Hybrid RPA:DFT Approach for Adsorption on Transition Metal Surfaces: Methane and Ethane on Platinum (111).

The hybrid QM:QM approach is extended to adsorption on transition metal surfaces. The random phase approximation (RPA) as the high-level method is applied to cluster models and, using the subtractive scheme, embedded in periodic models which are treated with density functional theory (DFT) that is the low-level method. The PBE functional, both without dispersion and augmented with the many-body dispersion (MBD), is employed. Adsorption of methane and ethane on the Pt(111) surface is studied. For methane in a 2 × 2 surface cell, the hybrid RPA:PBE and RPA:PBE+MBD results, -14.3 and -16.0 kJ mol-1, respectively, are in close agreement with the periodic RPA value of -13.8 kJ mol-1 at significantly reduced computational cost (factor of ∼50). For methane and ethane, the RPA:PBE results (-14.3 and -17.8 kJ mol-1, respectively) indicate underbinding relative to energies derived from experimental desorption barriers for relevant loadings (-15.6 ± 1.6 and -27.2 ± 2.9 kJ mol-1, respectively), whereas the hybrid RPA:PBE+MBD results (-16.0 and -24.9 kJ mol-1, respectively) agree with the experiment well within experimental uncertainty limits (deviation of -0.4 ± 1.5 and +2.3 ± 2.9 kJ mol-1, respectively). Finding a cluster that adequately and robustly represents the adsorbate at the bulk surface is important for the success of the RPA-based QM:QM scheme for metals.

Two Allogons of an O2 -activating Bis(disiloxido)ferrate(II) Accessible Selectively just by Variation of the Crystallization Temperature.

Deprotonation of O(iPr2 SiOH)2 (iPr LH2 ) with LiOtBu followed by reaction with FeCl2 in THF led to the complex [iPr L2 Fe][Li(THF)2 ]2 , 2, which represents a structural and spectroscopic model of the α-Fe sites of Fe/ZSM-5. Reaction with O2 in THF solution proceeds rather fast and is complete within 200 ms; an intermediate O2 adduct could not be identified by stopped-flow methods. Cooling blue solutions of 2 to -80 °C led to the growth of blue crystals of 2⋅THF, the analysis of which by XRD revealed a FeO4 core that is somewhat distorted from planarity towards a tetrahedral structure. By contrast, cooling such solutions to -30 °C led to pink crystals of an allogon featuring a perfectly square planar FeO4 entity. Hence, 2 represents a unique case where two different structural isomers (allogons) can be crystallized from the same solvent selectively, controlled by the temperature. DFT calculations were performed to understand this finding.

Plasma Functionalization of Silica Bilayer Polymorphs.

Ultrathin silica films are considered suitable two-dimensional model systems for the study of fundamental chemical and physical properties of all-silica zeolites and their derivatives, as well as novel supports for the stabilization of single atoms. In the present work, we report the creation of a new model catalytic support based on the surface functionalization of different silica bilayer (BL) polymorphs with well-defined atomic structures. The functionalization is carried out by means of in situ H-plasma treatments at room temperature. Low energy electron diffraction and microscopy data indicate that the atomic structure of the films remains unchanged upon treatment. Comparing the experimental results (photoemission and infrared absorption spectra) with density functional theory simulations shows that H2 is added via the heterolytic dissociation of an interlayer Si-O-Si siloxane bond and the subsequent formation of a hydroxyl and a hydride group in the top and bottom layers of the silica film, respectively. Functionalization of the silica films constitutes the first step into the development of a new type of model system of single-atom catalysts where metal atoms with different affinities for the functional groups can be anchored in the SiO2 matrix in well-established positions. In this way, synergistic and confinement effects between the active centers can be studied in a controlled manner.

Full configuration interaction quantum Monte Carlo treatment of fragments embedded in a periodic mean field.

We present an embedded fragment approach for high-level quantum chemical calculations on local features in periodic systems. The fragment is defined as a set of localized orbitals (occupied and virtual) corresponding to a converged periodic Hartree-Fock solution. These orbitals serve as the basis for the in-fragment post-Hartree-Fock treatment. The embedding field for the fragment, consisting of the Coulomb and exchange potential from the rest of the crystal, is included in the fragment's one-electron Hamiltonian. As an application of the embedded fragment approach, we investigate the performance of full configuration interaction quantum Monte Carlo (FCIQMC) with the adaptive shift. As the orbital choice, we use the natural orbitals from the distinguishable cluster method with singles and doubles. FCIQMC is a stochastic approximation to the full CI method and can be routinely applied to much larger active spaces than the latter. This makes this method especially attractive in the context of open shell defects in crystals, where fragments of adequate size can be rather large. As a test case, we consider dissociation of a fluorine atom from a fluorographane surface. This process poses a challenge for high-level electronic structure models as both the static and dynamic correlations are essential here. Furthermore, the active space for an adequate fragment (32 electrons in 173 orbitals) is already quite large even for FCIQMC. Despite this, FCIQMC delivers accurate dissociation and total energies.

Reaction barriers on non-conducting surfaces beyond periodic local MP2: Diffusion of hydrogen on α-Al2O3(0001) as a test case.

The quest for "chemical accuracy" is becoming more and more demanded in the field of structure and kinetics of molecules at solid surfaces. In this paper, as an example, we focus on the barrier for hydrogen diffusion on a α-Al2O3(0001) surface, aiming for a couple cluster singles, doubles, and perturbative triples [CCSD(T)]-level benchmark. We employ the density functional theory (DFT) optimized minimum and transition state structures reported by Heiden, Usvyat, and Saalfrank [J. Phys. Chem. C 123, 6675 (2019)]. The barrier is first evaluated at the periodic Hartree-Fock and local Møller-Plesset second-order perturbation (MP2) level of theory. The possible sources of errors are then analyzed, which includes basis set incompleteness error, frozen core, density fitting, local approximation errors, as well as the MP2 method error. Using periodic and embedded fragment models, corrections to these errors are evaluated. In particular, two corrections are found to be non-negligible (both from the chemical accuracy perspective and at the scale of the barrier value of 0.72 eV): the correction to the frozen core-approximation of 0.06 eV and the CCSD(T) correction of 0.07 eV. Our correlated wave function results are compared to barriers obtained from DFT. Among the tested DFT functionals, the best performing for this barrier is B3LYP-D3.

Insights into Reaction Kinetics in Confined Space: Real Time Observation of Water Formation under a Silica Cover.

We offer a comprehensive approach to determine how physical confinement can affect the water formation reaction. By using free-standing crystalline SiO2 bilayer supported on Ru(0001) as a model system, we studied the water formation reaction under confinement in situ and in real time. Low-energy electron microscopy reveals that the reaction proceeds via the formation of reaction fronts propagating across the Ru(0001) surface. The Arrhenius analyses of the front velocity yield apparent activation energies (Eaapp) of 0.32 eV for the confined and 0.59 eV for the nonconfined reaction. DFT simulations indicate that the rate-determining step remains unchanged upon confinement, therefore ruling out the widely accepted transition state effect. Additionally, H2O accumulation cannot explain the change in Eaapp for the confined cases studied because its concentration remains low. Instead, numerical simulations of the proposed kinetic model suggest that the H2 adsorption process plays a decisive role in reproducing the Arrhenius plots.

Growth and Atomic-Scale Characterization of Ultrathin Silica and Germania Films: The Crucial Role of the Metal Support.

The present review reports on the preparation and atomic-scale characterization of the thinnest possible films of the glass-forming materials silica and germania. To this end state-of-the-art surface science techniques, in particular scanning probe microscopy, and density functional theory calculations have been employed. The investigated films range from monolayer to bilayer coverage where both, the crystalline and the amorphous films, contain characteristic XO4 (X=Si,Ge) building blocks. A side-by-side comparison of silica and germania monolayer, zigzag phase and bilayer films supported on Mo(112), Ru(0001), Pt(111), and Au(111) leads to a more general comprehension of the network structure of glass former materials. This allows us to understand the crucial role of the metal support for the pathway from crystalline to amorphous ultrathin film growth.

The color center singlet state of oxygen vacancies in TiO2.

Oxygen vacancies are ubiquitous in TiO2 and play key roles in catalysis and magnetism applications. Despite being extensively investigated, the electronic structure of oxygen vacancies in TiO2 remains controversial both experimentally and theoretically. Here, we report a study of a neutral oxygen vacancy in TiO2 using state-of-the-art quantum chemical electronic structure methods. We find that the ground state is a color center singlet state in both the rutile and the anatase phases of TiO2. Specifically, embedded coupled cluster with singles, doubles, and perturbative triples calculations find, for an oxygen vacancy in rutile, that the lowest triplet state energy is 0.6 eV above the singlet state, and in anatase, the triplet state energy is higher by 1.4 eV. Our study provides fresh insights into the electronic structure of the oxygen vacancy in TiO2, clarifying earlier controversies and potentially inspiring future studies of defects with correlated wave function theories.

Fragment-Based Restricted Active Space Configuration Interaction with Second-Order Corrections Embedded in Periodic Hartree-Fock Wave Function.

We present a computational scheme for restricted-active-space configuration interaction (RASCI) calculations combined with second-order perturbation theory (RASCI-PT2) on a fragment of a periodic system embedded in the periodic Hartree-Fock (HF) wave function. This method allows one to calculate the electronic structure of localized strongly correlated features in crystals and surfaces. The scheme was implemented via an interface between the Cryscor and Q-Chem codes. To evaluate the performance of the embedding method, we explored dissociation of a fluorine atom from a lithium fluoride surface and partially fluorinated graphane layer. The results show that RASCI and RASCI-PT2 embedded in periodic HF are able to produce well-behaved potential energy surfaces and accurate dissociation energies.

Evolutionary Algorithm-Based Crystal Structure Prediction for Copper(I) Fluoride.

Despite numerous experimental studies since 1824, the binary copper(I) fluoride remains unknown. A crystal structure prediction has been carried out for CuF using the USPEX evolutionary algorithm and a dispersion-corrected hybrid density functional method. In total about 5000 hypothetical structures were investigated. The energetics of the predicted structures were also counter-checked with local second-order Møller-Plesset perturbation theory. Herein 39 new hypothetical copper(I) fluoride structures are reported that are lower in energy compared to the previously predicted cinnabar-type structure. Cuprophilic Cu-Cu interactions are present in all the low-energy structures, leading to ordered Cu substructures such as helical or zig-zag-type Cu-Cu motifs. The lowest-energy structure adopts a trigonal crystal structure with space group P31 21. From an electronic point of view, the predicted CuF modification is a semiconductor with an indirect band gap of 2.3 eV.

Chemically Accurate Adsorption Energies: CO and H2O on the MgO(001) Surface.

Hybrid MP2:DFT-D structure optimizations are performed at BSSE-free CBS-extrapolated potential energy surfaces for molecule-oxide surface interactions (BSSE, basis set superposition error; CBS, complete basis set limit). Subsequently single point MP2 calculations are performed to estimate the effects of increasing the basis set size in the CBS extrapolation and increasing the cluster model size. The resulting estimates of the periodic MP2 limit agree within 1 kJ/mol with Local MP2 calculations using periodic boundary conditions. Single point CCSD(T) calculations are performed to determine ΔCC = CCSD(T) - MP2 energy differences. The final hybrid MP2:DFT-D+ΔCC estimate for CO on the MgO(001) surface at low coverage, -21.2 ± 0.5 kJ/mol, is in close agreement with the reference energy derived from temperature-programmed desorption experiments, -20.6 ± 2.4 kJ/mol. For H2O on MgO(001), at limiting zero coverage, we predict an adsorption energy of -53.7 ± 4.2 kJ/mol which falls in the range of values, -55.8 ± 12.2 kJ/mol, derived from a high coverage low energy electron diffraction experiments and estimated lateral interactions.

On the exfoliation and anisotropic thermal expansion of black phosphorus.

Black phosphorus is a bulk solid allotrope of elemental phosphorus and can be seen as an infinite stack of phosphorene sheets. It is interesting from a technological point of view as well as from an electronic structure perspective due to the importance of electron correlation effects. In a recent paper [M. Schütz, L. Maschio, A. J. Karttunen and D. Usvyat, J. Phys. Chem. Lett., 2017, 8, 1290-1294] a highly accurate exfoliation energy has been computed. Building upon these results we carefully benchmark various dispersion-corrected density functional approximations. The choice of the range-separating function that suppresses London dispersion at short interatomic distances apparently has a substantial influence on the results. Having chosen the suitable functional, we have computed the thermal expansion coefficients of black phosphorous via a quasi-harmonic approximation. The computed coefficients manifest a strong anisotropy between the two in-plane directions. Our calculations, however, do not support the existence of negative thermal expansion in black phosphorus, as reported in some theoretical studies.

A Two-Dimensional 'Zigzag' Silica Polymorph on a Metal Support.

We present a new polymorph of the two-dimensional (2D) silica film with a characteristic 'zigzag' line structure and a rectangular unit cell which forms on a Ru(0001) metal substrate. This new silica polymorph may allow for important insights into growth modes and transformations of 2D silica films as a model system for the study of glass transitions. Based on scanning tunneling microscopy, low energy electron diffraction, infrared reflection absorption spectroscopy, and X-ray photoelectron spectroscopy measurements on the one hand, and density functional theory calculations on the other, a structural model for the 'zigzag' polymorph is proposed. In comparison to established monolayer and bilayer silica, this 'zigzag' structure system has intermediate characteristics in terms of coupling to the substrate and stoichiometry. The silica 'zigzag' phase is transformed upon reoxidation at higher annealing temperature into a SiO2 silica bilayer film which is chemically decoupled from the substrate.

A comparison between quantum chemistry and quantum Monte Carlo techniques for the adsorption of water on the (001) LiH surface.

We present a comprehensive benchmark study of the adsorption energy of a single water molecule on the (001) LiH surface using periodic coupled cluster and quantum Monte Carlo theories. We benchmark and compare different implementations of quantum chemical wave function based theories in order to verify the reliability of the predicted adsorption energies and the employed approximations. Furthermore we compare the predicted adsorption energies to those obtained employing widely used van der Waals density-functionals. Our findings show that quantum chemical approaches are becoming a robust and reliable tool for condensed phase electronic structure calculations, providing an additional tool that can also help in potentially improving currently available van der Waals density-functionals.

Dispersion interactions in silicon allotropes.

van der Waals interactions are known to play a key role in the formation of weakly bound solids, such as molecular or layered crystals. Here we show that the correct quantum-chemical description of van der Waals dispersion is also essential for a correct description of the relative stability between purely covalently-bound solids like silicon allotropes. To this end, we apply periodic local MP2 and DFT with Grimme's empirical -D3 correction to 11 experimentally determined or yet hypothetical crystalline silicon structures, including the most recently discovered silicon allotropes. Both methods provide similar energy ordering of the polymorphs, which, at the same time, noticeably deviate from the order predicted by standard DFT without an appropriate description of the van der Waals dispersion.

Exfoliation Energy of Black Phosphorus Revisited: A Coupled Cluster Benchmark.

Black phosphorus (black-P) consists of phosphorene sheets, stacked by van der Waals dispersion. In a recent study based on periodic local second-order Møller-Plesset perturbation theory (LMP2) with higher-order corrections evaluated on finite clusters, we obtained a value of -151 meV/atom for the exfoliation energy. This is almost twice as large as another recent theoretical result (around -80 meV/atom) obtained with quantum Monte Carlo (QMC). Here, we revisit this system on the basis of the recently implemented, periodically embedded ring coupled cluster (rCCD) model instead of LMP2. Higher-order coupled cluster corrections on top of rCCD are obtained from finite clusters by utilizing our new "unit-cell-in-cluster" scheme. Our new value of -92 meV/atom is noticeably lower than that based on LMP2 and in reasonably close agreement with the QMC result. However, in contrast to QMC, no strong effect from the second-neighbor and farther layers in black-P are observed in our calculations.

Fragment-Based Direct-Local-Ring-Coupled-Cluster Doubles Treatment Embedded in the Periodic Hartree-Fock Solution.

We present a periodic/finite-cluster interface for fragment-based direct local ring-coupled-cluster doubles (d-LrCCD) calculations embedded in the periodic mean field. The fragment is defined by a set of Wannier functions (WFs), obtained from a periodic Hartree-Fock calculation. The pair-specific virtual space is spanned by projected atomic orbitals (PAOs) truncated to pair domains. The computational procedure is initiated by a periodic local Møller-Plesset (LMP2) calculation. A subset of the WF pairs is then subsequently subjected to a finite-cluster d-LrCCD treatment using the local coupled cluster program of Molpro; this subset is specified by an interorbital cutoff distance. The orbital, pair, and domain lists, as well as other essential quantities needed for d-LrCCD such as the Fock and overlap matrices, and the electron repulsion integrals (ERIs) in the basis of WFs and PAOs are evaluated in the periodic framework and passed to Molpro via an interface. These periodic quantities provide the correct periodic mean-field embedding for the fragment d-LrCCD. Moreover, no expensive orbital transformations involving orbital coefficients related to large supporting clusters are necessary. ERIs appearing in the d-LrCCD diagrams are factorized via density fitting, which enables an efficient processing of the corresponding terms via three-index intermediates. The corresponding 3-index and the metric 2-index ERIs involving auxiliary functions are also computed and transformed to the WF-PAO basis (the 3-index ERI) on the periodic side. Although the direct ring-CCD method itself is not generally more accurate than MP2, it is more stable in the case of small band gap systems, as it sums up the ring diagrams to infinite order. Furthermore, this interface is a first step toward a high-level fragment-based quantum chemical treatment such as local CCSD(T) within a periodic embedding that is treated at a lower level. As two test examples we study the physisorption of H2 and argon on graphane.

A hierarchy of local coupled cluster singles and doubles response methods for ionization potentials.

We present a hierarchy of local coupled cluster (CC) linear response (LR) methods to calculate ionization potentials (IPs), i.e., excited states with one electron annihilated relative to a ground state reference. The time-dependent perturbation operator V(t), as well as the operators related to the first-order (with respect to V(t)) amplitudes and multipliers, thus are not number conserving and have half-integer particle rank m. Apart from calculating IPs of neutral molecules, the method offers also the possibility to study ground and excited states of neutral radicals as ionized states of closed-shell anions. It turns out that for comparable accuracy IPs require a higher-order treatment than excitation energies; an IP-CC LR method corresponding to CC2 LR or the algebraic diagrammatic construction scheme through second order performs rather poorly. We therefore systematically extended the order with respect to the fluctuation potential of the IP-CC2 LR Jacobian up to IP-CCSD LR, keeping the excitation space of the first-order (with respect to V(t)) cluster operator restricted to the m=½âŠ•3/2 subspace and the accuracy of the zero-order (ground-state) amplitudes at the level of CC2 or MP2. For the more expensive diagrams beyond the IP-CC2 LR Jacobian, we employ local approximations. The implemented methods are capable of treating large molecular systems with hundred atoms or more.

Toward an Accurate Estimate of the Exfoliation Energy of Black Phosphorus: A Periodic Quantum Chemical Approach.

The black phosphorus (black-P) crystal is formed of covalently bound layers of phosphorene stacked together by weak van der Waals interactions. An experimental measurement of the exfoliation energy of black-P is not available presently, making theoretical studies the most important source of information for the optimization of phosphorene production. Here, we provide an accurate estimate of the exfoliation energy of black-P on the basis of multilevel quantum chemical calculations, which include the periodic local Møller-Plesset perturbation theory of second order, augmented by higher-order corrections, which are evaluated with finite clusters mimicking the crystal. Very similar results are also obtained by density functional theory with the D3-version of Grimme's empirical dispersion correction. Our estimate of the exfoliation energy for black-P of -151 meV/atom is substantially larger than that of graphite, suggesting the need for different strategies to generate isolated layers for these two systems.