Why are time-dependent density functional theory excitations in solids equal to band structure energy gaps for semilocal functionals, and how does nonlocal Hartree–Fock-type exchange introduce excitonic effects?

A Perspective on the Simulation of Electronic Circular Dichroism and Circularly Polarized Luminescence Spectra in Chiral Solid Materials

Chiral materials have shown tremendous potential for many technological applications, such as optoelectronics, sensing, magnetism, information technology, and imaging. Characterization of these materials is mostly based on chiroptical spectroscopies, such as electronic circular dichroism (ECD) and circularly polarized luminescence (CPL). These experimental measurements would greatly benefit from theoretical simulations for interpretation of the spectra as well as predictions on new materials. While ECD and CPL simulations are well established for molecular systems, they are not for materials. In this Perspective, we describe the theoretical quantities necessary to simulate ECD and CPL spectra in oriented systems. Then, we discuss the approximate strategies currently used to perform these calculations, what computational machinery is already available to develop more general approaches, and some of the open challenges for the simulation of ECD and CPL spectra in solid materials. When methods that are as reliable and computationally efficient as those for molecules are developed, these simulations will provide invaluable insight and guidance for the rational design of optically active materials.

Inq, a Modern GPU-Accelerated Computational Framework for (Time-Dependent) Density Functional Theory

We present inq, a new implementation of density functional theory (DFT) and time-dependent DFT (TDDFT) written from scratch to work on graphic processing units (GPUs). Besides GPU support, inq makes use of modern code design features and takes advantage of newly available hardware. By designing the code around algorithms, rather than against specific implementations and numerical libraries, we aim to provide a concise and modular code. The result is a fairly complete DFT/TDDFT implementation in roughly 12 000 lines of open-source C++ code representing a modular platform for community-driven application development on emerging high-performance computing architectures.

Absorption Spectra of Solids from Periodic Equation-of-Motion Coupled-Cluster Theory

We present ab initio absorption spectra of six three-dimensional semiconductors and insulators calculated using Gaussian-based periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). The spectra are calculated efficiently by solving a system of linear equations at each frequency, giving access to an energy range of tens of electronvolts without explicit enumeration of excited states. We assess the impact of cost-saving approximations associated with Brillouin zone sampling, frozen orbitals, and the partitioned EOM-CCSD approximation. Although our most converged spectra exhibit line shapes that are in good agreement with experimental spectra, they are uniformly shifted to higher energies by about 1 eV, which is not explained by the remaining finite-size errors. We tentatively attribute this discrepancy to a combination of vibrational effects and the remaining electron correlation, i.e., triple excitations and above.

Pros and cons of the time-dependent hybrid density functional approach for calculating the optical spectra of solids: a case study of CeO2

The prediction of optical spectra of complex solids remains a great challenge for first-principles calculations due to the huge computational cost of the state-of-the-art many-body perturbation theory based GW-Bethe Salpeter equation (BSE) approach. An alternative method is the time-dependent density-functional theory (TDDFT) based on hybrid exchange-correlation functionals, which involves the essential ingredients of electron-hole interactions in its formalism in contrast to its local/semi-local functional counterparts. In this work, we investigate the optical absorption spectra of ceria (CeO2), a prototypical lanthanide oxide with a 4f0 configuration, utilizing TDDFT based on four well-established hybrid functionals for ground state DFT calculations. All four functionals reproduce well the excitonic features of the experimental optical spectra, in spite of the significant differences in their band structures arising from different hybridization parameters (i.e. the fraction of the Hartree-Fock exchange and the screening parameter). It is demonstrated that the apparently weak dependence of the resulting optical spectra on the employed functionals is quite universal and applies to simple semiconductors such as Si and GaAs and insulator LiF as well. This study highlights the feasibility of TDDFT based on existing hybrids to describe optical spectra of solids, and also, points out the difficulty of obtaining accurate exciton binding energies using these hybrid functionals due to the strong functional dependence of quasi-particle band structures.

Crystal Symmetry and Static Electron Correlation Greatly Accelerate Nonradiative Dynamics in Lead Halide Perovskites

Using a recently developed many-body nonadiabatic molecular dynamics (NA-MD) framework for large condensed matter systems, we study the phonon-driven nonradiative relaxation of excess electronic excitation energy in cubic and tetragonal phases of the lead halide perovskite CsPbI₃. We find that the many-body treatment of the electronic excited states significantly changes the structure of the excited states' coupling, promotes a stronger nonadiabatic coupling of states, and ultimately accelerates the relaxation dynamics relative to the single-particle description of excited states. The acceleration of the nonadiabatic dynamics correlates with the degree of configurational mixing, which is controlled by the crystal symmetry. The higher-symmetry cubic phase of CsPbI₃ exhibits stronger configuration mixing than does the tetragonal phase and subsequently yields faster nonradiative dynamics. Overall, using a many-body treatment of excited states and accounting for decoherence dynamics are important for closing the gap between the computationally derived and experimentally measured nonradiative excitation energy relaxation rates.

Exploring the Origin of the Axial-Conformation Preferences in the 3-Halopiperidinium Cations: the Importance of the Coulombic Potential Energies

Although there are some published conclusions in the literature concerning the origin of the axial-conformation preference in 3-fluoropiperidinium cations (charge-dipole orientation effect), the origin of the axial-conformation preferences in the 3-halopiperidinium cations [halogen = F (1), Cl (2), Br (3)] has remained an open question. To explore the origin of the axial-conformation preferences in compounds 1-3, we assessed the roles and contributions of the hyperconjugative interactions, the Coulombic electrostatic interactions, the electrostatic model associated with dipole-dipole interactions, and the steric effects associated with the Pauli exchange-type repulsions on the conformational properties of compounds 1-3 utilizing the G3MP2, LC-ωPBE, and B3LYP methods and natural bond orbital (NBO) interpretations. Natural Coulombic potential energies are in favor of the axial conformations of compounds 1-3, and justify their corresponding total energy differences. The through-space hyperconjugative interactions between the donor lone pairs of halogen atoms (LP3X) and the acceptor antibonding orbitals of H-N bonds [σ*(H-N) ⊕], LP3X → σ*(H-N) ⊕, increase from compound 1 to compound 3. The inspection of the dipole moments of the parallel C-X and H-N bonds in the axial conformations of compounds 1-3 revealed that the variations of their corresponding four-center dipole-dipole interactions correlate well with their corresponding conformational behaviors. The steric effects associated with the Pauli exchange-type repulsions are strongly in favor of the equatorial conformations of compounds 1-3. Accordingly, the charge-dipole orienting effect associated with the four-center dipole-dipole interactions is a dominant factor in the conformational behaviors of compounds 1-3.

Quantum plasmons and intraband excitons in doped nanoparticles: Insights from quantum chemistry

We use excited-state quantum chemistry techniques to investigate the intraband absorption of doped semiconductor nanoparticles as a function of doping density, nanoparticle radius, and material properties. Modeling the excess electrons as interacting electrons confined to a sphere, we find that the excitation evolves from single-particle to plasmonic with increasing number of electrons at fixed density, and the threshold number of electrons to produce a plasmon increases with density due to quantum confinement and electron-hole attraction. In addition, the excitation passes through an intermediate regime where it is best characterized as an intraband exciton. We compare equation-of-motion coupled-cluster theory with those of more affordable single-excitation theories and identify the inclusion of electron-hole interactions as essential to describing the evolution of the excitation. Despite the simplicity of our model, the results are in reasonable agreement with the experimental spectra of doped ZnO nanoparticles at a doping density of 1.4 × 10²⁰ cm^-3. Based on our quantum chemistry calculations, we develop a schematic model that captures the dependence of the excitation energy on nanoparticle radius and electron density.

Many-body perturbation theory for understanding optical excitations in organic molecules and solids

Semiconductors composed of organic molecules are promising as components for flexible and inexpensive optoelectronic devices, with many recent studies aimed at understanding their electronic and optical properties. In particular, computational modeling of these complex materials has provided new understanding of the underlying properties which give rise to their excited-state phenomena. This article provides an overview of recent many-body perturbation theory (MBPT) studies of optical excitations within organic molecules and solids. We discuss the accuracy of MBPT within the GW/BSE approach in predicting excitation energies and absorption spectra, and assess the impact of two commonly used approximations, the DFT starting point and the Tamm-Dancoff approximation. Moreover, we summarize studies that elucidate the role of solid-state structure on the nature of excitons in organic crystals. These studies show that a rich physical understanding of organic materials can be obtained from GW/BSE.

Intrinsic electron trapping in amorphous oxide

We demonstrate that electron trapping at intrinsic precursor sites is endemic in non-glass-forming amorphous oxide films. The energy distributions of trapped electron states in ultra-pure prototype amorphous (a)-HfO₂ insulator obtained from exhaustive photo-depopulation experiments demonstrate electron states in the energy range of 2-3 eV below the oxide conduction band. These energy distributions are compared to the results of density functional calculations of a-HfO₂ models of realistic density. The experimental results can be explained by the presence of intrinsic charge trapping sites formed by under-coordinated Hf cations and elongated Hf-O bonds in a-HfO₂. These charge trapping states can capture up to two electrons, forming polarons and bi-polarons. The corresponding trapping sites are different from the dangling-bond type defects responsible for trapping in glass-forming oxides, such as SiO₂, in that the traps are formed without bonds being broken. Furthermore, introduction of hydrogen causes formation of somewhat energetically deeper electron traps when a proton is immobilized next to the trapped electron bi-polaron. The proposed novel mechanism of intrinsic charge trapping in a-HfO₂ represents a new paradigm for charge trapping in a broad class of non-glass-forming amorphous insulators.

Exploring the Origin of the Generalized Anomeric Effects in the Acyclic Nonplanar Systems

Contrary to the published conclusions in the literature concerning the origin of the generalized anomeric relationships in open-chain nonplanar systems, its origin has remained an open question. In order to explore the origin of the generalized anomeric relationships in open-chain nonplanar systems, we assessed the roles and contributions of the effective factors on the conformational properties of methyl propargyl ether (1), methyl propargyl sulfide (2), and methyl propargyl selenide (3) by means of the G3MP2, CCSD(T), MP2, LC-ωPBE, and B3LYP methods and natural bond orbital (NBO) interpretations. We examined the contributions of the hyperconjugative interactions on the conformational preferences of compounds 1-3 by the deletions of the orbitals overlapping from the Fock matrices of the gauche- and anti-conformations. The trend observed for energy changes in the Fock matrices justify the variations of the gauche-conformations preferences going from compound 1 to compound 3, revealing that the hyperconjugative interactions are solely responsible for the generalized anomeric relationships in compounds 1-3. Accordingly, the conclusions published in the literature concerning the origin of the generalized anomeric effect in the acyclic nonplanar compounds should be revised by these findings. The Pauli exchange type repulsions (PETR) are in favors of the gauche-conformations and the variations of the PETR differences between the gauche- and anti-conformations of compounds 1-3 correlate well with their gauche-conformations preferences, revealing that the generalized anomeric relationships in compounds 1-3 have also the Pauli exchange-type repulsions origin. The resemblance between the preorthogonal natural bond orbitals (that are involved in the hyperconjugative interactions) and their corresponding molecular orbitals have been investigated.

Excited-State Properties of Molecular Solids from First Principles

Molecular solids have attracted attention recently in the context of organic (opto)electronics. These materials exhibit unique charge carrier generation and transport phenomena that are distinct from those of conventional semiconductors. Understanding these phenomena is fundamental to optoelectronics and requires a detailed description of the excited-state properties of molecular solids. Recent advances in many-body perturbation theory (MBPT) and density functional theory (DFT) have made such description possible and have revealed many surprising electronic and optical properties of molecular crystals. Here, we review this progress. We summarize the salient aspects of MBPT and DFT as well as various properties that can be described by these methods. These properties include the fundamental gap and its renormalization, hybridization and band dispersion, singlet and triplet excitations, optical spectra, and excitonic properties. For each, we present concrete examples, a comparison to experiments, and a critical discussion.

Assessment of a Middle-Range Hybrid Functional

While hybrid functionals are largely responsible for the utility of modern Kohn-Sham density functional theory, they are not without their weaknesses. In the solid state, the slow decay of their nonlocal Hartree-Fock-type exchange makes hybrids computationally demanding and can introduce unphysical effects. Both problems can be remedied by a screened hybrid which uses exact exchange only at short-range. Many molecular properties, in contrast, benefit from the inclusion of long-range exact exchange. Recently, the authors reconciled these two seemingly contradictory requirements by introducing the HISS functional [ J. Chem. Phys. 2007 , 127 , 221103 ], which uses exact exchange only in the middle range. In this paper, we expand upon our previous work, benchmarking the performance of the HISS functional for several simple properties and applying it to the dissociation of homonuclear diatomic cations and to the polarizability of linear H2 chains to determine the importance of middle-range exact exchange for these systems, which are expected to be sensitive to the asymptotic exchange potential.

Possible use of BN-modified fullerene as a nano-biosensor to detect adenine–thymine Watson–Crick base pair in mutagenic tautomeric form: Theoretical approach

The present work deals with the theoretical investigation of electronic structure features and stability of adenine–thymine (AT) and rare tautomer of adenine–thymine (rAT) base pairs along with their complexes with Cu 2+ cation and their interactions with BN doped fullerene ( C 58 BN ). All the calculations have been performed with density functional theory using B3LYP functional. Electronic structures of the two base pairs are almost identical. Hence, it is rather difficult to distinguish between the two base pairs on the basis of their electronic properties. As per our theoretical calculations, we have observed that, BN modified fullerene could act as a nano-biosensor for detection of mispairing between these two complementary bases as well as their Cu 2+ complexes.

Symmetry breaking in the planar configurations of disilicon tetrahalides: Pseudo-Jahn–Teller effect parameters, hardness and electronegativity

The correlations between the Pseudo-Jahn–Teller Effect (PJTE) parameters (i.e. F, Δ and K₀), structural and configurational properties, global hardness and global electronegativities in disilicon tetrahalides were investigated by means of ab initio and hybrid-DFT methods.

Quantum chemical investigations of AlN-doped C60 for use as a nano-biosensor in detection of mispairing between DNA bases

Quantum chemical calculations were carried out to study the electronic structure and stability of adenine-thymine and the rare tautomer of adenine-thymine base pairs along with their Cu 2+ complexes and their interactions with AlN-modified fullerene (C58AlN) using Density Functional Theory (B3LYP method). Since, these two forms of base pairs and their Cu 2+ complexes have almost similar electronic structures, their chemical differentiation is an extremely difficult task. In this investigation, we have observed that AlN-doped C 60 could be used as a potentially viable nanoscale sensor to detect these two base pairs as well as their Cu2+ complexes.

A minimal model for excitons within time-dependent density-functional theory

The accurate description of the optical spectra of insulators and semiconductors remains an important challenge for time-dependent density-functional theory (TDDFT). Evidence has been given in the literature that TDDFT can produce bound as well as continuum excitons for specific systems, but there are still many unresolved basic questions concerning the role of dynamical exchange and correlation (xc). In particular, the roles of the long spatial range and the frequency dependence of the xc kernel f(xc) for excitonic binding are still not very well explored. We present a minimal model for excitons in TDDFT, consisting of two bands from a one-dimensional (1D) Kronig-Penney model and simple approximate xc kernels, providing an easily accessible model system for studying excitonic effects in TDDFT. For the 1D model system, it is found that adiabatic xc kernels can produce at most two bound excitons, confirming that the long spatial range of f(xc) is not a necessary condition. It is shown how the Wannier model, featuring an effective electron-hole interaction, emerges from TDDFT. The collective, many-body nature of excitons is explicitly demonstrated.

Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

The recently developed SOGGA11 and M11-L density functionals have been tested for the prediction of bandgaps and lattice constants by comparing to databases containing 31 bandgaps and 34 lattice constants. To make a comparative assessment we also test several other density functionals against the same databases; in particular, we test the local spin density approximation, PBE, PBEsol, SOGGA, TPSS, revTPSS, and M06-L local density functionals and the HSE screened-exchange hybrid nonlocal density functional; and for a subset of 13 lattice constants we also compare the mean errors to those of the AM05 and WC local density functionals and the HISS and HSEsol nonlocal density functionals. The tests show that, of the ten functionals tested against all 65 data, the SOGGA, PBEsol, and HSE functionals are the most accurate for lattice constants, whereas the HSE, M11-L, and M06-L density functionals are the most accurate for bandgaps. However, the SOGGA11 density functional is the most accurate generalized gradient approximation for bandgaps.

Nonempirically Tuned Range-Separated DFT Accurately Predicts Both Fundamental and Excitation Gaps in DNA and RNA Nucleobases

Using a nonempirically tuned range-separated DFT approach, we study both the quasiparticle properties (HOMO–LUMO fundamental gaps) and excitation energies of DNA and RNA nucleobases (adenine, thymine, cytosine, guanine, and uracil). Our calculations demonstrate that a physically motivated, first-principles tuned DFT approach accurately reproduces results from both experimental benchmarks and more computationally intensive techniques such as many-body GW theory. Furthermore, in the same set of nucleobases, we show that the nonempirical range-separated procedure also leads to significantly improved results for excitation energies compared to conventional DFT methods. The present results emphasize the importance of a nonempirically tuned range-separation approach for accurately predicting both fundamental and excitation gaps in DNA and RNA nucleobases.

Accurate prediction of the electronic properties of low-dimensional graphene derivatives using a screened hybrid density functional

Over the last several years, low-dimensional graphene derivatives, such as carbon nanotubes and graphene nanoribbons, have played a central role in the pursuit of a plausible carbon-based nanotechnology. Their electronic properties can be either metallic or semiconducting depending purely on morphology, but predicting their electronic behavior has proven challenging. The combination of experimental efforts with modeling of these nanometer-scale structures has been instrumental in gaining insight into their physical and chemical properties and the processes involved at these scales. Particularly, approximations based on density functional theory have emerged as a successful computational tool for predicting the electronic structure of these materials. In this Account, we review our efforts in modeling graphitic nanostructures from first principles with hybrid density functionals, namely the Heyd-Scuseria-Ernzerhof (HSE) screened exchange hybrid and the hybrid meta-generalized functional of Tao, Perdew, Staroverov, and Scuseria (TPSSh). These functionals provide a powerful tool for quantitatively studying structure-property relations and the effects of external perturbations such as chemical substitutions, electric and magnetic fields, and mechanical deformations on the electronic and magnetic properties of these low-dimensional carbon materials. We show how HSE and TPSSh successfully predict the electronic properties of these materials, providing a good description of their band structure and density of states, their work function, and their magnetic ordering in the cases in which magnetism arises. Moreover, these approximations are capable of successfully predicting optical transitions (first and higher order) in both metallic and semiconducting single-walled carbon nanotubes of various chiralities and diameters with impressive accuracy. This versatility includes the correct prediction of the trigonal warping splitting in metallic nanotubes. The results predicted by HSE and TPSSh provide excellent agreement with existing photoluminescence and Rayleigh scattering spectroscopy experiments and Green's function-based methods for carbon nanotubes. This same methodology was utilized to predict the properties of other carbon nanomaterials, such as graphene nanoribbons. Graphene nanoribbons may be viewed as unrolled (and passivated) carbon nanotubes. However, the emergence of edges has a crucial impact on the electronic properties of graphene nanoribbons. Our calculations have shown that armchair nanoribbons are predicted to be nonmagnetic semiconductors with a band gap that oscillates with their width. In contrast, zigzag graphene nanoribbons are semiconducting with an electronic ground state that exhibits spin polarization localized at the edges of the carbon nanoribbon. The spatial symmetry of these magnetic states in graphene nanoribbons can give rise to a half-metallic behavior when a transverse external electric field is applied. Our work shows that these properties are enhanced upon different types of oxidation of the edges. We also discuss the properties of rectangular graphene flakes, which present spin polarization localized at the zigzag edges.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

Higher energy optical transitions in semiconducting carbon nanotubes

We have studied the high energy optical transitions of semiconducting single-walled carbon nanotubes using the nonorthogonal tight-binding model, which takes into account the exciton effect. It is found from our calculations that the exciton's binding energies for the high energy E(33) and E(44) transitions are large enough, indicating clearly they are also excitonic in nature. More importantly, the logarithmic Kane-Mele correction, successful for the low energy E(11) and E(22) transitions, is now found to fail for describing the many-body effects in the higher energy transitions, which is consistent with the experimental result of Araujo et al (2007 Phys. Rev. Lett. 98 067401). Finally, it is interesting to find the possibility of a crossover effect between the E(33) and E(44) energies for certain mod 1 chiralities and the family behavior of the many-body corrections in the E(33) and E(44) transitions, both of which are well supported by the recent experiment of Haroz et al (2008 Phys. Rev. B 77 125405).