ABSTRACT
The question of whether a solid-liquid phase transition occurs in small clusters poses a fundamental challenge. In this study, we attempt to elucidate this phenomenon through a thorough examination of the thermal behavior and structural stability of Pd8 clusters employing ab initio simulations. Initially, a systematic global search is carried out to identify the various isomers of the Pd8 cluster. This is accomplished by employing an ab initio basin-hopping algorithm and using the PBE/SDD scheme integrated in the Gaussian code. The resulting isomers are further refined through reoptimization using the deMon2k package. To ensure the structural firmness of the lowest-energy isomer, we calculated normal modes. The structural stability as a function of temperature is analyzed through the Born-Oppenheimer molecular dynamics (BOMD) approach. Multiple BOMD trajectories at distinct simulated temperatures are examined with data clustering analysis to determine cluster isomers. This analysis establishes a connection between the potential energy landscape and the simulated temperature. To address the question of cluster melting, canonical parallel-tempering BOMD runs are performed and analyzed with the multiple-histogram method. A broad maximum in the heat capacity curve indicates a melting transition between 500 and 600 K. To further examine this transition, the mean-squared displacement and the pair-distance distribution function are calculated. The results of these calculations confirm the existence of a solid-liquid phase transition, as indicated by the heat capacity curve.
ABSTRACT
Machine-learning force fields (MLFF) should be accurate, computationally and data efficient, and applicable to molecules, materials, and interfaces thereof. Currently, MLFFs often introduce tradeoffs that restrict their practical applicability to small subsets of chemical space or require exhaustive datasets for training. Here, we introduce the Bravais-Inspired Gradient-Domain Machine Learning (BIGDML) approach and demonstrate its ability to construct reliable force fields using a training set with just 10-200 geometries for materials including pristine and defect-containing 2D and 3D semiconductors and metals, as well as chemisorbed and physisorbed atomic and molecular adsorbates on surfaces. The BIGDML model employs the full relevant symmetry group for a given material, does not assume artificial atom types or localization of atomic interactions and exhibits high data efficiency and state-of-the-art energy accuracies (errors substantially below 1 meV per atom) for an extended set of materials. Extensive path-integral molecular dynamics carried out with BIGDML models demonstrate the counterintuitive localization of benzene-graphene dynamics induced by nuclear quantum effects and their strong contributions to the hydrogen diffusion coefficient in a Pd crystal for a wide range of temperatures.
ABSTRACT
Bimetallic Re-Pt is a widely used catalyst in petroleum reforming to obtain high-octane gasoline, but experimental and theoretical information of such systems at the subnanometer scale-namely, as cluster aggregates-is currently lacking. Thus, in this work, we performed a density functional theory-based global optimization study to determine the physicochemical properties of the most stable Re-Pt gas-phase clusters up to six atoms for all compositions. Our results indicate that in these putative global minima (GM) geometries, Re atoms tend to aggregate, while most Pt atoms remain separated from each other. This is even observed in Pt-rich clusters-an indication of the strength of the Re-Re and Re-Pt bonds over pure Pt-Pt ones-due to a strong, directional hybridization of the Re half-filled 5d and the nearly full Pt 5d states. We observe that doping monometallic Pt clusters even with a single Re atom increases their binding energy values and widens the bimetallic cluster highest occupied molecular orbital-lowest unoccupied molecular orbital gap. As catalysis occurs at elevated temperatures, we explore the concept of cluster fluxionality for Re-Pt minima in terms of the calculated isomer occupation probability, P(T). This allows us to quantify the abundance of GM and low-energy isomer configurations as a function of temperature. This is done at size 5 atoms due to the wide isomer observed variety. Our calculations indicate that for pure Re5, the P(T) of the GM configuration substantially decreases after 750 K. Especially, for Re4Pt1, the GM is the dominant structure up to nearly 700 K when the second-energy isomer becomes the stable one. Although no ordering changes are seen for Re3Pt2, Re2Pt3, and Re1Pt4, we do observe a structural transition-between the GM and the second isomer-for pure Pt5 above 1000 K. We expect this type of combined first-principles analysis to add to the overall, continuous understanding of the stability and energetics of ultrafine and highly-dispersed Re-Pt petroleum-reforming catalysts and the scarce available information on this particular bimetallic system.
ABSTRACT
Transition and noble metal clusters have proven to be critical novel materials, potentially offering major advantages over conventional catalysts in a range of value-added catalytic processess such as carbon dioxide transformation to methanol. In this work, a systematic computational study of CO2 adsorption on gas-phase Cu4-xPtx (x = 0-4) clusters is performed. An exhaustive potential energy surface exploration is initially performed using our recent density functional theory basin-hopping global optimization implementation. Ground-state and low-lying energy isomers are identified for Cu4-xPtx clusters. Secondly, a CO2 molecule adsorption process is analyzed on the ground-state Cu4-xPtx configurations, as a function of cluster composition. Our results show that the gas-phase linear CO2 molecule is deformed upon adsorption, with its bend angle varying from about 132° to 139°. Cu4-xPtx cluster geometries remain unchanged after CO2 adsorption, with the exception of Cu3Pt1 and Pt4 clusters. For these particular cases, a structural conversion between the ground-state geometry and the corresponding first isomer configurations is found to be assisted by the CO2 adsorption. For all clusters, the energy barriers between the ground-state and first isomer structures are explored. Our calculated CO2 adsorption energies are found to be larger for Pt-rich clusters, exhibiting a volcano-type plot. The overall effect of a hybrid functional including dispersion forces is also discussed.
