Discovering High Entropy Alloy Electrocatalysts in Vast Composition Spaces with Multiobjective Optimization.

High entropy alloys (HEAs) are a highly promising class of materials for electrocatalysis as their unique active site distributions break the scaling relations that limit the activity of conventional transition metal catalysts. Existing Bayesian optimization (BO)-based virtual screening approaches focus on catalytic activity as the sole objective and correspondingly tend to identify promising materials that are unlikely to be entropically stabilized. Here, we overcome this limitation with a multiobjective BO framework for HEAs that simultaneously targets activity, cost-effectiveness, and entropic stabilization. With diversity-guided batch selection further boosting its data efficiency, the framework readily identifies numerous promising candidates for the oxygen reduction reaction that strike the balance between all three objectives in hitherto unchartered HEA design spaces comprising up to 10 elements.

Neural graph distance embedding for molecular geometry generation.

This article introduces neural graph distance embedding (nGDE), a method for generating 3D molecular geometries. Leveraging a graph neural network trained on the OE62 dataset of molecular geometries, nGDE predicts interatomic distances based on molecular graphs. These distances are then used in multidimensional scaling to produce 3D geometries, subsequently refined with standard bioorganic forcefields. The machine learning-based graph distance introduced herein is found to be an improvement over the conventional shortest path distances used in graph drawing. Comparative analysis with a state-of-the-art distance geometry method demonstrates nGDE's competitive performance, particularly showcasing robustness in handling polycyclic molecules-a challenge for existing methods.

q-pac: A Python package for machine learned charge equilibration models.

Many state-of-the art machine learning (ML) interatomic potentials are based on a local or semi-local (message-passing) representation of chemical environments. They, therefore, lack a description of long-range electrostatic interactions and non-local charge transfer. In this context, there has been much interest in developing ML-based charge equilibration models, which allow the rigorous calculation of long-range electrostatic interactions and the energetic response of molecules and materials to external fields. The recently reported kQEq method achieves this by predicting local atomic electronegativities using Kernel ML. This paper describes the q-pac Python package, which implements several algorithmic and methodological advances to kQEq and provides an extendable framework for the development of ML charge equilibration models.

Science-Driven Atomistic Machine Learning.

Machine learning (ML) algorithms are currently emerging as powerful tools in all areas of science. Conventionally, ML is understood as a fundamentally data-driven endeavour. Unfortunately, large well-curated databases are sparse in chemistry. In this contribution, I therefore review science-driven ML approaches which do not rely on "big data", focusing on the atomistic modelling of materials and molecules. In this context, the term science-driven refers to approaches that begin with a scientific question and then ask what training data and model design choices are appropriate. As key features of science-driven ML, the automated and purpose-driven collection of data and the use of chemical and physical priors to achieve high data-efficiency are discussed. Furthermore, the importance of appropriate model evaluation and error estimation is emphasized.

CO2-Activation by size-selected tantalum cluster cations (Ta1-16+): thermalization governing reaction selectivity.

The reactions of tantalum cluster cations of different sizes toward carbon dioxide are studied in an ion trap under multi-collisional conditions. For all sizes studied, consecutive reactions with several CO2 molecules are observed. This reveals two different pathways, namely oxide formation and the pickup of an entire molecule. Supported by calculations of the thermochemistry of TanO+ formation upon reaction with CO2, changes in the branching ratios at a particular cluster size are related to heat effects due to the vibrational heat capacity of the clusters and the exothermicity of the reaction.

Regularized second-order correlation methods for extended systems.

Second-order Møller-Plesset perturbation theory (MP2) constitutes the simplest form of many-body wavefunction theory and often provides a good compromise between efficiency and accuracy. There are, however, well-known limitations to this approach. In particular, MP2 is known to fail or diverge for some prototypical condensed matter systems like the homogeneous electron gas (HEG) and to overestimate dispersion-driven interactions in strongly polarizable systems. In this paper, we explore how the issues of MP2 for metallic, polarizable, and strongly correlated periodic systems can be ameliorated through regularization. To this end, two regularized second-order methods (including a new, size-extensive Brillouin-Wigner approach) are applied to the HEG, the one-dimensional Hubbard model, and the graphene-water interaction. We find that regularization consistently leads to improvements over the MP2 baseline and that different regularizers are appropriate for the various systems.

Mapping Materials and Molecules.

The visualization of data is indispensable in scientific research, from the early stages when human insight forms to the final step of communicating results. In computational physics, chemistry and materials science, it can be as simple as making a scatter plot or as straightforward as looking through the snapshots of atomic positions manually. However, as a result of the "big data" revolution, these conventional approaches are often inadequate. The widespread adoption of high-throughput computation for materials discovery and the associated community-wide repositories have given rise to data sets that contain an enormous number of compounds and atomic configurations. A typical data set contains thousands to millions of atomic structures, along with a diverse range of properties such as formation energies, band gaps, or bioactivities.It would thus be desirable to have a data-driven and automated framework for visualizing and analyzing such structural data sets. The key idea is to construct a low-dimensional representation of the data, which facilitates navigation, reveals underlying patterns, and helps to identify data points with unusual attributes. Such data-intensive maps, often employing machine learning methods, are appearing more and more frequently in the literature. However, to the wider community, it is not always transparent how these maps are made and how they should be interpreted. Furthermore, while these maps undoubtedly serve a decorative purpose in academic publications, it is not always apparent what extra information can be garnered from reading or making them.This Account attempts to answer such questions. We start with a concise summary of the theory of representing chemical environments, followed by the introduction of a simple yet practical conceptual approach for generating structure maps in a generic and automated manner. Such analysis and mapping is made nearly effortless by employing the newly developed software tool ASAP. To showcase the applicability to a wide variety of systems in chemistry and materials science, we provide several illustrative examples, including crystalline and amorphous materials, interfaces, and organic molecules. In these examples, the maps not only help to sift through large data sets but also reveal hidden patterns that could be easily missed using conventional analyses.The explosion in the amount of computed information in chemistry and materials science has made visualization into a science in itself. Not only have we benefited from exploiting these visualization methods in previous works, we also believe that the automated mapping of data sets will in turn stimulate further creativity and exploration, as well as ultimately feed back into future advances in the respective fields.

Data-efficient iterative training of Gaussian approximation potentials: Application to surface structure determination of rutile IrO2 and RuO2.

Machine-learning interatomic potentials, such as Gaussian Approximation Potentials (GAPs), constitute a powerful class of surrogate models to computationally involved first-principles calculations. At a similar predictive quality but significantly reduced cost, they could leverage otherwise barely tractable extensive sampling as in global surface structure determination (SSD). This efficiency is jeopardized though, if an a priori unknown structural and chemical search space as in SSD requires an excessive number of first-principles data for the GAP training. To this end, we present a general and data-efficient iterative training protocol that blends the creation of new training data with the actual surface exploration process. Demonstrating this protocol with the SSD of low-index facets of rutile IrO2 and RuO2, the involved simulated annealing on the basis of the refining GAP identifies a number of unknown terminations even in the restricted sub-space of (1 × 1) surface unit cells. Particularly in an O-poor environment, some of these, then metal-rich terminations, are thermodynamically most stable and are reminiscent of complexions as discussed for complex ceramic materials.

Carbon Nanodots for Charge-Transfer Processes.

In recent years, carbon nanodots (CNDs) have emerged as an environmentally friendly, biocompatible, and inexpensive class of material, whose features sparked interest for a wide range of applications. Most notable is their photoactivity, as exemplified by their strong luminescence. Consequently, CNDs are currently being investigated as active components in photocatalysis, sensing, and optoelectronics. Charge-transfer interactions are common to all these areas. It is therefore essential to be able to fine-tune both the electronic structure of CNDs and the electronic communication in CND-based functional materials. The complex, but not completely deciphered, structure of CNDs necessitates, however, a multifaceted strategy to investigate their fundamental electronic structure and to establish structure-property relationships. Such investigations require a combination of spectroscopic methods, such as ultrafast transient absorption and fluorescence up-conversion techniques, electrochemistry, and modeling of CNDs, both in the absence and presence of other photoactive materials. Only a sound understanding of the dynamics of charge transfer, charge shift, charge transport, etc., with and without light makes much-needed improvements in, for example, photocatalytic processes, in which CNDs are used as either photosensitizers or catalytic centers, possible. This Account addresses the structural, photophysical, and electrochemical properties of CNDs, in general, and the charge-transfer chemistry of CNDs, in particular. Pressure-synthesized CNDs (pCNDs), for which citric acid and urea are used as inexpensive and biobased precursor materials, lie at the center of attention. A simple microwave-assisted thermolytic reaction, performed in sealed vessels, yields pCNDs with a fairly homogeneous size distribution of ∼1-2 nm. The narrow and excitation-independent photoluminescence of pCNDs contrasts with that seen in CNDs synthesized by other techniques, making pCNDs optimal for in-depth physicochemical analyses. The atomistic and electronic structures of CNDs were also analyzed by quantum chemical modeling approaches that led to a range of possible structures, ranging from heavily functionalized, graphene-like structures to disordered amorphous particles containing small sp2 domains. Both the electron-accepting and -donating performances of CNDs make the charge-transfer chemistry of CNDs rather versatile. Both covalent and noncovalent synthetic approaches have been explored, resulting in architectures of various sizes. CNDs, for example, have been combined with molecular materials ranging from electron-donating porphyrins and extended tetrathiafulvalenes to electron-accepting perylendiimides, or nanocarbon materials such as polymer-wrapped single-walled carbon nanotubes. In every case, charge-separated states formed as part of the reaction cascades initiated by photoexcitation. Charge-transfer assemblies including CNDs have also played a role in technological applications: for example, a proof-of-concept dye-sensitized solar cell was designed and tested, in which CNDs were adsorbed on the surface of mesoporous anatase TiO2. The wide range of reported electron-donor-acceptor systems documents the versatility of CNDs as molecular building blocks, whose electronic properties are tunable for the needs of emerging technologies.

Machine-Learning Coupled Cluster Properties through a Density Tensor Representation.

The introduction of machine-learning (ML) algorithms to quantum mechanics enables rapid evaluation of otherwise intractable expressions at the cost of prior training on appropriate benchmarks. Many computational bottlenecks in the evaluation of accurate electronic structure theory could potentially benefit from the application of such models, from reducing the complexity of the underlying wave function parameter space to circumventing the complications of solving the electronic Schrödinger equation entirely. Applications of ML to electronic structure have thus far been focused on learning molecular properties (mainly the energy) from geometric representations. While this line of study has been quite successful, highly accurate models typically require a "big data" approach with thousands of training data points. Herein, we propose a general, systematically improvable scheme for wave function-based ML of arbitrary molecular properties, inspired by the underlying equations that govern the canonical approach to computing the properties. To this end, we combine the established ML machinery of the t-amplitude tensor representation with a new reduced density matrix representation. The resulting model provides quantitative accuracy in both the electronic energy and dipoles of small molecules using only a few dozen training points per system.

Towards density functional approximations from coupled cluster correlation energy densities.

(Semi)local density functional approximations (DFAs) are the workhorse electronic structure methods in condensed matter theory and surface science. The correlation energy density ϵc(r) (a spatial function that yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, ϵc(r) is not uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection between ϵc(r) and ρ. Herein, we present a new such approach by deriving ϵc(r) directly from the coupled-cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron systems. As a proof-of-principle, we construct a semilocal functional to approximate the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as reference data but guide the choice of the functional form, leading to a remarkably simple and accurate correlation functional for the helium isoelectronic series. While the resulting functional is not transferable to many-electron systems (due to a lack of same-spin correlation), these results underscore the potential of the presented approach.

Vertical valence ionization potential benchmarks from equation-of-motion coupled cluster theory and QTP functionals.

The ionization potential (IP) of a molecule quantifies the energy required to remove an electron from the system. As such, it is a fundamental quantity in the context of redox chemistry, charge transfer, and molecular electronics. The accurate theoretical prediction of this property is therefore highly desirable for virtual materials design. Furthermore, vertical IPs are of interest in the development of many-body Green's function methods like the GW formalism, as well as density functionals and semiempirical methods. In this contribution, we report over 1468 vertical valence IPs calculated with the IP variant of equation-of-motion coupled cluster theory with singles and doubles (IP-EOM-CCSD) covering 155 molecules. The purpose of this is two-fold: First, the quality of the predicted IPs is compared with respect to experiments and higher-order coupled cluster theory. This confirms the overall high accuracy and robustness of this method, with some outliers which are discussed in detail. Second, a large set of consistent theoretical reference values for vertical valence IPs are generated. This addresses a lack of reliable reference data for lower-lying valence IPs, where experimental data are often unavailable or of dubious quality. The benchmark set is then used to assess the quality of the eigenvalues predicted by different density functional approximations (via Bartlett's IP-eigenvalue theorem) and the extended Koopmans' theorem approach. The QTP family of functionals are found to be remarkably accurate, low-cost alternatives to IP-EOM-CCSD.

Screening Supramolecular Interactions between Carbon Nanodots and Porphyrins.

We present an in-depth investigation regarding the electron-accepting nature of pressure-synthesized carbon nanodots (pCNDs) in combination with porphyrins as excited-state electron donors. To this end, electrostatic attractions involving negative charges, which are present on the pCND surface, are essential to govern the hybrid assembly, on one hand, and charge separation, on the other hand.

Making the Coupled Cluster Correlation Energy Machine-Learnable.

Calculating the electronic structure of molecules and solids has become an important pillar of modern research in diverse fields of research from biology and materials science to chemistry and physics. Unfortunately, increasingly accurate and thus reliable approximate solution schemes to the underlying Schrödinger equation scale steeply in computational cost, rendering most accurate approaches like "gold standard" coupled cluster theory, CC, quickly intractable for larger systems of interest. Here we show that this scaling can be significantly reduced by applying machine-learning to the CC correlation energy. We introduce a vector-based representation of CC wave functions and use potential energy surfaces of a small molecule test set to learn the correlation energy from this representation. Our results show that the CC correlation energy can be efficiently learned, even when the representation is constructed from approximate amplitudes provided by computationally less demanding Møller-Plesset (MP2) perturbation theory. Exploiting existing linear scaling MP2 implementations, this potentially opens the door to CC-quality molecular dynamics simulations.

Communication: Coupled cluster and many-body perturbation theory for fractional charges and spins.

The study of systems with fractional charges and spins has become an extremely important tool to understand errors in approximate electronic structure methods, particularly in the context of density functional theory. Meanwhile, similar studies with wavefunction (WF)-based methods beyond second-order perturbation theory have been lacking. In this contribution, we study the performance of different coupled cluster (CC) and many-body perturbation theory (MBPT)-based methods for fractional charges. The use of the conventional and renormalized formulations of fractional-charge MBPT is discussed. The fractional spin behavior of the coupled cluster doubles (CCD) method is also investigated. Overall, all tested WF methods show very promising performance for the fractional charge problem. CCD is also quite accurate for the fractional spin problem in He+ across most of the range, although it breaks down to near Hartree-Fock quality in the strongly correlated limit. Beyond the study of fractional charge and spin curves, the implementation of CC methods with fractional occupation numbers offers a promising route to treating problems with multi-reference character in a single-reference framework.

Valence and charge-transfer optical properties for some SinCm (m, n ≤ 12) clusters: Comparing TD-DFT, complete-basis-limit EOMCC, and benchmarks from spectroscopy.

Accurate optical characterization of the closo-Si12C12 molecule is important to guide experimental efforts toward the synthesis of nano-wires, cyclic nano-arrays, and related array structures, which are anticipated to be robust and efficient exciton materials for opto-electronic devices. Working toward calibrated methods for the description of closo-Si12C12 oligomers, various electronic structure approaches are evaluated for their ability to reproduce measured optical transitions of the SiC2, Si2Cn (n = 1-3), and Si3Cn (n = 1, 2) clusters reported earlier by Steglich and Maier [Astrophys. J. 801, 119 (2015)]. Complete-basis-limit equation-of-motion coupled-cluster (EOMCC) results are presented and a comparison is made between perturbative and renormalized non-iterative triples corrections. The effect of adding a renormalized correction for quadruples is also tested. Benchmark test sets derived from both measurement and high-level EOMCC calculations are then used to evaluate the performance of a variety of density functionals within the time-dependent density functional theory (TD-DFT) framework. The best-performing functionals are subsequently applied to predict valence TD-DFT excitation energies for the lowest-energy isomers of SinC and Sin-1C7-n (n = 4-6). TD-DFT approaches are then applied to the SinCn (n = 4-12) clusters and unique spectroscopic signatures of closo-Si12C12 are discussed. Finally, various long-range corrected density functionals, including those from the CAM-QTP family, are applied to a charge-transfer excitation in a cyclic (Si4C4)4 oligomer. Approaches for gauging the extent of charge-transfer character are also tested and EOMCC results are used to benchmark functionals and make recommendations.

Strain-Promoted Reactivity of Alkyne-Containing Cycloparaphenylenes.

A new class of macrocyclic angle-strained alkynes whose size and reactivity can be precisely tuned by modular organic synthesis is disclosed. Detailed analysis of the size-dependent structural and electronic properties provides evidence for considerable distortion of the alkyne units incorporated into the cycloparaphenylene (CPP)-derived macrocycles. The remarkable increase of the alkyne reactivity with decreasing macrocycle size in [2+2]cycloaddition-retrocyclization was investigated by joint experimental and theoretical studies and the thermodynamic and kinetic parameters that govern this reaction were unraveled. Additionally, even the largest, least strained macrocycle in this series was found to undergo strain-promoted azide-alkyne cycloaddition (SPAAC) efficiently under mild conditions, thereby paving the way to the application of alkyne-containing CPPs as fluorescent "clickable" macrocyclic architectures.

Automatic generation of reaction energy databases from highly accurate atomization energy benchmark sets.

In this contribution, we discuss how reaction energy benchmark sets can automatically be created from arbitrary atomization energy databases. As an example, over 11 000 reaction energies derived from the W4-11 database, as well as some relevant subsets are reported. Importantly, there is only very modest computational overhead involved in computing >11 000 reaction energies compared to 140 atomization energies, since the rate-determining step for either benchmark is performing the same 140 quantum chemical calculations. The performance of commonly used electronic structure methods for the new database is analyzed. This allows investigating the relationship between the performances for atomization and reaction energy benchmarks based on an identical set of molecules. The atomization energy is found to be a weak predictor for the overall usefulness of a method. The performance of density functional approximations in light of the number of empirically optimized parameters used in their design is also discussed.

Single-reference coupled cluster theory for multi-reference problems.

Coupled cluster (CC) theory is widely accepted as the most accurate and generally applicable approach in quantum chemistry. CC calculations are usually performed with single Slater-determinant references, e.g., canonical Hartree-Fock (HF) wavefunctions, though any single determinant can be used. This is an attractive feature because typical CC calculations are straightforward to apply, as there is no potentially ambiguous user input required. On the other hand, there can be concern that CC approximations give unreliable results when the reference determinant provides a poor description of the system of interest, i.e., when the HF or any other single determinant ground state has a relatively low weight in the full CI expansion. However, in many cases, the reported "failures" of CC can be attributed to an unfortunate choice of reference determinant, rather than intrinsic shortcomings of CC itself. This is connected to well-known effects like spin-contamination, wavefunction instability, and symmetry-breaking. In this contribution, a particularly difficult singlet/triplet splitting problem in two phenyldinitrene molecules is investigated, where CC with singles, doubles and perturbative triples [CCSD(T)] was reported to give poor results. This is analyzed by using different reference determinants for CCSD(T), as well as performing higher level CCSDT-3 and CCSDT calculations. We show that doubly electron attached and doubly ionized equation-of-motion (DEA/DIP-EOM) approaches are powerful alternatives for treating such systems. These are operationally single-determinant methods that adequately take the multi-reference nature of these molecules into account. Our results indicate that CC remains a powerful tool for describing systems with both static correlation and dynamic correlation, when pitfalls associated with the choice of the reference determinant are avoided.

Does the ionization potential condition employed in QTP functionals mitigate the self-interaction error?

Though contrary to conventional wisdom, the interpretation of all occupied Kohn-Sham eigenvalues as vertical ionization potentials is justified by several formal and numerical arguments. Similarly, the performance of density functional approximations (DFAs) for fractionally charged systems has been extensively studied as a measure of one- and many-electron self-interaction errors (MSIEs). These complementary perspectives (initially recognized in ab initio dft) are shown to lead to the unifying concept that satisfying Bartlett's IP theorem in DFA's mitigates self-interaction errors. In this contribution, we show that the IP-optimized QTP functionals (reparameterization of CAM-B3LYP where all eigenvalues are approximately equal to vertical IPs) display reduced self-interaction errors in a variety of tests including the He2+ potential curve. Conversely, the MSIE-optimized rCAM-B3LYP functional also displays accurate orbital eigenvalues. It is shown that the CAM-QTP and rCAM-B3LYP functionals show improved dissociation limits, fundamental gaps and thermochemical accuracy compared to their parent functional CAM-B3LYP.