01. Optimisation of decision sequences from selection of elements to chemical formulae of functional materials

A. Vasylenko*, D. Antypov, V. Gusev, G. Darling, M. S. Dyer, M. J. Rosseinsky

The workflow for materials discovery – from selection of chemical elements to combine  to identification of functional high-performing candidates to establishing experimentally accessible formulae  – presents a complex hierarchy of consequential decisions. Development of quantitative guides is thus imperative to aid decision-making, increase the success rate and accelerate the discovery workflow. Recent advances in learning the patterns of properties-materials relationships from historical data have enabled a range of powerful techniques for prediction of functional performance for materials. Applied at the level of the periodic table, these techniques have enabled ranking of elemental combinations regarding the likelihood of forming new materials [1]. 

Here, I will present new capabilities for learning from materials data at two stages of the discovery workflow: phase field selection (PhaseSelect[2]) and stoichiometry optimisation (PhaseBO[3]). PhaseSelect learns from data about chemical elements themselves and discovers their contributions to functional properties of materials, e.g., such as superconductivity or magnetism; then it identifies the promising elemental combinations for new materials in terms of their functional performance. PhaseBO accelerates the exploration of all possible combinations of selected elements and increases the probability of the discovery of practically accessible new materials.

References
1. Vasylenko, A. et al. Element selection for crystalline inorganic solid discovery guided by unsupervised machine learning of experimentally explored chemistry. Nat. Commun. 12, 5561 (2021).
2. Vasylenko, A. et al. Element selection for functional materials discovery by integrated machine learning of atomic contributions to properties. arXiv:2202.01051 [cond-mat] (2022). 
3. Vasylenko, A. et. al., Exploring energy-composition relationships with Bayesian optimization for accelerated discovery of inorganic materials. arXiv:2302:00710 [cond-mat.mtrl-sci] (2023).

02. Data-driven discovery of 2D materials by deep generative models

Peder Lyngby* and Kristian Sommer Thygesen

Efficient algorithms to generate candidate crystal structures with good stability properties can play a key role in data-driven materials discovery. Here, we show that a crystal diffusion variational autoencoder (CDVAE) is capable of generating two-dimensional (2D) materials of high chemical and structural diversity and formation energies mirroring the training structures. Specifically, we train the CDVAE on 2615 2D materials with energy above the convex hull ΔH_hull < 0.3 eV/atom, and generate 5003 materials that we relax using density functional theory (DFT). We also generate 14192 new crystals by systematic element substitution of the training structures. We find that the generative model and lattice decoration approach are complementary and yield materials with similar stability properties but very different crystal structures and chemical compositions. In total we find 11630 predicted new 2D materials, where 8599 of these have ΔH_hull < 0.3 eV/atom as the seed structures, while 2004 are within 50 meV of the convex hull and could potentially be synthesised. The relaxed atomic structures of all the materials are available in the open Computational 2D Materials Database (C2DB). Our work establishes the CDVAE as an efficient and reliable crystal generation machine, and significantly expands the space of 2D materials.

03. Data-driven estimation of transfer integrals in undoped cuprates

Denys Kononenko*, Ulrich Rößler, Jeroen van den Brink, Oleg Janson

Undoped cuprates exhibit various low-dimensional and frustrated spin models. When the corresponding transfer integral is known, the dominant antiferromagnetic contribution to a magnetic exchange can be accurately estimated. However, calculating the transfer integral computationally has been a cumbersome process. Our study shows how a Gaussian Process Regression (GPR) model, trained on density functional theory calculations results, can predict transfer integrals by using crystal structure as the sole input. The GPR model takes in descriptors of the local crystal environment of two copper sites based on the truncated expansion of the site position functions using three-dimensional Zernike functions. Incorporating information on the local crystal environment's spatial configuration and chemical composition into the descriptor facilitates the quick screening of spin models with desirable features among a wide range of known and unknown cuprates.

04. Exploring O-vacancy defects in BaSnO₃ by a cluster-expansion approach

Manish Kumar*, Santiago Rigamonti, and Claudia Draxl

BaSnO₃ has high potential for being used as a photocatalytic and optoelectronic material due to its suitable band-edge positions, high mobility, excellent thermal stability, and being non-toxic. However, its wide band gap of 3.1 eV [1] limits its optical response to UV irradiation. Oxygen vacancies have the potential to reduce the band gap [2], but their role in facilitating visible-light absorption remains unclear. This study aims at understanding the influence of O vacancies on the structural and electronic properties of BaSnO₃. To explore the vast configurational space of possible vacancy arrangements, we construct a cluster-expansion (CE) model of the formation energy, based on density functional theory (DFT) calculations. By performing configurational samplings in the concentration range between 0 and 25%, we find that O vacancies are predominantly stable in a cis configuration (nearest-neighbour O vacancies) and a sep configuration, where the vacancies are at a third nearest-neighbor position in the Sn-O plane. The volume increases with the addition of O vacancies, reaching a maximum of 5.4% at a concentration of ~21%. This confirms previous experimental findings [3]. Additionally, the Sn-O average bond lengths of stable structures exhibit two characteristic values, namely ~2.07 Å and ~2.17 Å. The electronic structure of the material reveals a complex dependence on configuration, with band gaps differing by as much as 0.58 eV for structures with the same concentration and similar formation energy. Detailed analysis of a set of configurations at 2.47% vacancy concentration, reveals the appearance of in-gap states. The size of the band-gap depends on their respective position relative to the conduction band minimum. The dependence of the latter on the vacancy configuration is analyzed.

[1] W. Aggoune, A. Eljarrat, D. Nabok, K. Irmscher, M. Zupancic, Z. Galazka, M. Albrecht, C. Koch, and C. Draxl, Commun. Mater. 3, 12 (2022).
[2] M. Kim, B. Lee, H. Ju, J. Y. Kim, J. Kim, and S. W. Lee, Adv. Mater. 31, 1903316 (2019).
[3] Q. Liu, J. Dai, Y. Zhang, H. Li, B. Li, Z. Liu, and W. Wang, J. Alloys Compd. 655, 389 (2016).

05. Machine learning for additive manufacturing: Predicting materials characteristics and their uncertainty

Dmitry Chernyavsky*, Denys Kononenko, Jun Hee Han, Hwi Jun Kim, Jeroen van den Brink, Konrad Kosiba

Additive manufacturing (AM) is known for versatile fabrication of complex parts, while also allowing the synthesis of materials with desired microstructures and resulting properties. These benefits come at a cost: process control to manufacture parts within given specifications is very challenging due to the relevance of a large number of processing parameters. Efficient predictive machine learning (ML) models trained on small datasets, can minimize this cost. They also allow to assess the quality of the dataset inclusive of uncertainty. This is important in order for additively manufactured parts to meet property specifications not only on average, but also within a given variance or uncertainty. In our recent work, we demonstrate this strategy by developing a heteroscedastic Gaussian process (HGP) model, from a dataset based on laser powder bed fusion of a glass-forming alloy at varying processing parameters. Using amorphicity as the microstructural descriptor, we train the model on our Zr_52.5Cu_17.9Ni_14.6Al₁₀Ti₅ (at.%) alloy dataset. The HGP model not only accurately predicts the mean value of amorphicity, but also provides the respective uncertainty. The quantification of the aleatoric and epistemic uncertainty contributions allows to assess intrinsic inaccuracies of the dataset, as well as identify underlying physical phenomena. 

06. Flow Annealed Importance Sampling Bootstrap

Laurence Illing Midgley, Vincent Stimper*, Gregor N. C. Simm, Bernhard Schölkopf, José Miguel Hernández-Lobato

Normalizing flows are tractable density models that can approximate complicated target distributions, e.g. Boltzmann distributions of physical systems. However, current methods for training flows either suffer from mode-seeking behavior, use samples from the target generated beforehand by expensive MCMC methods, or use stochastic losses that have high variance. To avoid these problems, we augment flows with annealed importance sampling (AIS) and minimize the mass-covering α-divergence with α=2, which minimizes importance weight variance. Our method, Flow AIS Bootstrap (FAB), uses AIS to generate samples in regions where the flow is a poor approximation of the target, facilitating the discovery of new modes. We apply FAB to multimodal targets and show that we can approximate them very accurately where previous methods fail. To the best of our knowledge, we are the first to learn the Boltzmann distribution of the alanine dipeptide molecule using only the unnormalized target density, without access to samples generated via Molecular Dynamics (MD) simulations: FAB produces better results than training via maximum likelihood on MD samples while using 100 times fewer target evaluations. After reweighting the samples, we obtain unbiased histograms of dihedral angles that are almost identical to the ground truth. 

07. Elastocaloric effect of Sr2RuO4: entropy mapping and order parameter symmetry

Zhenhai Hu*, You-Sheng Li, Fabian Jerzembeck, Andreas Rost, Michael Nicklas, Andrew P. Mackenzie, Clifford W. Hicks

Elastocaloric effect (ECE) provides people a powerful tool to probe the strain and temperature dependence of entropy. With experimental 100-Sr₂RuO₄ ECE data, we successfully extracted the absolute entropy as a function of strain and temperature. The entropy map reproduces the entropy quench near the van Hove singularity point and indicates the first-order nature of the magnetic order at high strain. On the other hand, whether the superconducting (SC) order parameter is one-/two- component remains an unsolved issue. If the SC order parameter is degenerate and protected by lattice symmetry, the degeneracy will be lifted when the lattice symmetry is broken. Here we report the latest progress on elastocaloric measurement of Sr₂RuO₄ crystal with strain applied along <110>. Within our experimental precision, no signal indicating a second phase transition below Tc is observed. Combined with previous ECE measurements with strain applied along <100>, more stringent constraints on the nature of SC states at zero strain were placed by the absence of the second transition.

08. Machine learning experimental and modeling approaches for exotic phases of matter

S. Salomoni*, A. France-Lanord, F. Datchi, A. M. Saitta

Liquid is one of the three fundamental states of matter, together with solids and gases; but among them, it is the most poorly understood because of the intrinsic difficulty in its physical description. Thus it is not surprising that there remain some not properly understood phenomena, including liquid polymorphism. The main objective of this project is to significantly advance our understanding of liquid polymorphism and liquid-liquid transitions, and, by extension, of the liquid state itself, by providing accurate experimental and first-principles data sets that will constitute a solid basis from which the systematics of LLT can be extracted, and eventually will aid the emergence of theories from which predictions can be made. Mixed DFT-ML approaches have already proved to be particularly successful in the study of liquids at high pressures and temperatures, thus they will be our main investigative tools.

09. 3D CNN based crystal structure recognition

Ziyuan Rao*, Yue Li, Hongbin Zhang, Timoteo Colnaghi, Andreas Marek, Markus Rampp, Baptiste Gault

Computational methods and machine learning algorithms for automatic information extraction are crucial to enable data-driven materials science. These approaches are changing materials characterization and analytics, which often require a user-specified threshold to e.g. detect structure or symmetries in structures with defects. Here, we present a machine learning-based approach that directly works on the original periodic arrangements of atoms based on a three-dimensional convolutional neural network without any transformation of descriptors. Our approach shows a high classification accuracy and tolerance to the presence of random displacements and missing atoms. Experimentally, we successfully reconstruct the ordered L12 precipitates extracted from atom probe tomography data, consistent with segmentation based on isocomposition surfaces. The convolutional layers are essential for the simultaneous identification of compositional and structural information, which also give rise to its high tolerance. Our work advances machine learning-based crystal structure identification for incomplete crystal structural data.

10. Systematic exploration of quaternary MAB phases

Adam Carlsson*, Johanna Rosén, Martin Dahlqvist

A desired prerequisite when performing a quantum mechanical calculation is to have an initial idea of the atomic positions within an approximate crystal structure. The atomic positions combined should result in a system located in, or close to, an energy minimum. However, designing low-energy structures may be a challenging task when prior knowledge is scarce, specifically for large multi-component systems where the degrees of freedom are close to infinite. The low-energy basins of the (M’_xM’’_1-x)₃AlB₄ material system are herein explored by combining cluster expansion and crystal structure predictions with density functional theory calculations. Crystal structure prediction searches are applied to ternary systems to identify candidate structures which are subsequently used to explore the quaternary (pseudo-binary) (Mo_xSc_1-x)₃AlB₄ and (Ti_xV_1-x)₃AlB₄ systems through the cluster expansion formalism utilizing the ground-state search approach. Low-energy structures are specifically found at the (M’_1/3M’’_2/3)₃AlB₄ and (M’_2/3M’’_1/3)₃AlB₄ compositions and this for multiple crystal symmetries. Subsequent high-throughput phase stability and have been evaluated at identified compositions and structures for M’ and M’’ set to Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Mn, Fe, and Co. In addition, chemical solid-solution disorder has been considered and its stability have been evaluated at finite temperatures.  

11. Band-gap regression with architecture-optimized message-passing neural networks

Tim Bechtel*, Daniel T. Speckhard, Jonathan Godwin and Claudia Draxl

Graph-based neural networks and, specifically, message-passing neural networks (MPNNs) have shown great promise in predicting physical properties of solids. In this work, we train a MPNN to first classify materials through density-functional-theory data from the AFLOW database as being metallic or semiconducting/insulating. We then train another MPNN to predict the band gaps of those identified as non-metals. The network is optimized using a neural-architecture search using a random search algorithm over the number of message-passing steps, embedding size, and activation-function choice. Monte-Carlo dropout is employed to add uncertainty estimates to the model predictions. Our model significantly outperforms previous models from the literature in terms of classification and band-gap prediction. The model domain of applicability is analyzed with respect to the crystal systems, the inclusion of a Hubbard parameter in the density functional, and the atomic species building up the materials.11. 

12. Fingerprint enabled hyperdimensional optimization of atomic structures

Casper Larsen*, Sami Kaappa, Karsten Wedel Jacobsen

Construction of potential energy surrogate surfaces by means of Gaussian processes allows for a tremendous speedup of atomic structure relaxations compared to conventional DFT-relaxations. Combining this approach with fractionalization of atomic properties in an interpolation-enabling fingerprint space allows for further performance enhancement by allowing structure optimizations to bypass energy barriers encountered in the conventional energy landscape.

13. Investigating the Mineralization Mechanisms of Forming Human Osteons

Giacomo Rossato, Mahdi Ayoubi, Peter Fratzl, Angelo Valleriani, Richard Weinkamer Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Potsdam, Germany 

In adult humans the bone is constantly resorbed and newly formed in a process called bone remodeling. A basic building block of bone is called an osteon, a cylindrical structure of roughly 200 µm diameter created during the remodeling. This structure is composed by a central canal called Haversian canal that can accommodate blood vessels and nerves surrounded by a mineralized matrix. The creation of a new osteon happens in two distinct phases: in a first moment a matrix composed mainly by collagen, called osteoid, is deposited around the Harversian canal and in a second stage nanoscopic mineral particles are incorporated into the collagen. Osteoid is deposited by cells called osteoblasts; some of these osteoblasts remain encapsulated within the osteoid and differentiate into osteocytes. The osteocytes encapsulated in the bone lie in cavities called lacunae and are connected to each other through channels called canaliculi. The network formed by lacunae and canaliculi is called the lacunocanalicular network (LCN). To study the kinetics of the mineralization process, we imaged forming human osteons in 3D using high-resolution Focused Ion Beam - Scanning Electron Microscopy (FIB-SEM). Staining techniques allow to discriminate not only the mineralized and the unmineralized matrix, but also the cellular component within the bone. In a previous study [1], we observed that there is a mineralization-free halo around canaliculi hosting osteocyte processes. 

The purpose of the present study is to describe the mineralization process as resulting from the competition between mineral precursor and inhibitor. We combined image analysis of mineralization patterns around single canaliculi with a reaction-diffusion model. In the mathematical model, both mineral precursor and inhibitor diffuse from the canaliculus and mineralization occurs wherever the local concentration of the precursor exceeds the one of the inhibitor. 

We developed an adaptive thresholding algorithm in order to segment the canaliculi in the FIB-SEM image stacks and to analyze the mineralization patterns around different canaliculi. We observed that mineralization begins predominantly in the interstitial regions between the canaliculi and then progresses with time towards each canaliculus. And we confirmed this behavior for all the canaliculi under consideration. The data obtained from the image analysis were then used to compare the model outcomes with the experimental images. Model exploration demonstrated that a similar mineralization kinetics occurs by assuming a different regulation of precursor and inhibitor at the canaliculus and by interaction between cell processes in neighboring canaliculi. 

This model could allow for a deeper understanding of the underlying mechanisms of mineralization and can also be used to better understand known mineralization disorders. 

[1] Ayoubi et al. (2021), Advanced Healthcare Materials, 10, p.2100113

14. Towards machine learning potentials for field evaporation

Shyam Katnagallu*, Jӧrg Neugebauer and Christoph Freysoldt

Field evaporation, an electrostatic field induced ionization and subsequent evaporation of surface atoms, is the underlying principle of atom probe tomography. Ab initio simulations including 1-10 V/Å fields on metallic slabs have recently shed light [1] in to the intricacies of the field evaporation process. These simulations underscore the importance of knowing the path of the evaporating atom prior to complete ionization to improve the spatial resolution of the technique. However, to properly sample the extremely shallow potential energy surface due to electrostatic field extensive simulations with computationally expensive ab initio accuracy are needed. We therefore combine machine learning interatomic potentials with a charge equilibration scheme. To demonstrate the performance and accuracy of our scheme, we validate the Rappe et al charge equilibration model [2] using Hirshfeld decomposed DFT reference charges acquired from (13,5,7) Pt slab under electric fields ranging from (1-4.5 V/Å) and  develop potentials for field evaporation in Al.

References:

[1] M. Ashton, A. Mishra, J. Neugebauer, and C. Freysoldt, Ab Initio Description of Bond Breaking in Large Electric Fields, Phys. Rev. Lett. 124, (2020).

[2] A. K. Rappe and W. A. G. Iii, Charge Equilibration for Molecular Dynamics Simulations, J. Phys. Chem 95, 3358 (1991).

15. Development of Moment Tensor Interatomic Potentials to Study Interphase Interactions Between a Li6PS5Cl Electrolyte and a Li-metal Anode 

G. Chaney*, N. Mingo, A. van Roekeghem, A. Golov, and J. Carrasco

High energy and high power Li-ion batteries are essential to developing a “green” economy, involving electric vehicles and energy backups to photovoltaic devices.  However, conventional Li-ion batteries contain flammable liquid electrolytes that present safety concerns. All solid-state Li-ion batteries (ASSLMBs) are safe, energy dense alternatives that use solid electrolytes and Li-metal anodes. Argyrodite-type electrolytes feature high ionic conductivities (1-6 mS/cm for Li₆PS₅Cl)[1-3] and are easily prepared. However, electrochemical instabilities between these electrolytes and the Li-metal anode cause interphase side reactions that hinder their practical application to ASSLMBs. These reactions can be modeled computationally via molecular dynamics with interatomic potentials developed from machine learning (MLIPs). A suite of MLIPs have been designed to construct relationships between the atomic structure of a material and its potential energy surface. Moment tensor potentials (MTPs) are a type of MLIP that uses polynomial-like functions as basis sets to describe interatomic distances and angles, and allow researchers to model large-scale systems relatively inexpensively [4, 5]. Here I will discuss the background, and present preliminary results in our use of MTPs to study the interactions between Li₆PS₅Cl and a Li-metal anode. We will focus on the structural rearrangement of the anode surface as well as the diffusion of the Li-ions into Li₆PS₅Cl at long time-scales.  Our initial ab initio data was provided by Andrey Golov and Javier Carrrasco from CIC Energigune, Spain [6].

[1] Wang, S.; Zhang, Y.; Zhang, X.; Liu, T.; Lin, Y.-H.; Shen, Y.; Li, L.; Nan, C.-W. High-Conductivity Argyrodite Li₆PS₅Cl Solid Electrolytes Prepared via Optimized Sintering Processes for All- Solid-State Lithium−Sulfur Batteries. ACS Appl. Mater. Interfaces 2018, 10, 42279−42285.

[2] Yu, C.; van Eijck, L.; Ganapathy, S.; Wagemaker, M. Synthesis, Structure and Electrochemical Performance of the Argyrodite Li6PS5Cl Solid Electrolyte for Li-Ion Solid State Batteries. Electrochim. Acta 2016, 215, 93−99.

[3] Liu, G.; Weng, W.; Zhang, Z.; Wu, L.; Yang, J.; Yao, X. Densified Li6PS5Cl Nanorods with High Ionic Conductivity and Improved Critical Current Density for All-Solid-State Lithium Batteries. Nano Lett. 2020, 20, 6660−6665.

[4] Alexander V Shapeev. Moment tensor potentials: a class of systematically improvable interatomic potentials. Multiscale Modeling & Simulation, 14(3):1153–1173, 2016.

[5] Yunxing Zuo, Chi Chen, Xiangguo Li, Zhi Deng, Yiming Chen, Jörg Behler, Gábor Csányi, Alexander V. Shapeev, Aidan P. Thompson, Mitchell A. Wood, and Shyue Ping Ong. Performance and cost assessment of machine learning interatomic potentials. The Journal of Physical Chemistry A, 124(4):731–745, 2020. 

[6] Golov, A. & Carrasco, J. Molecular-Level Insight into the Interfacial Reactivity and Ionic Conductivity of a Li-Argyrodite Li₆PS₅Cl Solid Electrolyte at Bare and Coated Li-Metal Anodes. ACS Appl. Mater. Interfaces 13, 43734–43745 (2021).

16. Withdrawn

17. Delta-learning potentials for gas diffusion in metal organic frameworks

Beliz Sertcan*, Vincente Della Balda, Jürg Hutter

The accurate prediction of activation barriers of rare events is limited by the computational cost of high-level quantum chemistry methods. A cost-efficient strategy called delta-learning [1] was proposed that adds machine learned corrections to an inexpensive approximate method, capable of predicting accurate thermochemical properties and electron correlation energies. Therefore, we are working on a model that elevates GFN_1-xTB [3] electronic structure calculations to PBEsol [2] accuracy, to determine barrier energies of noble gas diffusion in a metal organic framework called MFU-4 [4]. 

[1] R. Ramakrishnan, PO. Dral, M. Rupp, OA. vin Lilienfeld, J. Chem. Theory Comput., 11, 2087-209 (2015).
[2] JP. Perdew, A. Ruzsinszky, GI. Csonka, OA. Vydrov, GE. Scuseria, LA. Constantin, X. Zhou, K. Burke, Phys. Rev. Lett., 100, 13, 136406-136409 (2008).
[3] S. Grimme, C. Bannwarth, P. Shushkov, J. Chem. Theory Comput., 13, 1989-2009 (2017).
[4] H. Bunzen, F. Kolbe, A. Kalytta-Mewes, G. Sastre, E. Brunner, D. Volkmer, J. Am. Chem. Soc., 140, 10191-10197 (2018).

18. Non-Local DFT calculations towards the discovery of stable water-splitting catalysts

Akhil S. Nair*, Lucas Foppa, Matthias Scheffler

Efficient prediction of the thermodynamic and aqueous stability of materials is essential for leveraging the catalyst discovery for the water splitting reaction. In particular, the oxygen evolution half-reaction is usually carried out using oxide catalysts under harsh potential and pH conditions.[1] This necessitates the application of DFT methods which can predict the oxide stability under experimentally relevant conditions without any ad hoc corrections.[2] In this regard, herein, we employ a non-local DFT method using the hybrid HSE functional for calculating the stability of oxide catalysts. Crucially, we scrutinize the effect of the HSE mixing parameter on the formation energies and aqueous stability of oxides and compare to higher-level calculations using coupled-cluster theory for reference systems. Through this approach, we attempt to standardize the application of HSE method for accurate oxide stability prediction which could augment the large-scale catalyst discovery.

19. Ab initio modeling and understanding of molecular beam epitaxy growth of Ga₂O₃

Qaem Hassanzada*, Konstantin Lion, Claudia Draxl, Matthias Scheffler

Nowadays, Ga₂O₃ is attracting much attention as a promising candidate for various types of optoelectronic, electronic, and sensing devices, including light-emitting diodes, solar cells, field-effect transistors, photodetectors, and gas sensors [1-4]. Despite the growing importance of this material and the significant advances that have been made in its growth techniques, there is still little theoretical research that can provide answers to the key questions that arise in the growth of Ga₂O₃. Although Ga₂O₃ crystallizes mostly in the monoclinic structure, several polymorphs, including the corundum α-Ga₂O₃ , the defective spinel γ-Ga₂O₃ , the hexagonal ε-Ga₂O₃ , and the orthorhombic κ-Ga₂O₃ have been described [1,4]. Thus, a change in substrate and growth conditions can lead to the appearance of different phases during growth [1]. The atomic-level mechanisms for the stabilization of these different phases are not yet known. For these reasons, it is important to understand the growth processes at the atomic level. In this project, we study the growth of Ga₂O₃ at the most stable surface, β-Ga₂O₃ (100). Using density functional theory (DFT), we investigate all stable adsorption sites for single Ga and O atoms as well as multi-atom clusters at the surface. We find that the stable sites for single atoms adsorbate are drastically different from the stable sites for two-adatom clusters. However, for more than two adatoms, the stable sites are the same as the stable sites for the two-adatom cluster with slight distortions. By calculating the potential energy surface (PES) for Ga and O atoms, we calculate the energy barriers for all possible diffusion paths. Our calculations suggest that Ga adatoms diffuse freely along the a direction without facing a high energy barrier. However, in general, the energy barrier is higher for O than for Ga. Based on the rates derived from the DFT calculations, the growth is finally modeled by the kinetic Monte Carlo method.

[1] S. J. Pearton, J. Yang, P. H. Cary, F. Ren, J. Kim, M. J. Tadjer, and M. A. Mastro, Applied Physics Reviews 5, 011301 (2018)
[2] Z. Galazka, Semiconductor Science and Technology 33, 113001 (2018).
[3] M. Higashiwaki and S. Fujita, Gallium Oxide: Materials Properties, Crystal Growth, and Devices, Springer Series in Materials Science (Springer International Publishing, 2020).
[4] H. von Wenckstern, Advanced Electronic Materials 3, 1600350 (2017)

20. Adaptively Compressed Exchange in LAPW

Davis Zavickis*, Kristians Kacars, Janis Cimurs, Andris Gulans

We address precision and reproducibility issues in DFT calculations with hybrid functionals. Linearized augmented plane waves (LAPW) method currently serves as the de facto reference tool within the electronic structure community. In the current implementation of the Fock exchange in LAPW, the total and band energies depend on the number of orbitals used. We overcome these issues by implementing the adaptively compressed exchange (ACE) method [Lin Lin, J. Chem. Comput., 2016, 12, 5] in exciting code that introduces a low rank approximation and apply it to light atoms, molecules and solids [D. Zavickis et al., Phys. Rev. B., 2022, 106, 165101]. In case of atoms and molecules, we show that ACE leads to highly precise total energies which are within a few microhartrees off the results obtained by multi-resolution analysis method. In solids we calculate band structures that are compared with other all-electron hybrid implementations. Lastly, we apply optimizations and fine tuning to ACE, analyze its complexity and computational performance by comparing it to the previous Fock-exchange implementation in the exciting code.

21. Coulomb potential truncation in electronic structure calculations

Kristians Kacars*, Andris Gulans

Solving Poisson’s equation is a fundamentally important part of electronic structure calculations. The long-range character of the Coulomb potential makes this task non-trivial in a range of applications. It leads to diverging Fock exchange and spurious interactions of periodic images of low-dimensional systems in supercell calculations. We address this problem in the context of linearized augmented plane waves(LAPW), considering two different approaches. In the first of them, we employ a wavelet-based Poisson equation solver from the psolver library. In the second one, we use Coulomb potential truncation schemes. Both approaches are implemented and tested in the LAPW code exciting. We apply and compare these methods for bulk materials and low-dimensional systems in calculations with local and hybrid functionals.

22. Radial Kohn-Sham problem via integral-equation approach

Jānis Užulis*, Andris Gulans

We present a highly precise numerical tool for solving the Kohn-Sham problem for spherically symmetric atoms. It reduces the Schrödinger equation to the screened Poisson equation. The solver is interfaced with the libxc library, and it supports local and hybrid exchange-correlation functionals including screened and long-range corrected hybrids. To consider range-separated exchange, we employ a new approach by approximating the error function kernel as a linear combination of complex exponents. The calculations can be done in non-relativistic case and in the scalar relativistic case within the zero-order regular approximation. We show that our tool achieves up to 14-digit precision for the total energy. We use the solver for generating high precision reference data that can be used for verification of other DFT codes and radial solvers.

23. Crystal-phase engineering of silicene by Sn-modified Ag(111)

F. Orlando*, S. Achilli, G. Fratesi, D.S. Dhungana, C. Grazianetti, C. Martella, A. Molle c

The emergence of graphene on the condensed matter scenario has boosted the search for novel 2D materials termed Xenes, with carbon replaced by other elements but within the same honeycomb structure. Extensive theoretical and experimental effort revealed such materials to feature a variety of structural phases and exotic optoelectronic properties, as well as being amenable to fine tuning and engineering, for instance via coupling to selected substrates and assembling into Xene-Xene interfaces (Van der Waals heterostructures). Silicene – the silicon-based equivalent of graphene – deserves even more special interest in that it should be more easily integrable into existing Si-based technology. First addressed in its ideal freestanding form, it has however attracted the most attention when adsorbed as a thin overlayer on substrates, such as (111) surfaces of FCC metals as well as other 2D crystals. 

Recently, experimental works reporting on functionalizing the silicene/Ag(111) interface highlighted a change in silicene reconstruction upon inserting an entire monolayer of stanene (2D honeycomb Sn) atop the clean Ag substrate, through the intermediate case of a partial-only coverage, resulting in the formation of a surface Ag₂Sn alloy. In such context, we address the stability of various configurations of the Si/Sn/Ag heterostructure from a theoretical perspective, showing via Density Functional Theory numerical simulations how the structural and electronic properties of silicene change depending on the nature of the substrate. We investigate the energy ordering of five different silicene reconstructions, obtaining outcomes in good accord with experiments. Two such reconstructions – namely, a √7 × √7 (matched to a √13 × √13 of Ag) and a 3x3 (matched to a 4x4 of Ag) – emerge as competing in energy on the clean Ag substrate; conversely, single ones are stabilized both on Ag₂Sn (the 3x3 - 4x4) and on Sn/Ag₂Sn (a √3 × √3 of silicene). Our results therefore provide a viable route to suppress the otherwise multiphasic character in the silicene/Ag(111) interface, expected to pose severe constraints on the charge conduction process. 

24. Withdrawn

25. Withdrawn

26. Ab Initio Green-Kubo Calculations for High-Throughput Materials Exploration

Shuo Zhao*, Matthias Scheffler, Christian Carbogno

For accurately assessing vibrational heat transport in strongly anharmonic thermal insulator, ab initio Green-Kubo (aiGK) calculations [1, 2] are the method of choice, since all orders of anharmonicity are accounted for via first-principle molecular dynamics. We herein present a streamlined automatic workflow for high-throughput aiGK calculations that is based on FHI-aims [3] and FHI-vibes. [4] We discuss and demonstrate the proposed workflow by computing the anisotropic thermal conductivity of α-, β-, and κ-Ga₂O₃. Furthermore, we discuss how the proposed workflow can be coupled to artificial-intelligence schemes [5] for high-throughput materials’ space exploration.

References
[1] C. Carbogno, R. Ramprasad, and M. Scheffler, Phys. Rev. Lett. 118, 175901 (2017).
[2] F. Knoop, M. Scheffler, and C. Carbogno, Phys. Rev. B (accepted), arXiv:2209.01139 (2022).
[3] V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, K. Reuter, and M. Scheffler, Comput. Phys. Commun. 180, 2175 (2009).
[4] F. Knoop, T. A. R. Purcell, M. Scheffler, and C. Carbogno, J. Open Source Softw. 5, 2671 (2020).
[5] T. A. R. Purcell, M. Scheffler, L. M. Ghiringhelli, and C. Carbogno, arXiv preprint arXiv:2204.12968 (2022).

27. Data-centeric approach for uncovering rules to describe the CO₂ activation at metal catalysts

Herzain I. Rivera Arrieta*, Lucas Foppa, and Matthias Scheffler

Using CO₂ as a building block in the production of chemicals and fuels requires, in a first step, the activation of this molecule. The materials space is practically infinite, but only a handful of them may enable an effective CO₂ activation. Therefore, this work focuses on the use of artificial intelligence to speed up finding new catalysts for this process. Single-atom alloys (SAA) of transition metals not only provide good model systems, but also show potential as heterogeneous catalysts. Using the mBEEF functional to perform the DFT modeling of the interaction between CO₂ and different surface terminations in Cu-, Zn-, and Pd-based SAA, we generated a dataset including 50 physicochemical parameters characterizing the geometry, and electronic properties of the adsorption sites where the molecule is activated in each material. Then, we applied the subgroup-discovery (SGD) approach to uncover rules correlating key parameters in the SAA with indicators of the CO₂ activation, e.g., a large C−O bond elongation. Having access to these SGD-rules, which only depend on the material, allows a fast screening and prediction of potentially effective catalysts.

28. Identifying materials genes describing selectivity of catalytic CO₂ hydrogenation: an AI approach with theoretical and experimental data

Ray Miyazaki*, Kendra Belthle, Harun Tuysuz, Lucas Foppa, and Matthias Scheffler

Investigating CO₂ hydrogenation by heterogeneous catalysis that mimics hydrothermal vents leads to a deeper understanding of the origin of organic molecules at the early earth [1]. We focus on cobalt nanoparticles supported on M-SiO₂ where hetero atoms (e.g., Ti or Al) are incorporated into SiO₂. However, heterogeneous catalysis is governed by an intricate interplay among multi-scale processes. Thus, it is rather difficult, if not impossible, to identify the key physical parameters correlated with the catalytic performance (materials genes) directly by theoretical or experimental approaches. In this study, materials properties obtained from density functional theory calculations and experiments, such as adsorption energy of CO₂ and measured pore volume, are used to model the experimental selectivity of each organic molecule (e.g., CH₃OH, CH₄) by the sure-independence screening and sparsifying operator (SISSO) AI approach [2]. In order to accelerate catalyst design, we also investigate the accuracy of the models using input parameter sets with the different acquisition cost.

[1] K. S. Belthle et al., J. Am. Chem. Soc., 144, 21232–21243 (2022).
[2] R. Ouyang et al., Phys. Rev. Mater., 2, 083802 (2018).