Isomerisation and phase transitions in small sodium clusters

Structural and electronic changes in Ga-In and Ga-Sn alloys on melting

The melting behaviour of surface slabs of Ga-In and Ga-Sn is studied using periodic density functional theory and ab initio molecular dynamics. Analysis of the structure and electronics of the solid and liquid phases gives insight into the properties of these alloys, and why they may act as promising CO₂ reduction catalysts. We report melting points for slabs of hexa-layer Ga-In (386 K) and Ga-Sn (349 K) that are substantially lower than the pure hexa-layer Ga system (433 K), and attribute the difference to the degree to which the dopant (In or Sn) disrupts the layered Ga network. In molecular dynamics trajectories of the liquid structures, we find that dopant tends to migrate from the centre of the slab towards the surface and accumulate there. Bader charge calculations reveal that the surface dopant atoms have increased positive charge, and density of states analyses suggest the liquid alloys maintain metallic electronic behaviour. Thus, surface In and Sn may provide good binding sites for intermediates in CO₂ reduction. This work contributes to our understanding of the properties of liquid metal systems, and provides a foundation for modelling catalysis on these materials.

Modulating the thermal and structural stability of gallenene via variation of atomistic thickness

Using ab initio molecular dynamics, we show that a recently discovered form of 2D Ga-gallenene-exhibits highly variable thickness dependent properties. Here, 2D Ga of four, five and six atomic layers thick are found to be thermally stable to 457 K, 350 K and 433 K, respectively; all well above that of bulk Ga. Analysis of the liquid structure of 2D Ga shows a thickness dependent ordering both parallel and perpendicular to the Ga/vacuum interface. Furthermore, ground state optimisations of 2D Ga to 12 atomic layers thick shows a return to a bulk-like bonding structure at 10 atoms thick, therefore we anticipate that up to this thickness 2D Ga structures will each exhibit novel properties as discrete 2D materials. Gallenene has exciting potential applications in plasmonics, sensors and electrical contacts however, for the potential of 2D Ga to be fully realised an in depth understanding of its thickness dependent properties is required.

Evidencing the relationship between isomer spectra and melting: the 20- and 55-atom silver and gold cluster cases

The present work highlights the links between melting properties and structural excitation spectra of small gold and silver clusters. The heat capacity curves are computed for Ag₂₀, Au₂₀, Ag₅₅, Au₅₅ and their ions, using a parallel-tempering molecular dynamics scheme to explore the density functional based tight binding (DFTB) potential energy surfaces and the multiple histogram method. It is found that clusters having very symmetric lowest energy structures (Au₂₀, Ag₅₅ and their ions) present sharp or relatively sharp solid-to-liquid transitions and large melting temperatures, important structural excitation energies and a discrete isomer spectrum. Opposite trends are observed for less ordered clusters (Ag₂₀, Au₅₅ and their ions). Regarding the structural evolution with temperature, very symmetric clusters exhibit minor evolution up to the starting melting temperature. The present study also highlights that, in contrast with the case of Au₂₀, a single electron excess or deficiency is not determinant regarding the melting characteristics, even quantitatively, for clusters containing 55 atoms, for gold as for silver.

Thickness dependent thermal stability of 2D gallenene

Freestanding 2D metallic gallenene exhibits remarkable stability when the thickness is three atomic layers.

Neural network potentials for dynamics and thermodynamics of gold nanoparticles

For understanding the dynamical and thermodynamical properties of metal nanoparticles, one has to go beyond static and structural predictions of a nanoparticle. Accurate description of dynamical properties may be computationally intensive depending on the size of nanoparticle. Herein, we demonstrate the use of atomistic neural network potentials, obtained by fitting quantum mechanical data, for extensive molecular dynamics simulations of gold nanoparticles. The fitted potential was tested by performing global optimizations of size selected gold nanoparticles (Au_n, 17 ≤ n ≤ 58). We performed molecular dynamics simulations in canonical (NVT) and microcanonical (NVE) ensembles on Au₁₇, Au₃₄, Au₅₈ for a total simulation time of around 3 ns for each nanoparticle. Our study based on both NVT and NVE ensembles indicate that there is a dynamical coexistence of solid-like and liquid-like phases near melting transition. We estimate the probability at finite temperatures for set of isomers lying below 0.5 eV from the global minimum structure. In the case of Au₁₇ and Au₅₈, the properties can be estimated using global minimum structure at room temperature, while for Au₃₄, global minimum structure is not a dominant structure even at low temperatures.

Temperature- and field-induced structural transitions in magnetic colloidal clusters

Magnetic colloidal clusters can form chain, ring, and more compact structures depending on their size. In the present investigation we examine the combined effects of temperature and external magnetic field on these configurations by means of extensive Monte Carlo simulations and a dedicated analysis based on inherent structures. Various thermodynamical, geometric, and magnetic properties are calculated and altogether provide evidence for possibly multiple structural transitions at low external magnetic field. Temperature effects are found to overcome the ordering effect of the external field, the melted stated being associated with low magnetization and a greater compactness. Tentative phase diagrams are proposed for selected sizes.

Phase changes of the water hexamer and octamer in the gas phase and adsorbed on polycyclic aromatic hydrocarbons

We investigate thermodynamic properties of small water clusters adsorbed on polycyclic aromatic hydrocarbons (PAHs), which are relevant systems in the context of astrophysical and atmospheric chemistry. We present heat capacity curves computed from parallel-tempering molecular dynamics and Monte Carlo simulations that were performed using the self-consistent-charge density-functional based tight-binding method. These curves are characteristic of the phase changes occurring in the aggregates and provide useful information on the evolution of the interaction between the water molecules and the PAHs as a function of temperature. After benchmarking our approach on the water hexamer and octamer in the gas phase, we present some results for these same clusters adsorbed on coronene and circumcoronene. When compared to the curves obtained for the isolated water clusters, the phase change temperature significantly decreases for the (H2O)8-PAH clusters whereas it depends on the nature of the PAH in the case of the hexamer. We analyse these differences as connected to the relative energies of the optimized characteristic isomers and to their dynamical behavior. We also evidence the population changes of the various cluster isomers as a function of temperature.

Sigma method for the microcanonical entropy or density of states

We introduce a simple improvement on the method to calculate equilibrium entropy differences between classical energy levels proposed by Davis [S. Davis, Phys. Rev. E 84, 050101 (2011)]. We demonstrate that the modification is superior to the original whenever the energy levels are sufficiently closely spaced or whenever the microcanonical averaging needed in the method is carried out by importance sampling Monte Carlo. We also point out the necessary adjustments if Davis's method (improved or not) is to be used with molecular dynamics simulations.

Perturbation method to calculate the density of states

Monte Carlo switching moves ("perturbations") are defined between two or more classical Hamiltonians sharing a common ground-state energy. The ratio of the density of states (DOS) of one system to that of another is related to the ensemble averages of the microcanonical acceptance probabilities of switching between these Hamiltonians, analogously to the case of Bennett's acceptance ratio method for the canonical ensemble [C. H. Bennett, J. Comput. Phys. 22, 245 (1976)]. Thus, if the DOS of one of the systems is known, one obtains those of the others and, hence, the partition functions. As a simple test case, the vapor pressure of an anharmonic Einstein crystal is computed, using the harmonic Einstein crystal as the reference system in one dimension; an auxiliary calculation is also performed in three dimensions. As a further example of the algorithm, the energy dependence of the ratio of the DOS of the square-well and hard-sphere tetradecamers is determined, from which the temperature dependence of the constant-volume heat capacity of the square-well system is calculated and compared with canonical Metropolis Monte Carlo estimates. For these cases and reference systems, the perturbation calculations exhibit a higher degree of convergence per Monte Carlo cycle than Wang-Landau (WL) sampling, although for the one-dimensional oscillator the WL sampling is ultimately more efficient for long runs. Last, we calculate the vapor pressure of liquid gold using an empirical Sutton-Chen many-body potential and the ideal gas as the reference state. Although this proves the general applicability of the method, by its inherent perturbation approach the algorithm is suitable for those particular cases where the properties of a related system are well known.

Statistical analysis of ion mobility spectrometry. I. Unbiased and guided replica-exchange molecular dynamics

Achieving (bio)macromolecular structural assignment from the interpretation of ion mobility spectrometry (IMS) experiments requires successful comparison with computer modeling. Replica-exchange molecular dynamics simulations with suitable force fields not only offer a convenient framework to locate relevant conformations, especially in the case of multiple-funnel energy landscapes, but they are also well suited to statistical analyses. In the present paper, we discuss two extensions of the method used to improve its efficiency in the context of IMS. Two doubly-protonated polyalanines [RA(4)XA(4)K + 2H](2+) with X=V and D appear as favorable cases for which the calculated collision cross-section distributions naturally agree with the measurements, providing reliable candidate structures. For these compounds, a careful consideration of other order parameters based on the weighted histogram method resolves several otherwise hidden underlying conformational families. In the case of a much larger peptide exhibiting bistability, assignment is more difficult but could be achieved by guiding the sampling with an umbrella potential using the square gyration radius as the biasing coordinate. Applied to triply protonated bradykinine, the two presented methods indicate that different conformations compatible with the measurements are very close in energy.

Melting and Freezing of Metal Clusters

Recent developments allow heat capacities to be measured for size-selected clusters isolated in the gas phase. For clusters with tens to hundreds of atoms, the heat capacities determined as a function of temperature usually have a single peak attributed to a melting transition. The melting temperatures and latent heats show large size-dependent fluctuations. In some cases, the melting temperatures change by hundreds of degrees with the addition of a single atom. Theory has played a critical role in understanding the origin of the size-dependent fluctuations, and in understanding the properties of the liquid-like and solid-like states. In some cases, the heat capacities have extra features (an additional peak or a dip) that reveal a more complex behavior than simple melting. In this article we provide a description of the methods used to measure the heat capacities and provide an overview of the experimental and theoretical results obtained for sodium and aluminum clusters.

Liquid-liquid phase coexistence in gold clusters: 2D or not 2D?

The thermodynamics of gold cluster anions (AuN-, N=11,...,14) is investigated using quantum molecular dynamics. Our simulations suggest that AuN- may exhibit a novel, freestanding planar liquid phase which dynamically coexists with a normal three-dimensional liquid. Upon cooling with experimentally realizable cooling rates, the entropy-favored three-dimensional liquid clusters often supercool and solidify into the "wrong" dimensionality. This indicates that experimental validation of theoretically predicted AuN- ground states might be more complicated than hitherto expected.

Quantum Effects on the Caloric Curves of Lithium Clusters

A tight-binding quantum Hamiltonian and an empirical embedded-atom model (EAM) potential are used to get insight into the finite-temperature behavior of small Lin clusters, n = 8, 20, and 55. Exchange Monte Carlo simulations provide an extensive sampling of configuration space, including the putative global minimum and many relevant isomers. The heat capacities obtained from the classical simulations are corrected for low-temperature quantum delocalization using the Pitzer-Gwinn approximation. Alternatively, the caloric curves are estimated from the database of local minima using the quantum harmonic superposition approximation. While the two atomistic models predict qualitatively similar features, including some premelting effects in Li20 but none in Li55, strong variations are observed in the melting temperatures, the EAM potential giving unexpectedly low values.

Specific heat and Lindemann-like parameter of metallic clusters: Mono- and polyvalent metals

The Brownian-type molecular dynamics simulation is revisited and applied to study the thermal and geometric properties of four mono- and two polyvalent metallic clusters. For the thermal property, we report the specific heat at constant volume CV and study the solid-liquid-like transition by scrutinizing its characteristic. For the geometric property, we calculate the root mean square relative bond-length fluctuation delta as a function of increasing temperature. The thermal change in delta reflects the movement of atoms and hence is a relevant parameter in understanding the phase transition in clusters. The simulated results for the CV of alkali and aluminum clusters whose ground state structures exhibit icosahedral symmetry generally show one phase transition. In contrast, the tetravalent lead is quite often seen to exhibit two phase transitions, a premelting process followed by a progressive melting. In connection with the premelting scenario, it is found here that those (magic number) clusters identified to be of lesser stability (among other stable ones) according to the second energy difference are clusters showing a greater possibility of undergoing premelting process. This energy criterion applies to aluminum clusters nAl=28 and 38. To delve further into the thermal behavior of clusters, we have analyzed also the thermal variation of deltaT and attempted to correlate it with CV(T). It turns out that the premelting (if exist) and melting temperatures of the smaller size clusters (n less, similar 50) extracted from CV do not always agree quantitatively with that deduced from delta.

Thermal expansion in small metal clusters and its impact on the electric polarizability

The thermal expansion coefficients of Na(N) clusters with 8</=N</=40, and Al7, Al-13, and Al-14 clusters are obtained from ab initio Born-Oppenheimer local-density-approximation molecular dynamics. Thermal expansion of small metal clusters is considerably larger than that in the bulk and is size dependent. We demonstrate that the average static electric dipole polarizability of Na clusters depends linearly on the mean interatomic distance and only to a minor extent on the detailed ionic configuration when the overall shape of the electron density is enforced by electronic shell effects. Taking thermal expansion into account brings theoretical and experimental polarizabilities into quantitative agreement.

Molecular mechanisms for cooperative folding of proteins

The folding of single-domain globular proteins exhibits the character of first-order or two-state thermodynamics. The origin of such high cooperativity in relatively small polymer systems is still not well understood. Recently, the statistical mechanics of protein folding has been studied extensively with simple protein models such as short cubic-lattice chains with contact-based interactions. While many valuable insights about protein folding were gained with such models, some concerns have also arisen, viz. that they lack the character of protein backbones whose interactions would limit the folding patterns of proteins. Here, a comparative study of the conventional cubic-lattice chain model and a fine-grained more realistic lattice protein model with both backbone and side-chain interactions is carried out. It is found that, even though both types of models exhibit a cooperative two-state folding transition to the native structure with optimized force fields, the character and origin of cooperativity of the two models are different. In the simple contact-based model, the free-energy barrier occurs at the low end of the energy scale, and the cooperativity arises from a concerted formation of native contacts among many residues in a compact state. In the other more complicated model, the free-energy barrier occurs in the intermediate energy region, and the folding cooperativity arises from collective orientational arrangements of locally structured units in semi-open conformational states. On the basis of these results, two limiting molecular mechanisms for protein folding emerge, which can be used for analyzing the folding process of real proteins.