Pairwise Repulsive Interactions Research Articles

Machine Learning Assisted Monte Carlo Simulation: Efficient Overlap Determination for Nonspherical Hard Bodies

AbstractStandard molecular dynamics (MD) and Monte Carlo (MC) simulations deal with spherical particles. Extending the standard simulation methodologies to the nonspherical objects is non‐trivial. To circumvent this problem, nonspherical bodies are often treated as a collection of constituent spherical objects. As the number of these constituent objects becomes large, the computational burden to simulate the system also increases. Here, an alternative way is proposed to simulate nonspherical rigid bodies having pairwise repulsive interactions. This approach is based on a machine learning (ML)‐based model, which predicts the overlap between two nonspherical bodies. The ML model is easy to train and the computation cost of its implementation remains independent of the number of constituent spheres used to represent a nonspherical rigid body. When used in MC simulation, this method is faster than the standard implementation, where overlap determination is based on calculating the distance between constituent spheres. This proposed ML‐based MC method produces similar structural features (in comparison to the standard implementation) in both two and three dimensions, and can qualitatively capture the isotropic to nematic transition of rigid rods in three dimensions. It is believed that this work is a step toward a time‐efficient simulation of non‐spherical rigid bodies.

Rotational transition, domain formation, dislocations, and defects in vortex systems with combined sixfold and twelvefold anisotropic interactions

We introduce a new model for a pairwise repulsive interaction potential of vortices in a type-II superconductor, consisting of superimposed six- and 12-fold anisotropies. Using numerical simulations we study how the vortex lattice configuration varies as the magnitudes of the two anisotropic interaction terms change. A triangular lattice appears for all values, and rotates through 30 degrees as the ratio of the six- and 12-fold anisotropy amplitudes is varied. The transition causes the VL to split into domains that have rotated clockwise or counter-clockwise, with domain boundaries that are "decorated" by dislocations consisting of five- and seven-fold coordinated vortices. We also find intra-domain dislocations and defects, and characterize them in terms of their energy cost. We discuss how this model could be generalized to other particle-based systems with anisotropic interactions, such as colloids, and consider the limit of very large anisotropy where it is possible to create cluster crystal states.

Third-Order Phase Transition: Random Matrices and Screened Coulomb Gas with Hard Walls

Consider the free energy of a d-dimensional gas in canonical equilibrium under pairwise repulsive interaction and global confinement, in presence of a volume constraint. When the volume of the gas is forced away from its typical value, the system undergoes a phase transition of the third order separating two phases (pulled and pushed). We prove this result (i) for the eigenvalues of one-cut, off-critical random matrices (log-gas in dimension d=1) with hard walls; (ii) in arbitrary dimension dge 1 for a gas with Yukawa interaction (aka screened Coulomb gas) in a generic confining potential. The latter class includes systems with Coulomb (long range) and delta (zero range) repulsion as limiting cases. In both cases, we obtain an exact formula for the free energy of the constrained gas which explicitly exhibits a jump in the third derivative, and we identify the ‘electrostatic pressure’ as the order parameter of the transition. Part of these results were announced in Cunden et al. (J Phys A 51:35LT01, 2018).

Unidirectional laning and migrating cluster crystals in confined self-propelled particle systems

One standard approach to describe the collective behaviour of self-propelled particles is the Vicsek model: point-like self-propelled particles tend to align their migration directions to the ones of their nearer neighbours at each time-step. Here we use a variant of the Vicsek model that includes pairwise repulsive interactions. Confining the system between parallel walls can qualitatively change its appearance: a laning state can emerge that is different from the ones previously reported. All lanes show on average the same migration direction of the contained particles with a finite separation distance between the lanes. Furthermore, in certain parameter ranges we observe collectively migrating clusters that arrange in an approximately hexagonal way. We suggest that the mechanism behind these regular textures is an overreaction in the alignment mechanism. Considering the more realistic scenario of non-point-like particles in the presence of confining surfaces is generally important for the comparison to experimental systems.

Continuous structural transitions in quasi-one-dimensional classical Wigner crystals

We study the structural phase transitions in confined systems of strongly interacting particles. We consider infinite quasi-one-dimensional systems with different pairwise repulsive interactions in the presence of an external confinement following a power law. Within the framework of Landau's theory, we find the necessary conditions to observe continuous transitions and demonstrate that the only allowed continuous transition is between the single- and the double-chain configurations and that it only takes place when the confinement is parabolic. We determine analytically the behavior of the system at the transition point and calculate the critical exponents. Furthermore, we perform Monte Carlo simulations and find a perfect agreement between theory and numerics.

Nambu-Goldstone mode in a rotating dilute Bose-Einstein condensate

The Nambu-Goldstone mode (NGM), associated with vortex nucleation in a harmonically confined, two-dimensional dilute Bose-Einstein condensate is studied. We argue, based on exact diagonalization calculations, that the NGM manifests in the lowest-lying envelope of the quasidegenerate spectrum that emerges as the vortex is about to enter the condensate. The quasidegenerate states constitute a series of octupole-mode branches that originate primarily from pairwise repulsive interactions between octupole excitations and are distinguished by the number of admixed quadrupolar excitations. As the vortex approaches the center of the condensate and the system's axisymmetry is restored, the NGM becomes massive due to its coupling to higher rotational bands. We clarify the mechanism of this mass acquisition by using a newly developed projection-operator method.

Quantification of lateral repulsion between coadsorbed CO and N on Rh(100) using temperature-programmed desorption, low-energy electron diffraction, and Monte Carlo simulations

Temperature programmed desorption of CO coadsorbed with atomic N on Rh(100), reveals both long- and short-range interactions between adsorbed CO and N. For CO desorption from Rh(100) at low coverage we find an activation energy Ea of 137±2 kJ/mol and a preexponential factor of 1013.8±0.2 s−1. Coadsorption with N partially blocks CO adsorption and destabilizes CO by lowering Ea for CO desorption. Destabilization at low N coverage is explained by long-range electronic modification of the Rh(100) surface. At high N and CO coverage, we find evidence for a short-range repulsive lateral interaction between COads and Nads in neighboring positions. We derive a pairwise repulsive interaction ωCO–NNN=19 kJ/mol for CO coadsorbed to a c(2×2) arrangement of N atoms. This has important implications for the lateral distribution of coadsorbed CO and N at different adsorbate coverages. Regarding the different lateral interactions and mobility of adsorbates, we propose a structural model which satisfactorily explains the observed effects of atomic N on the desorption of CO. Dynamic Monte Carlo simulations were used to verify the experimentally obtained value for the CO–N interaction, by using the kinetic parameters and interaction energy derived from the temperature-programmed desorption experiments.

Low-lying excitations from the yrast line of weakly interacting trapped bosons

Through an extensive numerical study, we find that the low-lying, quasi-degenerate eigenenergies of weakly-interacting trapped N bosons with total angular momentum L are given in case of small L/N and sufficiently small L by E = L hbar omega + g[N(N-L/2-1)+1.59 n(n-1)/2], where omega is the frequency of the trapping potential and g is the strength of the repulsive contact interaction; the last term arises from the pairwise repulsive interaction among n octupole excitations and describes the lowest-lying excitation spectra from the Yrast line. In this case, the quadrupole modes do not interact with themselves and, together with the octupole modes, exhaust the low-lying spectra which are separated from others by N-linear energy gaps.

Bose-Einstein condensation in an external potential at zero temperature: General theory

Bose-Einstein condensation is described in terms of the condensate wave function and the pair-excitation function, the latter being responsible for the existence of phonons. This minimal description in terms of these two functions is generalized to the case with an external potential. For a dilute gas with short-range pairwise repulsive interaction and at very low temperatures when the Bose-Einstein condensation is nearly complete, a partial differential equation is obtained for the condensate wave function and an integro-differential equation for the pair excitation. Experimentally, the external potential is used to trap the atoms, i.e., to keep them together. Since the trap is of macroscopic dimensions, the resulting external potential is often slowly varying. In these cases and when the condensate is in the lowest state, the partial differential equation for the condensate wave function and the integro-differential equation for the pair excitation are solved approximately for the case of a time-independent trap.

Site symmetry dependence of repulsive interactions between chemisorbed oxygen atoms on Pt{100}-(1×1)

Ab initio total energy calculations using density functional theory with the generalized gradient approximation have been performed for the chemisorption of oxygen atoms on a Pt{100}-(1×1) slab. Binding energies for the adsorption of oxygen on different high-symmetry sites are presented. The bridge site is the most stable at a coverage of 0.5 ML, followed by the fourfold hollow site. The atop site is the least stable. This finding is rationalized by analyzing the “local structures” formed upon oxygen chemisorption. The binding energies and heats of adsorption at different oxygen coverages show that pairwise repulsive interactions are considerably stronger between oxygen atoms occupying fourfold sites than those occupying bridge sites. Analysis of the partial charge densities associated with Bloch states demonstrates that the O–Pt bond is considerably more localized at the bridge site. These effects cause a sharp drop in the heats of adsorption for oxygen on hollow sites when the coverage is increased from 0.25 to 0.5 ML. Mixing between oxygen p orbitals and Pt d orbitals can be observed over the whole metal d-band energy range.

Adatom bond energies and lateral interaction energies from calorimetry: NO, O2, and N2 adsorption on Ni{100}

Heats of adsorption and sticking probabilities have been measured for NO and O2 on clean and oxygen precovered Ni{100} at room temperature by single crystal adsorption calorimetry (SCAC). Adsorption is initially dissociative for both species and the initial heat of adsorption is 536 kJ/mol for O2 and 426 kJ/mol for NO. From these data the initial heat of dissociative adsorption of N2 on Ni{100} is estimated to be 136 kJ/mol. With increasing coverage the adsorption heat for both NO and O2 decreases due to repulsive interactions between adsorbed adatoms; the magnitude of the pairwise repulsive interactions between oxygen adatoms in nnn sites is estimated to be about 40 kJ/mol by fitting the experimental data for O2 dissociative adsorption with a Monte Carlo simulation. The pairwise repulsive interaction between nitrogen and oxygen and between nitrogen adatoms in nnn sites is obtained as about 100 kJ/mol. Due to the high magnitude of lateral repulsive interactions between adatoms, a critical coverage of NO is reached for which molecular adsorption is energetically favored with respect to dissociative adsorption. This coverage is ∼0.16 ML for a 1:1 O:N adatom coverage decreasing to ∼0.07 ML for 3:1 O:N adatom ratio. For O2 adsorption, the lower magnitude of repulsive interactions allows dissociative adsorption to take place up to a coverage of about 0.3–0.4 ML; above this coverage the bulk oxide is more energetically favorable and an oxide layer is formed. NO dissociative adsorption is precursor mediated, whereas for O2 the precursor plays only a limited role.

A simple approach to the calculation of surface defect energies in transition metals

In order to understand the energetics of various atomic processes involved in crystal growth, we have developed a simple approach for calculating surface defect energies in transition metals. The total energy of each system is split into two contributions: an attractive term which is due to the broadening of d atomic levels (band contribution) and a repulsive one written as a sum of pairwise interactions (Born-Mayer potential). The band contribution is calculated in the tight-binding approximation. Both the pairwise repulsive interaction and the tight-binding hopping integrals are assumed to decrease exponentially when the interatomic distance increases and the equilibrium geometry can be determined from total energy minimization. A few examples aiming at interpreting some field ion microscopy experiments carried out on transition metals will be presented: interaction of an adsorbate with a surface step, relative stability of normal (bulk) and fault (surface) adsorption sites on the close-packed (111) fcc and (0001) hcp surfaces and of islands of adatoms on (111) fcc surfaces.

Calorimetric adsorption heats on low-index nickel surfaces

A new method has been devised for detecting the heat evolved when a gas is adsorbed onto a crystal surface. The method forms the basis of an adsorption calorimeter which provides, for the first time, accurate heats of adsorption for adsorbates on metal single crystal surfaces as a detailed function of surface coverage. Coverage-dependent calorimetric heats of adsorption and sticking probabilities for CO on the {111} {100} and {110} planes of nickel have been obtained, enabling comparisons to be made with literature values for isosteric heats. Data for CO adsorption onto nickel surfaces with varying amounts of predosed K have been obtained, demonstrating an unexpectedly large effect of promotion on the heat of adsorption. A model is presented to explain this data. Finally, heats of adsorption for oxygen chemisorption have been obtained for the clean and K predosed nickel surfaces. The data provide a direct measure of the lateral interaction energies between adatoms. Unexpectedly large values for the pairwise repulsive interaction between O adatoms on Ni surfaces have been obtained.

Lateral interactions and structural phase transitions in ultrathin Hg films

We have investigated the energetics and lateral interactions of ordered mercury overlayers on Cu(100) and Ag(100) by thermal desorption spectroscopy (TDS). We find evidence for the coexistence of phases on Cu(100) from thermal desorption spectroscopy. Hg adsorbs on both Cu(100) and Ag(100) with a coverage-independent sticking coefficient indicative of a mobile precursor state. Hg on Cu(100) is observed to have a barrier to desorption consistent with the existence of a precursor state. The two equilibrium phases of Hg on Cu(100) have zero coverage heats of desorption of 0.74 eV (c(2×2)) and 0.70 eV (c(4×4)) with pairwise attractive interactions of 0.21 and 0.13 eV, respectively. The ordered 1×1 phase of Hg on Ag(100) has a zero coverage heat of desorption of 0.63 eV with pairwise repulsive interactions of 0.38 eV.