Density functional theory for modelling large molecular adsorbate–surface interactions: a mini-review and worked example

Benchmarking a Molecular Flake Model on the Road to Programmable Graphene-Based Single-Atom Catalysts

Single-atom catalysts (SACs) of embedding an active metal in nitrogen-doped graphene are emergent catalytic materials in various applications. The rational design of efficient SACs necessitates an electronic and mechanistic understanding of those materials with reliable quantum mechanical simulations. Conventional computational methods of modeling SACs involve using an infinite slab model with periodic boundary condition, limiting to the selection of generalized gradient approximations as the exchange correlation (XC) functional within density functional theory (DFT). However, these DFT approximations suffer from electron self-interaction error and delocalization error, leading to errors in predicted charge-transfer energetics. An alternative strategy is using a molecular flake model, which carved out the important catalytic center by cleaving C-C bonds and employing a hydrogen capping scheme to saturate the innocent dangling bonds at the molecular boundary. By doing so, we can afford more accurate hybrid XC functionals, or even high-level correlated wavefunction theory, to study those materials. In this work, we compared the structural, electronic, and catalytic properties of SACs simulated using molecular flake models and periodic slab models with first-row transition metals as the active sites. Molecular flake models successfully reproduced structural properties, including both global distortion and local metal-coordination environment, as well as electronic properties, including spin magnetic moments and metal partial charges, for all transition metals studied. In addition, we calculated CO binding strength as a descriptor for electrochemical CO2 reduction reactivity and noted qualitatively similar trends between two models. Using the computationally efficient molecular flake models, we investigated the effect of tuning Hartree-Fock exchange in a global hybrid functional on the CO binding strength and observed system-dependent sensitivities. Overall, our calculations provide valuable insights into the development of accurate and efficient computational tools to simulate SACs.

ChemSpaX: exploration of chemical space by automated functionalization of molecular scaffold

Exploration of the local chemical space of molecular scaffolds by post-functionalization (PF) is a promising route to discover novel molecules with desired structure and function. PF with rationally chosen substituents based on known electronic and steric properties is a commonly used experimental and computational strategy in screening, design and optimization of catalytic scaffolds. Automated generation of reasonably accurate geometric representations of post-functionalized molecular scaffolds is highly desirable for data-driven applications. However, automated PF of transition metal (TM) complexes remains challenging. In this work a Python-based workflow, ChemSpaX, that is aimed at automating the PF of a given molecular scaffold with special emphasis on TM complexes, is introduced. In three representative applications of ChemSpaX by comparing with DFT and DFT-B calculations, we show that the generated structures have a reasonable quality for use in computational screening applications. Furthermore, we show that ChemSpaX generated geometries can be used in machine learning applications to accurately predict DFT computed HOMO-LUMO gaps for transition metal complexes. ChemSpaX is open-source and aims to bolster and democratize the efforts of the scientific community towards data-driven chemical discovery.

Eliminating Delocalization Error to Improve Heterogeneous Catalysis Predictions with Molecular DFT + U

Approximate semilocal density functional theory (DFT) is known to underestimate surface formation energies yet paradoxically overbind adsorbates on catalytic transition-metal oxide surfaces due to delocalization error. The low-cost DFT + U approach only improves surface formation energies for early transition-metal oxides or adsorption energies for late transition-metal oxides. In this work, we demonstrate that this inefficacy arises due to the conventional usage of metal-centered atomic orbitals as projectors within DFT + U. We analyze electron density rearrangement during surface formation and O atom adsorption on rutile transition-metal oxides to highlight that a standard DFT + U correction fails to tune properties when the corresponding density rearrangement is highly delocalized across both metal and oxygen sites. To improve both surface properties simultaneously while retaining the simplicity of a single-site DFT + U correction, we systematically construct multi-atom-centered molecular-orbital-like projectors for DFT + U. We demonstrate this molecular DFT + U approach for tuning adsorption energies and surface formation energies of minimal two-dimensional models of representative early (i.e., TiO₂) and late (i.e., PtO₂) transition-metal oxides. Molecular DFT + U simultaneously corrects adsorption energies and surface formation energies of multilayer models of rutile TiO₂(110) and PtO₂(110) to resolve the paradoxical description of surface stability and surface reactivity of semilocal DFT.

Stabilization and activation of molecular oxygen at biomimetic tetrapyrroles on surfaces: from UHV to near-ambient pressure

Recent advances in the development of surface science methods have allowed bridging, at least partially, the pressure gap between the ultra-high vacuum environment and some applicative conditions. This step has been particularly critical for the characterization of heterogenous catalytic systems (solid-liquid, solid-gas interfaces) and, specifically, of the electronic, structural, and chemical properties of tetrapyrroles at surfaces when arranged in 2D networks. Within a biomimetic picture, in which 2D metalorganic frameworks are expected to model and reproduce in a tailored way the activity of their biochemical proteic counterparts, the fundamental investigation of the adsorption and activation of small ligands at the single-metal atom reaction sites has progressively gained increasing attention. Concerning oxygen, biology offers a variety of tetrapyrrole-based transport and reaction pockets, as e.g. in haemoglobin, myoglobin or cytochrome proteins. Binding and activation of O2 are accomplished thanks to complex charge transfer and spin realignment processes, sometimes requiring cooperative mechanisms. Within the framework of surface science at near-ambient pressure (towards and beyond the mbar regime), recent progress has unveiled novel and interesting properties of 2D metalorganic frameworks and heterostacks based on self-assembled tetrapyrroles, thus opening possible, effective applicative routes in the fields of light harvesting, heterogenous (electro-)catalysts, chemical sensing, and spintronics.

Dioxygen at Biomimetic Single Metal-Atom Sites: Stabilization or Activation? The Case of CoTPyP/Au(111)

By means of a combined experimental and computational approach, we show that a 2D metal–organic framework self-assembled at the Au(111) termination is able to mimic the O2 stabilization and activation mechanisms that are typical of the biochemical environment of proteins and enzymes. 5,10,15,20-tetra(4-pyridyl)21H,23H-porphyrin cobalt(III) chloride (CoTPyP) molecules on Au(111) bind dioxygen forming a covalent bond at the Co center, yielding charge injection into the ligand by exploiting the surface trans-effect. A weakening of the O–O bond occurs, together with the development of a dipole moment, and a change in the molecule’s magnetic moment. Also the bonding geometry is similar to the biological counterpart, with the O2 molecule sitting on-top of the Co atom and the molecular axis tilted by 118°. The ligand configuration lays between the oxo- and the superoxo-species, in agreement with the observed O–O stretching frequency measured in situ at near-ambient pressure conditions.

Accelerated decomposition of the fungicide, iprodione, on TiO2 surface under solar irradiation: experimental study and DFT mechanisms

In the present work we have studied photo-induced decomposition of iprodione on silica support with different additions of titanium dioxide. Both the experimental and theoretical (DFT) approaches have been applied. It was found that 16 hours visible light exposure of the samples with 0.1% and 1.0% of TiO₂ leads respectively to 48.28% and 21.05% of residual amounts of iprodione in these samples. A number of intermediates and end products were identified by means of GS-MS and LC-MS chromatography. The iprodione isomer (RP 30228) and its decay product 1-(3,5-dichlorophenyl)-5-isopropyl biuret (RP 36221) were identified among them. Our DFT calculations have revealed the detailed mechanisms of formation of the above products and the mechanism of accelerated proton-induced decomposition of iprodione molecules adsorbed on the TiO₂ surface. Also, the intra-molecular reasons for iprodione stability in acidic media were clarified together with the mechanism of hydantoin cycle opening under the action of hydroxyl anions.

Seeing Is Believing: Experimental Spin States from Machine Learning Model Structure Predictions

Determination of ground-state spins of open-shell transition-metal complexes is critical to understanding catalytic and materials properties but also challenging with approximate electronic structure methods. As an alternative approach, we demonstrate how structure alone can be used to guide assignment of ground-state spin from experimentally determined crystal structures of transition-metal complexes. We first identify the limits of distance-based heuristics from distributions of metal–ligand bond lengths of over 2000 unique mononuclear Fe(II)/Fe(III) transition-metal complexes. To overcome these limits, we employ artificial neural networks (ANNs) to predict spin-state-dependent metal–ligand bond lengths and classify experimental ground-state spins based on agreement of experimental structures with the ANN predictions. Although the ANN is trained on hybrid density functional theory data, we exploit the method-insensitivity of geometric properties to enable assignment of ground states for the majority (ca. 80–90%) of structures. We demonstrate the utility of the ANN by data-mining the literature for spin-crossover (SCO) complexes, which have experimentally observed temperature-dependent geometric structure changes, by correctly assigning almost all (>95%) spin states in the 46 Fe(II) SCO complex set. This approach represents a promising complement to more conventional energy-based spin-state assignment from electronic structure theory at the low cost of a machine learning model.

Structure, Properties, and Reactivity of Porphyrins on Surfaces and Nanostructures with Periodic DFT Calculations

Porphyrins are fascinating molecules with applications spanning various scientific fields. In this review we present the use of periodic density functional theory (PDFT) calculations to study the structure, electronic properties, and reactivity of porphyrins on ordered two dimensional surfaces and in the formation of nanostructures. The focus of the review is to describe the application of PDFT calculations for bridging the gaps in experimental studies on porphyrin nanostructures and self-assembly on 2D surfaces. A survey of different DFT functionals used to study the porphyrin-based system as well as their advantages and disadvantages in studying these systems is presented.

Large-scale comparison of 3d and 4d transition metal complexes illuminates the reduced effect of exchange on second-row spin-state energetics

The origin of distinct 3d vs. 4d transition metal complex sensitivity to exchange is explored over a large data set.

Stable Surfaces That Bind Too Tightly: Can Range-Separated Hybrids or DFT+U Improve Paradoxical Descriptions of Surface Chemistry?

Approximate, semilocal density functional theory (DFT) suffers from delocalization error that can lead to a paradoxical model of catalytic surfaces that both overbind adsorbates yet are also too stable. We investigate the effect of two widely applied approaches for delocalization error correction, (i) affordable DFT+U (i.e., semilocal DFT augmented with a Hubbard U) and (ii) hybrid functionals with an admixture of Hartree-Fock (HF) exchange, on surface and adsorbate energies across a range of rutile transition metal oxides widely studied for their promise as water-splitting catalysts. We observe strongly row- and period-dependent trends with DFT+U, which increases surface formation energies only in early transition metals (e.g., Ti and V) and decreases adsorbate energies only in later transition metals (e.g., Ir and Pt). Both global and local hybrids destabilize surfaces and reduce adsorbate binding across the periodic table, in agreement with higher-level reference calculations. Density analysis reveals why hybrid functionals correct both quantities, whereas DFT+U does not. We recommend local, range-separated hybrids for the accurate modeling of catalysis in transition metal oxides at only a modest increase in computational cost over semilocal DFT.

Bridging the Homogeneous-Heterogeneous Divide: Modeling Spin for Reactivity in Single Atom Catalysis

Single atom catalysts (SACs) are emergent catalytic materials that have the promise of merging the scalability of heterogeneous catalysts with the high activity and atom economy of homogeneous catalysts. Computational, first-principles modeling can provide essential insight into SAC mechanism and active site configuration, where the sub-nm-scale environment can challenge even the highest-resolution experimental spectroscopic techniques. Nevertheless, the very properties that make SACs attractive in catalysis, such as localized d electrons of the isolated transition metal center, make them challenging to study with conventional computational modeling using density functional theory (DFT). For example, Fe/N-doped graphitic SACs have exhibited spin-state dependent reactivity that remains poorly understood. However, spin-state ordering in DFT is very sensitive to the nature of the functional approximation chosen. In this work, we develop accurate benchmarks from correlated wavefunction theory (WFT) for relevant octahedral complexes. We use those benchmarks to evaluate optimal DFT functional choice for predicting spin state ordering in small octahedral complexes as well as models of pyridinic and pyrrolic nitrogen environments expected in larger SACs. Using these guidelines, we determine Fe/N-doped graphene SAC model properties and reactivity as well as their sensitivities to DFT functional choice. Finally, we conclude with broad recommendations for computational modeling of open-shell transition metal single-atom catalysts.

The effect of translation on the binding energy for transition-metal porphyrines adsorbed on Ag(111) surface

The characteristics of interaction between six transition-metal porphyrines and the Ag(111) surface are detailed here as resulted from DFT calculations. Van der Waals interactions as well as the strong correlation in 3d orbitals of transition metals were taken into account in all calculations, including the structural relaxation. For each system we investigate four relative positions of the metallic atom on top the surface. We show that the interaction between the transition metal and silver is the result of a combination between the dispersion interaction, charge transfer and weak chemical interaction. The detailed analysis of the physical properties, such as dipolar and magnetic moments and the molecule-surface charge transfer, analyzed for different geometric configurations allows us to propose qualitative models, relevant for the understanding of the self-assembly processes and related phenomena.

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

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

Adsorption of Hydrogen Sulfide, Hydrosulfide and Sulfide at Cu(110) - Polarizability and Cooperativity Effects. First Stages of Formation of a Sulfide Layer

Understanding the surface site preference for single adsorbates, the interactions between adsorbates, how these interactions affect surface site specificity in adsorption and perturb the electronic states of surfaces is important for rationalizing the structure of interfaces and the growth of surface products. Herein, using density functional theory (DFT) calculations, we investigated the adsorption of H₂ S, HS and, S onto Cu(110). The surface site specificity observed for single adsorbates can be largely affected by the presence of other adsorbates, especially S that can affect the adsorption of other species even at distances of 13 Å. The large supercell employed with a surface periodicity of (6×6) allowed us to safely use the Helmholtz method for the determination of the dipole of the surface-adsorbate complex at low adsorbate coverages. We found that the surface perturbation induced by S can be explained by the charge transfer model, H₂ S leads to a perturbation of the surface that arises mostly from Pauli exclusion effects, whereas HS shows a mix of charge transfer and Pauli exclusion effects. These effects have a large contribution to the long range adsorbate-adsorbate interactions observed. Further support for the long range adsorbate-adsorbate interactions are the values of the adsorption energies of adsorbate pairs that are larger than the sum of the adsorption energies of the single adsorbates that constitute the pair. This happens even for large distances and thus goes beyond the H-bond contribution for the H-bond capable adsorbate pairs. Exploiting this knowledge we investigated two models for describing the first stages of growth of a layer of S-atoms at the surface: the formation of islands versus the formation of more homogeneous surface distributions of S-atoms. We found that for coverages lower than 0.5 ML the S-atoms prefer to cluster as islands that evolve to stripes along the [1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mn>1</mml:mn><mml:mo>‾</mml:mo></mml:mover></mml:math> 0] direction with increasing coverage. At 0.5 ML a homogeneous distribution of S-atoms becomes more stable than the formation of stripes. For the coverage equivalent to 1 ML, the formation of two half-monolayers of S-atoms that disrupt the Cu-Cu bonds between the first and second layer is more favorable than the formation of 1 ML homogeneous coverage of S-atoms. Here the S-Cu bond distances and geometries are reminiscent of pyrite, covellite, and to some extent chalcocite. The small energy difference of ≈0.1 eV that exists between this structure and the formation of 1 ML suggests that in a real system at finite temperature both structures may coexist leading to a structure with even lower symmetry.

Translation of metal-phthalocyanines adsorbed on Au(111): from van der Waals interaction to strong electronic correlation

Using first-principles calculations, we investigate the binding energy for six transition metal - phthalocyanine molecules adsorbed on Au(111). We focus on the effect of translation on molecule - surface physical properties; van der Waals interactions as well as the strong correlation in d orbitals of transition metals are taken into account in all calculations. We found that dispersion interaction and charge transfer have the dominant role in the molecule-surface interaction, while the interaction between the transition metal and gold has a rather indirect influence over the physics of the molecule-surface system. A detailed analysis of the physical properties of the adsorbates at different geometric configurations allows us to propose qualitative models to account for all values of interface dipole charge transfer and magnetic moment of metal-phthalocyanines adsorbed on Au(111).

Microscopy with a single-molecule scanning electrometer

The vibrational spectrum of a single carbon monoxide molecule, adsorbed on the tip apex of a scanning tunneling microscope, is used to image electrostatic fields with submolecular spatial resolution. The method takes advantage of the vibrational Stark effect to image local electrostatic fields and the single-molecule sensitivity of tip-enhanced Raman scattering (TERS) to optically relay the signal. We apply the method to single metalloporphyrins adsorbed on Au(111) to image molecular charges, intramolecular polarization, local photoconductivity, atomically resolved hydrogen bonds, and surface electron density waves.

Where Does the Density Localize in the Solid State? Divergent Behavior for Hybrids and DFT+U

Approximate density functional theory (DFT) is widely used in chemistry and physics, despite delocalization errors that affect energetic and density properties. DFT+U (i.e., semilocal DFT augmented with a Hubbard U correction) and global hybrid functionals are two commonly employed practical methods to address delocalization error. Recent work demonstrated that in transition-metal complexes both methods localize density away from the metal and onto surrounding ligands, regardless of metal or ligand identity. In this work, we compare density localization trends with DFT+U and global hybrids on a diverse set of 34 transition-metal-containing solids with varying magnetic state, electron configuration and valence shell, and coordinating-atom orbital diffuseness (i.e., O, S, Se). We also study open-framework solids in which the metal is coordinated by molecular ligands, i.e., MCO₃, M(OH)₂, M(NCNH)₂, K₃M(CN)₆ (M = V-Ni). As in transition-metal complexes, incorporation of Hartree-Fock exchange consistently localizes density away from the metal, but DFT+U exhibits diverging behavior, localizing density (i) onto the metal in low-spin and late transition metals and (ii) away from the metal in other cases in agreement with hybrids. To isolate the effect of the crystal environment, we extract molecular analogues from open-framework transition-metal solids and observe consistent localization of the density away from the metal in all cases with both DFT+U and hybrid exchange. These observations highlight the limited applicability of trends established for functional tuning on transition-metal complexes even to equivalent coordination environments in the solid state.

Tip-Enhanced Raman Spectromicroscopy of Co(II)-Tetraphenylporphyrin on Au(111): Toward the Chemists' Microscope

Atomically terminated and nanoscopically smooth silver tips effectively focus light on the angstrom scale, allowing tip-enhanced Raman spectromicroscopy (TER-sm) with single molecule sensitivity and submolecular spatial resolution. Through measurements carried out on cobalt-tetraphenylporphyrin (CoTPP) adsorbed on Au(111), we highlight peculiarities of vibrational spectromicroscopy with light confined on the angstrom scale. Field-gradient-driven spectra, orientational fingerprinting, and sculpting of local fields by atomic morphology of the junction are elucidated through measurements that range from 2D arrays at room temperature to single molecule manipulations at 5 K. Notably, vibrational Stark tuning within molecules, reflecting intramolecular charge distributions, becomes accessible when light is more localized than the interrogated normal modes. The Stark images of CoTPP reveal that it is saddled, and the distortion is accompanied by charge transfer to gold through the two anchoring pyrroles.

Adsorption of iron tetraphenylporphyrin on (111) surfaces of coinage metals: a density functional theory study

The adsorption of the iron tetraphenylporphyrin (FeTPP) molecule in its deckchair conformation was investigated on Au(111), Ag(111) and Cu(111) surfaces by performing spin-polarized density functional theory (DFT) calculations taking into account both van der Waals (vdW) interaction and on-site Coulomb repulsion. The deckchair conformation of the molecule favours intermolecular π-π-type interactions in a less densely packed monolayer than the saddle conformation. The activation barrier between the two stable magnetic states (high spin, S = 2 and intermediate spin, S = 1) of the molecule in vacuum disappears upon adsorption on the metal surfaces. The high-spin state of physisorbed FeTPP is stable on all adsorption sites. This result reveals that an external permanent element such as a STM tip or an additional molecule is needed to use FeTPP or similar molecules as model system for molecular spin switches.