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

Toward size-dependent thermodynamics of nanoparticles from quantum chemical calculations of small atomic clusters: a case study of (B2O3)n

We present a method for obtaining canonical partition functions and, accordingly, temperature-dependent thermodynamics of arbitrary-sized (nano) particles from electronic structure calculations of the corresponding small size atomic clusters. The guiding idea here is to extrapolate the basic properties underlying the thermochemistry of clusters (electronic energies, rotational constants, and vibrational frequencies) rather than the thermodynamic functions themselves. The thus obtained scaling dependences for these basic properties expressed in a simple analytical form provide an efficient tool for fast evaluation of the size-selected thermochemical data for particles of any nuclearity. To exemplify the performance of the methodology, neutral stoichiometric boron oxide clusters are considered. To this end, the geometry and various physical properties of the energetically lowest-lying (B₂O₃)_n (n = 1,…,8) structures are found using density functional theory and the authors' multistage hierarchical procedure customized for global optimization of quite large cluster structures. With these data and based on the physically consistent scaling regularities for the principal cluster properties, the size-selected thermodynamic functions of boron oxide particles in the gas phase, such as enthalpy, entropy, and specific heat capacity, are derived. The variation of these characteristics with increasing cluster size is discussed in detail as well. To facilitate handling of the temperature and size dependences we have found here in further chemical kinetic and equilibrium modeling, the tabulated thermodynamic functions of interest are fitted for n = 1,…,1000 to the standard seven-parameter Chemkin polynomials.

Periodic DFTB for Supported Clusters: Implementation and Application on Benzene Dimers Deposited on Graphene

The interest for properties of clusters deposited on surfaces has grown in recent years. In this framework, the Density Functional based Tight Binding (DFTB) method appears as a promising tool due to its ability to treat extended systems at the quantum level with a low computational cost. We report the implementation of periodic boundary conditions for DFTB within the deMonNano code with k-points formalism and corrections for intermolecular interactions. The quality of DFTB results is evaluated by comparison with dispersion-corrected DFT calculations. Optimized lattice properties for a graphene sheet and graphite bulk are in agreement with reference data. The deposition of both benzene monomer and dimers on graphene are investigated and the observed trends are similar at the DFT and DFTB levels. Moreover, interaction energies are of similar orders of magnitude for these two levels of calculation. This study has evidenced the high stability of a structure made of two benzene molecules deposited close to each other on the graphene sheet. This work demonstrates the ability of the new implementation to investigate surface-deposited molecular clusters properties.

Theoretical insights into C-H bond activation of methane by transition metal clusters: the role of anharmonic effects

In heterogeneous catalysis, the determination of active phases has been a long-standing challenge, as materials' properties change under operational conditions (i.e. temperature (T) and pressure (p) in an atmosphere of reactive molecules). As a first step towards materials design for methane activation, we study the T and p dependence of the composition, structure, and stability of metal oxide clusters in a reactive atmosphere at thermodynamic equilibrium using a prototypical model catalyst having wide practical applications: free transition metal (Ni) clusters in a combined oxygen and methane atmosphere. A robust methodological approach is employed, where the starting point is systematic scanning of the potential energy surface (PES) to obtain the global minimum structures using a massively parallel cascade genetic algorithm (cGA) at the hybrid density functional level. The low energy clusters are further analyzed to estimate their thermodynamic stability at realistic T, p O2 and p CH4 using ab initio atomistic thermodynamics (aiAT). To incorporate the anharmonicity in the vibrational free energy contribution to the configurational entropy, we evaluate the excess free energy of the clusters numerically by a thermodynamic integration method with ab initio molecular dynamics (aiMD) simulation inputs. By analyzing a large dataset, we show that the conventional harmonic approximation miserably fails for this class of materials, and capturing the anharmonic effects on the vibration free energy contribution is indispensable. The latter has a significant impact on detecting the activation of the C-H bond, while the harmonic infrared spectrum fails to capture this, due to the wrong prediction of the vibrational modes.

Pd Single-Atom Sites on the Surface of PdAu Nanoparticles: A DFT-Based Topological Search for Suitable Compositions

Structure of model bimetallic PdAu nanoparticles is analyzed aiming to find Pd:Au ratios optimal for existence of Pd1 single-atom surface sites inside outer Au atomic shell. The analysis is performed using density-functional theory (DFT) calculations and topological approach based on DFT-parameterized topological energy expression. The number of the surface Pd1 sites in the absence of adsorbates is calculated as a function of Pd concentration inside the particles. At low Pd contents none of the Pd atoms emerge on the surface in the lowest-energy chemical orderings. However, surface Pd1 sites become stable, when Pd content inside a Pd-Au particle reaches ca. 60%. Further Pd content increase up to almost pure Pd core is accompanied by increased concentration of surface Pd atoms, mostly as Pd1 sites, although larger Pd ensembles as dimers and linear trimers are formed as well. Analysis of the chemical orderings inside PdAu nanoparticles at different Pd contents revealed that enrichment of the subsurface shell by Pd with predominant occupation of its edge positions precedes emergence of Pd surface species.

Evolution of the structural, energetic, and electronic properties of the 3d, 4d, and 5d transition-metal clusters (30 TMn systems for n = 2–15): a density functional theory investigation

Subnanometric transition-metal (TM) clusters have attracted great attention due to their unexpected physical and chemical properties, leastwise compared to their bulk counterparts.