Excited states properties of organic molecules: from density functional theory to the GW and Bethe-Salpeter Green's function formalisms

All-Electron BSE@GW Method with Numeric Atom-Centered Orbitals for Extended Periodic Systems

Green's function theory has emerged as a powerful many-body approach not only in condensed matter physics but also in quantum chemistry in recent years. We have developed a new all-electron implementation of the BSE@GW formalism using numeric atom-centered orbital basis sets (Liu, C. J. Chem. Phys. 2020, 152, 044105). We present our recent developments in implementing this formalism for extended periodic systems. We discuss its numerical implementation and various convergence tests pertaining to numerical atom-centered orbitals, auxiliary basis sets for the resolution-of-identity formalism, and Brillouin zone sampling. Several proof-of-principle examples are presented to compare with other formalisms, illustrating the new all-electron BSE@GW method for extended periodic systems.

Nonempirical Prediction of the Length-Dependent Ionization Potential in Molecular Chains

The ionization potential of molecular chains is well-known to be a tunable nanoscale property that exhibits clear quantum confinement effects. State-of-the-art methods can accurately predict the ionization potential in the small molecule limit and in the solid-state limit, but for intermediate, nanosized systems prediction of the evolution of the electronic structure between the two limits is more difficult. Recently, optimal tuning of range-separated hybrid functionals has emerged as a highly accurate method for predicting ionization potentials. This was first achieved for molecules using the ionization potential theorem (IPT) and more recently extended to solid-state systems, based on an ansatz that generalizes the IPT to the removal of charge from a localized Wannier function. Here, we study one-dimensional molecular chains of increasing size, from the monomer limit to the infinite polymer limit using this approach. By comparing our results with other localization-based methods and where available with experiment, we demonstrate that Wannier-localization-based optimal tuning is highly accurate in predicting ionization potentials for any chain length, including the nanoscale regime.

Excited-State Charge Transfer Coupling from Quasiparticle Energy Density Functional Theory

The recently developed Quasiparticle Energy (QE) scheme, based on a DFT calculation with one more (or less) electron, offers a good description of excitation energies, even with charge transfer characters. In this work, QE is further extended to calculate electron transfer (ET) couplings involving two excited states. We tested it with a donor-acceptor complex, consisting of a furan and a 1,1-dicyanoethylene (DCNE), in which two low lying charge transfer and local excitation states are involved. With generalized Mülliken-Hush and fragment charge-difference schemes, couplings from the QE approach generally agree well with those obtained from TDDFT, except that QE couplings exhibit better exponential distance dependence. Couplings from half-energy gaps with an external field are also calculated and reported. Our results show that the QE scheme is robust in calculating ET couplings with greatly reduced computational time.

Computational Discovery of Intermolecular Singlet Fission Materials Using Many-Body Perturbation Theory

Intermolecular singlet fission (SF) is the conversion of a photogenerated singlet exciton into two triplet excitons residing on different molecules. SF has the potential to enhance the conversion efficiency of solar cells by harvesting two charge carriers from one high-energy photon, whose surplus energy would otherwise be lost to heat. The development of commercial SF-augmented modules is hindered by the limited selection of molecular crystals that exhibit intermolecular SF in the solid state. Computational exploration may accelerate the discovery of new SF materials. The GW approximation and Bethe-Salpeter equation (GW+BSE) within the framework of many-body perturbation theory is the current state-of-the-art method for calculating the excited-state properties of molecular crystals with periodic boundary conditions. In this Review, we discuss the usage of GW+BSE to assess candidate SF materials as well as its combination with low-cost physical or machine learned models in materials discovery workflows. We demonstrate three successful strategies for the discovery of new SF materials: (i) functionalization of known materials to tune their properties, (ii) finding potential polymorphs with improved crystal packing, and (iii) exploring new classes of materials. In addition, three new candidate SF materials are proposed here, which have not been published previously.

Variational Active Space Selection with Multiconfiguration Pair-Density Functional Theory

The selection of an adequate set of active orbitals for modeling strongly correlated electronic states is difficult to automate because it is highly dependent on the states and molecule of interest. Although many approaches have shown some success, no single approach has worked well in all cases. In light of this, we present the "discrete variational selection" (DVS) approach to active space selection, in which one generates multiple trial wave functions from a diverse set of systematically constructed active spaces and then selects between these wave functions variationally. We apply this DVS approach to 207 vertical excitations of small-to-medium-sized organic and inorganic molecules (with 3 to 18 atoms) in the QUESTDB database by (i) constructing various sets of active space orbitals through diagonalization of parametrized operators and (ii) choosing the result with the lowest average energy among the states of interest. This approach proves ineffective when variationally selecting between wave functions using the density matrix renormalization group (DMRG) or complete active space self-consistent field (CASSCF) energy but is able to provide good results when variationally selecting between wave functions using the energy of the translated PBE (tPBE) functional from multiconfiguration pair-density functional theory (MC-PDFT). Applying this DVS-tPBE approach to selection among state-averaged DMRG wave functions, we obtain a mean unsigned error of only 0.17 eV using hybrid MC-PDFT. This result matches that of our previous benchmark without the need to filter out poor active spaces and with no further orbital optimization following active space selection of the SA-DMRG wave functions. Furthermore, we find that DVS-tPBE is able to robustly and effectively select between the new SA-DMRG wave functions and our previous SA-CASSCF results.

Linearized Pair-Density Functional Theory for Vertical Excitation Energies

Multiconfiguration pair-density functional theory (MC-PDFT) is a computationally efficient method that computes the energies of electronic states in a state specific or state average framework via an on-top functional. However, MC-PDFT does not include state interaction among these states since the final energies do not come from the diagonalization of an effective model-space Hamiltonian. Recently, multistate extensions such as linearized PDFT (L-PDFT) have been developed to accurately model the potentials near conical intersections and avoided crossings. However, there has not been any systematic study evaluating their performance for predicting vertical excitations at the equilibrium geometry of a molecule, when the excited states are generally well separated. In this paper, we report the performance of L-PDFT on the extensive QUESTDB data set of vertical excitations using a database of automatically selected active spaces. We show that L-PDFT performs well on all these excitations and successfully reproduces the performance of MC-PDFT. These results further demonstrate the potential of L-PDFT, as its scaling is constant with the number of states included in the state-average manifold, whereas MC-PDFT scales linearly in this regard.

Theoretical Study on the Optoelectronic Properties of Merocyanine-Dyes

Merocyanines, as prototypes of highly polar π-conjugated molecules, have been intensively investigated for their self-assembly and optoelectronic properties, both experimentally and theoretically. However, an accurate description of their structural and electronic properties remains challenging for quantum-chemical methods. We assessed several theoretical approaches, TD-DFT, GW-BSE, STEOM-DLPNO-CCSD, and CASSCF/NEVPT2-FIC for their reliability in reproducing optoelectronic properties of a series of donor/acceptor (D/A) merocyanines, focusing on the first excitation energy. Additionally, we tested an all-electron perturbative method based on time-dependent coupled-perturbed density functional theory, denoted as TDCP-DFT. Particular focus was set on direct and indirect solvent effects, which affect excited-state energies by electrostatic interaction and molecular geometry. The molecular configuration space was sampled at the semiempirical tight-binding level. Our results corroborate previous investigations, showing that the S0 - S1 excitation energy strongly depends on the merocyanine molecular structure and the dielectric constant of the solvent. We found significant effects of the polar solution environment on the geometry of the merocyanines, which strongly affect the calculated excitation energies. Taking these effects into account, the best agreement between calculated and measured excitation energies was obtained with TDCP-DFT and GW-BSE. We also calculated excitation energies of molecular crystals at the TDCP-DFT level and compared the results to the corresponding monomers.

Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures

We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(Ne3), where Ne is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

Rational Design, Stabilities and Nonlinear Optical Properties of Non-Conventional Transition Metalides; New Entry into Nonlinear Optical Materials

Electronic and nonlinear optical properties of endohedral metallofullerenes are presented. The endohedral metallofullerenes contain transition metal encapsulated in inorganic fullerenes X₁₂Y₁₂ (X = B, Al & Y = N, P). The endohedral metallofullerenes (endo-TM@X₁₂Y₁₂) possess quite interesting geometric and electronic properties, which are the function of the nature of the atom and the size of fullerene. NBO charge and frontier molecular orbital analyses reveal that the transition metal encapsulated Al₁₂N₁₂ fullerenes (endo-TM@Al₁₂N₁₂) are true metalides when the transition metals are Ni, Cu and Zn. Endo-Cr@Al₁₂N₁₂ and endo-Co@Al₁₂N₁₂ are at the borderline between metalides and electrides with predominantly electride characteristics. The other members of the series are excess electron systems, which offer interesting electronic and nonlinear optical properties. The diversity of nature possessed by endo-TM@Al₁₂N₁₂ is not prevalent for other fullerenes. Endo-TM@Al₁₂P₁₂ are true metalides when the transition metals are (Cr-Zn). HOMO-LUMO gaps (E_H-L) are reduced significantly for these endohedral metallofullerenes, with a maximum percent decrease in E_H-L of up to 70%. Many complexes show odd-even oscillating behavior for E_H-L and dipole moments. Odd electron species contain large dipole moments and small E_H-L, whereas even electron systems have the opposite behavior. Despite the decrease in E_H-L, these systems show high kinetic and thermodynamic stabilities. The encapsulation of transition metals is a highly exergonic process. These endo-TM@X₁₂Y₁₂ possess remarkable nonlinear optical response in which the first hyperpolarizability reaches up to 2.79 × 10⁵ au for endo-V@Al₁₂N₁₂. This study helps in the comparative analysis of the potential nonlinear optical responses of electrides, metalides and other excess electron systems. In general, the potential nonlinear optical response of electrides is higher than metalides but lower than those of simple excess electron compounds. The higher non-linear optical response and interesting electronic characteristics of endo-TM@Al₁₂N₁₂ complexes may be promising contenders for potential NLO applications.

Assessing the Role of the Kohn-Sham Density in the Calculation of the Low-Lying Bethe-Salpeter Excitation Energies

We adopt the GW many-body perturbation theory in conjunction with the Bethe-Salpeter equation (BSE) to compute 57 excitation energies of a set of 37 molecules. By using the PBEh global hybrid functional and a self-consistent scheme on the eigenvalues in GW, we show a strong dependence of the BSE energy on the starting Kohn-Sham (KS) density functional. This arises from both the quasiparticle energies and the spatial localization of the frozen KS orbitals employed to compute the BSE. In order to address the arbitrariness in the mean field choice, we adopt an orbital-tuning scheme where the amount of Fock exchange, α, is tuned to impose that the KS HOMO matches the GW quasiparticle eigenvalue, thus fulfilling the ionization potential theorem in DFT. The performance of the proposed scheme yields excellent results and it is similar to M06-2X and PBEh with α = 75%, consistent with tuned values of α ranging between 60% and 80%.

Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection

We have calculated state-averaged complete-active-space self-consistent-field (SA-CASSCF), multiconfiguration pair-density functional theory (MC-PDFT), hybrid MC-PDFT (HMC-PDFT), and n-electron valence state second-order perturbation theory (NEVPT2) excitation energies with the approximate pair coefficient (APC) automated active-space selection scheme for the QUESTDB benchmark database of 542 vertical excitation energies. We eliminated poor active spaces (20-40% of calculations) by applying a threshold to the SA-CASSCF absolute error. With the remaining calculations, we find that NEVPT2 performance is significantly impacted by the size of the basis set the wave functions are converged in, regardless of the quality of their description, which is a problem absent in MC-PDFT. Additionally, we find that HMC-PDFT is a significant improvement over MC-PDFT with the translated PBE (tPBE) density functional and that it performs about as well as NEVPT2 and second-order coupled cluster on a set of 373 excitations in the QUESTDB database. We optimized the percentage of SA-CASSCF energy to include in HMC-PDFT when using the tPBE on-top functional, and we find the 25% value used in tPBE0 to be optimal. This work is by far the largest benchmarking of MC-PDFT and HMC-PDFT to date, and the data produced in this work are useful as a validation of HMC-PDFT and of the APC active-space selection scheme. We have made all the wave functions produced in this work (orbitals and CI vectors) available to the public and encourage the community to utilize this data as a tool in the development of further multireference model chemistries.

Time-Dependent Second-Order Green's Function Theory for Neutral Excitations

We develop a time-dependent second-order Green's function theory (GF2) for calculating neutral excited states in molecules. The equation of motion for the lesser Green's function (GF) is derived within the adiabatic approximation to the Kadanoff-Baym (KB) equation, using the second-order Born approximation for the self-energy. In the linear response regime, we recast the time-dependent KB equation into a Bethe-Salpeter-like equation (GF2-BSE), with a kernel approximated by the second-order Coulomb self-energy. We then apply our GF2-BSE to a set of molecules and atoms and find that GF2-BSE is superior to configuration interaction with singles (CIS) and/or time-dependent Hartree-Fock (TDHF), particularly for charge-transfer excitations, and is comparable to CIS with perturbative doubles (CIS(D)) in most cases.

Bethe-Salpeter equation insights into the photo-absorption function and exciton structure of chlorophyll a and b in light-harvesting complex II

The photo-absorption process and the excitation of chlorophyll (Chl) is the primary and essential step of photosynthesis in green plants. By solving the Bethe-Salpeter equation (BSE) on top of the GW approximation within ab initio many-body perturbation theory, we calculate the photo-absorption function and the excitons structure of Chl a and b in their in vivo conformations as measured by X-ray diffraction in the light-harvesting complex (LHC) II. BSE optical absorption spectra are in good agreement with the experiment and we discuss residual discrepancies. The experimental evidence of multiple Chla forms in vivo is explained by BSE. The Chla and Chlb BSE exciton wavefunctions present important charge-transfer differences on the Soret band. Q excitons are almost identical, apart from charge (both electron and hole) localization on the Chlb C7 aldheide formyl group, absent on the Chla methyl C7, that is exactly the group where the two chlorophylls differ.

Simplified GW/BSE Approach for Charged and Neutral Excitation Energies of Large Molecules and Nanomaterials

Inspired by Grimme's simplified Tamm-Dancoff density functional theory approach [Grimme, S. J. Chem. Phys. 2013, 138, 244104], we describe a simplified approach to excited-state calculations within the GW approximation to the self-energy and the Bethe-Salpeter equation (BSE), which we call sGW/sBSE. The primary simplification to the electron repulsion integrals yields the same structure as with tensor hypercontraction, such that our method has a storage requirement that grows quadratically with system size and computational timing that grows cubically with system size. The performance of sGW is tested on the ionization potential of the molecules in the GW100 test set, for which it differs from ab initio GW calculations by only 0.2 eV. The performance of sBSE (based on the sGW input) is tested on the excitation energies of molecules in Thiel's set, for which it differs from ab initio GW/BSE calculations by about 0.5 eV. As examples of the systems that can be routinely studied with sGW/sBSE, we calculate the band gap and excitation energy of hydrogen-passivated silicon nanocrystals with up to 2650 electrons in 4678 spatial orbitals and the absorption spectra of two large organic dye molecules with hundreds of atoms.

Combining localized orbital scaling correction and Bethe-Salpeter equation for accurate excitation energies

We applied localized orbital scaling correction (LOSC) in Bethe-Salpeter equation (BSE) to predict accurate excitation energies for molecules. LOSC systematically eliminates the delocalization error in the density functional approximation and is capable of approximating quasiparticle (QP) energies with accuracy similar to or better than GW Green's function approach and with much less computational cost. The QP energies from LOSC, instead of commonly used G0W0 and evGW, are directly used in BSE. We show that the BSE/LOSC approach greatly outperforms the commonly used BSE/G0W0 approach for predicting excitations with different characters. For the calculations of Truhlar-Gagliardi test set containing valence, charge transfer, and Rydberg excitations, BSE/LOSC with the Tamm-Dancoff approximation provides a comparable accuracy to time-dependent density functional theory (TDDFT) and BSE/evGW. For the calculations of Stein CT test set and Rydberg excitations of atoms, BSE/LOSC considerably outperforms both BSE/G0W0 and TDDFT approaches with a reduced starting point dependence. BSE/LOSC is, thus, a promising and efficient approach to calculate excitation energies for molecular systems.

Optimal Tuning Perspective of Range-Separated Double Hybrid Functionals

We study the optimal tuning of the free parameters in range-separated double hybrid functionals, based on enforcing the exact conditions of piecewise linearity and spin constancy. We find that introducing the range separation in both the exchange and the correlation terms allows for the minimization of both fractional charge and fractional spin errors for singlet atoms. The optimal set of parameters is system specific, underlining the importance of the tuning procedure. We test the performance of the resulting optimally tuned functionals for the dissociation curves of diatomic molecules. We find that they recover the correct dissociation curve for the one-electron system, H2+, and improve the dissociation curves of many-electron molecules such as H2 and Li2, but they also yield a nonphysical maximum and only converge to the correct dissociation limit at very large distances.

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.

Full-frequency dynamical Bethe-Salpeter equation without frequency and a study of double excitations

The Bethe-Salpeter equation (BSE) that results from the GW approximation to the self-energy is a frequency-dependent (nonlinear) eigenvalue problem due to the dynamically screened Coulomb interaction between electrons and holes. The computational time required for a numerically exact treatment of this frequency dependence is O(N6), where N is the system size. To avoid the common static screening approximation, we show that the full-frequency dynamical BSE can be exactly reformulated as a frequency-independent eigenvalue problem in an expanded space of single and double excitations. When combined with an iterative eigensolver and the density fitting approximation to the electron repulsion integrals, this reformulation yields a dynamical BSE algorithm whose computational time is O(N5), which we verify numerically. Furthermore, the reformulation provides direct access to excited states with dominant double excitation character, which are completely absent in the spectrum of the statically screened BSE. We study the 21Ag state of butadiene, hexatriene, and octatetraene and find that GW/BSE overestimates the excitation energy by about 1.5-2 eV and significantly underestimates the double excitation character.

Calculated linear and nonlinear optical absorption spectra of phosphine-ligated gold clusters

Although prediction of optical excitations of ligated gold clusters by time-dependent density functional theory (TDDFT) is relatively well-established, limitations still exist, for example in the choice of the exchange-correlation functional....

LiF Nanoparticles Enhance Targeted Degradation of Organic Material under Low Dose X-ray Irradiation

The targeted irradiation of structures by X-rays has seen application in a variety of fields. Herein, the use of 5–10 nm LiF nanoparticles to locally enhance the degradation of an organic thin film, diindenoperylene, under hard X-ray irradiation, at relatively low ionizing radiation doses, is shown. X-ray reflectivity analysis indicated that the film thickness increased 12.04 Å in air and 11.34 Å in a helium atmosphere, under a radiation dose of ∼65 J/cm2 for 3 h illumination with a bi-layer structure that contained submonolayer coverage of thermally evaporated LiF. This was accompanied by significant modification of the surface topography for the organic film, which initially formed large flat islands. Accelerated aging experiments suggested that localized heating was not a major mechanism for the observed changes, suggesting a photochemical mechanism due to the formation of reactive species from LiF under irradiation. As LiF has a tendency to form active defects under radiation across the energy spectrum, this could could open a new direction to explore the efficacy of LiF or similar optically active materials that form electrically active defects under irradiation in various applications that could benefit from enhanced activity, such as radiography or targeted X-ray irradiation therapies.

Photoelectron spectra of early 3d-transition metal dioxide molecular anions from GW calculations

Photoelectron spectra of early 3d-transition metal dioxide anions, ScO₂ ^-, TiO₂ ^-, VO₂ ^-, CrO₂ ^-, and MnO₂ ^-, are calculated using semilocal and hybrid density functional theory (DFT) and many-body perturbation theory within the GW approximation using one-shot perturbative and eigenvalue self-consistent formalisms. Different levels of theory are compared with each other and with available photoelectron spectra. We show that one-shot GW with a PBE0 starting point (G₀W₀@PBE0) consistently provides very good agreement for all experimentally measured binding energies (within 0.1 eV-0.2 eV or less). We attribute this to the success of PBE0 in mitigating self-interaction error and providing good quasiparticle wave functions, which renders a first-order perturbative GW correction effective. One-shot GW calculations with a Perdew-Burke-Ernzerhof (PBE) starting point do poorly in predicting electron removal energies by underbinding orbitals with typical errors near 1.5 eV. A higher exact exchange amount of 50% in the DFT starting point of one-shot GW does not provide very good agreement with experiment by overbinding orbitals with typical errors near 0.5 eV. While not as accurate as G₀W₀@PBE0, the G-only eigenvalue self-consistent GW scheme with W fixed to the PBE level provides a reasonably predictive level of theory (typical errors near 0.3 eV) to describe photoelectron spectra of these 3d-transition metal dioxide anions. Adding eigenvalue self-consistency also in W, on the other hand, worsens the agreement with experiment overall. Our findings on the performance of various GW methods are discussed in the context of our previous studies on other transition metal oxide molecular systems.

Ab Initio Many-Body Perturbation Theory Calculations of the Electronic and Optical Properties of Cyclometalated Ir(III) Complexes

Cyclometalated Ir(III) compounds are the preferred choice as organic emitters in organic light-emitting diodes. In practice, the presence of the transition metal surrounded by carefully designed ligands allows fine-tuning of the emission frequency as well as good efficiency of the device. To support the development of new compounds, experimental measurements are generally compared with absorption and emission spectra obtained from ab initio calculations. The standard approach for these calculations is time-dependent density functional theory (TDDFT) with a hybrid exchange-correlation functional like B3LYP. Because of the size of these compounds, the application of more complex quantum chemistry approaches can be challenging. In this work, we used many-body perturbation theory approaches, in particular the GW approximation with the Bethe-Salpeter equation (BSE) implemented in Gaussian basis sets, to calculate the quasiparticle properties and the absorption spectra of six cyclometalated Ir(III) complexes, going beyond TDDFT. In the presented results, we compared standard TDDFT simulations with BSE calculations performed on top of perturbative G₀W₀ and accounting for eigenvalue self-consistency. Moreover, in order to investigate in detail the effect of the DFT starting point, we concentrated on Ir(ppy)₃ and performed GW-BSE simulations starting from different DFT exchange-correlation potentials.

Piecewise linearity, freedom from self-interaction, and a Coulomb asymptotic potential: three related yet inequivalent properties of the exact density functional

Three properties of the exact energy functional of DFT are important in general and for spectroscopy in particular, but are not necessarily obeyed by approximate functionals. We explain what they are, why they are important, and how they are related yet inequivalent.

A comparison between observed and DFT calculations on structure of 5-(4-chlorophenyl)-2-amino-1,3,4-thiadiazole

The crystal and molecular structure of 5-(4-chlorophenyl)-2-amino-1,3,4-thiadiazole 3 was reported, which was characterized by various spectroscopic techniques (FT-IR, NMR and HRMS) and single-crystal X-ray diffraction. The crystal structure 3 (C₈H₆ClN₃S) crystallized in the orthorhombic space group Pna2₁ and the unit cell consisted of 8 asymmetric molecules. The unit cell parameters were a = 11.2027(2) Å, b = 7.6705(2) Å, c = 21.2166(6) Å, α = β = γ = 90°, V = 1823.15(8) ų, Z = 8. In addition, the structural geometry (bond lengths, bond angles, and torsion angles), the electronic properties of mono and dimeric forms of compound 3 were calculated by using the density functional theory (DFT) method at B3LYP level 6-31+ G(d,p), 6-31++ G(d,p) and 6-311+ G(d,p) basis sets in ground state. A good correlation was found (R² = 0.998) between the observed and theoretical vibrational frequencies. Frontier molecular orbitals (HOMO and LUMO) and Molecular Electrostatic Potential map of the compound was produced by using the optimized structures. The NBO analysis was suggested that the molecular system contains N-H…N hydrogen bonding, strong conjugative interactions and the molecule become more polarized owing to the movement of π-electron cloud from donor to acceptor. The calculated structural and geometrical results were in good rational agreement with the experimental X-ray crystal structure data of 1,3,4-thiadiazol-2-amine, 3. The compound 3 exhibited n→π* UV absorption peak of UV cutoff edge, and great magnitude of the first-order hyperpolarizability was observed. The obtained results suggest that compound 3 could have potential application as NLO material. Therefore, this study provides valuable insight experimentally and theoretically, for designing new chemical entities to meet the demands of specific applications.

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

The GW approximation in electronic structure theory has become a widespread tool for predicting electronic excitations in chemical compounds and materials. In the realm of theoretical spectroscopy, the GW method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The number of GW calculations in the past two decades has exploded with increased computing power and modern codes. The success of GW can be attributed to many factors: favorable scaling with respect to system size, a formal interpretation for charged excitation energies, the importance of dynamical screening in real systems, and its practical combination with other theories. In this review, we provide an overview of these formal and practical considerations. We expand, in detail, on the choices presented to the scientist performing GW calculations for the first time. We also give an introduction to the many-body theory behind GW, a review of modern applications like molecules and surfaces, and a perspective on methods which go beyond conventional GW calculations. This review addresses chemists, physicists and material scientists with an interest in theoretical spectroscopy. It is intended for newcomers to GW calculations but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.

Toward Design of Novel Materials for Organic Electronics

Materials for organic electronics are presently used in prominent applications, such as displays in mobile devices, while being intensely researched for other purposes, such as organic photovoltaics, large-area devices, and thin-film transistors. Many of the challenges to improve and optimize these applications are material related and there is a nearly infinite chemical space that needs to be explored to identify the most suitable material candidates. Established experimental approaches struggle with the size and complexity of this chemical space. Herein, the development of simulation methods is addressed, with a particular emphasis on predictive multiscale protocols, to complement experimental research in the identification of novel materials and illustrate the potential of these methods with a few prominent recent applications. Finally, the potential of machine learning and methods based on artificial intelligence is discussed to further accelerate the search for new materials.

Excitation Energies from the Single-Particle Green's Function with the GW Approximation

Quasi-particle energies are important in predicting molecular ionization energies and bulk band structures. The state-of-the-art method for quasi-particle energy calculations, particularly for bulk systems, is the GW approximation. For excited state calculations, one needs to go beyond the GW approximation. The Bethe-Salpeter equation (BSE) is the commonly used approach for bulk-system excited state calculations beyond the GW approximation, which is accurate but computationally cumbersome. In this Article, we develop a new method to extract excitation energies directly from the quasi-particle energies based on the GW approximation. Starting from the ( N - 1)-electron system, we are able to calculate molecular excitation energies with orbital energies at the GW level for HOMO excitations. Our calculations demonstrate that this method can accurately capture low-lying local excitations as well as charge transfer excitations in many molecular systems. Our method is shown to outperform the time-dependent density functional theory (TDDFT) and are comparable with higher level excited state calculations, including the equation-of-motion couple cluster (EOM-CC) theory and the BSE, but with less computational effort. This new approach provides an efficient alternative to the BSE method for accurate excited state calculations.

Transport and Optical Gaps in Amorphous Organic Molecular Materials

The standard procedure to identify the hole- or electron-acceptor character of amorphous organic materials used in OLEDs is to look at the values of a pair of basic parameters, namely, the ionization potential (IP) and the electron affinity (EA). Recently, using published experimental data, the present authors showed that only IP matters, i.e., materials with IP > 5.7 (<5.7) showing electron (hole) acceptor character. Only three materials fail to obey this rule. This work reports ab initio calculations of IP and EA of those materials plus two materials that behave according to that rule, following a route which describes the organic material by means of a single molecule embedded in a polarizable continuum medium (PCM) characterized by a dielectric constant ε . PCM allows to approximately describe the extended character of the system. This "compound" system was treated within density functional theory (DFT) using several combinations of the functional/basis set. In the preset work ε was derived by assuming Koopmans' theorem to hold. Optimal ε values are in the range 4.4⁻5.0, close to what is expected for this material family. It was assumed that the optical gap corresponds to the excited state with a large oscillator strength among those with the lowest energies, calculated with time-dependent DFT. Calculated exciton energies were in the range 0.76⁻1.06 eV, and optical gaps varied from 3.37 up to 4.50 eV. The results are compared with experimental data.

Electronic Excitations in Complex Molecular Environments: Many-Body Green's Functions Theory in VOTCA-XTP

Many-body Green's functions theory within the GW approximation and the Bethe-Salpeter Equation (BSE) is implemented in the open-source VOTCA-XTP software, aiming at the calculation of electronically excited states in complex molecular environments. Based on Gaussian-type atomic orbitals and making use of resolution of identity techniques, the code is designed specifically for nonperiodic systems. Application to a small molecule reference set successfully validates the methodology and its implementation for a variety of excitation types covering an energy range from 2 to 8 eV in single molecules. Further, embedding each GW-BSE calculation into an atomistically resolved surrounding, typically obtained from Molecular Dynamics, accounts for effects originating from local fields and polarization. Using aqueous DNA as a prototypical system, different levels of electrostatic coupling between the regions in this GW-BSE/MM setup are demonstrated. Particular attention is paid to charge-transfer (CT) excitations in adenine base pairs. It is found that their energy is extremely sensitive to the specific environment and to polarization effects. The calculated redshift of the CT excitation energy compared to a nucelobase dimer treated in vacuum is of the order of 1 eV, which matches expectations from experimental data. Predicted lowest CT energies are below that of a single nucleobase excitation, indicating the possibility of an initial (fast) decay of such an UV excited state into a binucleobase CT exciton. The results show that VOTCA-XTP's GW-BSE/MM is a powerful tool to study a wide range of types of electronic excitations in complex molecular environments.

Screening mixing GW/Bethe-Salpeter approach for triplet states of organic molecules

We recently proposed a screening mixing many-body ansatz (Ziaei and Bredow 2017 Phys. Rev. B 96 195115) to decrease the typical overestimation of the Hartree-Fock based GW/Bethe-Salpeter equation (BSE) singlet-singlet excitation energies in molecular systems. Now we have evaluated the accuracy of the proposed scheme for triplet states of a set of 20 organic molecules known as the Thiel set. We show that by mixing different screenings into GW and BSE calculated within random phase approximation (in order to ensure best gap and an optimal exciton binding energy), the total mean absolute error of 0.59 eV in the standard Hartree-Fock based eigenvalue GW/BSE approach is reduced to 0.26 eV for 63 triplet states. We further demonstrate that the quasi-particle self-consistent GW/BSE approach in which orbitals and energies are updated in the Green's function and the dynamically screened interaction mostly and considerably underestimates the excitation energies as shown for a few molecules.

Dielectric Screening Meets Optimally Tuned Density Functionals

A short overview of recent attempts at merging two independently developed methods is presented. These are the optimal tuning of a range-separated hybrid (OT-RSH) functional, developed to provide an accurate first-principles description of the electronic structure and optical properties of gas-phase molecules, and the polarizable continuum model (PCM), developed to provide an approximate but computationally tractable description of a solvent in terms of an effective dielectric medium. After a brief overview of the OT-RSH approach, its combination with the PCM as a potentially accurate yet low-cost approach to the study of molecular assemblies and solids, particularly in the context of photocatalysis and photovoltaics, is discussed. First, solvated molecules are considered, with an emphasis on the challenge of balancing eigenvalue and total energy trends. Then, it is shown that the same merging of methods can also be used to study the electronic and optical properties of molecular solids, with a similar discussion of the pros and cons. Tuning of the effective scalar dielectric constant as one recent approach that mitigates some of the difficulties in merging the two approaches is considered.

Photoelectron spectra of copper oxide cluster anions from first principles methods

We present results and analyses for the photoelectron spectra of small copper oxide cluster anions (CuO^-, Cu O2- , Cu O3- , and Cu₂O^-). The spectra are computed using various techniques, including density functional theory (DFT) with semi-local, global hybrid, and optimally tuned range-separated hybrid functionals, as well as many-body perturbation theory within the GW approximation based on various DFT starting points. The results are compared with each other and with the available experimental data. We conclude that as in many metal-organic systems, self-interaction errors are a major issue that is mitigated by hybrid functionals. However, these need to be balanced against a strong role of non-dynamical correlation-especially in smaller, more symmetric systems-where errors are alleviated by semi-local functionals. The relative importance of the two phenomena, including practical ways of balancing the two constraints, is discussed in detail.

Combining Wave Function Methods with Density Functional Theory for Excited States

We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.

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.

Intermolecular Singlet and Triplet Exciton Transfer Integrals from Many-Body Green's Functions Theory

A general approach to determine orientation and distance-dependent effective intermolecular exciton transfer integrals from many-body Green's functions theory is presented. On the basis of the GW approximation and the Bethe-Salpeter equation (BSE), a projection technique is employed to obtain the excitonic coupling by forming the expectation value of a supramolecular BSE Hamiltonian with electron-hole wave functions for excitations localized on two separated chromophores. Within this approach, accounting for the effects of coupling mediated by intermolecular charge transfer (CT) excitations is possible via perturbation theory or a reduction technique. Application to model configurations of pyrene dimers shows an accurate description of short-range exchange and long-range Coulomb interactions for the coupling of singlet and triplet excitons. Computational parameters, such as the choice of the exchange-correlation functional in the density-functional theory (DFT) calculations that underly the GW-BSE steps and the convergence with the number of included CT excitations, are scrutinized. Finally, an optimal strategy is derived for simulations of full large-scale morphologies by benchmarking various approximations using pairs of dicyanovinyl end-capped oligothiophenes (DCV5T), which are used as donor material in state-of-the-art organic solar cells.

Accurate description of the electronic structure of organic semiconductors by GW methods

Electronic properties associated with charged excitations, such as the ionization potential (IP), the electron affinity (EA), and the energy level alignment at interfaces, are critical parameters for the performance of organic electronic devices. To computationally design organic semiconductors and functional interfaces with tailored properties for target applications it is necessary to accurately predict these properties from first principles. Many-body perturbation theory is often used for this purpose within the GW approximation, where G is the one particle Green's function and W is the dynamically screened Coulomb interaction. Here, the formalism of GW methods at different levels of self-consistency is briefly introduced and some recent applications to organic semiconductors and interfaces are reviewed.