Incorporating solvent effects in DFT: insights from cation exchange in faujasites.

Zeolites are versatile materials renowned for their extra-framework cation exchange capabilities, with applications spanning diverse fields, including nuclear waste treatment. While detailed experimental characterization offers valuable insight, density functional theory (DFT) proves particularly adept at investigating ion exchange in zeolites, owing to its atomic and electronic resolution. However, the prevalent occurrence of zeolitic ion exchange in aqueous environments poses a challenge to conventional DFT modeling, traditionally conducted in a vacuum. This study seeks to enhance zeolite modeling by systematically evaluating predictive differences across varying degrees of aqueous solvent inclusion. Specifically focusing on monovalent cation exchange in Na-X zeolites, we explore diverse modeling approaches. These range from simple dehydrated systems (representing bare reference states in vacuum) to more sophisticated models that incorporate aqueous solvent effects through explicit water molecules and/or a dielectric medium. Through comparative analysis of DFT and semi-empirical DFT approaches, along with their validation against experimental results, our findings underscore the necessity to concurrently consider explicit and implicit solvent effects for accurate prediction of zeolitic ionic exchange.

Tailoring the Angular Mismatch in MoS2 Homobilayers through Deformation Fields.

Ultrathin MoS2 has shown remarkable characteristics at the atomic scale with an immutable disorder to weak external stimuli. Ion beam modification unlocks the potential to selectively tune the size, concentration, and morphology of defects produced at the site of impact in 2D materials. Combining experiments, first-principles calculations, atomistic simulations, and transfer learning, it is shown that irradiation-induced defects can induce a rotation-dependent moiré pattern in vertically stacked homobilayers of MoS2 by deforming the atomically thin material and exciting surface acoustic waves (SAWs). Additionally, the direct correlation between stress and lattice disorder by probing the intrinsic defects and atomic environments are demonstrated. The method introduced in this paper sheds light on how engineering defects in the lattice can be used to tailor the angular mismatch in van der Waals (vdW) solids.

Transition Temperature for Spin-Crossover Materials with the Mean Value Ensemble Hubbard-U Correction.

Calculation of transition temperatures T1/2 for thermally driven spin-crossover in condensed phases is challenging, even with sophisticated state-of-the-art density functional approximations. The first issue is the accuracy of the adiabatic crossover energy difference ΔEHL between the low- and high-spin states of the bistable metal-organic complexes. The other is the proper inclusion of entropic contributions to the Gibbs free energy from the electronic and vibrational degrees of freedom. We discuss the effects of treatments of both contributions upon the calculation of thermochemical properties for a set of 20 spin-crossover materials using a Hubbard-U correction obtained from a reference ensemble spin-state. The U values obtained from a simplest bimolecular representation may overcorrect, somewhat, the ΔEHL values, hence giving somewhat excessive reduction of the T1/2 results with respect to their U = 0 values in the crystalline phase. We discuss the origins of the discrepancies by analyzing different sources of uncertainties. By use of a first-coordination-sphere approximation and the assumption that vibrational contributions from the outermost atoms in a metal-organic complex are similar in both low- and high-spin states, we achieve T1/2 results with the low-cost, widely used PBE generalized gradient density functional approximation comparable to those from the more costly, more sophisticated r2SCAN meta-generalized gradient approximation. The procedure is promising for use in high-throughput materials screening, because it combines rather low computational effort requirements with freedom from user manipulation of parameters.

Ligand Optimization of Exchange Interaction in Co(II) Dimer Single Molecule Magnet by Machine Learning.

Designing single-molecule magnets (SMMs) for potential applications in quantum computing and high-density data storage requires tuning their magnetic properties, especially the strength of the magnetic interaction. These properties can be characterized by first-principles calculations based on density functional theory (DFT). In this work, we study the experimentally synthesized Co(II) dimer (Co2(C5NH5)4(µ-PO2(CH2C6H5)2)3) SMM with the goal to control the exchange energy, ΔEJ, between the Co atoms through tuning of the capping ligands. The experimentally synthesized Co(II) dimer molecule has a very small ΔEJ < 1 meV. We assemble a DFT data set of 1081 ligand substitutions for the Co(II) dimer. The ligand exchange provides a broad range of exchange energies, ΔEJ, from +50 to -200 meV, with 80% of the ligands yielding a small ΔEJ < 10 meV. We identify descriptors for the classification and regression of ΔEJ using gradient boosting machine learning models. We compare one-hot encoded, structure-based, and chemical descriptors consisting of the HOMO/LUMO energies of the individual ligands and the maximum electronegativity difference and bond order for the ligand atom connecting to Co. We observe a similar overall performance with the chemical descriptors outperforming the other descriptors. We show that the exchange coupling, ΔEJ, is correlated to the difference in the average bridging angle between the ferromagnetic and antiferromagnetic states, similar to the Goodenough-Kanamori rules.

Implicit self-consistent electrolyte model in plane-wave density-functional theory.

The ab initio computational treatment of electrochemical systems requires an appropriate treatment of the solid/liquid interfaces. A fully quantum mechanical treatment of the interface is computationally demanding due to the large number of degrees of freedom involved. In this work, we develop a computationally efficient model where the electrode part of the interface is described at the density-functional theory (DFT) level, and the electrolyte part is represented through an implicit solvation model based on the Poisson-Boltzmann equation. We describe the implementation of the linearized Poisson-Boltzmann equation into the Vienna Ab initio Simulation Package, a widely used DFT code, followed by validation and benchmarking of the method. To demonstrate the utility of the implicit electrolyte model, we apply it to study the surface energy of Cu crystal facets in an aqueous electrolyte as a function of applied electric potential. We show that the applied potential enables the control of the shape of nanocrystals from an octahedral to a truncated octahedral morphology with increasing potential.

Two-Dimensional Intrinsic Half-Metals With Large Spin Gaps.

Through a systematic search of all layered bulk compounds combined with density functional calculations employing hybrid exchange-correlation functionals, we predict a family of three magnetic two-dimensional (2D) materials with half-metallic band structures. The 2D materials, FeCl2, FeBr2, and FeI2, are all sufficiently stable to be exfoliated from bulk layered compounds. The Fe2+ ions in these materials are in a high-spin octahedral d6 configuration leading to a large magnetic moment of 4 µB. Calculations of the magnetic anisotropy show an easy-plane for the magnetic moment. A classical XY model with nearest neighbor coupling estimates critical temperatures, Tc, for the Berezinskii-Kosterlitz-Thouless transition ranging from 122 K for FeI2 to 210 K for FeBr2. The quantum confinement of these 2D materials results in unusually large spin gaps, ranging from 4.0 eV for FeI2 to 6.4 eV for FeCl2, which should defend against spin current leakage even at small device length scales. Their purely spin-polarized currents and dispersive interlayer interactions should make these materials useful for 2D spin valves and other spintronic applications.

Topology-Scaling Identification of Layered Solids and Stable Exfoliated 2D Materials.

The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic clusters in a structure's unit cell, and determines their scaling with cell size. The search yielded 826 stable layered materials that are considered as candidates for the formation of two-dimensional monolayers via exfoliation. Density-functional theory was used to calculate the exfoliation energy of each material and 680 monolayers emerge with exfoliation energies below those of already-existent two-dimensional materials. The crystal structures of these two-dimensional materials provide templates for future theoretical searches of stable two-dimensional materials. The optimized structures and other calculated data for all 826 monolayers are provided at our database (https://materialsweb.org).

Interface-Driven Structural Distortions and Composition Segregation in Two-Dimensional Heterostructures.

The discovery of emergent phenomena in 2D materials has sparked substantial research efforts in the materials community. A significant experimental challenge for this field is exerting atomistic control over the structure and composition of the constituent 2D layers and understanding how the interactions between layers drive both structure and properties. While no segregation for single bilayers was observed, segregation of Pb to the surface of three bilayer thick PbSe-SnSe alloy layers was discovered within [(Pbx Sn1-x Se)1+δ ]n (TiSe2 )1 heterostructures using electron microscopy. This segregation is thermodynamically favored to occur when Pbx Sn1-x Se layers are interdigitated with TiSe2 monolayers. DFT calculations indicate that the observed segregation depends on what is adjacent to the Pbx Sn1-x Se layers. The interplay between interface- and volume-free energies controls both the structure and composition of the constituent layers, which can be tuned using layer thickness.

ReaxFF molecular dynamics simulations on lithiated sulfur cathode materials.

Sulfur is a very promising cathode material for rechargeable energy storage devices. However, sulfur cathodes undergo a noticeable volume variation upon cycling, which induces mechanical stress. In spite of intensive investigation of the electrochemical behavior of the lithiated sulfur compounds, their mechanical properties are not very well understood. In order to fill this gap, we developed a ReaxFF interatomic potential to describe Li-S interactions and performed molecular dynamics (MD) simulations to study the structural, mechanical, and kinetic behavior of the amorphous lithiated sulfur (a-LixS) compounds. We examined the effect of lithiation on material properties such as ultimate strength, yield strength, and Young's modulus. Our results suggest that with increasing lithium content, the strength of lithiated sulfur compounds improves, although this increment is not linear with lithiation. The diffusion coefficients of both lithium and sulfur were computed for the a-LixS system at various stages of Li-loading. A grand canonical Monte Carlo (GCMC) scheme was used to calculate the open circuit voltage profile during cell discharge. The Li-S binary phase diagram was constructed using genetic algorithm based tools. Overall, these simulation results provide insight into the behavior of sulfur based cathode materials that are needed for developing lithium-sulfur batteries.

Density functional theory study of the electrochemical interface between a Pt electrode and an aqueous electrolyte using an implicit solvent method.

We present a computational study of the interface of a Pt electrode and an aqueous electrolyte employing semi-empirical dispersion corrections and an implicit solvent model within first-principles calculations. The electrode potential is parametrized within the computational hydrogen electrode scheme. Using one explicit layer, we find that the most realistic interface configuration is a water bilayer in the H-up configuration. Furthermore, we focus on the contribution of the dispersion interaction and the presence of water on H, O, and OH adsorption energies. This study demonstrates that the implicit water scheme represents a computationally efficient method to take the presence of an aqueous electrolyte interface with a metal electrode into account.

The nanocrystal superlattice pressure cell: a novel approach to study molecular bundles under uniaxial compression.

Ordered assemblies of inorganic nanocrystals coated with organic linkers present interesting scientific challenges in hard and soft matter physics. We demonstrate that a nanocrystal superlattice under compression serves as a nanoscopic pressure cell to enable studies of molecular linkers under uniaxial compression. We developed a method to uniaxially compress the bifunctional organic linker by attaching both ends of aliphatic chains to neighboring PbS nanocrystals in a superlattice. Pressurizing the nanocrystal superlattice in a diamond anvil cell thus results in compression of the molecular linkers along their chain direction. Small-angle and wide-angle X-ray scattering during the compression provide insights into the structure of the superlattice and nanocrystal cores under compression, respectively. We compare density functional theory calculations of the molecular linkers as basic Hookean springs to the experimental force-distance relationship. We determine the density of linkers on the nanocrystal surfaces. We demonstrate our method to probe the elastic force of single molecule as a function of chain length. The methodology introduced in this paper opens doors to investigate molecular interactions within organic molecules compressed within a nanocrystal superlattice.

Solid-solid phase transformations induced through cation exchange and strain in 2D heterostructured copper sulfide nanocrystals.

We demonstrate dual interface formation in nanocrystals (NCs) through cation exchange, creating epitaxial heterostructures within spherical NCs. The thickness of the inner-disk layer can be tuned to form two-dimensional (2D), single atomic layers (<1 nm). During the cation exchange reaction from copper sulfide to zinc sulfide (ZnS), we observe a solid-solid phase transformation of the copper sulfide phase in heterostructured NCs. As the cation exchange reaction is initiated, Cu ions replaced by Zn ions at the interfaces are accommodated in intrinsic Cu vacancy sites present in the initial roxbyite (Cu1.81S) phase of copper sulfide, inducing a full phase transition to djurleite (Cu1.94S)/low chalcocite (Cu2S), a more thermodynamically stable phase than roxbyite. As the reaction proceeds and reduces the size of the copper sulfide layer, the epitaxial strain at the interfaces between copper sulfide and ZnS increases and is maximized for a copper sulfide disk ∼ 5 nm thick. To minimize this strain energy, a second phase transformation occurs back to the roxbyite phase, which shares a similar sulfur sublattice to wurtzite ZnS. The observation of a solid-solid phase transformation in our unique heterostructured NCs provides a new pathway to control desired phases and an insight into the influence of cation exchange on nanoscale phase transitions in heterostructured materials.

Structure and stability prediction of compounds with evolutionary algorithms.

Crystal structure prediction is a long-standing challenge in the physical sciences. In recent years, much practical success has been had by framing it as a global optimization problem, leveraging the existence of increasingly robust and accurate free energy calculations. This optimization problem has often been solved using evolutionary algorithms (EAs). However, many choices are possible when designing an EA for structure prediction, and innovation in the field is ongoing. We review the current state of evolutionary algorithms for crystal structure and composition prediction and discuss the details of methodological and algorithmic choices. Finally, we review the application of these algorithms to many systems of practical and fundamental scientific interest.

Emergent reduction of electronic state dimensionality in dense ordered Li-Be alloys.

High pressure is known to influence electronic structure and crystal packing, and can in some cases even induce compound formation between elements that do not bond under ambient conditions. Here we present a computational study showing that high pressure fundamentally alters the reactivity of the light elements lithium (Li) and beryllium (Be), which are the first of the metals in the condensed state and immiscible under normal conditions. We identify four stoichiometric Li(x)Be(1-x) compounds that are stable over a range of pressures, and find that the electronic density of states of one of them displays a remarkable step-like feature near the bottom of the valence band and then remains almost constant with increasing energy. These characteristics are typical of a quasi-two-dimensional electronic structure, the emergence of which in a three-dimensional environment is rather unexpected. We attribute this observation to large size differences between the ionic cores of Li and Be: as the density increases, the Li cores start to overlap and thereby expel valence electrons into quasi-two-dimensional layers characterized by delocalized free-particle-like states in the vicinity of Be ions.

Implicit solvation model for density-functional study of nanocrystal surfaces and reaction pathways.

Solid-liquid interfaces are at the heart of many modern-day technologies and provide a challenge to many materials simulation methods. A realistic first-principles computational study of such systems entails the inclusion of solvent effects. In this work, we implement an implicit solvation model that has a firm theoretical foundation into the widely used density-functional code Vienna ab initio Software Package. The implicit solvation model follows the framework of joint density functional theory. We describe the framework, our algorithm and implementation, and benchmarks for small molecular systems. We apply the solvation model to study the surface energies of different facets of semiconducting and metallic nanocrystals and the SN2 reaction pathway. We find that solvation reduces the surface energies of the nanocrystals, especially for the semiconducting ones and increases the energy barrier of the SN2 reaction.

Charge state-dependent symmetry breaking of atomic defects in transition metal dichalcogenides.

The functionality of atomic quantum emitters is intrinsically linked to their host lattice coordination. Structural distortions that spontaneously break the lattice symmetry strongly impact their optical emission properties and spin-photon interface. Here we report on the direct imaging of charge state-dependent symmetry breaking of two prototypical atomic quantum emitters in mono- and bilayer MoS2 by scanning tunneling microscopy (STM) and non-contact atomic force microscopy (nc-AFM). By changing the built-in substrate chemical potential, different charge states of sulfur vacancies (VacS) and substitutional rhenium dopants (ReMo) can be stabilized. Vac S - 1 as well as Re Mo 0 and Re Mo - 1 exhibit local lattice distortions and symmetry-broken defect orbitals attributed to a Jahn-Teller effect (JTE) and pseudo-JTE, respectively. By mapping the electronic and geometric structure of single point defects, we disentangle the effects of spatial averaging, charge multistability, configurational dynamics, and external perturbations that often mask the presence of local symmetry breaking.

Angle-resolved Raman imaging of interlayer rotations and interactions in twisted bilayer graphene.

Few-layer graphene is a prototypical layered material, whose properties are determined by the relative orientations and interactions between layers. Exciting electrical and optical phenomena have been observed for the special case of Bernal-stacked few-layer graphene, but structure-property correlations in graphene which deviates from this structure are not well understood. Here, we combine two direct imaging techniques, dark-field transmission electron microscopy (DF-TEM) and widefield Raman imaging, to establish a robust, one-to-one correlation between twist angle and Raman intensity in twisted bilayer graphene (tBLG). The Raman G band intensity is strongly enhanced due to a previously unreported singularity in the joint density of states of tBLG, whose energy is exclusively a function of twist angle and whose optical transition strength is governed by interlayer interactions, enabling direct optical imaging of these parameters. Furthermore, our findings suggest future potential for novel optical and optoelectronic tBLG devices with angle-dependent, tunable characteristics.

Predicting chiral nanostructures, lattices and superlattices in complex multicomponent nanoparticle self-assembly.

"Bottom up" type nanoparticle (NP) self-assembly is expected to provide facile routes to nanostructured materials for various, for example, energy related, applications. Despite progress in simulations and theories, structure prediction of self-assembled materials beyond simple model systems remains challenging. Here we utilize a field theory approach for predicting nanostructure of complex and multicomponent hybrid systems with multiple types of short- and long-range interactions. We propose design criteria for controlling a range of NP based nanomaterial structures. In good agreement with recent experiments, the theory predicts that ABC triblock terpolymer directed assemblies with ligand-stabilized NPs can lead to chiral NP network structures. Furthermore, we predict that long-range Coulomb interactions between NPs leading to simple NP lattices, when applied to NP/block copolymer (BCP) assemblies, induce NP superlattice formation within the phase separated BCP nanostructure, a strategy not yet realized experimentally. We expect such superlattices to be of increasing interest to communities involved in research on, for example, energy generation and storage, metamaterials, as well as microelectronics and information storage.

Unintended phosphorus doping of nickel nanoparticles during synthesis with TOP: a discovery through structural analysis.

We report the discovery of unintentional phosphorus (P) doping when tri-n-octylphosphine (TOP) ligands are used in Ni nanoparticle synthesis, which is the most common method for monodisperse Ni nanoparticle synthesis. The nanoparticles appear pure face-centered cubic (fcc) Ni in X-ray diffraction despite the surprisingly high level (5 atomic %) of P. We find that the P doping follows a direct relationship with increased reaction time and temperature and that the P doping can be estimated with the degree of lattice expansion shown from a peak shift in the XRD spectrum. Through EXAFS modeling and density-functional (DFT) calculations of defect formation energies we find that the P atoms are preferentially located on the fcc lattice as substitutional dopants with oxidation state of zero. Magnetic and catalytic properties are shown to be greatly affected by this doping; DFT calculations show magnetization losses in the Ni system, as well as in Fe and Co systems. These findings are likely relevant for other metal syntheses that employ phosphine ligands.

Softened elastic response and unzipping in chemical vapor deposition graphene membranes.

We use atomic force microscopy to image grain boundaries and ripples in graphene membranes obtained by chemical vapor deposition. Nanoindentation measurements reveal that out-of-plane ripples effectively soften graphene's in-plane stiffness. Furthermore, grain boundaries significantly decrease the breaking strength of these membranes. Molecular dynamics simulations reveal that grain boundaries are especially weakening when subnanometer voids are present in the lattice. Finally, we demonstrate that two graphene membranes brought together form membranes with higher resistance to breaking.