Cluster embedding in an elastic polarizable environment: Density functional study of Pd atoms adsorbed at oxygen vacancies of MgO(001)

Molecules in Environments: Toward Systematic Quantum Embedding of Electrons and Drude Oscillators

We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational Ansatz for the correlated ground state of the fully interacting molecule-environment system. This wave function is optimized via the variational Monte Carlo method and the ground state energy is subsequently estimated through the diffusion Monte Carlo method. The proposed scheme allows an explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the molecule and the environment. We study solvation energies and excitation energies of benzene derivatives, obtaining excellent agreement with explicit ab initio calculations and experiments.

Embedding Methods for Quantum Chemistry: Applications from Materials to Life Sciences

Quantum mechanical embedding methods hold the promise to transform not just the way calculations are performed, but to significantly reduce computational costs and improve scaling for macro-molecular systems containing hundreds if not thousands of atoms. The field of embedding has grown increasingly broad with many approaches of different intersecting flavors. In this perspective, we lay out the methods into two streams: QM:MM and QM:QM, showcasing the advantages and disadvantages of both. We provide a review of the literature, the underpinning theories including our contributions, and we highlight current applications with select examples spanning both materials and life sciences. We conclude with prospects and future outlook on embedding, and our view on the use of universal test case scenarios for cross-comparisons of the many available (and future) embedding theories.

A comparative study of AumRhn (4 ≤ m + n ≤ 6) clusters in the gas phase versus those deposited on (100) MgO

The combined use of a genetic algorithm and Density Functional Theory (DFT) calculations allows us to explore the potential energy surface. Our results show interesting effects on the geometries of the clusters on deposition. Two-dimensional clusters in the gas phase become three-dimensional and vice versa.

Size-dependent properties of transition metal clusters: from molecules to crystals and surfaces--computational studies with the program ParaGauss

In the so-called scalable regime the size-dependent behavior of the physical and chemical properties of transition metal clusters is described by scaling relationships. For most quantities this scalable regime is reached for cluster sizes between a few tens and a few hundreds of atoms, hence for systems for which an accurate treatment by density functional theory is still feasible. Thus, by invoking scaling relations one is able to obtain properties of very large nanoparticles and even the bulk limit from the results of a series of smaller cluster models. In this invited review we illustrate this strategy by exploiting results from computational studies that mostly were carried out with the density functional theory software ParaGauss. We address mainly the size-dependent behavior of the properties of transition metal clusters. To this end, we first present benchmark studies probing various approximations that are used in such density functional calculations. Subsequently we show how physical insight may be gained by exploring less understood types of systems. These applications range from bare clusters to nanoislands and nanoalloys to adsorption complexes.

Pd(n)Ag(4-n) and Pd(n)Pt(4-n) clusters on MgO (100): a density functional surface genetic algorithm investigation

The novel surface mode of the Birmingham Cluster Genetic Algorithm (S-BCGA) is employed for the global optimisation of noble metal tetramers upon an MgO (100) substrate at the GGA-DFT level of theory. The effect of element identity and alloying in surface-bound neutral subnanometre clusters is determined by energetic comparison between all compositions of PdnAg(4-n) and PdnPt(4-n). While the binding strengths to the surface increase in the order Pt > Pd > Ag, the excess energy profiles suggest a preference for mixed clusters for both cases. The binding of CO is also modelled, showing that the adsorption site can be predicted solely by electrophilicity. Comparison to CO binding on a single metal atom shows a reversal of the 5σ-d activation process for clusters, weakening the cluster-surface interaction on CO adsorption. Charge localisation determines homotop, CO binding and surface site preferences. The electronic behaviour, which is intermediate between molecular and metallic particles allows for tunable features in the subnanometre size range.

Density functional calculations of extended, periodic systems using Coulomb corrected molecular fractionation with conjugated caps method (CC-MFCC)

A consistent DFT based formulation of the order-N molecular fractionation with conjugated caps method in which a molecular system is calculated considering a set of finite fragments, is proposed. Here we apply the method and test its performance on a periodic metal–organic framework system.

Characterization of hydrogen dissociation over aluminium-doped zinc oxide using an efficient massively parallel framework for QM/MM calculations

A task-farm parallelization framework has been implemented in the ChemShell computational chemistry environment to provide a facility for parallelizing common chemical calculations, including finite-difference Hessian evaluation, the nudged elastic band method for reaction path optimization, and population-based methods for global optimization. The optimization methods are provided by a parallel interface to the DL-FIND optimization library. As ChemShell can already exploit parallel external programs for energy and gradient evaluations, the new methods result in a two-level approach to parallelization that gives significantly improved performance for massively parallel calculations. For typical systems, speed-up factors of five to eight times have been observed compared with non-task-farmed calculations. The task-farming version of ChemShell has been used to study the heterolytic dissociation of a hydrogen molecule over a polar oxygen-terminated surface of aluminium-doped zinc oxide using an embedded cluster hybrid QM/MM approach. We calculate a 42 kcal mol −1 heat of reaction and a 30 kcal mol −1 activation energy, which is equivalent to a high backward reaction barrier of 72 kcal mol −1 per H 2 molecule, in close agreement with temperature programmed desorption experiments. The dissociation path includes a stable intermediate comprising a hydride ion in an oxygen vacancy and physisorbed atomic hydrogen.

Quantum chemical modeling of uranyl adsorption on mineral surfaces

We overview quantum mechanical simulations that model the adsorption of actinide ions at solvated mineral surfaces. Pertinent examples illustrate the status of this emerging field of computational chemistry. In particular, we describe our own studies on uranyl adsorption on kaolinite. Already the few available results, from applications of density functional methods to cluster models or periodic slab models, show that such calculations are a useful complement to experimental investigations. Detailed information at the atomic level from accurate electronic structure calculations on well defined model systems helps to refine current interpretations of the chemical nature of uranyl adsorption species and to discover new features of these interface systems. Results from quantum mechanical simulations also provide a valuable reference for future experimental investigations.

Advances in correlated electronic structure methods for solids, surfaces, and nanostructures

Calculations of the electronic structure of solids began decades ago, but only recently have solid-state quantum techniques become sufficiently reliable that their application is nearly as routine as quantum chemistry is for molecules. We aim to introduce chemists to the pros and cons of first-principles methods that can provide atomic-scale insight into the properties and chemistry of bulk materials, interfaces, and nanostructures. The techniques we review include the ubiquitous density functional theory (DFT), which is often sufficient, especially for metals; extensions such as DFT + U and hybrid DFT, which incorporate exact exchange to rid DFT of its spurious self-interactions (critical for some semiconductors and strongly correlated materials); many-body Green's function (GW and Bethe-Salpeter) methods for excited states; quantum Monte Carlo, in principle an exact theory but for which forces (hence structure optimization and dynamics) are problematic; and embedding theories that locally refine the quantum treatment to improve accuracy.

Density-functional model cluster studies of EPR g tensors of Fs+ centers on the surface of MgO

We report g tensors of surface color centers, so-called F(s) (+) centers, of MgO calculated with two density-functional approaches using accurately embedded cluster models. In line with recent UHV measurements on single-crystalline MgO film, we determined only small g-tensor anisotropies and negative shifts Deltag identical with g-g(e) for all F(s) (+) sites considered, namely, (001)-terrace, step, edge, and corner sites. The g values are very sensitive to the local structure of the defect: relaxation reverses the sign of Deltag. However, accounting for the spin-orbit interaction either self-consistently or perturbatively yields very similar results. In addition to the values of the tensor components, their direction with respect to the surface was determined. In contrast to edges, significant deviations from ideal C(2v) symmetry were found for F(s) (+) centers at steps. Recent data on single-crystalline thin films are reevaluated in the light of these results.

Structure of Ag Clusters Grown on Fs-Defect Sites of an MgO(1 0 0) Surface

The structure of AgN clusters (N=1-4, 6, 8, 10), both in the gas phase and grown on the MgO(1 0 0) surface containing Fs-defects, has been investigated by a density functional basin-hopping (DF-BH) approach. In analogy with what observed in the case of gold clusters, it is found that the presence of the defect implies a double frustration and a cylindrical invariance of the metal-surface interaction, causing small Ag clusters growing around the Fs defect to be highly fluxional. Nevertheless, two different structural crossovers are found to be induced by the metal-defect interaction for the adsorbed clusters such that: 1) planar structures prevail for N<or=4 (as in the gas phase); 2) noncrystalline (fivefold symmetric) structures, which are the lowest energy ones in the gas phase for medium sized AgN clusters (N>or=7), prevail for N=6 and N=8; 3) distorted face-centered cubic (fcc) structures grown pseudomorphically on the defected surface prevail for N=10. The transition from fivefold to fcc motifs is rationalized in terms of the double-frustration effect, which increases the bond strain of the noncrystalline structures. Detrapping energies from the defect were also calculated; the lowest energy pathway corresponds to the detachment of a dimer.

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.

Infrared Characterization of Hydroxyl Groups on MgO: A Periodic and Cluster Density Functional Theory Study

The infrared OH stretching frequencies of the various types of hydroxyl groups on MgO surfaces have been calculated by periodic (VASP) and cluster (Gaussian) DFT simulations. Surface irregularities (mono and diatomic steps, corners, step divacancies, and kinks) have been considered to model the IR spectra of hydroxylated MgO powders. A good correspondence between calculated and experimental frequencies is obtained with the B3LYP functional. Hydrogen-bonding is the parameter which influences most the IR frequency of OH groups, followed by location of OH groups in concave or convex areas of the surface and then oxygen coordination. The evolution of experimental IR spectra upon evacuation at increasing temperature can be rationalized on the basis of calculated thermal stabilities of each kind of OH groups. A new model is finally proposed to help assign the experimental bands, in terms of hydrogen-bonding, local topology of the hydroxylated sites, and coordination of oxygen.

Density Functional Embedded Cluster Study of Cu4, Ag4and Au4Species Interacting with Oxygen Vacancies on the MgO(001) Surface

Cu(4), Ag(4), and Au(4) species adsorbed on an MgO(001) surface that exhibits neutral (F(s)) and charged (F(s) (+)) oxygen vacancies have been studied using a density functional approach and advanced embedding models. The gas-phase rhombic-planar structure of the coinage metal tetramers is only moderately affected by adsorption. In the most stable surface configuration, the plane of the tetramers is oriented perpendicular to the MgO(001) surface; one metal atom is attached to an oxygen vacancy and another one is bound to a nearby surface oxygen anion. A very similar structural motif was recently found on defect-free MgO(001), where two O(2-) ions serve as adsorption sites. Following the trend of the interactions with the regular MgO(001) surface, Au(4) and Cu(4) bind substantially stronger to F(s) and F(s) (+) sites than Ag(4). This stronger adsorption interaction at oxygen vacancies, in particular at F(s), is partly due to a notable accumulation of electron density on the adsorbates. We also examined the propensity of small supported metal species to aggregate to adsorbed di-, tri- and tetramers. Furthermore, we demonstrated that core-level ionization potentials offer the possibility for detecting experimentally supported metal tetramers and characterizing them structurally with the help of calculated data.

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.

A combined molecular dynamics+quantum mechanics method for investigation of dynamic effects on local surface structures

A combined molecular dynamics (MD)+quantum mechanics (QM) method for studying processes on ionic surfaces is presented. Through the combination of classical MD and ab initio embedded-cluster calculations, this method allows the modeling of surface processes involving both the structural and dynamic features of the substrate, even for large-scale systems. The embedding approach used to link the information from the MD simulation to the cluster calculation is presented, and rigorous tests have been carried out to ensure the feasibility of the method. The electrostatic potential and electron density resulting from our embedded-cluster model have been compared with periodic slab results, and confirm the satisfying quality of our embedding scheme as well as the importance of applying embedding in our combined MD+QM approach. We show that a highly accurate representation of the Madelung potential becomes a prerequisite when the embedded-cluster approach is applied to temperature-distorted surface snapshots from the MD simulation.

Nucleation of Pd dimers at defect sites of the MgO(100) surface

Point defects on oxide surfaces are presumed to be preferential nucleation sites for supported metal clusters. Under typical growth conditions, dimers constitute the first step in island nucleation. First-principles calculations on the formation of Pd dimers on regular and defect sites of the MgO(100) surface show that nucleation occurs with large dimer binding energies at divacancies and charged oxygen vacancies (F+ centers), while it is less favorable on steps and neutral F centers. The extensive database of defect trapping/attachment properties gives a firm basis to rationalize recent atomic-force microscopy findings and provides guidelines valid, in general, for ionic substrates.

Models for the treatment of crystalline solids and surfaces

Crystalline solids and surfaces have become a subject of growing interest. The difficulty of a comprehensive description of a variety of phenomena by a single method has led to the development of many models. These models can be classified as nonperiodic and periodic models. The former include free clusters, saturated clusters, and embedded clusters. The latter two models serve to remove the boundary effects of the free clusters. No perfect avoidance of such effects can be achieved in this way. The cyclic cluster model overcomes this difficulty in a natural way. It is periodic with a finite periodicity. An embedding can take into account a long-range effect in ionic crystals. Previous periodic approaches relied on the large unit cell model, which is related to the supercell approach. For perfect crystals the conventional unit cell approach is a well-known standard. However, its disadvantage is the unphysical periodicity of defects, which is avoided in the cyclic cluster model. The present article presents a description of these models together with selective applications to solid-state systems and surfaces.