論文

We devise an ideal three-dimensional octagonal quasicrystal that is based upon the two-dimensional Ammann–Beenker tiling and that is potentially suitable for realization with patchy particles. Based on an analysis of its local environments, we design a binary system of five- and eight-patch particles that in simulations assembles into a three-dimensional octagonal quasicrystal. The local structure is subtly different from the original ideal quasicrystal possessing a narrower coordination-number distribution; in fact, the eight-patch particles are not needed and a one-component system of the five-patch particles assembles into an essentially identical octagonal quasicrystal. We also consider a one-component system of the eight-patch particles; this assembles into a cluster with a number of crystalline domains, which, because of the coherent boundaries between the crystallites, has approximate eightfold order. We envisage that these systems could be realized using DNA origami or protein design.

The replica exchange method is a powerful tool for overcoming slow relaxation in molecular simulations, but its efficiency depends strongly on the choice of the number and interval of replicas and their exchange probabilities. Here, we propose a new optimization scheme based on the Dijkstra algorithm that constructs an optimal exchange path by representing replicas and their exchange probabilities on a graph. Inspired by path-finding techniques widely used in computer science, including applications in game algorithms, our approach ensures that transitions follow a minimum entropy gradient path and effectively speeds up sampling even in systems exhibiting slow relaxation near critical points or phase transition regions. The method provides a systematic way to improve replica exchange efficiency and offers new insights into the control of relaxation dynamics, as demonstrated through applications to the solid–liquid phase transition of the Lennard-Jones bulk system.

We systematically investigate the thermodynamic landscape of the 38-atom Lennard-Jones cluster LJ38 using Population Annealing (PA), a method suited for systems with challenging double-funnel energy landscapes. By employing an adaptive temperature schedule, we demonstrate that thermodynamic observables, such as internal energy and heat capacity, converge robustly when the population size is sufficiently large. To gain deeper insights into the competing basins, we introduce an integrated framework that combines PA reweighting factors with structure-resolved analysis. Using quenched configurations characterized by potential energy and Steinhardt’s bond-orientational order parameters, we identify three structural basins, face-centered cubic-like, icosahedral, and liquid-like, via dimensionality reduction and clustering. This framework enables the direct computation of structure-resolved free energy differences from population fractions, providing a quantitative mapping of the thermodynamic competition between the funnels. The resulting structural crossovers are consistent with the heat-capacity peak, demonstrating PA as a promising and scalable framework for structure-resolved thermodynamics in complex molecular systems.

The phenomenon of hysteresis in simulations, in which a system’s current state is correlated to previous states and inhibits the transition to a more stable phase, may often lead to misleading results in physical chemistry. In this study, in addition to the replica exchange method (REM), a novel approach was taken by combining an evolution strategy based on the evolutionary principles of nature to predict phase transitions for the Hess-Su liquid-crystal model. In this model, an anisotropy term is added to the simple 6-12 Lennard-Jones model to intuitively reproduce the behavior of liquid crystals. We first applied the pressure-temperature REM to the Hess-Su model and optimized the replica spacing for the energy distribution to gain the maximum advantage from the REM. We then used the same approach as for the Hamiltonian REM, seeking to optimize the replica spacing in the same way. Based on both results, we attempted to predict this coarse-grained liquid-crystal model’s exact phase transition point. In the Hamiltonian REM, replicas were prepared with different molecular aspect ratios corresponding to the values of the anisotropy terms in the potential function. The Hess-Su liquid-crystal model, which undergoes a direct transition from the nematic to the solid phase without going through a smectic phase, is a challenging research target for understanding phase transitions. Despite the tremendous computational difficulty in overcoming the strong hysteresis present in this system, our method could predict the phase transition point clearly and significantly reduce the extent of hysteresis. Our approach is beneficial when simulating more complex systems and, above all, shows great potential for more accurate and efficient phase transition predictions in the field of molecular simulation in the future.

We have incorporated Evolution Strategies into the Replica-Exchange Monte Carlo simulation method to predict the phase behavior of several example fluids. The replica-exchange method allows one system to exchange temperatures with its neighbors to search for the most stable structure relatively efficiently in a single simulation. However, if the temperature intervals of the replicas are not positioned carefully, there is an issue that local exchange does not occur. Our results for a simple Lennard-Jones fluid and the liquid-crystal Yukawa model demonstrate the utility of the approach when compared to conventional methods. When Evolution Strategies were applied to the Replica-Exchange Monte Carlo simulation, the problem of a significant localized decrease in exchange probability near the phase transition was avoided. By obtaining the optimal temperature intervals, the system efficiently traverses a broader parameter space with a small number of replicas. This is equivalent to accelerating molecular simulations with limited computational resources and can be useful when attempting to predict the phase behavior of complex systems.

In this work, the advantages of applying the temperature and pressure replica-exchange method to investigate the phase transitions and the hysteresis for liquid-crystal fluids were demonstrated. In applying this method to the commonly used Hess-Su liquid-crystal model, heat capacity peaks and points of phase co-existence were observed. The absence of a smectic phase at higher densities and a narrow range of the nematic phase were reported. The identity of the crystalline phase of this system was found to a hexagonal close-packed solid. Since the nematic-solid phase transition is strongly first order, care must be taken when using this model not to inadvertently simulate meta-stable nematic states at higher densities. In further analysis, the Weighted Histogram Analysis Method was applied to verify the precise locations of the phase transition points.

In this paper, molecular chirality is studied for liquid-crystal fluids represented by hard rods with the addition of an attractive chiral dispersion term. Chiral forces between molecular pairs are assumed to be long-ranged and are described in terms of the pseudotensor of Goossens [W. J. A. Goossens, Mol. Cryst. Liq. Cryst. 1971, 12, 237-244]. Following Varga and Jackson [S. Varga and G. Jackson, Chem. Phys. Lett. 2003, 377, 6-12], this is combined with a hard-spherocylinder core. We investigate the relationship between molecular chirality and the helical pitch of the system, which occurs in the absence of full three-dimensional periodic boundary conditions. The dependence of the wavenumber of this pitch on the thermodynamic variables, temperature, and density is measured. We also explore the use of a novel surface boundary interaction model. As a result of this approach, we are able to lower the temperature of the system without the occurrence of nematic droplets, which would interfere with the formation of a uniaxial pitch. Regarding the theoretical predictions of Wensink and Jackson [H. H. Wensink and G. Jackson, J. Chem. Phys. 2009, 130, 234911], on the one hand, we have qualitative agreement with the observed non-monotonic density dependence of the wavenumber. Initially increasing with density, the wavenumber reaches a maximum, before falling as the density moves toward the point of phase transition from cholesteric to smectic. However, further analysis for shorter rods, in the presence of novel boundary conditions, reveals some disagreement with the theory, at least in this case; the unwinding of the cholesteric helix in the cholesteric phase occurs simultaneously with subtle increases in smectic ordering. These pre-smectic fluctuations have not been accounted for so far in theories on cholesterics but turn out to play a key role in controlling the pitch of cholesteric phases of rod-shaped mesogens with a small to moderate aspect ratio.