Efficient all-electron hybrid density functionals for atomistic simulations beyond 10 000 atoms.

Hybrid density functional approximations (DFAs) offer compelling accuracy for ab initio electronic-structure simulations of molecules, nanosystems, and bulk materials, addressing some deficiencies of computationally cheaper, frequently used semilocal DFAs. However, the computational bottleneck of hybrid DFAs is the evaluation of the non-local exact exchange contribution, which is the limiting factor for the application of the method for large-scale simulations. In this work, we present a drastically optimized resolution-of-identity-based real-space implementation of the exact exchange evaluation for both non-periodic and periodic boundary conditions in the all-electron code FHI-aims, targeting high-performance central processing unit (CPU) compute clusters. The introduction of several new refined message passing interface (MPI) parallelization layers and shared memory arrays according to the MPI-3 standard were the key components of the optimization. We demonstrate significant improvements of memory and performance efficiency, scalability, and workload distribution, extending the reach of hybrid DFAs to simulation sizes beyond ten thousand atoms. In addition, we also compare the runtime performance of the PBE, HSE06, and PBE0 functionals. As a necessary byproduct of this work, other code parts in FHI-aims have been optimized as well, e.g., the computation of the Hartree potential and the evaluation of the force and stress components. We benchmark the performance and scaling of the hybrid DFA-based simulations for a broad range of chemical systems, including hybrid organic-inorganic perovskites, organic crystals, and ice crystals with up to 30 576 atoms (101 920 electrons described by 244 608 basis functions).

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.

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.

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.

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-BII-MIV-X (BII = Sr, Pb; MIV = 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 AI-BII-MIV-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-BII-MIV-X compositional family provide a basis for a broader understanding of the structure formation and optoelectronic properties within the quaternary chalcogenide semiconductor family.

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.

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 de-orbitalize 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 the use of the orbital-dependent kinetic energy density. The performance and transferability of the machine-learned functional are demonstrated for molecular and periodic systems.

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, 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.

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.

Highly Distorted Chiral Two-Dimensional Tin Iodide Perovskites for Spin Polarized Charge Transport.

Incorporating chiral organic molecules into organic/inorganic hybrid 2D metal-halide perovskites results in a novel family of chiral hybrid semiconductors with unique spin-dependent properties. The embedded chiral organic moieties induce a chiroptical response from the inorganic metal-halide sublattice. However, the structural interplay between the chiral organic molecules and the inorganic sublattice, as well as their synergic effect on the resulting electronic band structure need to be explored in a broader material scope. Here we present three new layered tin iodide perovskites templated by chiral (R/S-)methylbenzylammonium (R/S-MBA), i.e., (R-/S-MBA)2SnI4, and their racemic phase (rac-MBA)2SnI4. These MBA2SnI4 compounds exhibit the largest level of octahedral bond distortion compared to any other reported layered tin iodide perovskite. The incorporation of chiral MBA cations leads to circularly polarized absorption from the inorganic Sn-I sublattice, displaying chiroptical activity in the 300-500 nm wavelength range. The bandgap and chiroptical activity are modulated by alloying Sn with Pb, in the series of (MBA)2Pb1-xSnxI4. Finally, we show that vertical charge transport through oriented (R-/S-MBA)2SnI4 thin films is highly spin-dependent, arising from a chiral-induced spin selectivity (CISS) effect. We demonstrate a spin-polarization in the current-voltage characteristics as high as 94%. Our work shows the tremendous potential of these chiral hybrid semiconductors for controlling both spin and charge degrees of freedom.

Relativistic correction scheme for core-level binding energies from GW.

We present a relativistic correction scheme to improve the accuracy of 1s core-level binding energies calculated from Green's function theory in the GW approximation, which does not add computational overhead. An element-specific corrective term is derived as the difference between the 1s eigenvalues obtained from the self-consistent solutions to the non- or scalar-relativistic Kohn-Sham equations and the four-component Dirac-Kohn-Sham equations for a free neutral atom. We examine the dependence of this corrective term on the molecular environment and the amount of exact exchange in hybrid exchange-correlation functionals. This corrective term is then added as a perturbation to the quasiparticle energies from partially self-consistent and single-shot GW calculations. We show that this element-specific relativistic correction, when applied to a previously reported benchmark set of 65 core-state excitations [D. Golze et al., J. Phys. Chem. Lett. 11, 1840-1847 (2020)], reduces the mean absolute error (MAE) with respect to the experiment from 0.55 eV to 0.30 eV and eliminates the species dependence of the MAE, which otherwise increases with the atomic number. The relativistic corrections also reduce the species dependence for the optimal amount of exact exchange in the hybrid functional used as a starting point for the single-shot G0W0 calculations. Our correction scheme can be transferred to other methods, which we demonstrate for the delta self-consistent field (ΔSCF) approach based on density functional theory.

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.

All-electron ab initio Bethe-Salpeter equation approach to neutral excitations in molecules with numeric atom-centered orbitals.

The Bethe-Salpeter equation (BSE) based on GW quasiparticle levels is a successful approach for calculating the optical gaps and spectra of solids and also for predicting the neutral excitations of small molecules. We here present an all-electron implementation of the GW+BSE formalism for molecules, using numeric atom-centered orbital (NAO) basis sets. We present benchmarks for low-lying excitation energies for a set of small organic molecules, denoted in the literature as "Thiel's set." Literature reference data based on Gaussian-type orbitals are reproduced to about one millielectron-volt precision for the molecular benchmark set, when using the same GW quasiparticle energies and basis sets as the input to the BSE calculations. For valence correlation consistent NAO basis sets, as well as for standard NAO basis sets for ground state density-functional theory with extended augmentation functions, we demonstrate excellent convergence of the predicted low-lying excitations to the complete basis set limit. A simple and affordable augmented NAO basis set denoted "tier2+aug2" is recommended as a particularly efficient formulation for production calculations. We finally demonstrate that the same convergence properties also apply to linear-response time-dependent density functional theory within the NAO formalism.

Siesta: Recent developments and applications.

A review of the present status, recent enhancements, and applicability of the Siesta program is presented. Since its debut in the mid-1990s, Siesta's flexibility, efficiency, and free distribution have given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of Siesta combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a real-space grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here, we describe the more recent implementations on top of that core scheme, which include full spin-orbit interaction, non-repeated and multiple-contact ballistic electron transport, density functional theory (DFT)+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as wannier90 and the second-principles modeling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering Siesta runs, and various post-processing utilities. Siesta has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low-level libraries, as well as data standards and support for them, particularly the PSeudopotential Markup Language definition and library for transferable pseudopotentials, and the interface to the ELectronic Structure Infrastructure library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments.

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.

Direct-Bandgap 2D Silver-Bismuth Iodide Double Perovskite: The Structure-Directing Influence of an Oligothiophene Spacer Cation.

Three-dimensional (3D) hybrid organic-inorganic lead halide perovskites (HOIPs) feature remarkable optoelectronic properties for solar energy conversion but suffer from long-standing issues of environmental stability and lead toxicity. Associated two-dimensional (2D) analogues are garnering increasing interest due to superior chemical stability, structural diversity, and broader property tunability. Toward lead-free 2D HOIPs, double perovskites (DPs) with mixed-valent dual metals are attractive. Translation of mixed-metal DPs to iodides, with their prospectively lower bandgaps, represents an important target for semiconducting halide perovskites, but has so far proven inaccessible using traditional spacer cations due to either intrinsic instability or formation of competing non-perovskite phases. Here, we demonstrate the first example of a 2D Ag-Bi iodide DP with a direct bandgap of 2.00(2) eV, templated by a layer of bifunctionalized oligothiophene cations, i.e., (bis-aminoethyl)bithiophene, through a collective influence of aromatic interactions, hydrogen bonding, bidentate tethering, and structural rigidity. Hybrid density functional theory calculations for the new material reveal a direct bandgap, consistent with the experimental value, and relatively flat band edges derived principally from Ag-d/I-p (valence band) and Bi-p/I-p (conduction band) states. This work opens up new avenues for exploring specifically designed organic cations to stabilize otherwise inaccessible 2D HOIPs with potential applications for optoelectronics.