the other hand there are significant discrepancies between experimental and calculated core binding energies when we consider structural models that maintain the H-Cl bond more or less intact. An analysis of models that allow for pre-dissociated and dissociated structures suggests that experimentally observed chemical shifts in binding energies between Cl^- and HCl would require that H⁺ (in the form of H₃O⁺) and Cl^- are separated by roughly 4-6 Å.

Green's Function Formulation of Quantum Defect Embedding Theory

We present a Green's function formulation of the quantum defect embedding theory (QDET) where a double counting scheme is rigorously derived within the G₀W₀ approximation. We then show the robustness of our methodology by applying the theory with the newly derived scheme to several defects in diamond. Additionally, we discuss a strategy to obtain converged results as a function of the size and composition of the active space. Our results show that QDET is a promising approach to investigate strongly correlated states of defects in solids.

Challenges of modeling nanostructured materials for photocatalytic water splitting

Understanding the water splitting mechanism in photocatalysis is a rewarding goal as it will allow producing clean fuel for a sustainable life in the future. However, identifying the photocatalytic mechanisms by modeling photoactive nanoparticles requires sophisticated computational techniques based on multiscale modeling. In this review, we will survey the strengths and drawbacks of currently available theoretical methods at different length and accuracy scales. Understanding the surface-active site through Density Functional Theory (DFT) using new, more accurate exchange-correlation functionals plays a key role for surface engineering. Larger scale dynamics of the catalyst/electrolyte interface can be treated with Molecular Dynamics albeit there is a need for more generalizations of force fields. Monte Carlo and Continuum Modeling techniques are so far not the prominent path for modeling water splitting but interest is growing due to the lower computational cost and the feasibility to compare the modeling outcome directly to experimental data. The future challenges in modeling complex nano-photocatalysts involve combining different methods in a hierarchical way so that resources are spent wisely at each length scale, as well as accounting for excited states chemistry that is important for photocatalysis, a path that will bring devices closer to the theoretical limit of photocatalytic efficiency.

Reaction Mechanisms, Kinetics, and Improved Catalysts for Ammonia Synthesis from Hierarchical High Throughput Catalyst Design

The Haber-Bosch (HB) process is the primary chemical synthesis technique for industrial production of ammonia (NH₃) for manufacturing nitrate-based fertilizer and as a potential hydrogen carrier. The HB process alone is responsible for over 2% of all global energy usage to produce more than 160 million tons of NH₃ annually. Iron catalysts are utilized to accelerate the reaction, but high temperatures and pressures of atmospheric nitrogen gas (N₂) and hydrogen gas (H₂) are required. A great deal of research has aimed at increased performance over the last century, but the rate of progress has been slow. This Account focuses on determining the atomic-level reaction mechanism for HB synthesis of NH₃ on the Fe catalysts used in industry and how to use this knowledge to suggest greatly improved catalysts via a novel paradigm of catalyst rational design.We determined the full reaction mechanism on the two most active surfaces for the HB process, Fe(111) and Fe(211)R. We used density functional theory (DFT) to predict the free-energy barriers for all 12 important reactions and the 34 most important 2 × 2 surface configurations. Then we incorporated the mechanism into kinetic Monte Carlo (kMC) simulations run for several hours of real time to predict turnover frequencies (TOFs). The predicted TOFs are within experimental error, indicating that the predicted barriers are within 0.04 eV of experiment.With this level of accuracy, we are poised to use DFT to improve the catalyst. Rather than forming bulk alloys with uniform concentration, we aimed at finding additives that strongly prefer near-surface sites so that minor amounts of the additive might lead to dramatic improvements. However, even for a single additive, the combinations of surface species and reactions multiplies significantly, with ∼48 reaction steps to examine and nearly 100 surface configurations per 2 × 2 site. To make it practical to examine tens of dopant candidates, we developed the hierarchical high-throughput catalysis screening (HHTCS) approach, which we applied to both the Fe(111) and Fe(211) surfaces. For HHTCS, we identified the most important 4 reaction steps out of 12 for the two surfaces to examine >50 dopant cases, where we required performance at each step no worse than for pure Fe. With HHTCS, the computational cost is about 1% of that for doing the full reaction mechanism, allowing us to do ≈50 cases in about 1/2 the time it took to do pure Fe(111). The new leads identified with HHTCS are then validated with full mechanistic studies.For Fe(111), we predict three high-performance dopants that strongly prefer the second layer: Co with a rate 8 times higher, Ni with a rate 16 times higher, and Si with a rate 43 times higher, at 400 °C and 20 atm. We also found four dopants that strongly prefer the top layer and improve performance: Pt or Rh 3 times faster and Pd or Cu 2 times faster. For Fe(211), the best dopant was found to be second-layer Co with a rate 3 times faster than that for the undoped surface.The DFT/kMC data were used to predict reshaping of the catalyst particles under reaction conditions and how to tune dopant content so as to maximize catalytic area and thus activity. Finally, we show how to validate our mechanistic modeling via a comparison between theoretical and experimental operando spectroscopic signatures.

Diffusion Barriers for Carbon Monoxide on the Cu(001) Surface Using Many-Body Perturbation Theory and Various Density Functionals

First-principles calculations play a key role in understanding the interactions of molecules with transition-metal surfaces and the energy profiles for catalytic reactions. However, many of the commonly used density functionals are not able to correctly predict the surface energy as well as the adsorption site preference for a key molecule such as CO, and it is not clear to what extent this shortcoming influences the prediction of reaction or diffusion pathways. Here, we report calculations of carbon monoxide diffusion on the Cu(001) surface along the [100] and [110] pathways, as well as the surface energy of Cu(001), and CO-adsorption energy and compare the performance of the Perdew-Burke-Ernzerhof (PBE), PBE + D2, PBE + D3, RPBE, Bayesian error estimation functional with van der Waals correlation (BEEF-vdW), HSE06 density functionals, and the random phase approximation (RPA), a post-Hartree-Fock method based on many-body perturbation theory. We critically evaluate the performance of these methods and find that RPA appears to be the only method giving correct site preference, overall barrier, adsorption enthalpy, and surface energy. For all of the other methods, at least one of these properties is not correctly captured. These results imply that many density functional theory (DFT)-based methods lead to qualitative and quantitative errors in describing CO interaction with transition-metal surfaces, which significantly impacts the description of diffusion pathways. It is well conceivable that similar effects exist when surface reactions of CO-related species are considered. We expect that the methodology presented here will be used to get more detailed insights into reaction pathways for CO conversion on transition-metal surfaces in general and Cu in particular, which will allow us to better understand the catalytic and electrocatalytic reactions involving CO-related species.

Flexible boundary layer using exchange for embedding theories. I. Theory and implementation

Embedding theory is a powerful computational chemistry approach to exploring the electronic structure and dynamics of complex systems, with Quantum Mechanical/Molecular Mechanics (QM/MM) being the prime example. A challenge arises when trying to apply embedding methodology to systems with diffusible particles, e.g., solvents, if some of them must be included in the QM region, for example, in the description of solvent-supported electronic states or reactions involving proton transfer or charge-transfer-to-solvent: without a special treatment, inter-diffusion of QM and MM particles will eventually lead to a loss of QM/MM separation. We have developed a new method called Flexible Boundary Layer using Exchange (FlexiBLE) that solves the problem by adding a biasing potential to the system that closely maintains QM/MM separation. The method rigorously preserves ensemble averages by leveraging their invariance to an exchange of identical particles. With a careful choice of the biasing potential and the use of a tree algorithm to include only important QM and MM exchanges, we find that the method has an MM-forcefield-like computational cost and thus adds negligible overhead to a QM/MM simulation. Furthermore, we show that molecular dynamics with the FlexiBLE bias conserves total energy, and remarkably, sub-diffusional dynamical quantities in the inner QM region are unaffected by the applied bias. FlexiBLE thus widens the range of chemistry that can be studied with embedding theory.

Direct orbital selection within the domain-based local pair natural orbital coupled-cluster method

Domain-based local pair natural orbital coupled cluster (DLPNO-CC) has become increasingly popular to calculate relative energies (e.g., reaction energies and reaction barriers). It can be applied within a multi-level DLPNO-CC-in-DLPNO-CC ansatz to reduce the computational cost and focus the available computational resources on a specific subset of the occupied orbitals. We demonstrate how this multi-level DLPNO-CC ansatz can be combined with our direct orbital selection (DOS) approach [M. Bensberg and J. Neugebauer, J. Chem. Phys. 150, 214106 (2019)] to automatically select orbital sets for any multi-level calculation. We find that the parameters for the DOS procedure can be chosen conservatively such that they are transferable between reactions. The resulting automatic multi-level DLPNO-CC method requires no user input and is extremely robust and accurate. The computational cost is easily reduced by a factor of 3 without sacrificing accuracy. We demonstrate the accuracy of the method for a total of 61 reactions containing up to 174 atoms and use it to predict the relative stability of conformers of a Ru-based catalyst.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Projector-Based Quantum Embedding for Molecular Systems: An Investigation of Three Partitioning Approaches

Projector-based embedding is a relatively recent addition to the collection of methods that seek to utilize chemical locality to provide improved computational efficiency. This work considers the interactions between the different proposed procedures for this method and their effects on the accuracy of the results. The interplay between the embedded background, projector type, partitioning scheme, and level of atomic orbital (AO) truncation are investigated on a selection of reactions from the literature. The Huzinaga projection approach proves to be more reliable than the level-shift projection when paired with other procedural options. Active subsystem partitioning from the subsystem projected AO decomposition (SPADE) procedure proves slightly better than the combination of Pipek-Mezey localization and Mulliken population screening (PMM). Along with these two options, a new partitioning criteria is proposed based on subsystem von Neumann entropy and the related subsystem orbital occupancy. This new method overlaps with the previous PMM method, but the screening process is computationally simpler. Finally, AO truncation proves to be a robust option for the tested systems when paired with the Huzinaga projection, with satisfactory results being acquired at even the most severe truncation level.

Natural Charge-Transfer Analysis: Eliminating Spurious Charge-Transfer States in Time-Dependent Density Functional Theory via Diabatization, with Application to Projection-Based Embedding

For many types of vertical excitation energies, linear-response time-dependent density functional theory (LR-TDDFT) offers a useful degree of accuracy combined with unrivaled computational efficiency, although charge-transfer excitation energies are often systematically and dramatically underestimated, especially for large systems and those that contain explicit solvent. As a result, low-energy electronic spectra of solution-phase chromophores often contain tens to hundreds of spurious charge-transfer states, making LR-TDDFT needlessly expensive in bulk solution. Intensity borrowing by these spurious states can affect intensities of the valence excitations, altering electronic bandshapes. At higher excitation energies, it is difficult to distinguish spurious charge-transfer states from genuine charge-transfer-to-solvent (CTTS) excitations. In this work, we introduce an automated diabatization that enables fast and effective screening of the CTTS acceptor space in bulk solution. Our procedure introduces "natural charge-transfer orbitals" that provide a means to isolate orbitals that are most likely to participate in a CTTS excitation. Projection of these orbitals onto solvent-centered virtual orbitals provides a criterion for defining the most important solvent molecules in a given excitation and be used as an automated subspace selection algorithm for projection-based embedding of a high-level description of the CTTS state in a lower-level description of its environment. We apply this method to an ab initio molecular dynamics trajectory of I^-(aq) and report the lowest-energy CTTS band in the absorption spectrum. Our results are in excellent agreement with the experiment, and only one-third of the water molecules in the I^-(H₂O)₉₆ simulation cell need to be described with LR-TDDFT to obtain excitation energies that are converged to <0.1 eV. The tools introduced herein will improve the accuracy, efficiency, and usability of LR-TDDFT in solution-phase environments.

Multiscale Quantum Refinement Approaches for Metalloproteins

Biomolecules with metal ion(s) (e.g., metalloproteins) play many important biological roles. However, accurate structural determination of metalloproteins, particularly those containing transition metal ion(s), is challenging due to their complicated electronic structure, complex bonding of metal ions, and high number of conformations in biomolecules. Quantum refinement, which was proposed to combine crystallographic data with computational chemistry methods by several groups, can improve the local structures of some proteins. In this study, a quantum refinement method combining several multiscale computational schemes with experimental (X-ray diffraction) information was developed for metalloproteins. Various quantum refinement approaches using different ONIOM (our own N-layered integrated molecular orbital and molecular mechanics) combinations of quantum mechanics (QM), semiempirical (SE), and molecular mechanics (MM) methods were conducted to assess the performance and reliability on the refined local structure in two metalloproteins. The structures for two (Cu- or Zn-containing) metalloproteins were refined by combining two-layer ONIOM2(QM1/QM2) and ONIOM2(QM/MM) and three-layer ONIOM3(QM1/QM2/MM) schemes with experimental data. The accuracy of the quantum-refined metal binding sites was also examined and compared in these multiscale quantum refinement calculations. ONIOM3(QM/SE/MM) schemes were found to give good results with lower computational costs and were proposed to be a good choice for the multiscale computational scheme for quantum refinement calculations of metal binding site(s) in metalloproteins with high efficiency. Additionally, a two-center ONIOM approach was employed to speed up the quantum refinement calculations for the Zn metalloprotein with two remote active sites/ligands. Moreover, a recent quantum-embedding wavefunction-in-density functional theory (WF-in-DFT) method was also adopted as the high-level method in unprecedented ONIOM2(CCSD-in-B3LYP/MM) and ONIOM3(CCSD-in-B3LYP/SE/MM) calculations, which can be regarded as novel pseudo-three- and pseudo-four-layer ONIOM methods, respectively, to refine the key Zn binding site at the coupled-cluster singles and doubles (CCSD) level. These refined results indicate that multiscale quantum refinement schemes can be used to improve the structural accuracy obtained for local metal binding site(s) in metalloproteins with high efficiency.

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.

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.

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.

First-principles calculations of hybrid inorganic-organic interfaces: from state-of-the-art to best practice

The computational characterization of inorganic-organic hybrid interfaces is arguably one of the technically most challenging applications of density functional theory. Due to the fundamentally different electronic properties of the inorganic and the organic components of a hybrid interface, the proper choice of the electronic structure method, of the algorithms to solve these methods, and of the parameters that enter these algorithms is highly non-trivial. In fact, computational choices that work well for one of the components often perform poorly for the other. As a consequence, default settings for one materials class are typically inadequate for the hybrid system, which makes calculations employing such settings inefficient and sometimes even prone to erroneous results. To address this issue, we discuss how to choose appropriate atomistic representations for the system under investigation, we highlight the role of the exchange-correlation functional and the van der Waals correction employed in the calculation and we provide tips and tricks how to efficiently converge the self-consistent field cycle and to obtain accurate geometries. We particularly focus on potentially unexpected pitfalls and the errors they incur. As a summary, we provide a list of best practice rules for interface simulations that should especially serve as a useful starting point for less experienced users and newcomers to the field.

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.