First-Principles Approach for Coupled Quantum Dynamics of Electrons and Protons in Heterogeneous Systems

The coupled quantum dynamics of electrons and protons is ubiquitous in many dynamical processes involving light-matter interaction, such as solar energy conversion in chemical systems and photosynthesis. A first-principles description of such nuclear-electronic quantum dynamics requires not only the time-dependent treatment of nonequilibrium electron dynamics but also that of quantum protons. Quantum mechanical correlation between electrons and protons adds further complexity to such coupled dynamics. Here we extend real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) to periodic systems and perform first-principles simulations of coupled quantum dynamics of electrons and protons in complex heterogeneous systems. The process studied is an electronically excited-state intramolecular proton transfer of o-hydroxybenzaldehyde in water and at a silicon (111) semiconductor-molecule interface. These simulations illustrate how environments such as hydrogen-bonding water molecules and an extended material surface impact the dynamical process on the atomistic level. Depending on how the molecule is chemisorbed on the surface, excited-state electron transfer from the molecule to the semiconductor surface can inhibit ultrafast proton transfer within the molecule. This Letter elucidates how heterogeneous environments influence the balance between the quantum mechanical proton transfer and excited electron dynamics. The periodic RT-NEO-TDDFT approach is applicable to a wide range of other photoinduced heterogeneous processes.

Thickness control of organic semiconductor-incorporated perovskites

Two-dimensional organic semiconductor-incorporated perovskites are a promising family of hybrid materials for optoelectronic applications, owing in part to their inherent quantum well architecture. Tuning their structures and properties for specific properties, however, has remained challenging. Here we report a general method to tune the dimensionality of phase-pure organic semiconductor-incorporated perovskite single crystals during their synthesis, by judicious choice of solvent. The length of the conjugated semiconducting organic cations and the dimensionality (n value) of the inorganic layers can be manipulated at the same time. The energy band offsets and exciton dynamics at the organic-inorganic interfaces can therefore be precisely controlled. Furthermore, we show that longer and more planar π-conjugated organic cations induce a more rigid inorganic crystal lattice, which leads to suppressed exciton-phonon interactions and better optoelectronic properties as compared to conventional two-dimensional perovskites. As a demonstration, optically driven lasing behaviour with substantially lower lasing thresholds was realized.

Chiral Cation Doping for Modulating Structural Symmetry of 2D Perovskites

Cation mixing in two-dimensional (2D) hybrid organic-inorganic perovskite (HOIP) structures represents an important degree of freedom for modifying organic templating effects and tailoring inorganic structures. However, the limited number of known cation-mixed 2D HOIP systems generally employ a 1:1 cation ratio for stabilizing the 2D perovskite structure. Here, we demonstrate a chiral-chiral mixed-cation system wherein a controlled small amount (<10%) of chiral cation S-2-MeBA (S-2-MeBA = (S)-(-)-2-methylbutylammonium) can be doped into (S-BrMBA)2PbI4 (S-BrMBA = (S)-(-)-4-bromo-α-methylbenzylammonium), modulating the structural symmetry from a higher symmetry (C2) to the lowest symmetry state (P1). This structural change occurs when the concentration of S-2-MeBA, measured by solution nuclear magnetic resonance, exceeds a critical level─specifically, for 1.4 ± 0.6%, the structure remains as C2, whereas 3.9 ± 1.4% substitution induces the structure change to P1 (this structure is stable to ∼7% substitution). Atomic occupancy analysis suggests that one specific S-BrMBA cation site is preferentially substituted by S-2-MeBA in the unit cell. Density functional theory calculations indicate that the spin splitting along different k-paths can be modulated by cation doping. A true circular dichroism band at the exciton energy of the 3.9% doping phase shows polarity inversion and a ∼45 meV blue shift of the Cotton-effect-type line-shape relative to (S-BrMBA)2PbI4. A trend toward suppressed melting temperature with higher doping concentration is also noted. The chiral cation doping system and the associated doping-concentration-induced structural transition provide a material design strategy for modulating and enhancing those emergent properties that are sensitive to different types of symmetry breaking.

Metal Halide Perovskite Heterostructures: Blocking Anion Diffusion with Single-Layer Graphene

The development of metal halide perovskite/perovskite heterostructures is hindered by rapid interfacial halide diffusion leading to mixed alloys rather than sharp interfaces. To circumvent this outcome, we developed an ion-blocking layer consisting of single-layer graphene (SLG) deposited between the metal halide perovskite layers and demonstrated that it effectively blocks anion diffusion in a CsPbBr₃/SLG/CsPbI₃ heterostructure. Spatially resolved elemental analysis and spectroscopic measurements demonstrate the halides do not diffuse across the interface, whereas control samples without the SLG show rapid homogenization of the halides and loss of the sharp interface. Ultraviolet photoelectron spectroscopy, DFT calculations, and transient absorbance spectroscopy indicate the SLG has little electronic impact on the individual semiconductors. In the CsPbBr₃/SLG/CsPbI₃, we find a type I band alignment that supports transfer of photogenerated carriers across the heterointerface. Light-emitting diodes (LEDs) show electroluminescence from both the CsPbBr₃ and CsPbI₃ layers with no evidence of ion diffusion during operation. Our approach provides opportunities to design novel all-perovskite heterostructures to facilitate the control of charge and light in optoelectronic applications.

Large Scale Quantum Chemistry with Tensor Processing Units

We demonstrate the use of Googles cloud-based Tensor Processing Units (TPUs) to accelerate and scale up conventional (cubic-scaling) density functional theory (DFT) calculations. Utilizing 512 TPU cores, we accomplish the largest such DFT computation to date, with 247848 orbitals, corresponding to a cluster of 10327 water molecules with 103270 electrons, all treated explicitly. Our work thus paves the way toward accessible and systematic use of conventional DFT, free of any system-specific constraints, at unprecedented scales.

Exact constraints and appropriate norms in machine learned exchange-correlation functionals

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to deorbitalize the strongly constrained and appropriately normed (SCAN) functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding use of the orbital dependent kinetic energy density. The performance and transferability of the machine learned functional are demonstrated for molecular and periodic systems.

Localized Resolution of Identity Approach to the Analytical Gradients of Random-Phase Approximation Ground-State Energy: Algorithm and Benchmarks

We develop and implement a formalism which enables calculating the analytical gradients of particle-hole random-phase approximation (RPA) ground-state energy with respect to the atomic positions within the atomic orbital basis set framework. Our approach is based on a localized resolution of identity (LRI) approximation for evaluating the two-electron Coulomb integrals and their derivatives, and the density functional perturbation theory for computing the first-order derivatives of the Kohn-Sham (KS) orbitals and orbital energies. Our implementation allows one to relax molecular structures at the RPA level using both Gaussian-type orbitals (GTOs) and numerical atomic orbitals (NAOs). Benchmark calculations against previous implementations show that our approach delivers adequate numerical precision, highlighting the usefulness of LRI in the context of RPA gradient evaluations. A careful assessment of the quality of RPA geometries for small molecules reveals that post-KS RPA systematically overestimates the bond lengths. We furthermore optimized the geometries of the four low-lying water hexamers-cage, prism, cyclic, and book isomers, and determined the energy hierarchy of these four isomers using RPA. The obtained RPA energy ordering is in good agreement with that yielded by the coupled cluster method with single, double and perturbative triple excitations, despite that the dissociation energies themselves are appreciably underestimated. The underestimation of the dissociation energies by RPA is well corrected by the renormalized single excitation correction.

Kinetically Controlled Structural Transitions in Layered Halide-Based Perovskites: An Approach to Modulate Spin Splitting

Two-dimensional hybrid organic-inorganic perovskite (HOIP) semiconductors with pronounced spin splitting, mediated by strong spin-orbit coupling and inversion symmetry breaking, offer the potential for spin manipulation in future spintronic applications. However, HOIPs exhibiting significant conduction/valence band splitting are still relatively rare, given the generally observed preference for (near)centrosymmetric inorganic (especially lead-iodide-based) sublattices, and few approaches are available to control this symmetry breaking within a given HOIP. Here, we demonstrate, using (S-2-MeBA)₂PbI₄ (S-2-MeBA = (S)-(-)-2-methylbutylammonium) as an example, that a temperature-induced structural transition (at ∼180 K) serves to change the degree of chirality transfer to and inversion symmetry breaking within the inorganic layer, thereby enabling modulation of HOIP structural and electronic properties. The cooling rate is shown to dictate whether the structural transition occurs─i.e., slow cooling induces the transition while rapid quenching inhibits it. Ultrafast calorimetry indicates a minute-scale structural relaxation time at the transition temperature, while quenching to lower temperatures allows for effectively locking in the metastable room-temperature phase, thus enabling kinetic control over switching between distinct states with different degrees of structural distortions within the inorganic layers at these temperatures. Density functional theory further highlights that the low-temperature phase of (S-2-MeBA)₂PbI₄ shows more significant spin splitting relative to the room-temperature phase. Our work opens a new pathway to use kinetic control of crystal-to-crystal transitions and thermal cycling to modulate spin splitting in HOIPs for future spintronic applications, and further points to using such "sluggish" phase transitions for switching and control over other physical phenomena, particularly those relying on structural distortions and lattice symmetry.

Nuclear-Electronic Orbital Approach to Quantization of Protons in Periodic Electronic Structure Calculations

The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the NEO method for periodic electronic structure calculations, particularly focused on multicomponent density functional theory (DFT). The NEO-DFT method is implemented in an all-electron electronic structure code, FHI-aims, using a combination of analytical and numerical integration techniques as well as a resolution of the identity scheme to enhance computational efficiency. After validating this implementation, proof-of-concept applications are presented to illustrate the effects of quantized protons on the physical properties of extended systems such as two-dimensional materials and liquid-semiconductor interfaces. Specifically, periodic NEO-DFT calculations are performed for a trans-polyacetylene chain, a hydrogen boride sheet, and a titanium oxide-water interface. The zero-point energy effects of the protons, as well as electron-proton correlation, are shown to noticeably impact the density of states and band structures for these systems. These developments provide a foundation for the application of multicomponent DFT to a wide range of other extended condensed matter systems.

All-Electron BSE@GW Method for K-Edge Core Electron Excitation Energies

We present an accurate computational approach to calculate absolute K-edge core electron excitation energies as measured by X-ray absorption spectroscopy. Our approach employs an all-electron Bethe-Salpeter equation (BSE) formalism based on GW quasiparticle energies (BSE@GW) using numeric atom-centered orbitals (NAOs). The BSE@GW method has become an increasingly popular method for the computation of neutral valence excitation energies of molecules. However, it was so far not applied to molecular K-edge excitation energies. We discuss the influence of different numerical approximations on the BSE@GW calculation and employ in our final setup (i) exact numeric algorithms for the frequency integration of the GW self-energy, (ii) G₀W₀ and BSE starting points with ∼50% of exact exchange, (iii) the Tamm-Dancoff approximation and (iv) relativistic corrections. We study the basis set dependence and convergence with common Gaussian-type orbital and NAO basis sets. We identify the importance of additional spatially confined basis functions as well as of diffuse augmenting basis functions. The accuracy of our BSE@GW method is assessed for a benchmark set of small organic molecules, previously used for benchmarking the equation-of-motion coupled cluster method [Peng et al., J. Chem. Theory Comput., 2015, 11, 4146], as well as the medium-sized dibenzothiophene (DBT) molecule. Our BSE@GW results for absolute excitation energies are in excellent agreement with the experiment, with a mean average error of only 0.63 eV for the benchmark set and with errors <1 eV for the DBT molecule.

Cubic Crystal Structure Formation and Optical Properties within the Ag-BII-MIV-X (BII = Sr, Pb; MIV = Si, Ge, Sn; X = S, Se) Family of Semiconductors

Quaternary chalcogenide semiconductors are promising materials for energy conversion and nonlinear optical applications, with properties tunable primarily by varying the elemental composition and crystal structure. Here, we first analyze the connections among several cubic crystal structure types, as well as the orthorhombic Ag₂PbGeS₄-type structure, reported for select members within the Ag-B^II-M^IV-X (B^II = Sr, Pb; M^IV = Si, Ge, Sn; X = S, Se) compositional space. Focusing on the Ag-Pb-Si-S and Ag-Sr-Sn-S systems, we show that one structure type, with the formulas Ag₂Pb₃Si₂S₈ and Ag₂Sr₃Sn₂S₈, is favored. We have prepared powder and single-crystal samples of Ag₂Pb₃Si₂S₈ and Ag₂Sr₃Sn₂S₈, showing that each takes on the noncentrosymmetric cubic space group I4̅3d and is isostructural to the previously reported compound Ag₂Sr₃Ge₂Se₈. Through hybrid density functional theory calculations, these cubic compounds are demonstrated to be (quasi-)direct band gap semiconductors with high densities of states at the band maxima. The band-gap energies are measured by reflectance spectroscopy as 1.95(3) and 2.66(4) eV for Ag₂Pb₃Si₂S₈ and Ag₂Sr₃Sn₂S₈, respectively. We further measure the optical properties and show the electronic band structures of three other isostructural A^I-B^II-M^IV-X-type materials, i.e., Ag₂Sr₃Si₂S₈, Ag₂Sr₃Ge₂S₈, and Ag₂Sr₃Ge₂Se₈, showing that the band gaps can be predictably tuned by element substitution. Detailed visual analyses of the different structures and of their relationships with other members of the Ag-B^II-M^IV-X compositional family provide a basis for a broader understanding of the structure formation and optoelectronic properties within the quaternary chalcogenide semiconductor family.

On the optical anisotropy in 2D metal-halide perovskites

Two-dimensional metal-halide perovskites (MHPs) are versatile solution-processed organic/inorganic quantum wells where the structural anisotropy creates profound anisotropy in their electronic and excitonic properties and associated optical constants. We here employ a wholistic framework, based on semiempirical modeling (k·p/effective mass theory calculations) informed by hybrid density functional theory (DFT) and multimodal spectroscopic ellipsometry on (C₆H₅(CH₂)₂NH₃)₂PbI₄ films and crystals, that allows us to link the observed optical properties and anisotropy precisely to the underlying physical parameters that shape the electronic structure of a layered MHP. We find substantial frequency-dependent anisotropy in the optical constants and close correspondence between experiment and theory, demonstrating a high degree of in-plane alignment of the two-dimensional planes in both spin-coated thin films and cleaved single crystals made in this study. Hybrid DFT results elucidate the degree to which organic and inorganic frontier orbitals contribute to optical transitions polarized along a particular axis. The combined experimental and theoretical approach enables us to estimate the fundamental electronic bandgap of 2.65-2.68 eV in this prototypical 2D perovskite and to determine the spin-orbit coupling (Δ_SO = 1.20 eV) and effective crystal field (δ = -1.36 eV) which break the degeneracy of the frontier conduction band states and determine the exciton fine structure. The methods and results described here afford a better understanding of the connection between structure and induced optical anisotropy in quantum-confined MHPs, an important structure-property relationship for optoelectronic applications and devices.

All-electron real-time and imaginary-time time-dependent density functional theory within a numeric atom-centered basis function framework

Real-time time-dependent density functional theory (RT-TDDFT) is an attractive tool to model quantum dynamics by real-time propagation without the linear response approximation. Sharing the same technical framework of RT-TDDFT, imaginary-time time-dependent density functional theory (it-TDDFT) is a recently developed robust-convergence ground state method. Presented here are high-precision all-electron RT-TDDFT and it-TDDFT implementations within a numerical atom-centered orbital (NAO) basis function framework in the FHI-aims code. We discuss the theoretical background and technical choices in our implementation. First, RT-TDDFT results are validated against linear-response TDDFT results. Specifically, we analyze the NAO basis sets' convergence for Thiel's test set of small molecules and confirm the importance of the augmentation basis functions for adequate convergence. Adopting a velocity-gauge formalism, we next demonstrate applications for systems with periodic boundary conditions. Taking advantage of the all-electron full-potential implementation, we present applications for core level spectra. For it-TDDFT, we confirm that within the all-electron NAO formalism, it-TDDFT can successfully converge systems that are difficult to converge in the standard self-consistent field method. We finally benchmark our implementation for systems up to ∼500 atoms. The implementation exhibits almost linear weak and strong scaling behavior.

Density Functional Theory Study of Reaction Equilibria in Signal Amplification by Reversible Exchange

The front cover artwork is provided by the groups of Prof. Thomas Theis (North Carolina State University) Prof. Volker Blum (Duke University). The image shows the reaction network of Signal Amplification by Reversible Exchange (SABRE), elucidated by density functional theory (DFT). Read the full text of the Review at 10.1002/cphc.202100204.

Density Functional Theory Study of Reaction Equilibria in Signal Amplification by Reversible Exchange

An in-depth theoretical analysis of key chemical equilibria in Signal Amplification by Reversible Exchange (SABRE) is provided, employing density functional theory calculations to characterize the likely reaction network. For all reactions in the network, the potential energy surface is probed to identify minimum energy pathways. Energy barriers and transition states are calculated, and harmonic transition state theory is applied to calculate exchange rates that approximate experimental values. The reaction network energy surface can be modulated by chemical potentials that account for the dependence on concentration, temperature, and partial pressure of molecular constituents (hydrogen, methanol, pyridine) supplied to the experiment under equilibrium conditions. We show that, under typical experimental conditions, the Gibbs free energies of the two key states involved in pyridine-hydrogen exchange at the common Ir-IMes catalyst system in methanol are essentially the same, i. e., nearly optimal for SABRE. We also show that a methanol-containing intermediate is plausible as a transient species in the process.

Structural descriptor for enhanced spin-splitting in 2D hybrid perovskites

Two-dimensional (2D) hybrid metal halide perovskites have emerged as outstanding optoelectronic materials and are potential hosts of Rashba/Dresselhaus spin-splitting for spin-selective transport and spin-orbitronics. However, a quantitative microscopic understanding of what controls the spin-splitting magnitude is generally lacking. Through crystallographic and first-principles studies on a broad array of chiral and achiral 2D perovskites, we demonstrate that a specific bond angle disparity connected with asymmetric tilting distortions of the metal halide octahedra breaks local inversion symmetry and strongly correlates with computed spin-splitting. This distortion metric can serve as a crystallographic descriptor for rapid discovery of potential candidate materials with strong spin-splitting. Our work establishes that, rather than the global space group, local inorganic layer distortions induced via appropriate organic cations provide a key design objective to achieve strong spin-splitting in perovskites. New chiral perovskites reported here couple a sizeable spin-splitting with chiral degrees of freedom and offer a unique paradigm of potential interest for spintronics.

Structural, Optical, and Electronic Properties of Two Quaternary Chalcogenide Semiconductors: Ag2SrSiS4 and Ag2SrGeS4

Quaternary chalcogenide materials have long been a source of semiconductors for optoelectronic applications. Recent studies on I₂-II-IV-X₄ (I = Ag, Cu, Li; II = Ba, Sr, Eu, Pb; IV = Si, Ge, Sn; X = S, Se) materials have shown particular versatility and promise among these compounds. These semiconductors take advantage of a diverse bonding scheme and chemical differences among cations to target a degree of antisite defect resistance. Within this set of compounds, the materials containing both Ag and Sr have not been experimentally studied and leave a gap in the full understanding of the family. Here, we have synthesized powders and single crystals of two Ag- and Sr-containing compounds, Ag₂SrSiS₄ and Ag₂SrGeS₄, each found to form in the tetragonal I4̅2m structure of Ag₂BaGeS₄. During the synthesis targeting the title compounds, two additional materials, Ag₂Sr₃Si₂S₈ and Ag₂Sr₃Ge₂S₈, have also been identified. These cubic compounds represent impurity phases during the synthesis of Ag₂SrSiS₄ and Ag₂SrGeS₄. We show through hybrid density functional theory calculations that Ag₂SrSiS₄ and Ag₂SrGeS₄ have highly dispersive band-edge states and indirect band gaps, experimentally measured as 2.08(1) and 1.73(2) eV, respectively. Second-harmonic generation measurements on Ag₂SrSiS₄ and Ag₂SrGeS₄ powders show frequency-doubling capabilities in the near-infrared range.

Accurate frozen core approximation for all-electron density-functional theory

We implement and benchmark the frozen core approximation, a technique commonly adopted in electronic structure theory to reduce the computational cost by means of mathematically fixing the chemically inactive core electron states. The accuracy and efficiency of this approach are well controlled by a single parameter, the number of frozen orbitals. Explicit corrections for the frozen core orbitals and the unfrozen valence orbitals are introduced, safeguarding against seemingly minor numerical deviations from the assumed orthonormality conditions of the basis functions. A speedup of over twofold can be achieved for the diagonalization step in all-electron density-functional theory simulations containing heavy elements, without any accuracy degradation in terms of the electron density, total energy, and atomic forces. This is demonstrated in a benchmark study covering 103 materials across the Periodic Table and a large-scale simulation of CsPbBr₃ with 2560 atoms. Our study provides a rigorous benchmark of the precision of the frozen core approximation (sub-meV per atom for frozen core orbitals below -200 eV) for a wide range of test cases and for chemical elements ranging from Li to Po. The algorithms discussed here are implemented in the open-source Electronic Structure Infrastructure software package.

Mechanism of Additive-Assisted Room-Temperature Processing of Metal Halide Perovskite Thin Films

Perovskite solar cells have received substantial attention due to their potential for low-cost photovoltaic devices on flexible or rigid substrates. Thiocyanate (SCN)-containing additives, such as MASCN (MA = methylammonium), have been shown to control perovskite film crystallization and the film microstructure to achieve effective room-temperature perovskite absorber processing. Nevertheless, the crystallization pathways and mechanisms of perovskite formation involved in MASCN additive processing are far from clear. Using in situ X-ray diffraction and photoluminescence, we investigate the crystallization pathways of MAPbI₃ and reveal the mechanisms of additive-assisted perovskite formation during spin coating and subsequent N₂ drying. We confirm that MASCN induces large precursor aggregates in solution and, during spin coating, promotes the formation of the perovskite phase with lower nucleation density and overall larger initial nuclei size, which forms upon reaching supersaturation in solution, in addition to intermediate solvent-complex phases. Finally, during the subsequent N₂ drying, MASCN facilitates the dissociation of these precursor aggregates and the solvate phases, leading to further growth of the perovskite crystals. Our results show that the nature of the intermediate phases and their formation/dissociation kinetics determine the nucleation and growth of the perovskite phase, which subsequently impact the film microstructure. These findings provide mechanistic insights underlying room-temperature, additive-assisted perovskite processing and help guide further development of such facile room-temperature synthesis routes.

Organic-to-inorganic structural chirality transfer in a 2D hybrid perovskite and impact on Rashba-Dresselhaus spin-orbit coupling

Translation of chirality and asymmetry across structural motifs and length scales plays a fundamental role in nature, enabling unique functionalities in contexts ranging from biological systems to synthetic materials. Here, we introduce a structural chirality transfer across the organic-inorganic interface in two-dimensional hybrid perovskites using appropriate chiral organic cations. The preferred molecular configuration of the chiral spacer cations, R-(+)- or S-(-)-1-(1-naphthyl)ethylammonium and their asymmetric hydrogen-bonding interactions with lead bromide-based layers cause symmetry-breaking helical distortions in the inorganic layers, otherwise absent when employing a racemic mixture of organic spacers. First-principles modeling predicts a substantial bulk Rashba-Dresselhaus spin-splitting in the inorganic-derived conduction band with opposite spin textures between R- and S-hybrids due to the broken inversion symmetry and strong spin-orbit coupling. The ability to break symmetry using chirality transfer from one structural unit to another provides a synthetic design paradigm for emergent properties, including Rashba-Dresselhaus spin-polarization for hybrid perovskite spintronics and related applications.

Rational ligand choice extends the SABRE substrate scope

Here we report on chelating ligands for Signal Amplification By Reversible Exchange (SABRE) catalysts that permit hyperpolarisation on otherwise sterically hindered substrates. We demonstrate 1H enhancements of ∼100-fold over 8.5 T thermal for 2-substituted pyridines, and smaller, yet significant enhancements for provitamin B6 and caffeine. We also show 15N-enhancements of ∼1000-fold and 19F-enhancements of 30-fold.

The CECAM electronic structure library and the modular software development paradigm

First-principles electronic structure calculations are now accessible to a very large community of users across many disciplines, thanks to many successful software packages, some of which are described in this special issue. The traditional coding paradigm for such packages is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, essentially from the compiler up, possibly with the exception of linear-algebra and message-passing libraries. This model has endured and been quite successful for decades. The successful evolution of the electronic structure methodology itself, however, has resulted in an increasing complexity and an ever longer list of features expected within all software packages, which implies a growing amount of replication between different packages, not only in the initial coding but, more importantly, every time a code needs to be re-engineered to adapt to the evolution of computer hardware architecture. The Electronic Structure Library (ESL) was initiated by CECAM (the European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure codes and redesign them as open-source libraries available to everybody. Such libraries include "heavy-duty" ones that have the potential for a high degree of parallelization and adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by, e.g., physicists and chemists when implementing new ideas. We envisage that this modular paradigm will improve overall coding efficiency and enable specialists (whether they be computer scientists or computational scientists) to use their skills more effectively and will lead to a more dynamic evolution of software in the community as well as lower barriers to entry for new developers. The model comes with new challenges, though. The building and compilation of a code based on many interdependent libraries (and their versions) is a much more complex task than that of a code delivered in a single self-contained package. Here, we describe the state of the ESL, the different libraries it now contains, the short- and mid-term plans for further libraries, and the way the new challenges are faced. The ESL is a community initiative into which several pre-existing codes and their developers have contributed with their software and efforts, from which several codes are already benefiting, and which remains open to the community.

Frenkel-Holstein Hamiltonian applied to absorption spectra of quaterthiophene-based 2D hybrid organic-inorganic perovskites

For the prototypical two-dimensional hybrid organic-inorganic perovskites (2D HOIPs) (AE4T)PbX₄ (X = Cl, Br, and I), we demonstrate that the Frenkel-Holstein Hamiltonian (FHH) can be applied to describe the absorption spectrum arising from the organic component. We first model the spectra using only the four nearest neighbor couplings between translationally inequivalent molecules in the organic herringbone lattice as fitting parameters in the FHH. We next use linear-response time-dependent density functional theory (LR-TDDFT) to calculate molecular transition densities, from which extended excitonic couplings are evaluated based on the atomic positions within the 2D HOIPs. We find that both approaches reproduce the experimentally observed spectra, including changes in their shape and peak positions. The spectral changes are correlated with a decrease in excitonic coupling from X = Cl to X = I. Importantly, the LR-TDDFT-based approach with extended excitonic couplings not only gives better agreement with the experimental absorption line shape than the approach using a restricted set of fitted parameters but also allows us to relate the changes in excitonic coupling to the underlying geometry. We accordingly find that the decrease in excitonic coupling from X = Cl to Br to I is due to an increase in molecular separation, which in turn can be related to the increasing Pb-X bond length from Cl to I. Our research opens up a potential pathway to predicting optoelectronic properties of new 2D HOIPs from ab initio calculations and to gain insight into structural relations from 2D HOIP absorption spectra.

DFTB+, a software package for efficient approximate density functional theory based atomistic simulations

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green's functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives.

Tunable Semiconductors: Control over Carrier States and Excitations in Layered Hybrid Organic-Inorganic Perovskites

For a class of 2D hybrid organic-inorganic perovskite semiconductors based on π-conjugated organic cations, we predict quantitatively how varying the organic and inorganic component allows control over the nature, energy, and localization of carrier states in a quantum-well-like fashion. Our first-principles predictions, based on large-scale hybrid density-functional theory with spin-orbit coupling, show that the interface between the organic and inorganic parts within a single hybrid can be modulated systematically, enabling us to select between different type-I and type-II energy level alignments. Energy levels, recombination properties, and transport behavior of electrons and holes thus become tunable by choosing specific organic functionalizations and juxtaposing them with suitable inorganic components.

Efficient Implicit Solvation Method for Full Potential DFT

With the advent of efficient electronic structure methods, effective continuum solvation methods have emerged as a way to, at least partially, include solvent effects into simulations without the need for expensive sampling over solvent degrees of freedom. The multipole moment expansion (MPE) model, while based on ideas initially put forward almost 100 years ago, has recently been updated for the needs of modern electronic structure calculations. Indeed, for an all-electron code relying on localized basis sets and-more importantly-a multipole moment expansion of the electrostatic potential, the MPE method presents a particularly cheap way of solving the macroscopic Poisson equation to determine the electrostatic response of a medium surrounding a solute. In addition to our implementation of the MPE model in the FHI-aims electronic structure theory code [ Blum , V. ; Comput. Phys. Commun. 2009 , 180 , 2175 - 2196 , DOI: 10.1016/j.cpc.2009.06.022 ], we describe novel algorithms for determining equidistributed points on the solvation cavity-defined as a charge density isosurface-and the determination of cavity surface and volume from just this collection of points and their local density gradients. We demonstrate the efficacy of our model on an analytically solvable test case, against high-accuracy finite-element calculations for a set of ≈140000 2D test cases, and finally against experimental solvation free energies of a number of neutral and singly charged molecular test sets [ Andreussi , O. ; J. Chem. Phys. 2012 , 136 , 064102 , DOI: 10.1063/1.3676407 ; Marenich , A. V. ; Minnesota Solvation Database , Version 2012; University of Minnesota : Minneapolis, MN, USA , 2012 . ]. In all test cases we find that our MPE approach compares very well with given references at computational overheads < 20% and sometimes much smaller compared to a plain self-consistency cycle.

Long-Lived 13C2 Nuclear Spin States Hyperpolarized by Parahydrogen in Reversible Exchange at Microtesla Fields

Parahydrogen is an inexpensive and readily available source of hyperpolarization used to enhance magnetic resonance signals by up to four orders of magnitude above thermal signals obtained at ∼10 T. A significant challenge for applications is fast signal decay after hyperpolarization. Here we use parahydrogen-based polarization transfer catalysis at microtesla fields (first introduced as SABRE-SHEATH) to hyperpolarize ¹³C₂ spin pairs and find decay time constants of 12 s for magnetization at 0.3 mT, which are extended to 2 min at that same field, when long-lived singlet states are hyperpolarized instead. Enhancements over thermal at 8.5 T are between 30 and 170 fold (0.02 to 0.12% polarization). We control the spin dynamics of polarization transfer by choice of microtesla field, allowing for deliberate hyperpolarization of either magnetization or long-lived singlet states. Density functional theory calculations and experimental evidence identify two energetically close mechanisms for polarization transfer: First, a model that involves direct binding of the ¹³C₂ pair to the polarization transfer catalyst and, second, a model transferring polarization through auxiliary protons in substrates.

Earth-Abundant Chalcogenide Photovoltaic Devices with over 5% Efficiency Based on a Cu2 BaSn(S,Se)4 Absorber

In recent years, Cu₂ ZnSn(S,Se)₄ (CZTSSe) materials have enabled important progress in associated thin-film photovoltaic (PV) technology, while avoiding scarce and/or toxic metals; however, cationic disorder and associated band tailing fundamentally limit device performance. Cu₂ BaSnS₄ (CBTS) has recently been proposed as a prospective alternative large bandgap (~2 eV), environmentally friendly PV material, with ~2% power conversion efficiency (PCE) already demonstrated in corresponding devices. In this study, a two-step process (i.e., precursor sputter deposition followed by successive sulfurization/selenization) yields high-quality nominally pinhole-free films with large (>1 µm) grains of selenium-incorporated (x = 3) Cu₂ BaSnS_4-x Se_x (CBTSSe) for high-efficiency PV devices. By incorporating Se in the sulfide film, absorber layers with 1.55 eV bandgap, ideal for single-junction PV, have been achieved within the CBTSSe trigonal structural family. The abrupt transition in quantum efficiency data for wavelengths above the absorption edge, coupled with a strong sharp photoluminescence feature, confirms the relative absence of band tailing in CBTSSe compared to CZTSSe. For the first time, by combining bandgap tuning with an air-annealing step, a CBTSSe-based PV device with 5.2% PCE (total area 0.425 cm² ) is reported, >2.5× better than the previous champion pure sulfide device. These results suggest substantial promise for the emerging Se-rich Cu₂ BaSnS_4-x Se_x family for high-efficiency and earth-abundant PV.

The Elephant in the Room of Density Functional Theory Calculations

Using multiwavelets, we have obtained total energies and corresponding atomization energies for the GGA-PBE and hybrid-PBE0 density functionals for a test set of 211 molecules with an unprecedented and guaranteed μHartree accuracy. These quasi-exact references allow us to quantify the accuracy of standard all-electron basis sets that are believed to be highly accurate for molecules, such as Gaussian-type orbitals (GTOs), all-electron numeric atom-centered orbitals (NAOs), and full-potential augmented plane wave (APW) methods. We show that NAOs are able to achieve the so-called chemical accuracy (1 kcal/mol) for the typical basis set sizes used in applications, for both total and atomization energies. For GTOs, a triple-ζ quality basis has mean errors of ∼10 kcal/mol in total energies, while chemical accuracy is almost reached for a quintuple-ζ basis. Due to systematic error cancellations, atomization energy errors are reduced by almost an order of magnitude, placing chemical accuracy within reach also for medium to large GTO bases, albeit with significant outliers. In order to check the accuracy of the computed densities, we have also investigated the dipole moments, where in general only the largest NAO and GTO bases are able to yield errors below 0.01 D. The observed errors are similar across the different functionals considered here.

Trends for isolated amino acids and dipeptides: Conformation, divalent ion binding, and remarkable similarity of binding to calcium and lead

We derive structural and binding energy trends for twenty amino acids, their dipeptides, and their interactions with the divalent cations Ca2+, Ba2+, Sr2+, Cd2+, Pb2+, and Hg2+. The underlying data set consists of more than 45,000 first-principles predicted conformers with relative energies up to ~4 eV (~400 kJ/mol). We show that only very few distinct backbone structures of isolated amino acids and their dipeptides emerge as lowest-energy conformers. The isolated amino acids predominantly adopt structures that involve an acidic proton shared between the carboxy and amino function. Dipeptides adopt one of two intramolecular-hydrogen bonded conformations C5 or . Upon complexation with a divalent cation, the accessible conformational space shrinks and intramolecular hydrogen bonding is prevented due to strong electrostatic interaction of backbone and side chain functional groups with cations. Clear correlations emerge from the binding energies of the six divalent ions with amino acids and dipeptides. Cd2+ and Hg2+ show the largest binding energies-a potential correlation with their known high acute toxicities. Ca2+ and Pb2+ reveal almost identical binding energies across the entire series of amino acids and dipeptides. This observation validates past indications that ion-mimicry of calcium and lead should play an important role in a toxicological context.

Quantitative Subsurface Atomic Structure Fingerprint for 2D Materials and Heterostructures by First-Principles-Calibrated Contact-Resonance Atomic Force Microscopy

Interfaces and subsurface layers are critical for the performance of devices made of 2D materials and heterostructures. Facile, nondestructive, and quantitative ways to characterize the structure of atomically thin, layered materials are thus essential to ensure control of the resultant properties. Here, we show that contact-resonance atomic force microscopy-which is exquisitely sensitive to stiffness changes that arise from even a single atomic layer of a van der Waals-adhered material-is a powerful experimental tool to address this challenge. A combined density functional theory and continuum modeling approach is introduced that yields sub-surface-sensitive, nanomechanical fingerprints associated with specific, well-defined structure models of individual surface domains. Where such models are known, this information can be correlated with experimentally obtained contact-resonance frequency maps to reveal the (sub)surface structure of different domains on the sample.

Reproducibility in density functional theory calculations of solids

The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements.

Direct and cost-efficient hyperpolarization of long-lived nuclear spin states on universal (15)N2-diazirine molecular tags

Conventional magnetic resonance (MR) faces serious sensitivity limitations which can be overcome by hyperpolarization methods, but the most common method (dynamic nuclear polarization) is complex and expensive, and applications are limited by short spin lifetimes (typically seconds) of biologically relevant molecules. We use a recently developed method, SABRE-SHEATH, to directly hyperpolarize (15)N2 magnetization and long-lived (15)N2 singlet spin order, with signal decay time constants of 5.8 and 23 minutes, respectively. We find >10,000-fold enhancements generating detectable nuclear MR signals that last for over an hour. (15)N2-diazirines represent a class of particularly promising and versatile molecular tags, and can be incorporated into a wide range of biomolecules without significantly altering molecular function.

Embedded-cluster calculations in a numeric atomic orbital density-functional theory framework

We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding quantum and molecular mechanical (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential functionality into FHI-aims to describe cations at the QM/MM boundary through effective core potentials and therewith prevent spurious overpolarization of the electronic density. Based on numeric atomic orbital basis sets, FHI-aims offers particularly efficient access to exact exchange and second order perturbation theory, rendering the established QM/MM setup an ideal tool for hybrid and double-hybrid level density functional theory calculations of solid systems. We illustrate this capability by calculating the reduction potential of Fe in the Fe-substituted ZSM-5 zeolitic framework and the reaction energy profile for (photo-)catalytic water oxidation at TiO2(110).

Approaching truly freestanding graphene: the structure of hydrogen-intercalated graphene on 6H-SiC(0001)

We measure the adsorption height of hydrogen-intercalated quasifreestanding monolayer graphene on the (0001) face of 6H silicon carbide by the normal incidence x-ray standing wave technique. A density functional calculation for the full (6√3×6√3)-R30° unit cell, based on a van der Waals corrected exchange correlation functional, finds a purely physisorptive adsorption height in excellent agreement with experiments, a very low buckling of the graphene layer, a very homogeneous electron density at the interface, and the lowest known adsorption energy per atom for graphene on any substrate. A structural comparison to other graphenes suggests that hydrogen-intercalated graphene on 6H-SiC(0001) approaches ideal graphene.