Embedded Cluster Model Research Articles

Computationally Effective Approach for Studies of Mechanism and Thermodynamics of Heterogeneous Catalytic Processes on Metal Oxides

ABSTRACTTo understand the nature of heterogeneous catalytic processes and improve their efficiency, it is necessary to conduct both experimental and theoretical studies. At the same time, there is no unified approach to obtaining the necessary data using quantum chemistry methods. In this work, problems of the existing calculational approaches are analyzed. The obtained information is used to develop the original three‐layer embedded cluster model approach, which is shown to be the most effective. The general algorithm for obtaining such models for various oxides is formulated. The sufficient accuracy of the proposed models in predicting geometric and energy characteristics, vibrational frequencies, activation barriers, and thermodynamic characteristics is verified. The specifics of calculating the thermodynamic characteristics of heterogeneous processes using the proposed cluster models is studied in detail. The developed approach is an effective tool for studying the mechanism of heterogeneous catalytic processes both by itself and in combination with experiment.

Oort Cloud and sednoid formation in an embedded cluster, I: Populations and size distributions

In this paper we report on massive computer simulations aimed to clarify the formation of an Oort Cloud and the adjoining sednoid population during the earliest times of the solar system due to the perturbing effects of the Sun’s birth aggregate, for which we use different embedded cluster models. We define the sednoid population to have semi-major axes between 100 and 1600 astronomical units, and it can be seen as the innermost extension of the Oort Cloud. By also restricting the orbits to perihelion distances exceeding 60 astronomical units, the sednoid population can be regarded as dynamically inert with respect to both planetary and Galactic influences. It includes the objects (90377) Sedna, 2012 VP113 and (541132) Leleākūhonua. We start by creating 12 cluster models, using the NBODY6++GPU code, with three random realisations of four physically different models. In each of these we select six random solar template stars and equip those with a planetary system composed of Jupiter, Saturn and 4000 massless planetesimals representing a population of stray planetesimals in the Jupiter–Saturn zone with a total mass assumed to be about 20 Earth masses. From dynamical simulations of all these 72 variants of the early solar system including the cluster perturbations, we derive the total numbers and orbital characteristics of the sednoid and Oort Cloud populations, including the size distributions resulting from the limiting effects of solar nebula gas drag on extraction efficiency. We find that the predicted number of sednoids varies dramatically depending on the orbital evolution of the solar template star in the cluster. In general, numbers consistent with the existence of the observed sednoids is an expected outcome only for a birth aggregate with a strong central condensation and a relatively long lifetime of the residual gas, whereas other cluster models tend to fail to explain this. In the most successful, concentrated cluster models, we predict the existence of an as yet unseen population of at least 108 km-sized sednoids. However, we note that these cluster models produce an overheated inclination distribution at variance with the observed inclinations. Hence, we conclude that our study points to a possible, severe problem of the embedded cluster scenario in explaining the origin of the sednoids. The Oort Cloud predicted to originate in local, Jupiter–Saturn planetesimals by our simulations amounts to ∼10% of the estimated, current size of the entire Oort Cloud. This shows that such comets, likely characterised by Earth-like D/H ratios, may be a minority though a significant one. In an accompanying paper we discuss the extraction dynamics in some detail, based on the same simulations as here.

Level-Shifted Embedded Cluster Method for Modeling the Chemistry of Metal Oxides.

The embedded cluster method has been used extensively in the study of the chemical and physical properties of metal oxides. This method has been a popular tool due to its relatively high accuracy and low computational cost. An even more promising option may entail integrating the embedded cluster method with the combined quantum mechanical and molecular mechanical (QM/MM) approach, thereby enabling further consideration of interactions within the entire system for superior results. We aim to accurately model the chemistry of metal oxides using this combined scheme. Here, using the prototypical MgO(100) surface as a test system, with Mg9O14 as the cluster in the quantum mechanical region, we show that the embedded cluster with untailored boundary effective core potentials (ECPs) can have frontier orbital energy levels that substantially deviate from the quantum mechanical reference results. This occurs even when Mg9O9, which retains the stoichiometry of MgO, is used as the cluster in the quantum mechanical region. As a result, the chemical properties of the embedded cluster models differ from those of the quantum mechanical reference model. To address this issue, we propose a new variant of the embedded cluster method called the level-shifted embedded cluster (LSEC) method, which allows the energy levels to be shifted to match the reference levels by tuning the boundary ECPs. Our validation calculations on the adsorption of various adsorbates with different properties on the MgO(100) surface show that the overall performance of QM/MM with the LSEC method is excellent for the adsorption energies, geometries, and charge properties. The excellent performance holds for both the nonstoichiometric and stoichiometric clusters (i.e., Mg9O14 and Mg9O9, respectively), demonstrating the robustness of the LSEC method. We expect that the LSEC method can be combined with QM/MM or used separately for future chemical studies of metal oxides and other ionically bonded systems.

A theoretical spectroscopy study of the photoluminescence properties of narrow band Eu2+-doped phosphors containing multiple candidate doping centers. Prediction of an unprecedented narrow band red phosphor.

We have previously presented a computational protocol that is based on an embedded cluster model and operates in the framework of TD-DFT in conjunction with the excited state dynamics (ESD) approach. The protocol is able to predict the experimental absorption and emission spectral shapes of Eu2+-doped phosphors. In this work, the applicability domain of the above protocol is expanded to Eu2+-doped phosphors bearing multiple candidate Eu doping centers. It will be demonstrated that this protocol provides full control of the parameter space that describes the emission process. The stability of Eu doping at various centers is explored through local energy decomposition (LED) analysis of DLPNO-CCSD(T) energies. This enables further development of the understanding of the electronic structure of the targeted phosphors, the diverse interactions between Eu and the local environment, and their impact on Eu doping probability, and control of the emission properties. Hence, it can be employed to systematically improve deficiencies of existing phosphor materials, defined by the presence of various intensity emission bands at undesired frequencies, towards classes of candidate Eu2+-doped phosphors with desired narrow band red emission. For this purpose, the chosen study set consists of three UCr4C4-based narrow-band phosphors, namely the known alkali lithosilicates RbNa[Li3SiO4]2:Eu2+ (RNLSO2), RbNa3[Li3SiO4]4:Eu2+ (RNLSO) and their isotypic nitridolithoaluminate phosphors consisting of CaBa[LiAl3N4]2:Eu2+ (CBLA2) and the proposed Ca3Ba[LiAl3N4]4:Eu2+ (CBLA), respectively. The theoretical analysis presented in this work led us to propose a modification of the CBLA2 phosphor that should have improved and unprecedented narrow band red emission properties. Finally, we believe that the analysis presented here is important for the future rational design of novel Eu2+-doped phosphor materials, with a wide range of applications in science and technology.

CombinedDFTand wave function theory approach to excited states of lanthanide luminescent materials: A case study ofLaF3:Ce3+

AbstractLanthanide luminescent materials play key roles in modern society, but their first‐principles treatment remains a great challenge due to complex manifold of electronic excited states and the difficulty in performing excited state structural relaxations that is necessary to model luminescent properties. Herein, we propose a practical approach that combines embedded cluster model (ECM) based multi‐configurational wave function theory (WFT) and occupancy constrained density‐functional theory plus the HubbardUcorrection (OC‐DFT + U) to treat lanthanide doped luminescent materials, using LaF3:Ce3+, a typical scintillator with low symmetry, as a case study. We show that the combined approach yields accurate absorption energies with an error on the order of 200 cm−1, but the emission energies are significantly underestimated, the origin of which is further clarified by vibrationally resolved absorption and emission spectra calculation. This work demonstrates the possibility of combining ECM‐based wave function theory and periodic DFT into a comprehensive computational scheme for lanthanide luminescent materials and highlights the limitations of the current implementation of OC‐DFT + Ufor excited state structural optimization.

Exploiting Phase Transitions in Catalysis: Adsorption of CO on doped VO2 -Polymorphs.

VO2 is well known for its low-temperature metal-insulator transition between two phases with tetragonal rutile and monoclinic structure. The adsorption of CO on the two polymorphs of Mo-doped VO2 is calculated to investigate the effect of a substrate phase change on the adsorption energy. The system is investigated theoretically at density-functional theory level using a hybrid functional with London dispersion correction. We establish a computational protocol applicable for the study of physisorption on open-shell transition metal oxides. The main task is to control the spin state of open-shell slab models used to model adsorption of closed-shell molecules in order to obtain numerically stable adsorption energies and to reduce spin contamination within the broken-symmetry unrestricted Kohn-Sham approximation. Applying this procedure, it is possible to identify the most stable adsorption positions of CO on both phases of VO2 . CO adsorbs vertically with the C atom on a surface V atom in the monoclinic phase with an adsorption energy of -56 kJ/mol. The same adsorption position has an adsorption energy of only -46 kJ/mol on the rutile phase. Similar differences were obtained with multireference methods using an embedded cluster model. This effect may inspire experimental strategies exploiting the rutile monoclinic VO2 phase transition in catalytic processes where CO is formed as product or as an intermediate.

Convergence of Electronic Structure Properties in Ionic Oxides Within a Fragment Approach

Embedded-cluster models of crystalline solids are important to allow accurate wave function methods to be applicable to solids. The ab-initio model potential method, in which the crystal is divided into three different fragments, one quantum fragment, one ab-initio model potential fragment and one point-charge fragment, has historically been shown to be a viable tool for describing the electronic structure in ionic solids. The optimal size of these regions is, of course, individual for each crystal. In this study we analyzed the convergence of the electronic structure properties with respect to an increase of the size of the quantum part and the layer of potentials. MgO crystal and Ni: MgO were used for this purpose as examples of an ideal crystal and a crystal with a point defect. We demonstrated that with an increase of the cluster size, the electron density in the inner part of the cluster becomes very similar to the electron density in the periodic model. Clusters, embedded into a layer of model potential and electrostatic field, are a good alternative to periodic description.

A program system for self-consistent embedded potentials for ionic crystals

Embedded-cluster models of crystalline solids are important to allow accurate wave function methods to be applicable to solids. The ab initio model potential method for embedding ionic solids has historically been shown to be a viable tool. While useful, the method has been limited by the need to generate such potentials for each crystal structure and the lack of a freely available program for generating ab initio model potentials. Herein, this is remedied by showcasing a new, AFL licensed, program, SCEPIC, which can be used in combination with Molcas or OpenMolcas codes to derive ab initio model potentials for ionic crystals.The applicability of ab initio model potentials derived via SCEPIC is evaluated for three simple ionic solids: MgO, CaO and CaF2. The following questions are addressed: (i) the capability of the method to reproduce the density matrix from periodic density functional theory calculations, (ii) the feasibility of performing geometry optimisations, (iii) the possibility to model band gaps of insulators and (iv) the ligand-field splitting of Ni-doped MgO. Going beyond the classical restriction of parametrising ab initio model potentials only at the Hartree–Fock level-of-theory, this work additionally address the sensitivity of results to the underlying Hamiltonian used to derive the potentials. The results demonstrate that good agreement with periodic density functional theory calculations can be achieved, geometry optimisations are feasible and accurate band gaps and ligand-field splittings can be computed.

Theoretical investigation of CH-bond activation by photocatalytic excited SO2 and the effects of C-, N-, S-, and Se-doped TiO2.

The photocatalytic sulfoxidation on TiO2 discovered by Parrino et al. represents a new, interesting and lower energy route for the synthesis of sulfonic acids. Sulfonic acids are important precursors for dyes, detergents and drugs. In the commonly known industrial process, SO2 and a specific hydrocarbon are converted into sulfonic acids using high-energy UV light. In this reaction, SO2 is excited into a metastable triplet state (3SO2), which has the potential to activate a CH-bond of hydrocarbons and start a radical reaction cycle. By introducing TiO2 as a photocatalyst, it has been shown that visible light can be used for the synthesis. This offers the potential to be a cost-effective reaction approach for industrial use. However, experimental studies indicate that the initial excitation mechanism of SO2 on TiO2 is significantly different from the catalyst-free mechanism. Parrino et al. were able to reveal first evidence for the existence of a charge-transfer process from SO2 to the TiO2 surface by means of electrochemical experiments. First theoretical investigations from first principles were able to further substantiate the existence of a charge-transfer. However, to fully understand this mechanism, more accurate methods such as Time Dependent Density Functional Theory (TD-DFT) or ab initio multireference methods such as the Complete Active Space Self Consistent Field (CASSCF) method are required. Furthermore, after understanding the charge-transfer mechanism, the introduction of dopants into TiO2 can be investigated in order to possibly redshift the excitation energy. This might open the route to using lower energy light for the sulfoxidation of hydrocarbons on TiO2 as a new potential industrial reaction for the synthesis of sulfonic acids. In this work, we will study the initial step of the photocatalytic sulfoxidation of hydrocarbons using the TD-DFT and CASSCF methods by using a combined approach consisting of calculations with periodic boundary conditions and a newly constructed embedded cluster model. Furthermore, we will explore the effects of doping by introducing four heteroatoms (C, N, S, and Se) into the TiO2 surfaces anatase[101] and rutile[110] to find a possible enhancement of the photocatalytic reactivity by lowering the electronic excitation energy.

Hybrid functional/embedded cluster study of uranium and actinide (actinide = Np, Pu, Am or Cm) mixed dioxides bulk and {110} surfaces

Understanding actinide (An) mixed oxides (MOX) is important for the development of minor An bearing U-Pu MOX nuclear fuel, and the long-term storage of spent nuclear fuel. In this work, we systematically simulate AnO2 (An = U, Np, Pu, Am, and Cm) and U-An MOX (An = Np, Pu, Am, and Cm) bulk and {110} surfaces using hybrid density functional theory within an embedded cluster model, focusing on the spin density of An and the density of states of AnO2 bulk and surface for the An series from U to Cm; spin density transfer is found between O and An and is discussed in detail. For U-An MOX bulk and surface, geometric structure, U and An spin densities and the densities of states are presented. Clear conclusions can be drawn regarding the oxidation state of An in the U-Np and U-Cm MOX systems, while U-Pu MOX and U-Am MOX are less clear but and sensitive to the simulation method, suggesting they are in a transition region between the U-Np and U-Cm systems.

Activation of Molecular O2 on CoFe2 O4 (001) Surfaces: An Embedded Cluster Study.

Dioxygen activation pathways on the (001) surfaces of cobalt ferrite, CoFe2O4, were investigated computationally using density functional theory and the hybrid Perdew‐Burke‐Ernzerhof exchange‐correlation functional (PBE0) within the periodic electrostatic embedded cluster model. We considered two terminations: the A‐layer exposing Fe2+ and Co2+ metal sites in tetrahedral and octahedral positions, respectively, and the B‐layer exposing octahedrally coordinated Co3+. On the A‐layer, molecular oxygen is chemisorbed as a superoxide on the Fe monocenter or bridging a Fe−Co cation pair, whereas on the B‐layer it is adsorbed at the most stable anionic vacancy. Activation is promoted by transfer of electrons provided by the d metal centers onto the adsorbed oxygen. The subsequent dissociation of dioxygen into monoatomic species and surface reoxidation have been identified as the most critical steps that may limit the rate of the oxidation processes. Of the reactive metal‐O species, [FeIII−O]2+ is thermodynamically most stable, while the oxygen of the Co−O species may easily migrate across the A‐layer with barriers smaller than the associative desorption.

Water Adsorption on Ideal Anatase-TiO2(101) – An Embedded Cluster Model for Accurate Adsorption Energetics and Excited State Properties

Abstract A combined theoretical approach towards the accurate description of water on anatase-TiO2(101) was pursued in this study. Firstly, periodic slab calculations on the basis of density hybrid functionals (PBE0, HSE06) were performed in order to gain insight into the adsorption sites and geometric structure of the surface. For submonolayer coverage of H2O, the molecular adsorption of water is found to be the most stable one with quite similar energetics in PBE0 and HSE06. Moreover, the transition states towards the less preferred dissociative adsorption forms are predicted to be greater than 0.7 eV. Thus, water will not spontaneously dissociate and based on the Computational Hydrogen Electrode model an overpotential of about 1.71 V is needed to drive the overall oxidation. In addition, to validate our results for molecular adsorption of H2O, an embedded cluster model is carefully evaluated for the a-TiO2(101) surface based on the periodic slab calculations. Subsequent high-level DLPNO-CCSD(T) results are in close agreement with our periodic slab calculations since the interaction is found to mainly consist of electrostatic contributions which are captured by hybrid functionals. Finally, first results on optimized geometries in the excited state based on the photogenerated charge-transfer state are presented.

The kinematics of star clusters undergoing gas expulsion in Newtonian and Milgromian dynamics

We study the kinematics of stars in clusters undergoing gas expulsion in standard Newtonian dynamics and also in Milgromian dynamics (MOND). Gas expulsion can explain the observed line-of-sight (LoS) velocity dispersion profile of NGC 2419 in Newtonian dynamics. For a given star formation efficiency (SFE), the shapes of the velocity dispersion profiles, which are normalised by the velocity dispersion at the projected half-mass radius, are almost indistinguishable for different SFE models in Newtonian dynamics. The velocity dispersion of a star cluster in the outer halo of a galaxy can indeed have a strong radial anisotropy in Newtonian dynamics after gas expulsion. MOND displays several different properties from Newtonian dynamics. In particular, the slope of the central velocity dispersion profile is less steep in MOND for the same SFE. Moreover, for a given SFE, more massive embedded cluster models result in more rapidly declining central velocity dispersion profiles for the final star clusters, while less massive embedded cluster models lead to flatter velocity dispersion profiles for the final products. The onset of the radial-orbit instability in post-gas-expulsion MOND models is discussed. SFEs as low as a few percent, typical of molecular clouds, lead to surviving ultra-diffuse objects. Gas expulsion alone is unlikely the physical mechanism for the observed velocity dispersion profile of NGC 2419 in MOND.

An ab initio study of the O1s and Mg1s, Mg2s, Mg2p core electron binding energies in bulk MgO

Embedded cluster models combined with wavefunction based quantum chemical ab initio methods were used to calculate the O1s and Mg1s, Mg2s, Mg2p core electron binding energies (CEBEs) of bulk MgO. The calculations were performed at three levels of theory: Koopmans' theorem (KT, initial state effects), ΔSCF (relaxation of the electronic wavefunction after core ionization, final state effects, with inclusion of scalar relativistic effects), and approximate coupled cluster (CC) approach to account for electron correlation. Several basis sets as well as MgO clusters of various design and size were employed to study their influence on the CEBEs. The contribution of electron correlation being in the order of 1 eV, but very much different for the different core levels, was analyzed in detail. Our final results are 529.5 eV for the O1s CEBE and 1303.5, 87.7 and 48.8 eV for Mg1s, Mg2s, Mg2p, respectively (all relative to the Fermi level). They agree with recent experimental XPS data within about 0.5 eV.

H2 Dissociation on H-Precovered Ni(100) Surface: Physisorbed State and Coverage Dependence

Hydrogen molecule dissociation on metal surfaces is a prototypical reaction for investigating the gas–surface interaction. To investigate the effect of lattice motion, the embedded cluster model is adopted to construct the quantum Ni(100) lattice, in which 11 Ni atoms are treated quantum mechanically. The direct and steady-state dissociation rates of H2 on H-precovered Ni(100) surface are calculated by quantum instanton method. Both the direct and steady-state dissociation rates on H-precovered Ni(100) are smaller than those on the clean Ni(100). This is because the repulsive interaction between H2 and the preadsorbed H raises the potential energy barrier. Moreover, this repulsive interaction is inversely proportional to the distance between H2 and the preadsorbed H. Owing to the classical relaxation and entropy effect of Ni atoms, the lattice motion promotes H2 dissociation by lowering the free-energy barrier but it hinders H2 recombination by raising the free-energy barrier. There are remarkable kinetic...

Developments of Interorbital–band Interaction Analysis and Embedded Cluster Model Incorporating Periodic Electrostatic Potential for Supported Metal Catalysts

Developments of Interorbital–band Interaction Analysis and Embedded Cluster Model Incorporating Periodic Electrostatic Potential for Supported Metal Catalysts

How intermolecular interactions influence electronic absorption spectra: insights from the molecular packing of uracil in condensed phases.

The photoexcitation mechanism in photochemistry and photophysics is a key to understanding the photostability and photoreaction of nucleobases. Using a combination of the generalized energy-based fragmentation (GEBF) and quantum mechanical and molecular mechanical (GEBF-QM/MM) approach and the QM/MM approach, we have investigated the electronic absorption spectra for the π-π* transition of uracil in aqueous solution, amorphous solid, and crystal. Our results indicate that the intermolecular interactions in terms of molecular packing are crucial for the investigation of the absorption spectra of uracil in different environments. There is a large red-shift (relative to uracil in the gas-phase) for uracil in the amorphous phase, which arises from hydrogen-bonding (HB) and close π-π stacking interactions. In contrast, the relatively smaller red-shift of uracil in aqueous solution can be attributed to the cooperative HB and long-range electrostatic and polarization interactions. Due to the HB and weak π-π interactions, the red-shift of the crystal is smaller than that of amorphous uracil. Furthermore, the results suggest that a large system is required to obtain the accurate absorption spectra of solutions, whereas small electrostatically embedded cluster models could be used to obtain the corresponding results for amorphous solids and molecular crystals.

Theoretical study of O2 interaction with subnanometer-sized Ag clusters supported on defective SiO2 surface

The effect of the nature of paramagnetic adsorption centers of the dehydroxylated silica surface - nonbridging oxygens (NBO) or silicon atoms with dangling bond (E′) - on the oxidation of adsorbed subnanometer-sized silver clusters Agn (n = 3, 4, 7) has been clarified by density functional theory using embedded cluster models. The interaction with NBO centers results in the formation of positively charged Ag moieties, while at E′ centers metal species remain rather neutral. At both surface defects, the electronic and structural properties of Ag species resemble the features of free Agn+ clusters. As a result, O2 molecular adsorption on the supported Ag clusters follows the trends established for cationic species. O2 is weakly adsorbed in a terminal mode on the Ag trimers and heptamers and is strongly bound to the Ag tetramers in a bridge mode. The stability of O2 molecular and dissociative adsorbed forms at the supported Ag3 and Ag7 species is similar, whereas on Ag4 cluster O2 dissociation is preferred. The heights of the O2 dissociation barriers are determined by the initial activation of molecularly adsorbed O2 and the deformation of supported metal clusters along the reaction pathway. The high activation energies make O2 dissociation unlikely and manifest that small Ag clusters trapped by silica paramagnetic defects highly resistant to the oxidation.

Acrolein oxidation to acrylic acid over the MoVOx material. Insights from DFT modeling

MoVOx-type catalysts are very active and very selective in the commercially important oxidation of acrolein to acrylic acid. To contribute to unravelling the thus far poorly understood mechanism, we carried out hybrid DFT calculations on embedded cluster models, focusing on the so-called pentameric unit as active site. In the absence of water, we calculated a large energy span, 169 kJ mol–1, for this transformation. After addressing the hydrolysis of the surface, we examined four scenarios of the acrolein conversion to explore the effect of water. The most favorable variant has a notably lower energy span, 146 kJ mol–1, in line with experimental observations that indicate a strong acceleration of the catalytic transformation in the presence of water.

Defect Structures, Electronic Properties, UV–Vis, and EPR Parameters for Rh2+ Centers in LiD: A DFT Study

The defect structures and electronic properties of orthorhombic elongated (OE) and tetragonal compressed (TC) Rh2+ centers in LiD are theoretically studied using Density Functional Theory (DFT) with the periodic CP2K program. The calculations demonstrate obvious differences in defect structure between the two centers. OE center with one next nearest neighbor (nnn) cation vacancy (VLi) in [100] axis shows the Jahn‐Teller elongation of about 0.076 Å along [001] axis, whereas TC center with one nnn VLi in [001] axis exhibits a compression of about 0.049 Å along this direction. The ligand between the central Rh2+ and the VLi is found to move away from the VLi by about 0.038 or 0.035 Å for O­­E or TC center. The larger magnitude of the overlap population (≈ −0.5907 or −0.5494 e) of the RhD bonds in OE or TC center than that (≈0.2373 e) of the host LiD bonds in pure LiD indicates much stronger covalency of the former. The simulated UV–Vis and electron paramagnetic resonance (EPR) spectra with the embedded cluster model in ORCA code are consistent with the experimental data. The present results are discussed and compared with those of the previous perturbation calculations.