First-Principles Atomistic Thermodynamics and Configurational Entropy

Vacancy enhanced Li, Na, and K clustering on graphene

The formation of metallic dendrites during battery cycling is a persistent challenge for alkali metal-ion batteries, reducing cycle life and posing safety risks. Although surface defects are often implicated in inhomogeneous metal nucleation, the atomic-scale mechanisms by which they promote metal clustering and subsequent dendrite formation remain poorly understood. Here, we use first-principles calculations to investigate how carbon monovacancies (VC) influence the clustering behaviour of alkali metals (Li, Na, and K) on graphene - a common basal-plane motif in graphite, hard carbons, and graphene-based anodes. Clusters of Li, Na, and K of varying size (M n for n ∈ {1-12}) are characterised on pristine and defective graphene to understand their stability. On pristine graphene, cluster formation is hindered for Li due to the instability of small clusters (n ≤ 3) and significant Li-Li repulsion, and suppressed for K due to weak K-K binding and its larger ionic radius. In contrast, Na exhibits spontaneous clustering, suggesting a higher propensity for dendrite formation even in the absence of defects. The introduction of a VC dramatically alters these trends: it stabilises small (n ≤ 3) clusters across all three metals by enhancing binding strength with the surface and modifying charge localisation. For Li, the vacancy overcomes the barrier to early-stage nucleation; for Na, it promotes growth at even lower metal loadings; and for K, clustering becomes locally favoured albeit only for the smallest cluster sizes (n ≤ 3). These results clarify the defect-facilitated pathways to metal clustering, offering atomistic insight that can inform the development of more dendrite-resistant carbon architectures.

Equilibrium densities of intrinsic defects in transition metal diselenides of molybdenum and tungsten

Point defects are thermodynamically stabilized in all crystalline materials, with increased densities negatively impacting the properties and performance of transition metal dichalcogenides (TMDs). While recent point defect reduction methods have led to considerable improvements in the optoelectronic properties of TMDs, there is a clear need for theoretical work to establish the lower limit of defect densities, as represented by thermal equilibrium. To that end, an ab initio and thermodynamic analysis of the equilibrium densities of intrinsic point defects in MoSe2 and WSe2 is presented. The intrinsic defect formation energies at the limits of the selenium and metal-rich regimes are determined by density functional theory (DFT) and then augmented with elemental chemical potential functions to determine temperature- and pressure-dependent formation energies. Equilibrium defect densities are determined for MSe, SeM, vM, and vSe, where M and v, respectively, represent the metal and the vacancy, as a function of synthesis temperature and pressure. The effects of vibrational free energy contributions and treatment of the DFT exchange-correlation potential are found to be non-negligible. Calculated equilibrium densities are several orders of magnitude below reported defect densities in TMDs made by chemical vapor deposition, chemical vapor transport, and flux methods, thereby establishing that current synthesis methods are either kinetically limited or impurity dominated.

Exploration of Free Energy Surface of the Au10 Nanocluster at Finite Temperature

The first step in comprehending the properties of Au10 clusters is understanding the lowest energy structure at low and high temperatures. Functional materials operate at finite temperatures; however, energy computations employing density functional theory (DFT) methodology are typically carried out at zero temperature, leaving many properties unexplored. This study explored the potential and free energy surface of the neutral Au10 nanocluster at a finite temperature, employing a genetic algorithm coupled with DFT and nanothermodynamics. Furthermore, we computed the thermal population and infrared Boltzmann spectrum at a finite temperature and compared it with the validated experimental data. Moreover, we performed the chemical bonding analysis using the quantum theory of atoms in molecules (QTAIM) approach and the adaptive natural density partitioning method (AdNDP) to shed light on the bonding of Au atoms in the low-energy structures. In the calculations, we take into consideration the relativistic effects through the zero-order regular approximation (ZORA), the dispersion through Grimme's dispersion with Becke-Johnson damping (D3BJ), and we employed nanothermodynamics to consider temperature contributions. Small Au clusters prefer the planar shape, and the transition from 2D to 3D could take place at atomic clusters consisting of ten atoms, which could be affected by temperature, relativistic effects, and dispersion. We analyzed the energetic ordering of structures calculated using DFT with ZORA and single-point energy calculation employing the DLPNO-CCSD(T) methodology. Our findings indicate that the planar lowest energy structure computed with DFT is not the lowest energy structure computed at the DLPN0-CCSD(T) level of theory. The computed thermal population indicates that the 2D elongated hexagon configuration strongly dominates at a temperature range of 50-800 K. Based on the thermal population, at a temperature of 100 K, the computed IR Boltzmann spectrum agrees with the experimental IR spectrum. The chemical bonding analysis on the lowest energy structure indicates that the cluster bond is due only to the electrons of the 6 s orbital, and the Au d orbitals do not participate in the bonding of this system.

Mixed Enthalpy-Entropy Descriptor for the Rational Design of Synthesizable High-Entropy Materials Over Vast Chemical Spaces

The practically unlimited high-dimensional composition space of high-entropy materials (HEMs) has emerged as an exciting platform for functional material design and discovery. However, the identification of stable and synthesizable HEMs and robust design rules remains a daunting challenge. Here, we propose a mixed enthalpy-entropy descriptor (MEED) that enables highly efficient, robust, high-throughput prediction of synthesizable HEMs across vast chemical spaces from first-principles. The MEED is based on two parameters: the relative formation enthalpy with respect to the most stable competing compound and the spread of the point-defect formation energy spectrum. The former measures the relative synthesizability of an HEM to its most stable competing phase, going beyond the conventional thermodynamic understanding. The latter gauges the relative entropy forming ability of an HEM, entailing no sampling over numerous alloy configurations. By applying the MEED to two structurally distinct representative material systems (i.e., 3D rocksalt carbides and 2D layered sulfides), we not only successfully identify all experimentally reported HEMs within these systems but also reveal a cutoff criterion for assessing their relative synthesizability within each system. By the MEED, tens of new high-entropy carbides and 2D high-entropy sulfides are also predicted, which have the potential for a wide variety of applications such as coating in aerospace devices, energy conversion and storage, and flexible electronics.

Cation Dynamics as Structure Explorer in Hybrid Perovskites-The Case of MAPbI3

Hybrid organic-inorganic perovskites exhibit remarkable potential as cost-effective and high-efficiency materials for photovoltaic applications. Their exceptional chemical tunability opens further routes for optimizing their optical and electronic properties through structural engineering. Nevertheless, the extraordinary softness of the lattice, stemming from its interconnected organic-inorganic composition, unveils formidable challenges in structural characterization. Here, by focusing on the quintessential methylammonium lead triiodide, MAPbI3, we combine first-principles modeling with high-resolution neutron scattering data to identify the key stationary points on its shallow potential energy landscape. This combined experimental and computational approach enables us to benchmark the performance of a collection of semilocal exchange-correlation functionals and to track the local distortions of the perovskite framework, hallmarked by the inelastic neutron scattering response of the organic cation. By conducting a thorough examination of structural distortions, we introduce the IKUR-PVP-1 structural data set. This data set contains nine mechanically stable structural models, each manifesting a distinct vibrational response. IKUR-PVP-1 constitutes a valuable resource for assessing thermal behavior in the low-temperature perovskite phase. In addition, it paves the way for the development of accurate force fields, enabling a comprehensive understanding of the interplay between the structure and dynamics in MAPbI3 and related hybrid perovskites.

Study on the physical and chemical properties of lead passivating agent in soil

With the rapid development of industry, heavy metal pollution has seriously damaged the health of soil, and heavy metals spread through the food chain, posing a threat to human health. The firm existence of heavy metals in soil under earthy conditions is a center trouble faced by soil dense metal pollution solidification and correction technology. However, the existing investigation results are mostly controlled to soil passivation experiments using various materials. Macroscopically, heavy metal passivation materials have been selected, but the intrinsic mechanisms of different compound functional groups in soil passivation have been ignored. With the common heavy metal ion Pb2+ as an example, the stability of the combination of heavy metal ions and common ion groups in soil was analyzed in this study by using quantum chemical calculation as the theoretical guidance. The results show that SO42- and PO43-, as functional groups of passivating agents, are used to control lead pollution and have been verified to have good effects. When the pollution is particularly serious and not easy to passivation and precipitation, Fe3+ can be considered to enhance the passivation effect.

Block sparsity promoting algorithm for efficient construction of cluster expansion models for multicomponent alloys

Multicomponent alloys are gaining significance as drivers of technological breakthroughs especially in structural and energy storage materials. The vast configuration space of these materials prohibit computational modeling using first-principles based methods alone. The cluster expansion (CE) method is the most widely used tool for modeling configurational disorder in alloys. CE relies on machine learning algorithms to train Hamiltonians and uses first-principles calculated data as training sets. In this paper we present a new compressive sensing-based algorithm for the efficient construction of CE Hamiltonians of multicomponent alloys. Our algorithm constructs highly sparse and physically reasonable models from a carefully selected small training set of alloy structures. Compared to conventional fitting algorithms, the algorithm achieves more than 50% reduction in the training set size. The resultant sparse models can sample the configuration space at least 3 × faster. We demonstrate this algorithm on 4 different alloy systems, namely Ag-Au, Ag-Au-Cu, Ag-Au-Cu-Pd and (Ge,Sn)(S,Se,Te).The sparse CE models for these alloys can rapidly reproduce known ground state orderings and order-disorder transitions. Our method can truly enable high-throughput multicomponent alloy thermodynamics by reducing the cost associated with model construction and configuration sampling.

Imperfections are not 0 K: free energy of point defects in crystals

Defects determine many important properties and applications of materials, ranging from doping in semiconductors, to conductivity in mixed ionic-electronic conductors used in batteries, to active sites in catalysts. The theoretical description of defect formation in crystals has evolved substantially over the past century. Advances in supercomputing hardware, and the integration of new computational techniques such as machine learning, provide an opportunity to model longer length and time-scales than previously possible. In this Tutorial Review, we cover the description of free energies for defect formation at finite temperatures, including configurational (structural, electronic, spin) and vibrational terms. We discuss challenges in accounting for metastable defect configurations, progress such as machine learning force fields and thermodynamic integration to directly access entropic contributions, and bottlenecks in going beyond the dilute limit of defect formation. Such developments are necessary to support a new era of accurate defect predictions in computational materials chemistry.

Speciation and Reactivity Control of Cu-Oxo Clusters via Extraframework Al in Mordenite for Methane Oxidation

The stoichiometric conversion of methane to methanol by Cu-exchanged zeolites can be brought to highest yields by the presence of extraframework Al and high CH4 chemical potentials. Combining theory and experiments, the differences in chemical reactivity of monometallic Cu-oxo and bimetallic Cu-Al-oxo nanoclusters stabilized in zeolite mordenite (MOR) are investigated. Cu-L3 edge X-ray absorption near-edge structure (XANES), infrared (IR), and ultraviolet-visible (UV-vis) spectroscopies, in combination with CH4 oxidation activity tests, support the presence of two types of active clusters in MOR and allow quantification of the relative proportions of each type in dependence of the Cu concentration. Ab initio molecular dynamics (MD) calculations and thermodynamic analyses indicate that the superior performance of materials enriched in Cu-Al-oxo clusters is related to the activity of two μ-oxo bridges in the cluster. Replacing H2O with ethanol in the product extraction step led to the formation of ethyl methyl ether, expanding this way the applicability of these materials for the activation and functionalization of CH4. We show that competition between different ion-exchanged metal-oxo structures during the synthesis of Cu-exchanged zeolites determines the formation of active species, and this provides guidelines for the synthesis of highly active materials for CH4 activation and functionalization.

Pressure-induced structural phase transitions of zirconium: anab initiostudy based on statistical ensemble theory

Recently, we put forward a direct integral approach to solve the partition function with ultrahigh efficiency and precision, which enables the rigorous ensemble theory to investigate phase behaviors of realistic condensed matters and has been successfully applied to the phase transition of vanadium metal (Ninget al2022J. Phys.: Condens. Matter34425404). In this work, the approach is applied to the structural phase transitions of zirconium metal under compressions up to 160 GPa and ultrahigh calculation precision is achieved. For the obtained equation of state with pressure over 40 GPa, the deviations from latest experiments are within0.7%and the computed transition pressure ofα→ωis 6.93 GPa, which is about five times larger than previous theoretical predictions and in excellent agreement with the measured range of 5-15 GPa. Our results support the argument that there is no existence of the isostructural phase transition of Zr metal that was asserted by recent experimental observations.

Vacancy driven surface disorder catalyzes anisotropic evaporation of ZnO (0001) polar surface

The evaporation and crystal growth rates of ZnO are highly anisotropic and are fastest on the Zn-terminated ZnO (0001) polar surface. Herein, we study this behavior by direct atomic-scale observations and simulations of the dynamic processes of the ZnO (0001) polar surface during evaporation. The evaporation of the (0001) polar surface is accelerated dramatically at around 300 °C with the spontaneous formation of a few nanometer-thick quasi-liquid layer. This structurally disordered and chemically Zn-deficient quasi-liquid is derived from the formation and inward diffusion of Zn vacancies that stabilize the (0001) polar surface. The quasi-liquid controls the dissociative evaporation of ZnO with establishing steady state reactions with Zn and O2 vapors and the underlying ZnO crystal; while the quasi-liquid catalyzes the disordering of ZnO lattice by injecting Zn vacancies, it facilitates the desorption of O2 molecules. This study reveals that the polarity-driven surface disorder is the key structural feature driving the fast anisotropic evaporation and crystal growth of ZnO nanostructures along the [0001] direction.

Vibrational Entropy of Crystalline Solids from Covariance of Atomic Displacements

The vibrational entropy of a solid at finite temperature is investigated from the perspective of information theory. Ab initio molecular dynamics (AIMD) simulations generate ensembles of atomic configurations at finite temperature from which we obtain the N-body distribution of atomic displacements, ρN. We calculate the information-theoretic entropy from the expectation value of lnρN. At a first level of approximation, treating individual atomic displacements independently, our method may be applied using Debye-Waller B-factors, allowing diffraction experiments to obtain an upper bound on the thermodynamic entropy. At the next level of approximation we correct the overestimation through inclusion of displacement covariances. We apply this approach to elemental body-centered cubic sodium and face-centered cubic aluminum, showing good agreement with experimental values above the Debye temperatures of the metals. Below the Debye temperatures, we extract an effective vibrational density of states from eigenvalues of the covariance matrix, and then evaluate the entropy quantum mechanically, again yielding good agreement with experiment down to low temperatures. Our method readily generalizes to complex solids, as we demonstrate for a high entropy alloy. Further, our method applies in cases where the quasiharmonic approximation fails, as we demonstrate by calculating the HCP/BCC transition in Ti.

Metal Release Mechanism and Electrochemical Properties of Lix(Ni1/3Mn1/3Co1/3)O2

Complex metal oxides (CMOs) are used broadly in applications including electroreactive forms found in lithium-ion battery technology. Computational chemistry can provide unique information about how the properties of CMO cathode materials change in response to changes in stoichiometry, for example, changes of the lithium (Li) content during the charge–discharge cycle of the battery. However, this is difficult to measure experimentally due to the small cross-sectional area of the cations. Outside of operational conditions, the Li content can influence the transformations of the CMO when exposed to the environment. For example, metal release from CMOs in aqueous settings has been identified as a cross-cutting mechanism important to CMO degradation. Computational studies investigating metal release from CMOs show that the thermodynamics depend on the oxidation states of lattice cations, which is expected to vary with the lithium content. In this work, computational studies track changes in metal release trends as a function of Li content in Lix(Ni1/3Mn1/3Co1/3)O2 (NMC). The resulting dataset is used to construct a random forest tree (RFT) machine learning (ML) model. A modeling challenge in delithiation studies is the large configurational space to sample. Through investigating multiple configurations at each lithium fraction, we find structural features associated with favorable energies to chemically guide the identification of relevant structures and adequately predict voltage values.

Relative Populations and IR Spectra of Cu38 Cluster at Finite Temperature Based on DFT and Statistical Thermodynamics Calculations

The relative populations of Cu38 isomers depend to a great extent on the temperature. Density functional theory and nanothermodynamics can be combined to compute the geometrical optimization of isomers and their spectroscopic properties in an approximate manner. In this article, we investigate entropy-driven isomer distributions of Cu38 clusters and the effect of temperature on their IR spectra. An extensive, systematic global search is performed on the potential and free energy surfaces of Cu38 using a two-stage strategy to identify the lowest-energy structure and its low-energy neighbors. The effects of temperature on the populations and IR spectra are considered via Boltzmann factors. The computed IR spectrum of each isomer is multiplied by its corresponding Boltzmann weight at finite temperature. Then, they are summed together to produce a final temperature-dependent, Boltzmann-weighted spectrum. Our results show that the disordered structure dominates at high temperatures and the overall Boltzmann-weighted spectrum is composed of a mixture of spectra from several individual isomers.

Along the road to Crystal Structure Prediction (CSP) of pharmaceutical-like molecules

Computational methods used for predicting crystal structures of organic compounds are mature enough to be routinely used with many rigid and semi-rigid organic molecules. The usefulness of Crystal Structure Prediction...

Theoretical Prediction of Structures, Vibrational Circular Dichroism, and Infrared Spectra of Chiral Be4B8 Cluster at Different Temperatures

Lowest-energy structures, the distribution of isomers, and their molecular properties depend significantly on geometry and temperature. Total energy computations using DFT methodology are typically carried out at a temperature of zero K; thereby, entropic contributions to the total energy are neglected, even though functional materials work at finite temperatures. In the present study, the probability of the occurrence of one particular Be4B8 isomer at temperature T is estimated by employing Gibbs free energy computed within the framework of quantum statistical mechanics and nanothermodynamics. To identify a list of all possible low-energy chiral and achiral structures, an exhaustive and efficient exploration of the potential/free energy surfaces is carried out using a multi-level multistep global genetic algorithm search coupled with DFT. In addition, we discuss the energetic ordering of structures computed at the DFT level against single-point energy calculations at the CCSD(T) level of theory. The total VCD/IR spectra as a function of temperature are computed using each isomer's probability of occurrence in a Boltzmann-weighted superposition of each isomer's spectrum. Additionally, we present chemical bonding analysis using the adaptive natural density partitioning method in the chiral putative global minimum. The transition state structures and the enantiomer-enantiomer and enantiomer-achiral activation energies as a function of temperature evidence that a change from an endergonic to an exergonic type of reaction occurs at a temperature of 739 K.