Elastic Polarizable Environment Research Articles

Interaction of silica-supported small silver clusters with molecular oxygen. A computational study

The effect of nonbridging oxygen centers (NBOs) of a silica surface on the interaction of O2 with small Agn clusters (n=3,4) has been studied computationally, using a scalar relativistic density functional method and embedding in an elastic polarizable environment described by molecular mechanics. Two types of O2 adsorption, molecular and dissociative, were analyzed. The electrostatic interaction of the metal clusters with the silica surface stabilizes adsorbed oxygen species, particularly those obtained via dissociative adsorption. O2 dissociation seems feasible on both silver clusters, Ag3 and Ag4, but relatively high activation barriers render O2 dissociation less probable than O2 desorption.

Small silver clusters at paramagnetic defects of silica surfaces: A density functional embedded-cluster study

We studied the interaction of small Ag n clusters (n = 1–4) with paramagnetic defect centers of a dehydroxylated silica surface using an all-electron scalar relativistic density functional method. The surface and adsorption complexes on it were modeled with an accurate quantum mechanics/molecular mechanics (QM/MM) scheme of embedding QM clusters in an elastic polarizable environment, described at the molecular mechanics level (MM). We analyzed two types of frequent point defects as sites for trapping and growing of Ag clusters: a silicon atom with a dangling bond (E′ center), ≡ Si•, and a non-bridging oxygen center (NBO), ≡ Si–O•. The Ag clusters interact with these paramagnetic centers forming strong covalent metal-defect bonds. The high adsorption energy allows one to consider the NBO and E′ sites as traps of single Ag atoms and as centers of cluster growth. We also explored the effect of adsorption on observable electronic properties of the silver clusters and of the defects of the silica surface.

Small gold species at hydroxylated alumina surfaces. A computational study using embedded-cluster models of α-Al 2O 3(0001)

We calculated equilibrium structures for adsorption complexes of gold monomers, dimers, and trimers on a α-Al 2O 3(0001) model surface, partially covered by μ 1 and μ 3 hydroxyl groups. We applied a scalar-relativistic gradient-corrected density functional method to cluster models of the support that were embedded in an elastic polarizable environment. The most stable structures, with calculated adsorption energies in the range 0.81–1.74 eV, feature coordination bonds to surface μ 1-OH group and are 0.24–0.79 eV more stable than the corresponding Au n complexes on a dehydrated surface. Isomeric rearrangements of the most stable complexes are hindered by barriers of 0.65–1.08 eV.

Small gold species supported on alumina. A computational study of α‐Al2O3(0001) and γ‐Al2O3(001) using an embedded‐cluster approach

AbstractWe calculated the structures of and analyzed the bonding in adsorption complexes of small gold species Aun on α‐Al2O3(0001), n = 1–6, and γ‐Al2O3(001), n = 1–5. We applied a scalar‐relativistic gradient‐corrected density functional (DF) method to cluster models of the support that were embedded in an extended elastic polarizable environment (EPE). The shortest AuO distances, 204–211 pm, are consistent with extended X‐ray adsorption fine structure (EXAFS) data for gold clusters on alumina surfaces. The calculated total adsorption energies increase with cluster nuclearity, up to n = 4, but drop for larger adsorbed species. In the gas phase, these small gold clusters exhibit a planar structure which they keep, oriented parallel to the surface, as adsorbates on α‐Al2O3(0001). Unfavorable energy contributions result for larger clusters as their planar shape is notably distorted by the interaction with the support which amounts to 0.5–1.5 eV. On γ‐Al2O3(001), also the larger gold clusters retain their intrinsic planar structure as they adsorb oriented perpendicular to the surface. The corresponding adsorption energies are slightly smaller, 0.3–1.2 eV.

Effect of the size of the quantum region in a hybrid embedded-cluster scheme for zeolite systems

Recently we presented an improved scheme for constructing the border region within the covEPE hybrid quantum mechanics/molecular mechanics (QM/MM) embedded cluster approach for zeolites and covalent oxides in the framework of the elastic polarizable environment method. In the present study we explored how size and shape of the embedded QM cluster affect the results for structural features, energies, and characteristic vibrational frequencies of two model systems, adsorption complexes of H 2O and Rh 6 in faujasite frameworks that contain Brønsted acid sites. Comparison of calculated characteristics of different QM cluster models suggests that the local structure and vibrational frequencies of acid sites in adsorbate-free zeolite are well reproduced with all embedded QM clusters, which contain from 5T to 14T atoms. A proper description of systems with an H 2O adsorbate requires larger QM clusters, with at least 8T atoms, whereas vibrational frequencies of OH groups participating in hydrogen bonds demand even larger quantum clusters, preferably with 12T or 14T atoms. The structure of the metal particle in adsorbed rhodium species is well reproduced with all QM clusters scrutinized, from 12T atoms. Larger QM models, with 18T or 24T atoms, are recommended when one aims at a high accuracy of Rh–O and Rh–H distances and characteristic energies.

Characterization of optical spectra of interacting systems: Application to oxide‐supported metal clusters

AbstractWe present a general strategy for interpreting optical spectra of interacting systems on the basis of linear‐response time‐dependent density functional theory (TDDFT) calculations. For this purpose, we combined a natural transition orbitals (NTO) analysis with a fragment molecular orbital (FMO) analysis. The NTO transformation allows one to identify leading contributions of particle‐hole excitations in the spectral bands, whereas the FMO analysis characterizes each pair in terms of (leading) contributions of the corresponding fragments. We applied this procedure to assign and characterize optical transitions of coinage metal dimers M2 (M = Cu, Ag, Au) adsorbed at regular oxygen sites of MgO(001) as well as at oxygen vacancies, Fs and F. The TDDFT calculations were carried out at the generalized‐gradient level on structures that had been obtained with cluster models embedded in an elastic polarizable environment. The combined NTO and FMO results allowed us to analyze the spectra both qualitatively and quantitatively. The qualitative results agree very well with a previous assignment carried out by our group (Bosko et al., J Phys Chem A, 2007, 111, 6870), whereas the present approach yields a straightforward and transparent quantitative characterization of the main spectral bands. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

First Hybrid Embedding Scheme for Polar Covalent Materials Using an Extended Border Region To Minimize Boundary Effects on the Quantum Region.

We present an improved scheme for constructing the border region within a hybrid quantum mechanics/molecular mechanics (QM/MM) embedded cluster approach for zeolites and covalent oxides that ensures proper modeling of adsorption complexes with QM regions of moderate size. The procedure employs a flexible orbital basis set on monovalent oxygen pseudoatoms at the boundary of the QM cluster and introduces a pseudopotential description without explicit representation of valence electrons for their immediate Si neighbors in the MM region. This novel QM/MM border scheme, implemented in the elastic polarizable environment method for polar covalent materials (covEPE), provides an accurate description of the local structure of zeolites and other silica based materials. We assessed the performance of the novel border scheme by comparing calculated and experimental results for structures, vibrational frequencies, and binding energies of CO adsorption complexes at bridging OH groups in zeolites with FAU and MFI structures. In addition, when modeling zeolite-supported metal clusters, the new approach implies considerably reduced corrections due to the basis set superposition error, compared to our previous scheme for treating the border region of the QM partition [J. Phys. Chem. B 2003, 107, 2228].

Reverse Hydrogen Spillover onto Zeolite-Supported Metal Clusters: An Embedded Cluster Density Functional Study of Models M6(M = Rh, Ir, or Au)

A density functional study using isolated cluster models of the zeolite framework (Vayssilov, G. N.; Rosch, N. Phys. Chem. Chem. Phys. 2005, 7, 4019) on supported metal clusters M6/zeo in a hydroxylated faujasite cage showed that for 12 metals M of the groups 8−11 the hydrogenated state, M6(3H)/zeo, is energetically preferred over the bare form M6/zeo(3H). The former state was obtained as result of reverse hydrogen spillover from zeolite OH groups onto the metal particle. In the present work, we reinvestigated this problem of identifying the favorable chemical state of zeolite-supported metal species for selected M6 model clusters (M = Rh, Ir, or Au) using an accurate quantum mechanics/molecular mechanics (QM/MM) approach where a QM partition is embedded in an extended zeolite lattice (MM). The embedding method covEPE, an improved variant of the elastic polarizable environment model EPE, adapted for polar-covalent materials, properly accounts for both the mechanical rigidity of the zeolite framework and t...

Optical Spectra of Cu, Ag, and Au Monomers and Dimers at Regular Sites and Oxygen Vacancies of the MgO(001) Surface. A Systematic Time-Dependent Density Functional Study Using Embedded Cluster Models

Polarization-resolved optical spectra of coinage metal monomers and dimers Mn (M=Cu, Ag, Au; n=1, 2) at ideal O2- sites of MgO(001) as well as at oxygen vacancies, Fs and Fs+, of that surface were established using a computational approach based on linear response time-dependent density functional theory. Calculations were performed for structures determined by applying a generalized-gradient density functional method to cluster models embedded in an elastic polarizable environment. This embedding scheme provides an accurate description of substrate relaxation and long-range electrostatic interaction. We compared the optical properties of adsorbed atoms and dimers with those of the corresponding gas-phase species and we systematically analyzed trends among congeners.

Comparison of All Sites for Ti Substitution in Zeolite TS-1 by an Accurate Embedded-Cluster Method

We studied the preferential location of Ti centers in the framework of the Ti-containing MFI zeolite TS-1 using a hybrid DFT/MM embedding method developed recently. This "covalent elastic polarizable environment" (covEPE) cluster embedding allows a complete and self-consistent treatment of solid covalent systems such as zeolites. For the present study, we used a gradient-corrected density functional approach. The resulting structural features of both Si- and Ti-substituted forms of the zeolite framework fit well with available experimental information. The calculated substitution energy of Ti at the 12 crystallographically different tetrahedral sites of the MFI structure vary within 19 kJ/mol with T12 and T2 as most and least preferred sites, respectively. On the basis of these computational results and the preferential sites for Ti substitution reported from different experimental investigations, we concluded that the Ti distribution in the TS-1 framework is not governed by the thermodynamic stability of the pure material.

Adsorption of dimers and trimers of Cu, Ag, and Au on regular sites and oxygen vacancies of the MgO(001) surface: a density functional study using embedded cluster models

We studied the adsorption of small coinage metal aggregates Mn (M = Cu, Ag, Au; n=2,3) on the ideal MgO(001) as well as on oxygen vacancies, Fs and Fs + using a first-principle computational approach. We applied a generalized-gradient density functional in combination with cluster embedding in an elastic polarizable environment, which provides an accurate description of substrate relaxation. In the same way as single adsorbed atoms, metal moieties on regular O2- surface sites are polarized and interact mainly by electrostatic attraction, counteracted by Pauli repulsion. However, adsorption on vacancies involves some transfer of electron density to the adsorbate, particularly for Au2. Our cluster results for Cu2 and Cu3 on regular O2- sites agree quantitatively with previous results of periodic slab models. The adsorption energy per atom decreases from dimers to trimers in line with the fact that metal-metal cohesion dominates over metal-oxide interaction. Compared to regular sites on flat terraces, dimerization is not particularly favorable on Fs sites and it is unfavorable on Fs + sites.

Adsorption of Cu 4, Ag 4 and Au 4 particles on the regular MgO(0 0 1) surface: A density functional study using embedded cluster models

Cu 4, Ag 4, and Au 4 species adsorbed on the regular MgO(0 0 1) surface are studied using a density functional method and cluster models embedded in an elastic polarizable environment. The structure of the coinage metal tetramers is only slightly distorted by adsorption on the oxide surface compared to the rhombic-planar arrangement in the gas phase. The most stable adsorption complexes of all three systems feature upright metal planar particles with the M 4 moiety orthogonal to the surface and two metal atoms attached to surface oxygen anions. Au 4 and Cu 4 exhibit substantially stronger binding to the surface than Ag 4.

Single d-Metal Atoms on Fs and Fs+ Defects of MgO(001): A Theoretical Study across the Periodic Table

Single d-metal atoms on oxygen defects F(s) and F(s+) of the MgO(001) surface were studied theoretically. We employed an accurate density functional method combined with cluster models, embedded in an elastic polarizable environment, and we applied two gradient-corrected exchange-correlation functionals. In this way, we quantified how 17 metal atoms from groups 6-11 of the periodic table (Cu, Ag, Au; Ni, Pd, Pt; Co, Rh, Ir; Fe, Ru, Os; Mn, Re; and Cr, Mo, W) interact with terrace sites of MgO. We found bonding with F(s) and F(s+) defects to be in general stronger than that with O2- sites, except for Mn-, Re-, and Fe/F(s) complexes. In M/F(s) systems, electron density is accumulated on the metal center in a notable fashion. The binding energy on both kinds of O defects increases from 3d- to 4d- to 5d-atoms of a given group, at variance with the binding energy trend established earlier for the M/O2- complexes, 4d < 3d < 5d. Regarding the evolution of the binding energy along a period, group 7 atoms are slightly destabilized compared to their group 6 congeners in both the F(s) and F(s+) complexes; for later transition elements, the binding energy increases gradually up to group 10 and finally decreases again in group 11, most strongly on the F(s) site. This trend is governed by the negative charge on the adsorbed atoms. We discuss implications for an experimental detection of metal atoms on oxide supports based on computed core-level energies.

Effects of the Aluminum Content of a Zeolite Framework: A DFT/MM Hybrid Approach Based on Cluster Models Embedded in an Elastic Polarizable Environment.

We report the first computational study with a sophisticated quantum mechanics/molecular mechanics (QM/MM) technique that addresses the effect of the aluminum content on the properties of acidic zeolites. To account for both electrostatic and mechanical interaction between the QM cluster and its MM environment, we used cluster models embedded in the covalent variant of the elastic polarizable environment (covEPE) [Nasluzov, V. A.; Ivanova, E. A.; Shor, A. M.; Vayssilov, G. N.; Birkenheuer, U.; Rösch, N. J. Phys. Chem. B 2003, 107, 2228]. For the practical application of the covEPE method, it was necessary to develop a new force field for Al containing zeolites. Two types of zeolite materials, FAU and MFI, were employed as examples. We modeled the variation of the Al content both in the MM environment and in the QM cluster, and we studied pertinent properties of bridging OH groups of the zeolite frameworks, OH vibrational frequencies, and deprotonation energies. The computational results suggest that the local structure and the location of the OH groups exert a stronger effect than the variation of the Al content of the framework.

Adsorption of d-metal atoms on the regular MgO(001) surface: Density functional study of cluster models embedded in an elastic polarizable environment

Structure and bonding of complexes formed by 17 different single transition metal atoms (Cu, Ag, Au; Ni, Pd, Pt; Co, Rh, Ir; Fe, Ru, Os; Mn, Re; Cr, Mo, W) with oxygen sites of the regular MgO(001) surface were studied computationally. We employed an all-electron scalar-relativistic density functional method in combination with our novel scheme of cluster models embedded in an elastic polarizable environment that allows one to account for substrate relaxation. Even on a rigid substrate such as ideal MgO(001), adsorbate-induced relaxation noticeably affects structure and stability of surface complexes. For more reliable estimates, we calculated adsorption energies with two different gradient-corrected exchange-correlation functionals, BP86 and PBEN. More than one electron configuration was considered for metal atoms exhibiting high-spin states adsorption complexes. Within one group of the periodic table, 3d-atoms, in general, were found to adsorb more strongly than 4d-atoms, but weaker than 5d-atoms. In line with our previous studies of selected d-metal atoms adsorbed on oxides, the surface complexes considered did now show any indication of metal oxidation.

Elastic polarizable environment cluster embedding approach for water adsorption on the α-Al2O3(0001) surface. A density functional study

Low coverage water adsorption on the α-Al2O3(0001) surface has been studied with a generalized-gradient density functional approach using embedded cluster and periodic slab methodologies. An advanced cluster embedding method in an elastic polarizable environment (EPE), which enables an accurate description of the adsorption-induced substrate relaxation, has been applied systematically at various density functional levels: PW91, BP, and PBEN. In addition, periodic slab model calculations based on the PW91 functional were carried out for varying surface supercell sizes, (2 × 2) and (3 × 3), which compare very well with the corresponding embedded-cluster results. In agreement with two recent studies employing integrated MO + MO (IMOMO) embedded cluster and periodic Car–Parrinello BLYP methodologies, our calculations predict the 1,2-dissociative adsorption to be about 10 kcal mol−1 more favorable than molecular adsorption; however, at variance with the latter study, we predict 1,4-dissociative adsorption to be least favorable. Analysis of adsorbate-induced relaxation renders the interaction energy with the unrelaxed substrate in the 1,4-dissociative case negative (unbound complex), thus rationalizing the smallest (by absolute value) interaction energy. Our best estimates for binding energies, at the PBEN level, for molecular, 1,2-dissociative, and 1,4-dissociative adsorption are −22.5, −31.2, and −17.2 kcal mol−1, respectively.

Pd 3 and Pt 3 species on the α-Al 2O 3(0 0 0 1) surface: cluster models embedded in an elastic polarizable environment

Adsorption of small metal particles Pd 3 and Pt 3 on an Al-terminated surface α-Al 2O 3(0 0 0 1) was studied by means of all-electron scalar relativistic density functional calculations. We employed stoichiometric model clusters and our recently developed embedding scheme which accurately accounts for the adsorption-induced substrate relaxation. We compared M 3 particles oriented parallel to and almost upright on the surface. The calculations show upright species which interact with two O anions and are stabilized by nearby Al cations to be most stable, with adsorption energies of 1.5 eV (Pd 3) and 2.6 eV (Pt 3). We also discuss the important role of substrate rearrangement.

Elastic Polarizable Environment Cluster Embedding Approach for Covalent Oxides and Zeolites Based on a Density Functional Method

We present a new quantum mechanics/molecular mechanics (QM/MM) embedding approach for systems with directional polar covalent bonds. This “covalent elastic polarizable environment” (covEPE) scheme features a variational treatment of an energy expression that includes all degrees of freedom of both the QM region (the “cluster”) and the MM regions (the “environment”). The method completely and explicitly includes both the electrostatic and mechanical interactions between a QM model cluster and its environment. Monovalent pseudoatoms that represent real atoms of the material saturate the dangling bonds of the cluster; these pseudoatoms belong simultaneously to the QM and MM regions. For a correct description of a pure silica environment, we constructed a new force field of the shell-model type based on potential derived charges instead of formal charges. We implemented the covEPE approach in the density functional program ParaGauss and applied it to pure-silica and Al-containing chabazite, employing a generalized gradient approximation. These applications showed that calculated structural parameters and OH frequencies of bridging hydroxyl groups reproduce experimental data with good accuracy compared to other contemporary computational methods.

Adsorption of Pd and Pt atoms on α-Al 2O 3( [formula omitted]): density functional study of cluster models embedded in an elastic polarizable environment

Complexes of single Pd and Pt atoms on a clean Al-terminated surface α-Al 2O 3(0 0 0 1) were calculated with a scalar relativistic density functional approach using the gradient-corrected BP86 exchange-correlation functional. Stoichiometric cluster models of the oxide substrate were designed, employing bare pseudopotential cations located at the cluster boundaries. Embedding of the clusters in an elastic polarizable environment (based on the shell model) accounted for the substrate relaxation in an accurate fashion. This relaxation notably affected structure and stability of the adsorption complexes. Stable complexes, with binding energies of 1.1 eV (Pd) and 1.7 eV (Pt), were calculated for metal atoms adsorbed on top of an O anion and also interacting with a nearby cation. A significant amount of the adsorption energy, 20% (Pd) and 33% (Pt), is due to substrate relaxation. The sites over the centers of equilateral oxygen triangles were not found to be minima of the potential surface; metal atoms in these positions are weakly bound. No indication was found for the oxidation of Pd or Pt atoms in equilibrium surface complexes at α-Al 2O 3(0 0 0 1).

Density functional embedded cluster calculations on Lewis acid centers of the α‐Al2O3(0001) surface: Adsorption of a CO probe

AbstractWe have investigated the adsorption of CO on the cation‐terminated (0001) surface of α‐Al2O3 with a generalized‐gradient density functional approach. We used cluster models that are consistently embedded in an elastic polarizable environment (EPE), employing a (classical) shell model scheme and bare pseudopotentials (Alpp*) for cations at the cluster boundary. The newly implemented EPE method was found to perform well for describing structure and adsorption properties of Lewis acidic centers of the polar (0001) surface known for its strong relaxation with respect to the bulk terminated geometry. The calculated data are stable with respect to the size of the cluster models. For the embedded stoichiometric clusters [Al4O6]/Al\documentclass{article}\pagestyle{empty}\begin{document}$_{6}^{\mathrm{pp}\ast}$\end{document} and [Al10O15]/Al\documentclass{article}\pagestyle{empty}\begin{document}$_{13}^{\mathrm{pp}\ast}$\end{document} of different structure, the adsorption induced shift Δν of the CO stretching vibration and the binding energy (BE) are 30–42 cm−1 and 0.38–0.47 eV, respectively. The results for the frequency shifts are in good agreement with the value of 39 cm−1 measured for CO/α‐Al2O3(0001) at low coverages. Judged by the frequency shift and the adsorption energy, the interaction of CO molecules with three‐coordinated Al3+ cations at the regular surface is very similar to that with Mg2+ corner sites of MgO polycrystallites, Δν=39 cm−1, BE=0.38 eV. © 2002 John Wiley &amp; Sons, Inc. Int J Quantum Chem, 2002