Ab Initio Bethe-Salpeter Equation Research Articles

Consequences of the Pb-S Bond Formation for Lead Halide Perovskites.

Lead halide perovskites are structurally not stable due to their ionic bonds. Using sulfur agents in the crystal growth improves the stability and performance of the photovoltaic and light-emitting devices. In this theoretical work, we use a small toy S-radical in place of A cation in the bulk of lead iodide perovskite, and highlight the significance of the Pb-S covalent-double-bond formation for: the charge redistribution on the neighboring bonds that also turn to be covalent, phase transformation to a stable non-perovskite structure, and superior optoelectronic properties. The chemical analysis was performed with the Quantum Theory of Atoms In Molecules (QTAIM) and Non-Covalent Interactions (NCI) index. Excitonic properties were obtained from the solution of ab initio Bethe-Salpeter equation. Presence of the spin-orbit coupling triggers an interplay between the Frenkel and charge-transfer multiexcitons, switching between the photovoltaic and laser applications. Multiexcitons obey the exciton-fission preconditions.

Exploring Epitaxial Structures for Electrically Pumped Perovskite Lasers: A Study of CsPb(Br,I)3 Based on the Ab Initio Bethe-Salpeter Equation.

Halide perovskites are widely used as components of electronic and optoelectronic devices such as solar cells, light-emitting diodes (LEDs), optically pumped lasers, field-effect transistors, photodetectors, and γ-detectors. Despite this wide range of applications, the construction of an electrically pumped perovskite laser remains challenging. In this paper, we numerically justify that mixing two perovskite compounds with different halide elements can lead to optical properties suitable for electrical pumping. As a reference, the chosen model material was CsPbBr3, whose performance as a part of lasers has been widely recognised, with some Br atoms substituted by I at specific sites. In particular, a strong enhancement of the low-energy absorption peaks has been obtained using the ab initio Bethe-Salpeter equation. Based on these results, we propose specific architectures of ordered doping that could be realised by epitaxial growth. Efficient light emission from the bottom of the conduction band is expected.

Phonon Screening of Excitons in Semiconductors: Halide Perovskites and Beyond.

The abinitio Bethe-Salpeter equation (BSE) approach, an established method for the study of excitons in materials, is typically solved in a limit where only static screening from electrons is captured. Here, we generalize this framework to include dynamical screening from phonons at lowest order in the electron-phonon interaction. We apply this generalized BSE approach to a series of inorganic lead halide perovskites, CsPbX_{3}, with X=Cl, Br, and I. We find that inclusion of screening from phonons significantly reduces the computed exciton binding energies of these systems. By deriving a simple expression for phonon screening effects, we reveal general trends for their importance in semiconductors and insulators, based on a hydrogenic exciton model. We demonstrate that the magnitude of the phonon screening correction in isotropic materials can be reliably predicted using four material specific parameters: the reduced effective mass, static and optical dielectric constants, and frequency of the most strongly coupled longitudinal-optical phonon mode. This framework helps to elucidate the importance of phonon screening and its relation to excitonic properties in a broad class of semiconductors.

Assessment of the Ab Initio Bethe-Salpeter Equation Approach for the Low-Lying Excitation Energies of Bacteriochlorophylls and Chlorophylls.

Bacteriochlorophyll and chlorophyll molecules are crucial building blocks of the photosynthetic apparatus in bacteria, algae, and plants. Embedded in transmembrane protein complexes, they are responsible for the primary processes of photosynthesis: excitation energy and charge transfer. Here, we use ab initio many-body perturbation theory within the GW approximation and Bethe–Salpeter equation (BSE) approach to calculate the electronic structure and optical excitations of bacteriochlorophylls a, b, c, d, and e and chlorophylls a and b. We systematically study the effects of the structure, basis set size, partial self-consistency in GW, and the underlying exchange–correlation approximation and compare our calculations with results from time-dependent density functional theory, multireference RASPT2, and experimental literature results. We find that optical excitations calculated with GW+BSE are in excellent agreement with experimental data, with an average deviation of less than 100 meV for the first three bright excitations of the entire family of (bacterio)chlorophylls. Contrary to state-of-the-art time-dependent density functional theory (TDDFT) with an optimally tuned range-separated hybrid functional, this accuracy is achieved in a parameter-free approach. Moreover, GW+BSE predicts the energy differences between the low-energy excitations correctly and eliminates spurious charge transfer states that TDDFT with (semi)local approximations is known to produce. Our study provides accurate reference results and highlights the potential of the GW+BSE approach for the simulation of larger pigment complexes.

The anisotropy in the optical constants of quartz crystals for soft X-rays.

The refractive index of a y-cut SiO2 crystal surface is reconstructed from orientation-dependent soft X-ray reflectometry measurements in the energy range from 45 to 620 eV. Owing to the anisotropy of the crystal structure in the (100) and (001) directions, a significant deviation of the measured reflectance at the Si L 2,3 and O K absorption edges is observed. The anisotropy in the optical constants reconstructed from these data is also confirmed by ab initio Bethe-Salpeter equation calculations for the O K edge. This new experimental data set expands the existing literature data for quartz crystal optical constants significantly, particularly in the near-edge regions.

Exciton-Phonon Interaction and Relaxation Times from First Principles.

Electron-phonon interactions are key to understanding the dynamics of electrons in materials and can be modeled accurately from first principles. However, when electrons and holes form Coulomb-bound states (excitons), quantifying their interactions and scattering processes with phonons remains an open challenge. Here we show a rigorous approach for computing exciton-phonon (ex-ph) interactions and the associated exciton dynamical processes from first principles. Starting from the abinitio Bethe-Salpeter equation, we derive expressions for the ex-ph matrix elements and relaxation times. We apply our method to bulk hexagonal boron nitride, for which we map the ex-ph relaxation times as a function of exciton momentum and energy, analyze the temperature and phonon-mode dependence of the ex-ph scattering processes, and accurately predict the phonon-assisted photoluminescence. The approach introduced in this work is general and provides a framework for investigating exciton dynamics in a wide range of materials.

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.

Mapping of the energetically lowest exciton in bulk1T−HfS2

By combining electron energy-loss spectroscopy and state-of-the-art computational methods, we were able to provide an extensive picture of the excitonic processes in $1T$-HfS$_2$. The results differ significantly from the properties of the more scrutinized group VI semiconducting transition metal dichalcogenides such as MoS$_2$ and WSe$_2$. The measurements revealed a parabolic exciton dispersion for finite momentum $\textbf{q}$ parallel to the $\Gamma$K direction which allowed the determination of the effective exciton mass. The dispersion decreases monotonically for momentum exchanges parallel to the $\Gamma$M high symmetry line. To gain further insight into the excitation mechanisms, we solved the ab-initio Bethe-Salpeter equation for the system. The results matched the experimental loss spectra closely, thereby confirming the excitonic nature of the observed transitions, and produced the momentumdependent binding energies. The simulations also demonstrated that the excitonic transitions for $\textbf{q}$ || $\Gamma$M occur exactly along that particular high symmetry line. For $\textbf{q}$ || $\Gamma$K on the other hand, the excitations traverse the Brillouin zone crossing various high symmetry lines. A particular interesting aspect of our findings was that the calculation of the electron probability density revealed that the exciton assumes a six-pointed star-like shape along the real space crystal planes indicating a mixed Frenkel-Wannier character.

Theory and Ab Initio Computation of the Anisotropic Light Emission in Monolayer Transition Metal Dichalcogenides.

Monolayer transition metal dichalcogenides (TMDCs) are direct gap semiconductors with a unique potential for use in ultrathin light emitters. However, their photoluminescence (PL) is not completely understood. We develop an approach to compute the radiative recombination rate in monolayer TMDCs as a function of photon emission direction and polarization. Using exciton wavefunctions and energies obtained with the ab initio Bethe-Salpeter equation, we obtain polar plots of the PL for different scenarios. Our results can explain the PL anisotropy and polarization dependence measured in recent experiments and predict that light is emitted with a peak intensity normal to the exciton dipole in monolayer TMDCs. We show that excitons emit light anisotropically upon recombination when they are in any quantum superposition state of the K and K' inequivalent valleys. When averaged over the emission angle and exciton momentum, our new treatment recovers the temperature-dependent radiative lifetimes that we previously derived. Our work demonstrates a generally applicable first-principles approach to studying anisotropic light emission in two-dimensional materials.

An assessment of low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach and the Tamm-Dancoff approximation.

The accurate prediction of singlet and triplet excitation energies is an area of intense research of significant fundamental interest and critical for many applications. Most calculations of singlet and triplet energies use time-dependent density functional theory (TDDFT) in conjunction with an approximate exchange-correlation functional. In this work, we examine and critically assess an alternative method for predicting low-lying neutral excitations with similar computational cost, the ab initio Bethe-Salpeter equation (BSE) approach, and compare results against high-accuracy wavefunction-based methods. We consider singlet and triplet excitations of 27 prototypical organic molecules, including members of Thiel's set, the acene series, and several aromatic hydrocarbons exhibiting charge-transfer-like excitations. Analogous to its impact in TDDFT, we find that the Tamm-Dancoff approximation (TDA) overcomes triplet instabilities in the BSE approach, improving both triplet and singlet energetics relative to higher level theories. Finally, we find that BSE-TDA calculations built on effective DFT starting points, such as those utilizing optimally tuned range-separated hybrid functionals, can yield accurate singlet and triplet excitation energies for gas-phase organic molecules.

A systematic benchmark of the ab initio Bethe-Salpeter equation approach for low-lying optical excitations of small organic molecules.

The predictive power of the ab initio Bethe-Salpeter equation (BSE) approach, rigorously based on many-body Green's function theory but incorporating information from density functional theory, has already been demonstrated for the optical gaps and spectra of solid-state systems. Interest in photoactive hybrid organic/inorganic systems has recently increased and so has the use of the BSE for computing neutral excitations of organic molecules. However, no systematic benchmarks of the BSE for neutral electronic excitations of organic molecules exist. Here, we study the performance of the BSE for the 28 small molecules in Thiel's widely used time-dependent density functional theory benchmark set [Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. We observe that the BSE produces results that depend critically on the mean-field starting point employed in the perturbative approach. We find that this starting point dependence is mainly introduced through the quasiparticle energies obtained at the intermediate GW step and that with a judicious choice of starting mean-field, singlet excitation energies obtained from BSE are in excellent quantitative agreement with higher-level wavefunction methods. The quality of the triplet excitations is slightly less satisfactory.

Ab initioBethe-Salpeter calculations of the x-ray absorption spectra of transition metals at theL-shell edges

We present ab initio Bethe-Salpeter equation (BSE) calculations of the ${L}_{2,3}$ edges of several insulating and metallic compounds containing Ca, V, Fe, Co, Ni, and Cu, spanning a range of 3$d$-electron occupations. Our approach includes the key ingredients of a unified treatment of both extended states and atomic multiplet effects, i.e., Bloch states, self-consistent crystal potentials, ground-state magnetism, $GW$ self-energy corrections, spin-orbit terms, and Coulomb interactions between the ${L}_{2}$ and ${L}_{3}$ levels. The method is implemented in the ocean package, which uses plane-wave pseudopotential wave functions as a basis, a projector-augmented-wave construction for the transition matrix elements, and a resolvent formalism for the BSE calculation. The results are in near quantitative agreement with experiment, including both fine structure at the edges and the nonstatistical ${L}_{3}$/${L}_{2}$ ratios observed for these systems. Approximations such as time-dependent density-functional theory are shown to be less accurate.