Implicit Solvation Methods for Catalysis at Electrified Interfaces.

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid-liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode's electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Correction: Photoelectron angular distributions as sensitive probes of surfactant layer structure at the liquid-vapor interface.

Correction for 'Photoelectron angular distributions as sensitive probes of surfactant layer structure at the liquid-vapor interface' by Rémi Dupuy et al., Phys. Chem. Chem. Phys., 2022, 24, 4796-4808, https://doi.org/10.1039/D1CP05621B.

Interpreting ultrafast electron transfer on surfaces with a converged first-principles Newns-Anderson chemisorption function.

We study the electronic coupling between an adsorbate and a metal surface by calculating tunneling matrix elements Had directly from first principles. For this, we employ a projection of the Kohn-Sham Hamiltonian upon a diabatic basis using a version of the popular projection-operator diabatization approach. An appropriate integration of couplings over the Brillouin zone allows the first calculation of a size-convergent Newns-Anderson chemisorption function, a coupling-weighted density of states measuring the line broadening of an adsorbate frontier state upon adsorption. This broadening corresponds to the experimentally observed lifetime of an electron in the state, which we confirm for core-excited Ar*(2p3/2-14s) atoms on a number of transition metal (TM) surfaces. Yet, beyond just lifetimes, the chemisorption function is highly interpretable and encodes rich information on orbital phase interactions on the surface. The model thus captures and elucidates key aspects of the electron transfer process. Finally, a decomposition into angular momentum components reveals the hitherto unresolved role of the hybridized d-character of the TM surface in the resonant electron transfer and elucidates the coupling of the adsorbate to the surface bands over the entire energy scale.

Photoelectron angular distributions as sensitive probes of surfactant layer structure at the liquid-vapor interface.

The characterization of liquid-vapor interfaces at the molecular level is an important underpinning for a basic understanding of fundamental heterogeneous processes in many areas, such as atmospheric science. Here we use X-ray photoelectron spectroscopy to study the adsorption of a model surfactant, octanoic acid, at the water-gas interface. In particular, we examine the information contained in photoelectron angular distributions and show that information about the relative depth of molecules and functional groups within molecules can be obtained from these measurements. Focusing on the relative location of carboxylate (COO-) and carboxylic acid (COOH) groups at different solution pH, the former is found to be immersed deeper into the liquid-vapor interface, which is confirmed by classical molecular dynamics simulations. These results help establish photoelectron angular distributions as a sensitive tool for the characterization of molecules at the liquid-vapor interface.

Cooperative Large-Hysteresis Spin-Crossover Transition in the Iron(II) Triazolate [Fe(ta)2] Metal-Organic Framework.

The metal-organic framework [Fe(ta)2] (Hta = 1H-1,2,3-triazole) containing Fe(II) ions and 1,2,3-triazolate ligands shows a reversible phase transition while retaining the cubic crystal symmetry and space group Fd3m (no. 227). The phase transition between room temperature (RT-[Fe(ta)2]; a = 16.6315(2) Å, V = 4600.39(8) Å3) and high temperature (HT-[Fe(ta)2]; a = 17.7566(4) Å, V = 5598.6(1) Å3) phases occurs at a temperature above 290 °C, whereas the phase transition between HT- and RT-[Fe(ta)2] starts at a temperature below 210 °C. Both [Fe(ta)2] polymorphs have identical bond topologies, but they differ by a large increase of the unit cell's volume of 22% for HT-[Fe(ta)2]. The compounds are characterized by powder X-ray diffraction, differential scanning calorimetry, and thermogravimetric analyses. Additionally, Mössbauer spectroscopy, magnetic studies, and the electronic structure of both phases are discussed in detail with respect to the spin-crossover transition from the low-spin (RT-[Fe(ta)2]) to the high-spin phase (HT-[Fe(ta)2]).

Formation and stability of small polarons at the lithium-terminated Li4Ti5O12 (LTO) (111) surface.

Zero strain insertion, high cycling stability, and a stable charge/discharge plateau are promising properties rendering Lithium Titanium Oxide (LTO) a possible candidate for an anode material in solid state Li ion batteries. However, the use of pristine LTO in batteries is rather limited due to its electronically insulating nature. In contrast, reduced LTO shows an electronic conductivity several orders of magnitude higher. Studying bulk reduced LTO, we could show recently that the formation of polaronic states can play a major role in explaining this improved conductivity. In this work, we extend our study toward the lithium-terminated LTO (111) surface. We investigate the formation of polarons by applying Hubbard-corrected density functional theory. Analyzing their relative stabilities reveals that positions with Li ions close by have the highest stability among the different localization patterns.

Charge Transport in Molecular Materials: An Assessment of Computational Methods.

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

Aspects of semiconductivity in soft, porous metal-organic framework crystals.

Metal-organic frameworks (MOFs) are known for their vast design space of possible structures, covering a wide range of often porous crystal structures and physical properties. Electrical conductivity, though, was-until very recently-not a feature usually associated with MOFs. On the other hand, well defined porous media such as MOFs, showing some measure of conductivity, could find uses in a huge number of fields ranging from electrochemistry to electronics and sensing. In this work, we therefore investigate the different aspects contributing to the bad conductivity in MOFs. Using Bardeen-Shockley deformation potential theory, we devise an approach that allows us to gauge all factors influencing the conductivity, including the availability of free charge carriers and their mobility. The latter itself is determined by the effective masses of the charge carriers, the material's elastic constants, and the deformation potential constants, which measure an effective electron-phonon coupling. Based on these parameters, we study charge carrier mobility in metal (1,2,3)-triazolate MOF crystals, M(ta)2, where the metal is either iron, zinc, or ruthenium. Thereby, Zn(ta)2 was experimentally shown to have little to no conductivity, while Fe(ta)2 is one of the best currently known MOF semiconductors. Disregarding the fact that all three investigated MOFs show near-zero carrier densities due to their large bandgaps, our calculations reproduce the trends between Zn(ta)2 and Fe(ta)2. In contrast to that we find the Ru(ta)2 MOF, which to date has not been synthesized experimentally, to yield even better performance than iron triazolate. In summary, assuming, fox example, light doping to counter the large bandgap, our analysis of the factors influencing conductivity in MOFs allows us not only to confirm experimental trends but also to predict new, as yet unknown semiconducting MOF crystals.

Generalized molecular solvation in non-aqueous solutions by a single parameter implicit solvation scheme.

In computer simulations of solvation effects on chemical reactions, continuum modeling techniques regain popularity as a way to efficiently circumvent an otherwise costly sampling of solvent degrees of freedom. As effective techniques, such implicit solvation models always depend on a number of parameters that need to be determined earlier. In the past, the focus lay mostly on an accurate parametrization of water models. Yet, non-aqueous solvents have recently attracted increasing attention, in particular, for the design of battery materials. To this end, we present a systematic parametrization protocol for the Self-Consistent Continuum Solvation (SCCS) model resulting in optimized parameters for 67 non-aqueous solvents. Our parametrization is based on a collection of ≈6000 experimentally measured partition coefficients, which we collected in the Solv@TUM database presented here. The accuracy of our optimized SCCS model is comparable to the well-known universal continuum solvation model (SMx) family of methods, while relying on only a single fit parameter and thereby largely reducing statistical noise. Furthermore, slightly modifying the non-electrostatic terms of the model, we present the SCCS-P solvation model as a more accurate alternative, in particular, for aromatic solutes. Finally, we show that SCCS parameters can, to a good degree of accuracy, also be predicted for solvents outside the database using merely the dielectric bulk permittivity of the solvent of choice.

Genarris: Random generation of molecular crystal structures and fast screening with a Harris approximation.

We present Genarris, a Python package that performs configuration space screening for molecular crystals of rigid molecules by random sampling with physical constraints. For fast energy evaluations, Genarris employs a Harris approximation, whereby the total density of a molecular crystal is constructed via superposition of single molecule densities. Dispersion-inclusive density functional theory is then used for the Harris density without performing a self-consistency cycle. Genarris uses machine learning for clustering, based on a relative coordinate descriptor developed specifically for molecular crystals, which is shown to be robust in identifying packing motif similarity. In addition to random structure generation, Genarris offers three workflows based on different sequences of successive clustering and selection steps: the "Rigorous" workflow is an exhaustive exploration of the potential energy landscape, the "Energy" workflow produces a set of low energy structures, and the "Diverse" workflow produces a maximally diverse set of structures. The latter is recommended for generating initial populations for genetic algorithms. Here, the implementation of Genarris is reported and its application is demonstrated for three test cases.

Transferable ionic parameters for first-principles Poisson-Boltzmann solvation calculations: Neutral solutes in aqueous monovalent salt solutions.

Implicit solvation calculations based on a Stern-layer corrected size-modified Poisson-Boltzmann (SMPB) model are an effective approach to capture electrolytic effects in first-principles electronic structure calculations. For a given salt solution, they require a range of ion-specific parameters, which describe the size of the dissolved ions as well as thickness and shape of the Stern layer. Out of this defined parameter space, we show that the Stern layer thickness expressed in terms of the solute's electron density and the resulting ionic cavity volume completely determine ion effects on the stability of neutral solutes. Using the efficient SMPB functionality of the full-potential density-functional theory package FHI-aims, we derive optimized such Stern layer parameters for neutral solutes in various aqueous monovalent electrolytes. The parametrization protocol relies on fitting to reference Setschenow coefficients that describe solvation free energy changes with ionic strength at low to medium concentrations. The availability of such data for NaCl solutions yields a highly predictive SMPB model that allows to recover the measured Setschenow coefficients with an accuracy that is comparable to prevalent quantitative regression models. Correspondingly derived SMPB parameters for other salts suffer from a much scarcer experimental data base but lead to Stern layer properties that follow a physically reasonable trend with ionic hydration numbers.

Perspective: On the active site model in computational catalyst screening.

First-principles screening approaches exploiting energy trends in surface adsorption represent an unparalleled success story in recent computational catalysis research. Here we argue that our still limited understanding of the structure of active sites is one of the major bottlenecks towards an ever extended and reliable use of such computational screening for catalyst discovery. For low-index transition metal surfaces, the prevalently chosen high-symmetry (terrace and step) sites offered by the nominal bulk-truncated crystal lattice might be justified. For more complex surfaces and composite catalyst materials, computational screening studies will need to actively embrace a considerable uncertainty with respect to what truly are the active sites. By systematically exploring the space of possible active site motifs, such studies might eventually contribute towards a targeted design of optimized sites in future catalysts.

First-Principles Free-Energy Barriers for Photoelectrochemical Surface Reactions: Proton Abstraction at TiO_{2}(110).

We explicitly calculate the free-energy barrier for the initial proton abstraction in the water splitting reaction at rutile TiO_{2}(110) through ab initio molecular dynamics. Combining solid-state embedding, an energy based reaction coordinate and state-of-the-art free-energy reconstruction techniques renders the calculation tractable at the hybrid density-functional theory level. The obtained free-energy barrier of approximately 0.2 eV, depending slightly on the orientation of the first acceptor water molecule, suggests a hindered reaction on the pristine rutile surface.

Thermal and Electronic Fluctuations of Flexible Adsorbed Molecules: Azobenzene on Ag(111).

We investigate the thermal and electronic collective fluctuations that contribute to the finite-temperature adsorption properties of flexible adsorbates on surfaces on the example of the molecular switch azobenzene C_{12}H_{10}N_{2} on the Ag(111) surface. Using first-principles molecular dynamics simulations, we obtain the free energy of adsorption that accurately accounts for entropic contributions, whereas the inclusion of many-body dispersion interactions accounts for the electronic correlations that govern the adsorbate binding. We find the adsorbate properties to be strongly entropy driven, as can be judged by a kinetic molecular desorption prefactor of 10^{24} s^{-1} that largely exceeds previously reported estimates. We relate this effect to sizable fluctuations across structural and electronic observables. A comparison of our calculations to temperature-programed desorption measurements demonstrates that finite-temperature effects play a dominant role for flexible molecules in contact with polarizable surfaces, and that recently developed first-principles methods offer an optimal tool to reveal novel collective behavior in such complex systems.

Critical analysis of fragment-orbital DFT schemes for the calculation of electronic coupling values.

We present a critical analysis of the popular fragment-orbital density-functional theory (FO-DFT) scheme for the calculation of electronic coupling values. We discuss the characteristics of different possible formulations or "flavors" of the scheme which differ by the number of electrons in the calculation of the fragments and the construction of the Hamiltonian. In addition to two previously described variants based on neutral fragments, we present a third version taking a different route to the approximate diabatic state by explicitly considering charged fragments. In applying these FO-DFT flavors to the two molecular test sets HAB7 (electron transfer) and HAB11 (hole transfer), we find that our new scheme gives improved electronic couplings for HAB7 (-6.2% decrease in mean relative signed error) and greatly improved electronic couplings for HAB11 (-15.3% decrease in mean relative signed error). A systematic investigation of the influence of exact exchange on the electronic coupling values shows that the use of hybrid functionals in FO-DFT calculations improves the electronic couplings, giving values close to or even better than more sophisticated constrained DFT calculations. Comparing the accuracy and computational cost of each variant, we devise simple rules to choose the best possible flavor depending on the task. For accuracy, our new scheme with charged-fragment calculations performs best, while numerically more efficient at reasonable accuracy is the variant with neutral fragments.

Electronic couplings for molecular charge transfer: benchmarking CDFT, FODFT and FODFTB against high-level ab initio calculations. II.

A new database (HAB7-) of electronic coupling matrix elements (Hab) for electron transfer in seven medium-sized negatively charged π-conjugated organic dimers is introduced. Reference data are obtained with spin-component scaled approximate coupled cluster method (SCS-CC2) and large basis sets. Assessed DFT-based approaches include constrained density functional theory (CDFT), fragment-orbital DFT (FODFT), self-consistent charge density functional tight-binding (FODFTB) and the recently described analytic overlap method (AOM). This complements the previously reported HAB11 database where only cationic dimers were considered. The CDFT method in combination with a functional based on PBE and including 50% of exact exchange (HFX) was found to provide best estimates, with a mean relative unsigned error (MRUE) of 8.2%. CDFT couplings systematically increase with decreasing fraction of HFX as a consequence of increasing delocalisation of the SOMO orbital. The FODFT method is found to be very robust underestimating electronic couplings by 28%. The FODFTB and AOM methods, although orders of magnitude more efficient in terms of computational effort than the DFT approaches, perform well with reasonably small errors of 54% and 29%, respectively, translating in errors in the non-adiabatic electron transfer rate of a factor of 2.4 and 1.7, respectively. We discuss carefully various sources of errors and the scope and limitations of all assessed methods taking into account the results obtained for both HAB7- and HAB11 databases.

Photoswitching in nanoporous, crystalline solids: an experimental and theoretical study for azobenzene linkers incorporated in MOFs.

In this article, we use the popular photoswitchable molecule, azobenzene, to demonstrate that the embedding in a nanoporous, crystalline solid enables a precise understanding of light-induced, reversible molecular motion. We investigate two similar azobenzene-containing, pillared-layer metal-organic frameworks (MOFs): Cu2(AzoBPDC)2(BiPy) and Cu2(NDC)2(AzoBiPy). Experimental results from UV-vis spectroscopy and molecular uptake experiments as well as theoretical results based on density-functional theory (DFT) show that in the Cu2(AzoBPDC)2(BiPy) MOF structure, the azobenzene side groups undergo photoisomerization when irradiated with UV or visible light. In a very similar MOF structure, Cu2(NDC)2(AzoBiPy), the experimental studies show an unexpected absence of photoisomerization. The DFT calculations reveal that in both MOFs the initial and final states of the photoswitching process (the trans and the cis conformation) have similar energies, which strongly suggests that the reason for the effective blocking of photoswitching in the AzoBiPy-based MOFs must be related to the switching process itself. More detailed calculations show that in Cu2(NDC)2(AzoBiPy) a naphthalene linker from the molecular framework blocks the photoisomerization trajectory which leads from the trans to the cis conformation. For Cu2(AzoBPDC)2(BiPy), as a result of the different geometry, such a steric hindrance is absent.

Electronic couplings for molecular charge transfer: benchmarking CDFT, FODFT, and FODFTB against high-level ab initio calculations.

We introduce a database (HAB11) of electronic coupling matrix elements (H(ab)) for electron transfer in 11 π-conjugated organic homo-dimer cations. High-level ab inito calculations at the multireference configuration interaction MRCI+Q level of theory, n-electron valence state perturbation theory NEVPT2, and (spin-component scaled) approximate coupled cluster model (SCS)-CC2 are reported for this database to assess the performance of three DFT methods of decreasing computational cost, including constrained density functional theory (CDFT), fragment-orbital DFT (FODFT), and self-consistent charge density functional tight-binding (FODFTB). We find that the CDFT approach in combination with a modified PBE functional containing 50% Hartree-Fock exchange gives best results for absolute H(ab) values (mean relative unsigned error = 5.3%) and exponential distance decay constants ß (4.3%). CDFT in combination with pure PBE overestimates couplings by 38.7% due to a too diffuse excess charge distribution, whereas the economic FODFT and highly cost-effective FODFTB methods underestimate couplings by 37.6% and 42.4%, respectively, due to neglect of interaction between donor and acceptor. The errors are systematic, however, and can be significantly reduced by applying a uniform scaling factor for each method. Applications to dimers outside the database, specifically rotated thiophene dimers and larger acenes up to pentacene, suggests that the same scaling procedure significantly improves the FODFT and FODFTB results for larger π-conjugated systems relevant to organic semiconductors and DNA.

Embedded-cluster calculations in a numeric atomic orbital density-functional theory framework.

We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding quantum and molecular mechanical (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential functionality into FHI-aims to describe cations at the QM/MM boundary through effective core potentials and therewith prevent spurious overpolarization of the electronic density. Based on numeric atomic orbital basis sets, FHI-aims offers particularly efficient access to exact exchange and second order perturbation theory, rendering the established QM/MM setup an ideal tool for hybrid and double-hybrid level density functional theory calculations of solid systems. We illustrate this capability by calculating the reduction potential of Fe in the Fe-substituted ZSM-5 zeolitic framework and the reaction energy profile for (photo-)catalytic water oxidation at TiO2(110).

First-principles thermodynamic screening approach to photo-catalytic water splitting with co-catalysts.

We adapt the computational hydrogen electrode approach to explicitly account for photo-generated charges and use it to computationally screen for viable catalyst/co-catalyst combinations for photo-catalytic water splitting. The hole energy necessary to thermodynamically drive the reaction is employed as descriptor for the screening process. Using this protocol and hybrid-level density-functional theory, we show that water oxidation on bare TiO2 surfaces is thermodynamically more complex than previously thought. This motivates a screening for suitable co-catalysts for this half-reaction, which we carry out for Au particles down to the non-scalable size regime. We find that almost all small Au clusters studied are better suited for water photo-oxidation than an extended Au(111) surface or bare TiO2 facets.