The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects

Atomistic simulations of out-of-equilibrium quantum nuclear dynamics

The rapid advancements in ultrafast laser technology have paved the way for pumping and probing the out-of-equilibrium dynamics of nuclei in crystals. However, interpreting these experiments is extremely challenging due to the complex nonlinear responses in systems where lattice excitations interact, particularly in crystals composed of light atoms or at low temperatures where the quantum nature of ions becomes significant. In this work, we address the nonequilibrium quantum ionic dynamics from first principles. Our approach is general and can be applied to simulate any crystal, in combination with a first-principles treatment of electrons or external machine-learning potentials. It is implemented by leveraging the nonequilibrium time-dependent self-consistent harmonic approximation (TD-SCHA), with a stable, energy-conserving, correlated stochastic integration scheme that achieves an accuracy of O ( d t 3 ) . We benchmark the method with both a simple one-dimensional model to test its accuracy and a realistic 40-atom cell of SrTiO3 under THz laser pump, paving the way for simulations of ultrafast THz-Xray pump-probe spectroscopy like those performed in synchrotron facilities.

Water Is Cool: Advanced Phonon Dynamics in Ice Ih and Ice XI via Machine Learning Potentials and Quantum Nuclear Vibrations

Low-dimensional water, despite the relative simplicity of its constituents, exhibits a vast range of phenomena that are of central importance in natural sciences. A large number of bulk as well as nanoscale polymorphs offer engineering possibilities for technological applications such as desalinization, drug delivery, or biological interfacing. However, little is known about the stability of such structures. Therefore, in this study, we employ an array of state-of-the-art computational techniques to study the vibrational properties of ice Ih and XI in their bulk and thin film forms in order to elucidate their structural stability and dynamic behavior. An efficient workflow, consisting of quantum mechanical simulations (based on density functional theory) and machine learning interatomic potentials (MTPs) coupled to temperature-dependent effective potentials (TDEP) and classical molecular dynamics, was verified necessary to capture the temperature-dependent stabilization of the phonons in bulk ice Ih and XI. Anharmonicity and nuclear quantum effects, incorporated in an efficient way through a quantum thermal bath technique, were found crucial to dynamically stabilize low-frequency lattice modes and high-frequency vibrational stretching involving hydrogen. We have identified three novel thin film structures that retain their stability up to at least 250 K and have shed light on their phonon characteristics. In addition, our examination of the Raman spectrum of ice underscores the shortcomings of predicting vibrational properties when relying entirely on the harmonic approximation or purely anharmonic effects. The corrected redistribution of vibrational intensities is found to be achieved only upon inclusion of quantum nuclear vibrations. This was found to be even more crucial for low-dimensional thin film (2D) structures. Overall, our findings demonstrate the significance of joining advanced computational methodologies in unraveling the intricate vibrational dynamics of crystalline ice materials, offering valuable insights into their thermodynamic and structural properties. Furthermore, we suggest a procedure based on MTPs coupled to a quantum thermal bath for the computationally efficient probing of nuclear effects in ice structures, although equally applicable to any other system.

Ultrafast dynamics of hot carriers: Theoretical approaches based on real-time propagation of carrier distributions

In recent years, computational approaches which couple density functional theory (DFT)-based description of the electron-phonon and phonon-phonon scattering rates with the Boltzmann transport equation have been shown to obtain the electron and thermal transport characteristics of many 3D and 2D semiconductors in excellent agreement with experimental measurements. At the same time, progress in the DFT-based description of the electron-phonon scattering has also allowed to describe the non-equilibrium relaxation dynamics of hot or photo-excited electrons in several materials, in very good agreement with time-resolved spectroscopy experiments. In the latter case, as the time-resolved spectroscopy techniques provide the possibility to monitor transient material characteristics evolving on the femtosecond and attosecond time scales, the time evolution of photo-excited, nonthermal carrier distributions has to be described. Similarly, reliable theoretical approaches are needed to describe the transient transport properties of devices involving high energy carriers. In this review, we aim to discuss recent progress in coupling the ab initio description of materials, especially that of the electron-phonon scattering, with the time-dependent approaches describing the time evolution of the out-of-equilibrium carrier distributions, in the context of time-resolved spectroscopy experiments as well as in the context of transport simulations. We point out the computational limitations common to all numerical approaches, which describe time propagation of strongly out-of-equilibrium carrier distributions in 3D materials, and discuss the methods used to overcome them.

Tracking anharmonic oscillations in the structure of β-1,3-diacetylpyrene

A recently discovered β polymorph of 1,3-diacetylpyrene has turned out to be a prominent negative thermal expansion material, with a linear thermal expansion coefficient of -199 (6) MK-1 at room temperature. Its unique properties can be linked to anharmonic oscillations in the crystal structure that can be attributed to several weak C-H...O interactions. The onset and development of anharmonic effects have been successfully tracked over a wide (90-390 K) temperature range using single-crystal X-ray diffraction. Experimental data of sufficient quality combined with Hirshfeld atom refinement of the crystal structures enabled a quantitative analysis of elusive anharmonic effects within the Gram-Charlier formalism. This example highlights that quantum crystallography tools can and should be applied in structural analysis even for data collected at high temperatures as well as of standard (∼0.8 Å) resolution.

The seventh blind test of crystal structure prediction: structure ranking methods

A seventh blind test of crystal structure prediction has been organized by the Cambridge Crystallographic Data Centre. The results are presented in two parts, with this second part focusing on methods for ranking crystal structures in order of stability. The exercise involved standardized sets of structures seeded from a range of structure generation methods. Participants from 22 groups applied several periodic DFT-D methods, machine learned potentials, force fields derived from empirical data or quantum chemical calculations, and various combinations of the above. In addition, one non-energy-based scoring function was used. Results showed that periodic DFT-D methods overall agreed with experimental data within expected error margins, while one machine learned model, applying system-specific AIMnet potentials, agreed with experiment in many cases demonstrating promise as an efficient alternative to DFT-based methods. For target XXXII, a consensus was reached across periodic DFT methods, with consistently high predicted energies of experimental forms relative to the global minimum (above 4 kJ mol-1 at both low and ambient temperatures) suggesting a more stable polymorph is likely not yet observed. The calculation of free energies at ambient temperatures offered improvement of predictions only in some cases (for targets XXVII and XXXI). Several avenues for future research have been suggested, highlighting the need for greater efficiency considering the vast amounts of resources utilized in many cases.

Integrating Newton's equations of motion in the reciprocal space

We here present the normal dynamics technique, which recasts the Newton's equations of motion in terms of phonon normal modes by exploiting a proper sampling of the reciprocal space. After introducing the theoretical background, we discuss how the reciprocal space sampling enables us to (i) obtain a computational speedup by selecting which and how many wave vectors of the Brillouin zone will be considered and (ii) account for distortions realized across large atomic distances without the use of large simulation cells. We implemented the approach into an open-source code, which we used to present three case studies: in the first one, we elucidate the general strategy for the sampling of the reciprocal space; in the second one, we illustrate the potential of the approach by studying the stabilization effect of temperature in α-uranium; and in the last one, we investigate the characterization of Raman spectra at different temperatures in MoS2/MX2 transition metal dichalcogenide heterostructures. Finally, we discuss how the procedure is general and can be used to simulate periodic, semiperiodic, and finite systems such as crystals, slabs, nanoclusters, or molecules.

Anomalous lattice thermal conductivity increase with temperature in cubic GeTe correlated with strengthening of second-nearest neighbor bonds

Understanding thermal transport mechanisms in phase change materials is critical to elucidating the microscopic picture of phase transitions and advancing thermal energy conversion and storage. Experiments consistently show that cubic phase germanium telluride (GeTe) has an unexpected increase in lattice thermal conductivity with rising temperature. Despite its ubiquity, resolving its origin has remained elusive. In this work, we carry out temperature-dependent lattice thermal conductivity calculations for cubic GeTe through efficient, high-order machine-learned models and additional corrections for coherence effects. We corroborate the calculated phonon properties with our inelastic X-ray scattering measurements. Our calculated lattice thermal conductivity values agree well with experiments and show a similar increasing trend. Through additional bonding strength calculations, we propose that a major contributor to the increasing lattice thermal conductivity is the strengthening of second-nearest neighbor interactions. The findings herein serve to deepen our understanding of thermal transport in phase-change materials.

Non-invasive detection of hazardous materials with a thermal-to-epithermal neutron station: a feasibility study towards practical application

The growing scale of the devastation that even a single terrorist attack can cause requires more effective methods for the detection of hazardous materials. In particular, there are no solutions for effectively monitoring threats at sea, both for the off-shore infrastructure and ports. Currently, state-of-the-art detection methods determine the density distribution and the shapes of tested subjects but only allow for a limited degree of substance identification. This work aims to present a feasibility study of the possible usage of several methods available on the thermal-to-epithermal neutron station, VESUVIO, at the ISIS neutron and muon spallation source, UK, for the detection of hazardous materials. To this end, we present the results of a series of experiments performed concurrently employing neutron transmission and Compton scattering using melamine, a commonly used explosive surrogate, in order to determine its signal characteristics and limits of detection and quantitation. The experiments are supported by first-principles modelling, providing detailed scrutiny of the material structure and the nuclear dynamics behind the neutron scattering observables.

Anharmonic and quantum effects in Pm3̄ AlM(M = Hf, Zr)H6 under high pressure: A first-principles study

First-principles calculations were employed to investigate the impact of quantum ionic fluctuations and lattice anharmonicity on the crystal structure and superconductivity of Pm3̄ AlM(M = Hf, Zr)H6 at pressures of 0.3-21.2 GPa (AlHfH6) and 4.7-39.5 GPa (AlZrH6) within the stochastic self-consistent harmonic approximation. A correction is predicted for the crystal lattice parameters, phonon spectra, and superconducting critical temperatures, previously estimated without considering ionic fluctuations on the crystal structure and assuming the harmonic approximation for lattice dynamics. The findings suggest that quantum ionic fluctuations have a significant impact on the crystal lattice parameters, phonon spectra, and superconducting critical temperatures. Based on our anharmonic phonon spectra, the structures will be dynamically stable at 0.3 GPa for AlHfH6 and 6.2 GPa for AlZrH6, ∼6 and 7 GPa lower than pressures given by the harmonic approximation, respectively. Due to the anharmonic correction of their frequencies, the electron-phonon coupling constants (λ) are suppressed by 28% at 11 GPa for AlHfH6 and 22% at 30 GPa for AlZrH6, respectively. The decrease in λ causes Tc to be overestimated by ∼12 K at 11 GPa for AlHfH6 and 30 GPa for AlZrH6. Even if the anharmonic and quantum effects are not as strong as those of Pm3̄n-AlH3, our results also indicate that metal hydrides with hydrogen atoms in interstitial sites are subject to anharmonic effects. Our results will inevitably stimulate future high-pressure experiments on synthesis, structural, and conductivity measurements.

Neural canonical transformations for vibrational spectra of molecules

The behavior of polyatomic molecules around their equilibrium positions can be regarded as that of quantum-coupled anharmonic oscillators. Solving the corresponding Schrödinger equations enables the interpretation or prediction of the experimental spectra of molecules. In this study, we developed a novel approach for solving the excited states of anharmonic vibrational systems. The normal coordinates of the molecules are transformed into new coordinates through a normalizing flow parameterized by a neural network. This facilitates the construction of a set of orthogonal many-body variational wavefunctions. This methodology has been validated on an exactly solvable 64-dimensional coupled harmonic oscillator, yielding numerical results with a relative error of 10-6. The neural canonical transformations are also applied to calculate the energy levels of two specific molecules, acetonitrile (CH3CN) and ethylene oxide (C2H4O). These molecules involve 12 and 15 vibrational modes, respectively. A key advantage of this approach is its flexibility concerning the potential energy surface, as it requires no specific form. Furthermore, this method can be readily implemented on large-scale distributed computing platforms, making it easy to extend to investigating complex vibrational structures.

Predicted hot superconductivity in LaSc2H24 under pressure

The recent theory-driven discovery of a class of clathrate hydrides (e.g., CaH6, YH6, YH9, and LaH10) with superconducting critical temperatures (Tc) well above 200 K has opened the prospects for "hot" superconductivity above room temperature under pressure. Recent efforts focus on the search for superconductors among ternary hydrides that accommodate more diverse material types and configurations compared to binary hydrides. Through extensive computational searches, we report the prediction of a unique class of thermodynamically stable clathrate hydrides structures consisting of two previously unreported H24 and H30 hydrogen clathrate cages at megabar pressures. Among these phases, LaSc2H24 shows potential hot superconductivity at the thermodynamically stable pressure range of 167 to 300 GPa, with calculated Tcs up to 331 K at 250 GPa and 316 K at 167 GPa when the important effects of anharmonicity are included. The very high critical temperatures are attributed to an unusually large hydrogen-derived density of states at the Fermi level arising from the newly reported peculiar H30 as well as H24 cages in the structure. Our predicted introduction of Sc in the La-H system is expected to facilitate future design and realization of hot superconductors in ternary clathrate superhydrides.

First-Order Rhombohedral-to-Cubic Phase Transition in Photoexcited GeTe

Photoexcited GeTe undergoes a nonthermal phase transition from a rhombohedral to a rocksalt crystalline phase. The microscopic mechanism and the nature of the transition are unclear. By using constrained density functional perturbation theory and by accounting for quantum anharmonicity within the stochastic self-consistent harmonic approximation, we show that the nonthermal phase transition is strongly first order and does not involve phonon softening, at odds with the thermal one. The transition is driven by the closure of the single particle gap in the photoexcited rhombohedral phase. Finally, we show that ultrafast x-ray diffraction data are consistent with a coexistence of the two phases, as expected in a first order transition. Our results are relevant for the understanding of phase transitions and bonding in phase change materials.

Feasible Route to High-Temperature Ambient-Pressure Hydride Superconductivity

A key challenge in materials discovery is to find high-temperature superconductors. Hydrogen and hydride materials have long been considered promising materials displaying conventional phonon-mediated superconductivity. However, the high pressures required to stabilize these materials have restricted their application. Here, we present results from high-throughput computation, considering a wide range of high-symmetry ternary hydrides from across the periodic table at ambient pressure. This large composition space is then reduced by considering thermodynamic, dynamic, and magnetic stability before direct estimations of the superconducting critical temperature. This approach has revealed a metastable ambient-pressure hydride superconductor, Mg_{2}IrH_{6}, with a predicted critical temperature of 160 K, comparable to the highest temperature superconducting cuprates. We propose a synthesis route via a structurally related insulator, Mg_{2}IrH_{7}, which is thermodynamically stable above 15 GPa, and discuss the potential challenges in doing so.

Photoinduced Electronic and Spin Topological Phase Transitions in Monolayer Bismuth

Ultrathin bismuth exhibits rich physics including strong spin-orbit coupling, ferroelectricity, nontrivial topology, and light-induced structural dynamics. We use ab initio calculations to show that light can induce structural transitions to four transient phases in bismuth monolayers. These light-induced phases exhibit nontrivial topological character, which we illustrate using the recently introduced concept of spin bands and spin-resolved Wilson loops. Specifically, we find that the topology changes via the closing of the electron and spin band gaps during photoinduced structural phase transitions, leading to distinct edge states. Our study provides strategies to tailor electronic and spin topology via ultrafast control of photoexcited carriers and associated structural dynamics.

Modeling Temperature-Dependent Electron Thermal Diffuse Scattering via Machine-Learned Interatomic Potentials and Path-Integral Molecular Dynamics

Electron thermal diffuse scattering is shown to be sensitive to subtle changes in atomic vibrations and shows promise in assessing lattice dynamics at nanometer resolution. Here, we demonstrate that machine-learned interatomic potentials (MLIPs) and path-integral molecular dynamics can accurately capture the potential energy landscape and lattice dynamics needed to describe electron thermal diffuse scattering. Using SrTiO_{3} as a test bed at cryogenic and room temperatures, we compare electron thermal diffuse scattering simulations using different approximations to incorporate thermal motion. Only when the simulations are based on quantum mechanically accurate MLIPs in combination with path-integral molecular dynamics that include nuclear quantum effects is there excellent agreement with experiments.

Temperature and quantum anharmonic lattice effects on stability and superconductivity in lutetium trihydride

In this work, we resolve conflicting experimental and theoretical findings related to the dynamical stability and superconducting properties of [Formula: see text]-LuH3, which was recently suggested as the parent phase harboring room-temperature superconductivity at near-ambient pressures. Including temperature and quantum anharmonic lattice effects in our calculations, we demonstrate that the theoretically predicted structural instability of the [Formula: see text] phase near ambient pressures is suppressed for temperatures above 200 K. We provide a p-T phase diagram for stability up to pressures of 6 GPa, where the required temperature for stability is reduced to T > 80 K. We also determine the superconducting critical temperature Tc of [Formula: see text]-LuH3 within the Migdal-Eliashberg formalism, using temperature- and quantum-anharmonically-corrected phonon dispersions, finding that the expected Tc for electron-phonon mediated superconductivity is in the range of 50-60 K, i.e., well below the temperatures required to stabilize the lattice. When considering moderate doping based on rigidly shifting the Fermi level, Tc decreases for both hole and electron doping. Our results thus provide evidence that any observed room-temperature superconductivity in pure or doped [Formula: see text]-LuH3, if confirmed, cannot be explained by a conventional electron-phonon mediated pairing mechanism.

Investigating the role of dispersion corrections and anharmonic effects on the phase transition in SrZrS3: A systematic analysis from AIMD free energy calculations

A thermally driven needle-like (NL) to distorted perovskite (DP) phase transition in SrZrS3 was investigated by means of ab initio free energy calculations accelerated by machine learning. As a first step, a systematic screening of the methods to include long-range interactions in semilocal density functional theory Perdew-Burke-Ernzerhof calculations was performed. Out of the ten correction schemes tested, the Tkatchenko-Scheffler method with iterative Hirshfeld partitioning method was found to yield the best match between calculated and experimental lattice geometries, while predicting the correct order of stability of NL and DP phases at zero temperature. This method was then used in free energy calculations, performed using several approaches, so as to determine the effect of various anharmonicity contributions, such as the anisotropic thermal lattice expansion or the thermally induced internal structure changes, on the phase transition temperature (TNP→DP). Accounting for the full anharmonicity by combining the NPT molecular dynamics data with thermodynamic integration with harmonic reference provided our best estimate of TNL→DP = 867 K. Although this result is ∼150 K lower than the experimental value, it still provides an improvement by nearly 300 K compared to the previous theoretical report by Koocher et al. [Inorg. Chem. 62, 11134-11141 (2023)].

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.

Sampling the Materials Space for Conventional Superconducting Compounds

A large scale study of conventional superconducting materials using a machine-learning accelerated high-throughput workflow is performed, starting by creating a comprehensive dataset of around 7000 electron-phonon calculations performed with reasonable convergence parameters. This dataset is then used to train a robust machine learning model capable of predicting the electron-phonon and superconducting properties based on structural, compositional, and electronic ground-state properties. Using this machine, the transition temperatures (Tc ) of approximately 200 000 metallic compounds are evaluated, all of which are on the convex hull of thermodynamic stability (or close to it) to maximize the probability of synthesizability. Compounds predicted to have Tc values exceeding 5 K are further validated using density-functional perturbation theory. As a result, 541 compounds with Tc values surpassing 10 K, encompassing a variety of crystal structures and chemical compositions, are identified. This work is complemented with a detailed examination of several interesting materials, including nitrides, hydrides, and intermetallic compounds. Particularly noteworthy is LiMoN2 , which is predicted to be superconducting in the stoichiometric trigonal phase, with a Tc exceeding 38 K. LiMoN2 has previously been synthesized in this phase, further heightening its potential for practical applications.

Observation of the most H2-dense filled ice under high pressure

Hydrogen hydrates are among the basic constituents of our solar system's outer planets, some of their moons, as well Neptune-like exo-planets. The details of their high-pressure phases and their thermodynamic conditions of formation and stability are fundamental information for establishing the presence of hydrogen hydrates in the interior of those celestial bodies, for example, against the presence of the pure components (water ice and molecular hydrogen). Here, we report a synthesis path and experimental observation, by X-ray diffraction and Raman spectroscopy measurements, of the most H[Formula: see text]-dense phase of hydrogen hydrate so far reported, namely the compound 3 (or C[Formula: see text]). The detailed characterisation of this hydrogen-filled ice, based on the crystal structure of cubic ice I (ice I[Formula: see text]), is performed by comparing the experimental observations with first-principles calculations based on density functional theory and the stochastic self-consistent harmonic approximation. We observe that the extreme (up to 90 GPa and likely beyond) pressure stability of this hydrate phase is due to the close-packed geometry of the hydrogen molecules caged in the ice I[Formula: see text] skeleton.

Light-Induced Nonthermal Phase Transition to the Topological Crystalline Insulator State in SnSe

Femtosecond pulses have been used to reveal hidden broken symmetry states and induce transitions to metastable states. However, these states are mostly transient and disappear after laser removal. Photoinduced phase transitions toward crystalline metastable states with a change of topological order are rare and difficult to predict and realize experimentally. Here, by using constrained density functional perturbation theory and accounting for light-induced quantum anharmonicity, we show that ultrafast lasers can permanently transform the topologically trivial orthorhombic structure of SnSe into the topological crystalline insulating rocksalt phase via a first-order nonthermal phase transition. We describe the reaction path and evaluate the critical fluence and possible decay channels after photoexcitation. Our simulations of the photoexcited structural and vibrational properties are in excellent agreement with recent pump-probe data in the intermediate fluence regime below the transition with an error on the curvature of the quantum free energy of the photoexcited state that is smaller than 2%.

Quantum lattice dynamics and their importance in ternary superhydride clathrates

The quantum nature of the hydrogen lattice in superconducting hydrides can have crucial effects on the material's properties. Taking a detailed look at the dynamic stability of the recently predicted BaSiH8 phase, we find that the inclusion of anharmonic quantum ionic effects leads to an increase in the critical dynamical pressure to 20 GPa as compared to 5 GPa within the harmonic approximation. We identify the change in the crystal structure due to quantum ionic effects to be the main driving force for this increase and demonstrate that this can already be understood at the harmonic level by considering zero-point energy corrections to the total electronic energy. In fact, the previously determined critical pressure of kinetic stability p kin = 30 GPa still poses a stricter bound for the synthesizability of BaSiH8 and similar hydride materials than the dynamical stability and therefore constitutes a more rigorous and accurate estimate for the experimental realizability of these structures.

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.

Exploring the High-Temperature Stabilization of Cubic Zirconia from Anharmonic Lattice Dynamics

Finite-temperature stability of crystals is of continuous relevance in solid-state chemistry with many important properties only emerging in high-temperature polymorphs. Currently, the discovery of new phases is largely serendipitous due to a lack of computational methods to predict crystal stability with temperature. Conventional methods use harmonic phonon theory, but this breaks down when imaginary phonon modes are present. Anharmonic phonon methods are required to describe dynamically stabilized phases. We investigate the high-temperature tetragonal-to-cubic phase transition of ZrO2 based on first-principles anharmonic lattice dynamics and molecular dynamics simulations as an archetypical example of a phase transition involving a soft phonon mode. Anharmonic lattice dynamics calculations and free energy analysis suggest that the stability of cubic zirconia cannot be attributed solely to anharmonic stabilization and is thus absent for the pristine crystal. Instead, an additional entropic stabilization is suggested to arise from spontaneous defect formation, which is also responsible for superionic conductivity at elevated temperatures.

Anharmonic Correction to Free Energy Barriers from DFT-Based Molecular Dynamics Using Constrained Thermodynamic Integration

For the calculation of anharmonic contributions to free energy barriers, constrained thermodynamic λ-path integration (λ-TI) from a harmonic reference force field to density functional theory is presented as an alternative to the established Blue Moon ensemble method (ξ-TI), in which free energy gradients along the reaction coordinate ξ are integrated. With good agreement in all cases, the λ-TI method is benchmarked against the ξ-TI method for several reactions, including the internal CH₃ group rotation in ethane, a nucleophilic substitution of CH₃Cl, a retro-Diels-Alder reaction, and a proton transfer in zeolite H-SSZ-13. An advantage of λ-TI is that one can use virtually any reference state to compute anharmonic contributions to reaction free energies or free energy barriers. This is particularly relevant for catalysis, where it is now possible to compute anharmonic corrections to the free energy of a transition state relative to any reference, for example, the most stable state of the active site and the reactants in the gas phase. This is in contrast to ξ-TI, where free energy barriers can only be computed relative to an initial state with all reactants coadsorbed. Finally, the Bennett acceptance ratio method combined with λ-TI is demonstrated to reduce the number of required integration grid points with tolerable accuracy, favoring thus λ-TI over ξ-TI in terms of computational efficiency.

Anharmonicity Reveals the Tunability of the Charge Density Wave Orders in Monolayer VSe2

VSe2 is a layered compound that has attracted great attention due to its proximity to a ferromagnetic state that is quenched by its charge density wave (CDW) phase. In the monolayer limit, unrelated experiments have reported different CDW orders with different transition temperatures, making this monolayer very controversial. Here we perform first-principles nonperturbative anharmonic phonon calculations in monolayer VSe2 in order to estimate the CDW order and the corresponding transition temperature. They reveal that monolayer VSe2 develops two independent charge density wave orders that compete as a function of strain. Variations of only 1.5% in the lattice parameter are enough to stabilize one order or the other. Moreover, we analyze the impact of external Lennard-Jones interactions, showing that these can act together with anharmonicity to suppress the CDW orders. Our results solve previous experimental contradictions, highlighting the high tunability and substrate dependency of the CDW orders of monolayer VSe2.

First-Principles Thermodynamics of CsSnI3

CsSnI₃ is a promising ecofriendly solution for energy harvesting technologies. It exists at room temperature in either a black perovskite polymorph or a yellow 1D double-chain, which irreversibly deteriorates in the air. In this work, we unveil the relative thermodynamic stability between the two structures with a first-principles sampling of the CsSnI₃ finite-temperature phase diagram, discovering how it is driven by anomalously large quantum and anharmonic ionic fluctuations. Thanks to a comprehensive treatment of anharmonicity, the simulations deliver a remarkable agreement with known experimental data for the transition temperatures of the orthorhombic, rhombohedral, and cubic perovskite structures and the thermal expansion coefficient. We disclose how the perovskite polymorphs are the ground state above 270 K and discover an abnormal decrease in heat capacity upon heating in the cubic black perovskite. Our results also significantly downplay the Cs⁺ rattling modes' contribution to mechanical instability. The remarkable agreement with experiments validates our methodology, which can be systematically applied to all metal halides.

Experimental absence of the non-perovskite ground state phases of MaPbI3 explained by a Funnel Hopping Monte Carlo study based on a neural network potential

Methylammonium lead iodide is a material known for its exceptional opto-electronic properties that make it a promising candidate for many high performance applications, such as light emitting diodes or solar cells. A recent computational structure search revealed two previously unknown non-perovskite polymorphs, that are lower in energy than the experimentally observed perovskite phases. To investigate the elusiveness of the non-perovskite phases in experimental studies, we extended our Funnel Hopping Monte Carlo (FHMC) method to periodic systems and performed extensive MC simulations driven by a machine learned potential. FHMC simulations that also include these newly discovered non-perovskite phases show that above temperatures of 200 K the perovskite phases are thermodynamically preferred. A comparison with the quasi-harmonic approximation highlights the importance of anharmonic effects captured by FHMC.

LO-mode phonon of KCl and NaCl at 300 K by inelastic x-ray scattering measurements and first principles calculations

Longitudinal-optical (LO) mode phonon branches of KCl and NaCl were measured using inelastic x-ray scattering (IXS) at 300 K and calculated by the first-principles phonon calculation with the stochastic self-consistent harmonic approximation. Spectral shapes of the IXS measurements and calculated spectral functions agreed well. We analyzed the calculated spectral functions that provide higher resolutions of the spectra than the IXS measurements. Due to strong anharmonicity, the spectral functions of these phonon branches have several peaks and the LO modes along Γ-L paths are disconnected.

Superconducting hydrides on a quantum landscape

Reaching superconductivity at ambient conditions is one of the biggest scientific dreams. The discoveries in the last few years at high pressures place hydrogen-based compounds as the best candidates for making it true. As the recent history shows, first-principles calculations are expected to continue guiding the experimental quest in the right track in the coming years. Considering that ionic quantum fluctuations largely affect the crystal structure and the vibrational properties of superconducting hydrides, in many cases making them thermodynamically stable at much lower pressures than expected, it will be crucial to include such effects on the futureab initiopredictions. The prospects for low-pressure high critical-temperature compounds are wide open, even at ambient pressure.

Local Symmetry Breaking Suppresses Thermal Conductivity in Crystalline Solids

Understanding the correlations of both the local and global structures with lattice dynamics is critical for achieving low lattice thermal conductivity (κ_lat ) in crystalline materials. Herein, we demonstrate local cationic off-centring within the global rock-salt structure of AgSbSe₂ by using synchrotron X-ray pair distribution function analysis and unravel the origin of its ultralow κ_lat ≈0.4 W mK^-1 at 300 K. The cations are locally off-centered along the crystallographic ⟨ 100 ⟩ direction by about ≈0.2 Å, which averages out as the rock-salt structure on the global scale. Phonon dispersion obtained by density functional theory (DFT) shows weak instabilities that cause local off-centering distortions within an anharmonic double-well potential. The local structural distortion arises from the stereochemically active 5s² lone pairs of Sb. Our findings open an avenue for understanding how the local structure influences the phonon transport and facilitates the design of next-generation crystalline materials with tailored thermal properties.

The microscopic origin of the anomalous isotopic properties of ice relies on the strong quantum anharmonic regime of atomic vibration

Water ice is a unique material presenting intriguing physical properties, such as negative thermal expansion and anomalous volume isotope effect (VIE). They arise from the interplay between weak hydrogen bonds and nuclear quantum fluctuations, making theoretical calculations challenging. Here, we employ the stochastic self-consistent harmonic approximation to investigate how thermal and quantum fluctuations affect the physical properties of ice XI with ab initio accuracy. Regarding the anomalous VIE, our work reveals that quantum effects on hydrogen are so strong to be in a nonlinear regime: When progressively increasing the mass of hydrogen from protium to infinity (classical limit), the volume first expands and then contracts, with a maximum slightly above the mass of tritium. We observe an anharmonic renormalization of about 10% in the bending and stretching phonon frequencies probed in IR and Raman experiments. For the first time, we report an accurate comparison of the low-energy phonon dispersion with the experimental data, possible only thanks to high-level accuracy in the electronic correlation and nuclear quantum and thermal fluctuations, paving the way for the study of thermal transport in ice from first-principles and the simulation of ice under pressure.

Dominant Role of Quantum Anharmonicity in the Stability and Optical Properties of Infinite Linear Acetylenic Carbon Chains

Carbyne, an infinite-length straight chain of carbon atoms, is supposed to undergo a second order phase transition from the metallic bond-symmetric cumulene (═C═C═)_∞ toward the distorted insulating polyyne chain (-C≡C-)_∞ displaying bond-length alternation. However, recent synthesis of ultra long carbon chains (∼6000 atoms, [Nat. Mater., 2016, 15, 634]) did not show any phase transition and detected only the polyyne phase, in agreement with previous experiments on capped finite carbon chains. Here, by performing first-principles calculations, we show that quantum-anharmonicity reduces the energy gain of the polyyne phase with respect to the cumulene one by 71%. The magnitude of the bond-length alternation increases by increasing temperature, in stark contrast with a second order phase transition, confining the cumulene-to-polyyne transition to extremely high and unphysical temperatures. Finally, we predict that a high temperature insulator-to-metal transition occurs in the polyyne phase confined in insulating nanotubes with sufficiently large dielectric constant due to a giant quantum-anharmonic bandgap renormalization.

TOLOMEO, a Novel Machine Learning Algorithm to Measure Information and Order in Correlated Networks and Predict Their State

We present ToloMEo (TOpoLogical netwOrk Maximum Entropy Optimization), a program implemented in C and Python that exploits a maximum entropy algorithm to evaluate network topological information. ToloMEo can study any system defined on a connected network where nodes can assume N discrete values by approximating the system probability distribution with a Pottz Hamiltonian on a graph. The software computes entropy through a thermodynamic integration from the mean-field solution to the final distribution. The nature of the algorithm guarantees that the evaluated entropy is variational (i.e., it always provides an upper bound to the exact entropy). The program also performs machine learning, inferring the system’s behavior providing the probability of unknown states of the network. These features make our method very general and applicable to a broad class of problems. Here, we focus on three different cases of study: (i) an agent-based model of a minimal ecosystem defined on a square lattice, where we show how topological entropy captures a crossover between hunting behaviors; (ii) an example of image processing, where starting from discretized pictures of cell populations we extract information about the ordering and interactions between cell types and reconstruct the most likely positions of cells when data are missing; and (iii) an application to recurrent neural networks, in which we measure the information stored in different realizations of the Hopfield model, extending our method to describe dynamical out-of-equilibrium processes.