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.

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.

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.

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 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.

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.

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.

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.

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 (ΔSO = 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.

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.

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.

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.

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.

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.

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.