Misbah Sarwar

Perspective: Methods for large-scale density functional calculations on metallic systems

Current research challenges in areas such as energy and bioscience have created a strong need for Density Functional Theory (DFT) calculations on metallic nanostructures of hundreds to thousands of atoms to provide understanding at the atomic level in technologically important processes such as catalysis and magnetic materials. Linear-scaling DFT methods for calculations with thousands of atoms on insulators are now reaching a level of maturity. However such methods are not applicable to metals, where the continuum of states through the chemical potential and their partial occupancies provide significant hurdles which have yet to be fully overcome. Within this perspective we outline the theory of DFT calculations on metallic systems with a focus on methods for large-scale calculations, as required for the study of metallic nanoparticles. We present early approaches for electronic energy minimization in metallic systems as well as approaches which can impose partial state occupancies from a thermal distribution without access to the electronic Hamiltonian eigenvalues, such as the classes of Fermi operator expansions and integral expansions. We then focus on the significant progress which has been made in the last decade with developments which promise to better tackle the length-scale problem in metals. We discuss the challenges presented by each method, the likely future directions that could be followed and whether an accurate linear-scaling DFT method for metals is in sight.

Predicting the oxygen-binding properties of platinum nanoparticle ensembles by combining high-precision electron microscopy and density functional theory

Many studies of heterogeneous catalysis, both experimental and computational, make use of idealized structures such as extended surfaces or regular polyhedral nanoparticles. This simplification neglects the morphological diversity in real commercial oxygen reduction reaction (ORR) catalysts used in fuel-cell cathodes. Here we introduce an approach that combines 3D nanoparticle structures obtained from high-throughput high-precision electron microscopy with density functional theory. Discrepancies between experimental observations and cuboctahedral/truncated-octahedral particles are revealed and discussed using a range of widely used descriptors, such as electron-density, d-band centers, and generalized coordination numbers. We use this new approach to determine the optimum particle size for which both detrimental surface roughness and particle shape effects are minimized.

A DFT study of Pt layer deposition on catalyst supports of titanium oxide, nitride and carbide

Due to carbon corrosion under the electrochemical conditions in PEMFCs, alternative ceramic supports to carbon such as TiO2 have been considered to improve the environmental resistance and catalyst durability. In this work, a series of metal oxides MO2 (M = Ti, Ir, Ru), doped and reduced TiO2 surfaces, titanium nitride and carbide ceramic supports have been chosen to study the Pt deposition behavior using density functional theory. The stacking orders and the electronic screening effect of Pt deposition layers on the different geometric structures of the support surfaces are discussed based on a simple periodic slab model. The structural stability and wetting tendency of Pt overlayers have been estimated via energetic descriptors. The interfacial bonding of catalyst-support has been investigated through the electron density analysis for a group of Ti containing substrates. This suggests a reduced Ti charge state as well as a stronger covalent character of the support material, facilitating Pt bonding.

A new type of scaling relations to assess the accuracy of computational predictions of catalytic activities applied to the oxygen evolution reaction

Experimentally, it is well known that the overpotentials for the oxygen evolution reaction (OER) on RuO2 and IrO2 are similar and rather low. The question is whether widespread computational electrochemistry models based on adsorption thermodynamics are capable of reproducing such observations. Making use of DFT results of revised Perdew–Burke–Ernzerhof (RPBE) and Perdew–Burke–Ernzerhof (PBE) functionals from six different codes and various types of pseudopotentials, we show that whereas IrO2 is consistently predicted to have low overpotentials, RuO2 is predicted to have large overpotentials. A new methodology based on adsorption‐energy scaling relations shows that the inaccurate prediction for RuO2 stems from its anomalous adsorption energies of oxygen/oxygenates. Including explicit water solvation and using functionals that account for van der Waals interactions such as vdW‐DF, vdW‐DF2 and optPBE‐vdW modifies appropriately the adsorption energies so that both oxides are predicted to be highly active.

Effect of graphene support on large Pt nanoparticles

State-of-the-art catalysts are often created via deposition of monolayers, sub-monolayers or nanoparticles of the catalytic material over supports, aiming to increase the surface area and decrease the loading of the catalytic material and therefore the overall cost. Here, we employ large-scale DFT calculations to simulate platinum clusters with up to 309 atoms interacting with single layer graphene supports with up to 880 carbon atoms. We compute the adsorption, cohesion and formation energies of two and three-dimensional Pt clusters interacting with the support, including dispersion interactions via a semi-empirical dispersion correction and a vdW functional. We find that three-dimensional Pt clusters are more stable than the two-dimensional when interacting with the support, and that the difference between their stabilities increases with the system size. Also, the dispersion interactions are more pronounced as we increase the nanoparticle size, being essential to a reliable description of larger systems. We observe inter-atomic expansion (contraction) on the closest (farthest) Pt facets from the graphene sheet and charge redistribution with overall charge being transferred from the platinum clusters to the support. The Pt-Pt expansion, which is related to the charge transfer in the system, correlates with the adsorption energy per Pt atom in contact with the graphene. These, and other electronic and structural observations show that the effect of the support cannot be neglected. Our study provides for the first time, to the best of our knowledge, quantitative results on the non-trivial combination of size and support effects for nanoparticles sizes which are relevant to catalyst design.

Theoretical exploration of novel catalyst support materials for fuel cell applications

In this work, a range of corrosion resistant materials have been assessed for their suitability as Pt catalyst supports using density functional theory. The influence of support materials on the catalytic activity has been disentangled into geometric and electronic effects via a correlation between the d-band centre of the supported Pt film and the interfacial lattice strain (lattice match). Two energetic descriptors, the Pt wetting parameter and the relative oxygen binding energy, have been used to describe the catalyst–support adhesion behaviour and the resultant activity. Taking both of the factors into account, some novel candidate materials, e.g. TiC and WC, are recommended as catalyst supports.

Atomic-Scale Modelling and its Application to Catalytic Materials Science

Computational methods are a burgeoning science within industry. In particular, recent advances have seen first-principles atomic-scale modelling leave the realm of the academic theory lab and enter mainstream industrial research. Herein we present an overview, focusing on catalytic applications in fuel cells, emission control and process catalysis and looking at some real industrial examples being undertaken within the Johnson Matthey Technology Centre. We proceed to discuss some underpinning research projects and give a perspective on where developments will come in the short to mid-term.

Ideal versus real: simulated annealing of experimentally derived and geometric platinum nanoparticles

Platinum nanoparticles find significant use as catalysts in industrial applications such as fuel cells. Research into their design has focussed heavily on nanoparticle size and shape as they greatly influence activity. Using high throughput, high precision electron microscopy, the structures of commercially available Pt catalysts have been determined, and we have used classical and quantum atomistic simulations to examine and compare them with geometric cuboctahedral and truncated octahedral structures. A simulated annealing procedure was used both to explore the potential energy surface at different temperatures, and also to assess the effect on catalytic activity that annealing would have on nanoparticles with different geometries and sizes. The differences in response to annealing between the real and geometric nanoparticles are discussed in terms of thermal stability, coordination number and the proportion of optimal binding sites on the surface of the nanoparticles. We find that annealing both experimental and geometric nanoparticles results in structures that appear similar in shape and predicted activity, using oxygen adsorption as a measure. Annealing is predicted to increase the catalytic activity in all cases except the truncated octahedra, where it has the opposite effect. As our simulations have been performed with a classical force field, we also assess its suitability to describe the potential energy of such nanoparticles by comparing with large scale density functional theory calculations.

From High-precision Imaging to High-performance Computing: Leveraging ADF-STEM Atom-counting and DFT for Catalyst Nano-metrology

Z-contrast imaging in the scanning transmission electron microscope (STEM) is a powerful tool to image precious metal heterogeneous catalysts at the atomic scale. When the annular dark-field (ADF) images from the STEM are quantified onto an absolute scale (Figure 1), it has been shown that it is possible to count the number of atoms in individual atomic columns of metallic nanoparticles and to estimate their three-dimensional structure [1]. In recent years further progress has been made in identifying the possible sources of error in the recording and analysis of quantitative annular dark-field (ADF STEM) images [2], in experiment-design, and in verifying the metrology by tomographic techniques. Of these developments, the move to fast multi-frame image-acquisition and -averaging has enabled the correction of experimental scanning-distortions, reductions in electron beam-damage of samples, and improvements in signal-noise ratio (SNR) [3]. Very recently, a new ADF image analysis best-practice, melding the benefits of both reference-simulation and unbiased statistical interpretation based analysis methods, has produced an atom counting method with even greater robustness [4,5]. Exploiting these recent technical developments, we obtain optimised raw data which is fed into highthroughput image processing tools revealing particle size, atom-counts etc. Unfortunately, our increased analysis throughput merely shifts the investigation bottleneck from data-processing to interpretation. To remedy this, we have developed a computationally-efficient genetic-algorithm based structure solving code (requiring a few tens of CPU hours per structure on a standard desktop PC) to retrieve likely lowenergy 3D particle structures which match the experimental observations.

Towards Statistically Representative Atomic Resolution 3D Nano-metrology for Materials Modelling and Catalyst Design

Metallic nanoparticles are used widely in a variety of catalyst applications and further improvement in their performance requires materials characterisation at the nano-scale. The aberration corrected scanning transmission electron microscope (STEM) now allows for the routine imaging of metallic nanoparticles at atomic resolution. Especially useful is the annular dark-field (ADF) imaging mode where image contrast is related to sample mass or atomic number. It has been shown that, for pure metals, this approach allows for the number of atoms in atomic-columns to be counted [1] and for the 3D structure of nanoparticles to be revealed [2]. Recently we presented a method for the highthroughput automated analysis of ADF STEM data to produce 3D models of nanoparticles at atomic resolution [3]. By utilising prior knowledge about the structures this allows information such as facet types and surface-atom coordination numbers to be determined on a particle by particle basis (Figure 1) without the need for the multiple frame imaging of tomography. However, in many electron microscopy studies, few unique nanostructures are presented and this may lead to unintended observational bias. The next logical step then is to survey a larger number of particles and to move towards more general measurements of ‘average’ particle properties.