Toward a correct treatment of core properties with local hybrid functionals.

In local hybrid functionals (LHs), a local mixing function (LMF) determines the position-dependent exact-exchange admixture. We report new LHs that focus on an improvement of the LMF in the core region while retaining or partly improving upon the high accuracy in the valence region exhibited by the LH20t functional. The suggested new pt-LMFs are based on a Padé form and modify the previously used ratio between von Weizsäcker and Kohn-Sham local kinetic energies by different powers of the density to enable flexibly improved approximations to the correct high-density and iso-orbital limits relevant for the innermost core region. Using TDDFT calculations for a set of K-shell core excitations of second- and third-period systems including accurate state-of-the-art relativistic orbital corrections, the core part of the LMF is optimized, while the valence part is optimized as previously reported for test sets of atomization energies and reaction barriers (Haasler et al., J Chem Theory Comput 2020, 16, 5645). The LHs are completed by a calibration function that minimizes spurious nondynamical correlation effects caused by the gauge ambiguities of exchange-energy densities, as well as by B95c meta-GGA correlation. The resulting LH23pt functional relates to the previous LH20t functional but specifically improves upon the core region.

Density Scaling of Translational and Rotational Molecular Dynamics in a Simple Ellipsoidal Model near the Glass Transition.

In this paper, we show that a simple anisotropic model of supercooled liquid properly reflects some density scaling properties observed for experimental data, contrary to many previous results obtained from isotropic models. We employ a well-known Gay-Berne model earlier parametrized to achieve a supercooling and glass transition at zero pressure to find the point of glass transition and explore volumetric and dynamic properties in the supercooled liquid state at elevated pressure. We focus on dynamic scaling properties of the anisotropic model of supercooled liquid to gain a better insight into the grounds for the density scaling idea that bears hallmarks of universality, as follows from plenty of experimental data collected near the glass transition for different dynamic quantities. As a result, the most appropriate values of the scaling exponent γ are established as invariants for a given anisotropy aspect ratio to successfully scale both the translational and rotational relaxation times considered as single variable functions of densityγ/temperature. These scaling exponent values are determined based on the density scaling criterion and differ from those obtained in other ways, such as the virial-potential energy correlation and the equation of state derived from the effective short-range intermolecular potential, which is qualitatively in accordance with the results yielded from experimental data analyses. Our findings strongly suggest that there is a deep need to employ anisotropic models in the study of glass transition and supercooled liquids instead of the isotropic ones very commonly exploited in molecular dynamics simulations of supercooled liquids over the last decades.

Isomorph Invariance of Higher-Order Structural Measures in Four Lennard-Jones Systems.

In the condensed liquid phase, both single- and multicomponent Lennard-Jones (LJ) systems obey the "hidden-scale-invariance" symmetry to a good approximation. Defining an isomorph as a line of constant excess entropy in the thermodynamic phase diagram, the consequent approximate isomorph invariance of structure and dynamics in appropriate units is well documented. However, although all measures of the structure are predicted to be isomorph invariant, with few exceptions only the radial distribution function (RDF) has been investigated. This paper studies the variation along isomorphs of the nearest-neighbor geometry quantified by the occurrence of Voronoi structures, Frank-Kasper bonds, icosahedral local order, and bond-orientational order. Data are presented for the standard LJ system and for three binary LJ mixtures (Kob-Andersen, Wahnström, NiY2). We find that, while the nearest-neighbor geometry generally varies significantly throughout the phase diagram, good invariance is observed along the isomorphs. We conclude that higher-order structural correlations are no less isomorph invariant than is the RDF.

Density scaling of phantom materials for a 3D dose verification system.

In this study, the optimum density scaling factors of phantom materials for a commercially available three-dimensional (3D) dose verification system (Delta4) were investigated in order to improve the accuracy of the calculated dose distributions in the phantom materials. At field sizes of 10 × 10 and 5 × 5 cm2 with the same geometry, tissue-phantom ratios (TPRs) in water, polymethyl methacrylate (PMMA), and Plastic Water Diagnostic Therapy (PWDT) were measured, and TPRs in various density scaling factors of water were calculated by Monte Carlo simulation, Adaptive Convolve (AdC, Pinnacle3 ), Collapsed Cone Convolution (CCC, RayStation), and AcurosXB (AXB, Eclipse). Effective linear attenuation coefficients (µeff ) were obtained from the TPRs. The ratios of µeff in phantom and water ((µeff )pl,water ) were compared between the measurements and calculations. For each phantom material, the density scaling factor proposed in this study (DSF) was set to be the value providing a match between the calculated and measured (µeff )pl,water . The optimum density scaling factor was verified through the comparison of the dose distributions measured by Delta4 and calculated with three different density scaling factors: the nominal physical density (PD), nominal relative electron density (ED), and DSF. Three plans were used for the verifications: a static field of 10 × 10 cm2 and two intensity modulated radiation therapy (IMRT) treatment plans. DSF were determined to be 1.13 for PMMA and 0.98 for PWDT. DSF for PMMA showed good agreement for AdC and CCC with 6 MV x ray, and AdC for 10 MV x ray. DSF for PWDT showed good agreement regardless of the dose calculation algorithms and x-ray energy. DSF can be considered one of the references for the density scaling factor of Delta4 phantom materials and may help improve the accuracy of the IMRT dose verification using Delta4.

De Novo Atomistic Discovery of Disordered Mechanical Metamaterials by Machine Learning.

Architected materials design across orders of magnitude length scale intrigues exceptional mechanical responses nonexistent in their natural bulk state. However, the so-termed mechanical metamaterials, when scaling bottom down to the atomistic or microparticle level, remain largely unexplored and conventionally fall out of their coarse-resolution, ordered-pattern design space. Here, combining high-throughput molecular dynamics (MD) simulations and machine learning (ML) strategies, some intriguing atomistic families of disordered mechanical metamaterials are discovered, as fabricated by melt quenching and exemplified herein by lightweight-yet-stiff cellular materials featuring a theoretical limit of linear stiffness-density scaling, whose structural disorder-rather than order-is key to reduce the scaling exponent and is simply controlled by the bonding interactions and their directionality that enable flexible tunability experimentally. Importantly, a systematic navigation in the forcefield landscape reveals that, in-between directional and non-directional bonding such as covalent and ionic bonds, modest bond directionality is most likely to promotes disordered packing of polyhedral, stretching-dominated structures responsible for the formation of metamaterials. This work pioneers a bottom-down atomistic scheme to design mechanical metamaterials formatted disorderly, unlocking a largely untapped field in leveraging structural disorder in devising metamaterials atomistically and, potentially, generic to conventional upscaled designs.

Forest demography and biomass accumulation rates are associated with transient mean tree size vs. density scaling relations.

Linking individual and stand-level dynamics during forest development reveals a scaling relationship between mean tree size and tree density in forest stands, which integrates forest structure and function. However, the nature of this so-called scaling law and its variation across broad spatial scales remain unquantified, and its linkage with forest demographic processes and carbon dynamics remains elusive. In this study, we develop a theoretical framework and compile a broad-scale dataset of long-term sample forest stands (n = 1,433) from largely undisturbed forests to examine the association of temporal mean tree size vs. density scaling trajectories (slopes) with biomass accumulation rates and the sensitivity of scaling slopes to environmental and demographic drivers. The results empirically demonstrate a large variation of scaling slopes, ranging from -4 to -0.2, across forest stands in tropical, temperate, and boreal forest biomes. Steeper scaling slopes are associated with higher rates of biomass accumulation, resulting from a lower offset of forest growth by biomass loss from mortality. In North America, scaling slopes are positively correlated with forest stand age and rainfall seasonality, thus suggesting a higher rate of biomass accumulation in younger forests with lower rainfall seasonality. These results demonstrate the strong association of the transient mean tree size vs. density scaling trajectories with forest demography and biomass accumulation rates, thus highlighting the potential of leveraging forest structure properties to predict forest demography, carbon fluxes, and dynamics at broad spatial scales.

Disrupting Density-Dependent Property Scaling in Hierarchically Architected Foams.

Creating lightweight architected foams as strong and stiff as their bulk constituent material has been a long-standing effort. Typically, the strength, stiffness, and energy dissipation capabilities of materials severely degrade with increasing porosity. We report nearly constant stiffness-to-density and energy dissipation-to-density ratios─a linear scaling with density─in hierarchical vertically aligned carbon nanotube (VACNT) foams with a mesoscale architecture of hexagonally close-packed thin concentric cylinders. We observe a transformation from an inefficient higher-order density-dependent scaling of the average modulus and energy dissipated to a desirable linear scaling as a function of the increasing internal gap between the concentric cylinders. From the scanning electron microscopy of the compressed samples, we observe an alteration in the deformation modality from local shell buckling at a smaller gap to column buckling at a larger gap, governed by an enhancement in the number density of CNTs with the increasing internal gap, leading to better structural stiffness at low densities. This transformation simultaneously improves the foams' damping capacity and energy absorption efficiency as well and allows us to access the ultra-lightweight regime in the property space. Such synergistic scaling of material properties is desirable for protective applications in extreme environments.