The Bethe-Salpeter formalism with polarisable continuum embedding: reconciling linear-response and state-specific features

Quantum-Quantum and Quantum-Quantum-Classical Schemes for Near-Gap Excitations with Projection-Based-Embedded GW-Bethe-Salpeter Equation

We present quantum-quantum and quantum-quantum-classical schemes based on many-body Green's functions theory in the GW approximation with the Bethe-Salpeter equation (GW-BSE) employing projection-based-embedding (PbE). Such approaches allow defining active and inactive subsystems of larger, complex molecular systems, with only the smaller active subsystem being explicitly treated by GW-BSE offering significant computational advantages. However, as PbE can modify the single-particle states in the Kohn-Sham (KS) ground state calculation and screening effects from the inactive region are not automatically included in GW-BSE, results from such PbE-GW-BSE calculations can deviate from a full-system reference. Here, we scrutinize in detail, e.g., the individual and combined effects of different choices of active regions, the influence of omitting the screening from the inactive region, and strategies for basis set truncation on frontier orbital and near-gap electron-hole excitation energies. As prototypical systems, we consider a diketopyrrolopyrrole bicyclic ring including side-chains, a polarity-sensitive dye (prodan) in aqueous environment, and a π-stacked dimer of benzene and tetracyanoethylene in water, respectively, covering a variety of excitation characters in molecular systems with complex chemical environments and photoinduced processes. Our results suggest that to obtain agreement of approximately 0.1 eV between near-gap excitation energies from embedded and full calculations, the active region should be chosen based on the Mulliken population of the full highest-occupied molecular orbital and that careful benchmarking should be done on the KS level before the actual GW-BSE steps when basis set truncation is used. We find that PbE-GW-BSE offers significant reductions in computation times and, more importantly, memory requirements, making calculations for considerably larger systems tractable.

Beyond Electrons: Correlation and Self-Energy in Multicomponent Density Functional Theory

Post-Kohn-Sham methods are used to evaluate the ground-state correlation energy and the orbital self-energy of systems consisting of multiple flavors of different fermions. Starting from multicomponent density functional theory, suitable ways to arrive at the corresponding multicomponent random-phase approximation and the multicomponent Green's functionG W ${GW}$ approximation, including relativistic effects, are outlined. Given the importance of both of this methods in the development of modern Kohn-Sham density functional approximations, this work will provide a foundation to design advanced multicomponent density functional approximations. Additionally, theG W ${GW}$ quasiparticle energies are needed to study light-matter interactions with the Bethe-Salpeter equation.

Electronic Couplings and Conversion Dynamics between Localized and Charge Transfer Excitations from Many-Body Green's Functions Theory

We investigate the determination of electronic coupling between localized excitations (LEs) and charge-transfer (CT) excitations based on many-body Green's functions theory in the GW approximation with the Bethe-Salpeter equation (GW-BSE). Using a small molecule dimer system, we first study the influence of different diabatization methods, as well as different model choices within GW-BSE, such as the self-energy models or different levels of self-consistency, and find that these choices affect the LE-CT couplings only minimally. We then consider a large-scale low-donor morphology formed from rubrene and fullerene and evaluate the LE-CT couplings based on coupled GW-BSE-molecular mechanics calculations. For these disordered systems of bulky molecules, we observe differences in the couplings based on the Edmiston-Ruedenberg diabatization compared to the more approximate Generalize Mulliken-Hush and fragment charge difference diabatization formalisms. In a kinetic model for the conversion between LE and CT states, these differences affect the details of state populations in an intermediate time scale but not the final populations.

Time-Dependent Multilevel Density Functional Theory

We present a novel three-layer approach based on multilevel density functional theory (MLDFT) and polarizable molecular mechanics to simulate the electronic excitations of chemical systems embedded in an external environment within the time-dependent DFT formalism. In our method, the electronic structure of a target system, the chromophore, is determined in the field of an embedded inactive layer, which is treated as frozen. Long-range interactions are described by employing the polarizable fluctuating charge (FQ) force field. The resulting MLDFT/FQ thus accurately describes both electrostatics (and polarization) and non-electrostatic target-environment interactions. The robustness and reliability of the approach are demonstrated by comparing our results with experimental data reported for various organic molecules in solution.

Elucidating Solvatochromic Shifts in Two-Dimensional Photocatalysts by Solving the Bethe-Salpeter Equation Coupled with Implicit Solvation Method

Many studies have focused on tailoring the photophysical properties of two-dimensional (2D) materials for photocatalytic (PC) or photoelectrochemical (PEC) applications. To understand the optical properties of 2D materials in solution, we established a computational method that combined the Bethe-Salpeter equation (BSE) calculations with our GW-GPE method, allowing for GW/BSE-level calculations with implicit solvation described using the generalized Poisson equation (GPE). We applied this method to MoS2, phosphorene (PP), and g-C3N4 and found that when the solvent dielectric increased, it reduced the exciton binding energy and quasiparticle bandgap, resulting in almost no solvatochromic shift in the excitonic peaks of MoS2 and PP, which is consistent with previous experiments. However, our calculations predicted that the solvent dielectric had a significant impact on the excitonic properties of g-C3N4, exhibiting a large solvatochromic shift. We expect that our GW/BSE-GPE method will offer insights into the design of 2D materials for PC and PEC applications.

Static versus dynamically polarizable environments within the many-body GW formalism

Continuum- or discrete-polarizable models for the study of optoelectronic processes in embedded subsystems rely mostly on the restriction of the surrounding electronic dielectric response to its low frequency limit. Such a description hinges on the assumption that the electrons in the surrounding medium react instantaneously to any excitation in the central subsystem, thus treating the environment in the adiabatic limit. Exploiting a recently developed embedded GW formalism with an environment described at the fully ab initio level, we assess the merits of the adiabatic limit with respect to an environment where the full dynamics of the dielectric response are considered. Furthermore, we show how to properly take the static limit of the environment's susceptibility by introducing the so-called Coulomb-hole and screened-exchange contributions to the reaction field. As a first application, we consider a C60 molecule at the surface of a C60 crystal, namely, a case where the dynamics of the embedded and embedding subsystems are similar. The common adiabatic assumption, when properly treated, generates errors below 10% on the polarization energy associated with frontier energy levels and associated energy gaps. Finally, we consider a water molecule inside a metallic nanotube, the worst case for the environment's adiabatic limit. The error on the gap polarization energy remains below 10%, even though the error on the frontier orbital polarization energies can reach a few tenths of an electronvolt.

Many-body GW calculations with very large scale polarizable environments made affordable: A fully ab initio QM/QM approach

We present a many-body GW formalism for quantum subsystems embedded in discrete polarizable environments containing up to several hundred thousand atoms described at a fully ab initio random phase approximation level. Our approach is based on a fragment approximation in the construction of the Green's function and independent-electron susceptibilities. Further, the environing fragments susceptibility matrices are reduced to a minimal but accurate representation preserving low order polarizability tensors through a constrained minimization scheme. This approach dramatically reduces the cost associated with inverting the Dyson equation for the screened Coulomb potential W, while preserving the description of short to long-range screening effects. The efficiency and accuracy of the present scheme is exemplified in the paradigmatic cases of fullerene bulk, surface, subsurface, and slabs with varying number of layers.

Effects of Solvent Dielectric on Thermally Activated Delayed Fluorescence: A Predictive Computational Polarization Consistent Approach

We study computationally thermally activated delayed fluorescence (TADF) in donor-acceptor compounds. The relevant electronic excited states that are strongly affected by the dielectric environment are treated by a polarization consistent framework. The high fidelity potential energy surfaces are used following a quantum-mechanical Fermi's golden rule (FGR) picture to calculate rates of intersystem crossing (ISC) and reverse intersystem crossing (RISC). To demonstrate the potency of the approach, we consider isomers of benzonitrile functionalized tert-butyl-substituted dimethylacridine (DMAC-BN), which were recently found to perform well as TADF emitters. The calculated excited state energies that appear to reproduce well measured spectral trends with respect to the dielectric constant are used to parametrize ISC/RISC FGR rates. The calculated rates reproduce well measured rates, whereas semiclassical based rates are grossly underestimated. In particular, we find in agreement with the recent experimental study [Phys. Rev. Appl.2019, 12, 044021] that the ortho and meta isomers are significantly more effective as TADF emitters. The computational framework provides valuable insight at the molecular level into RISC rates and therefore can contribute to the design of materials of increased TADF efficiency.

Flavonoids from the roots and rhizomes of Sophoratonkinensis and their in vitro anti-SARS-CoV-2 activity

Acute respiratory infection caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) had caused a global pandemic since 2019, and posed a serious threat to global health security. Traditional Chinese medicine (TCM) has played an indispensable role in the battle against the epidemic. Many components originated from TCMs were found to inhibit the production of SARS-CoV-2 3C-like protease (3CLpro) and papain-like protease (PLpro), which are two promising therapeutic targets to inhibit SARS-CoV-2. This study describes a systematic investigation of the roots and rhizomes of Sophora tonkinensis, which results in the characterization of 12 new flavonoids, including seven prenylated flavanones (1-7), one prenylated flavonol (8), two prenylated chalcones (9-10), one isoflavanone (11), and one isoflavan dimer (12), together with 43 known compounds (13-55). Their structures including the absolute configurations were elucidated by comprehensive analysis of MS, 1D and 2D NMR data, and time-dependent density functional theory electronic circular dichroism (TDDFT ECD) calculations. Compounds 12 and 51 exhibited inhibitory effects against SARS-CoV-2 3CLpro with IC₅₀ values of 34.89 and 19.88 μmol·L^-1, repectively while compounds 9, 43 and 47 exhibited inhibitory effects against PLpro with IC₅₀ values of 32.67, 79.38, and 16.74 μmol·L^-1, respectively.

Quasiparticle Self-Consistent GW-Bethe-Salpeter Equation Calculations for Large Chromophoric Systems

The GW-Bethe–Salpeter equation (BSE) method is promising for calculating the low-lying excitonic states of molecular systems. However, so far it has only been applied to rather small molecules and in the commonly implemented diagonal approximations to the electronic self-energy, it depends on a mean-field starting point. We describe here an implementation of the self-consistent and starting-point-independent quasiparticle self-consistent (qsGW)-BSE approach, which is suitable for calculations on large molecules. We herein show that eigenvalue-only self-consistency can lead to an unfaithful description of some excitonic states for chlorophyll dimers while the qsGW-BSE vertical excitation energies (VEEs) are in excellent agreement with spectroscopic experiments for chlorophyll monomers and dimers measured in the gas phase. Furthermore, VEEs from time-dependent density functional theory calculations tend to disagree with experimental values and using different range-separated hybrid (RSH) kernels does change the VEEs by up to 0.5 eV. We use the new qsGW-BSE implementation to calculate the lowest excitation energies of the six chromophores of the photosystem II (PSII) reaction center (RC) with nearly 2000 correlated electrons. Using more than 11,000 (6000) basis functions, the calculation could be completed in less than 5 (2) days on a single modern compute node. In agreement with previous TD-DFT calculations using RSH kernels on models that also do not include environmental effects, our qsGW-BSE calculations only yield states with local characters in the low-energy spectrum of the hexameric complex. Earlier works with RSH kernels have demonstrated that the protein environment facilitates the experimentally observed interchromophoric charge transfer. Therefore, future research will need to combine correlation effects beyond TD-DFT with an explicit treatment of environmental electrostatics.

Electronic Dynamics of a Molecular System Coupled to a Plasmonic Nanoparticle Combining the Polarizable Continuum Model and Many-Body Perturbation Theory

The efficiency of plasmonic metallic nanoparticles in harvesting and concentrating light energy in their proximity triggers a wealth of important and intriguing phenomena. For example, spectroscopies are able to reach single-molecule and intramolecule sensitivities, and important chemical reactions can be effectively photocatalyzed. For the real-time description of the coupled dynamics of a molecule's electronic system and of a plasmonic nanoparticle, a methodology has been recently proposed (J. Phys. Chem. C. 120, 2016, 28774-28781) which combines the classical description of the nanoparticle as a polarizable continuum medium with a quantum-mechanical description of the molecule treated at the time-dependent configuration interaction (TDCI) level. In this work, we extend this methodology by describing the molecule using many-body perturbation theory: the molecule's excitation energies, transition dipoles, and potentials computed at the GW/Bethe-Salpeter equation (BSE) level. This allows us to overcome current limitations of TDCI in terms of achievable accuracy without compromising on the accessible molecular sizes. We illustrate the developed scheme by characterizing the coupled nanoparticle/molecule dynamics of two prototype molecules, LiCN and p-nitroaniline.

NMR Coupling Constants Based on the Bethe-Salpeter Equation in the GW Approximation

We present the first steps to extend the Green's function GW method and the Bethe-Salpeter equation (BSE) to molecular response properties such as nuclear magnetic resonance (NMR) indirect spin-spin coupling constants. We discuss both a nonrelativistic one-component and a quasi-relativistic two-component formalism. The latter describes scalar-relativistic and spin-orbit effects and allows us to study heavy-element systems with reasonable accuracy. Efficiency is maintained by the application of the resolution of the identity approximation throughout. The performance is demonstrated using conventional central processing units (CPUs) and modern graphics processing units (GPUs) for molecules involving several thousand basis functions. Our results show that a large amount of Hartree-Fock exchange is vital to provide a sufficient Kohn-Sham starting point to compute the GW quasi-particle energies. As the GW-BSE approach is generally less accurate for triplet excitations or related properties such as the Fermi-contact interaction, the admixture of the Kohn-Sham correlation kernel through the contracted BSE (cBSE) method improves the results for NMR coupling constants. This leads to remarkable results when combined with the eigenvalue-only self-consistent variant (evGW) and Becke's half and half functional (BH&HLYP) or the CAM-QTP family. The developed methodology is used to calculate the Karplus curve of tin molecules, illustrating its applicability to extended chemically relevant molecules. Here, the GW-cBSE method improves upon the chosen BH&HLYP Kohn-Sham starting points.

Fragment-Based Excited-State Calculations Using the GW Approximation and the Bethe-Salpeter Equation

Herein, we present a fragment-based approach for calculating the charged and neutral excited states in molecular systems, based on the many-body Green's function method within the GW approximation and the Bethe-Salpeter equation (BSE). The implementation relies on the many-body expansion of the total irreducible polarizability on the basis of fragment molecular orbitals. The GW quasi-particle energies in complex molecular environments are obtained by the GW calculation for the target fragment plus induced polarization contributions of the surrounding fragments at the static Coulomb-hole plus screened exchange level. In addition, we develop a large-scale GW/BSE method for calculating the delocalized excited states of molecular aggregates, based on the fragment molecular orbital method and the exciton model. The accuracy of fragment-based GW and GW/BSE methods was evaluated on molecular clusters and molecular crystals. We found that the accuracy of the total irreducible polarizability can be improved systematically by including two-body correction terms, and the fragment-based calculations can reasonably reproduce the results of the corresponding unfragmented calculations with a relative error of less than 100 meV. The proposed approach enables efficient excited-state calculations for large molecular systems with reasonable accuracy.

Quantum Mechanics/Fluctuating Charge Protocol to Compute Solvatochromic Shifts

Despite the potentialities of the quantum mechanics (QM)/fluctuating charge (FQ) approach to model the spectral properties of solvated systems, its extensive use has been hampered by the lack of reliable parametrizations of solvents other than water. In this paper, we substantially extend the applicability of QM/FQ to solvating environments of different polarities and hydrogen-bonding capabilities. The reliability and robustness of the approach are demonstrated by challenging the model to simulate solvatochromic shifts of four organic chromophores, which display large shifts when dissolved in apolar, aprotic or polar, protic solvents.

Time-Resolved Excited-State Analysis of Molecular Electron Dynamics by TDDFT and Bethe-Salpeter Equation Formalisms

In this work, a theoretical and computational set of tools to study and analyze time-resolved electron dynamics in molecules, under the influence of one or more external pulses, is presented. By coupling electronic-structure methods with the resolution of the time-dependent Schrödinger equation, we developed and implemented the time-resolved induced density of the electronic wavepacket, the time-resolved formulation of the differential projection density of states (ΔPDOS), and of transition contribution map (TCM) to look at the single-electron orbital occupation and localization change in time. Moreover, to further quantify the possible charge transfer, we also defined the energy-integrated ΔPDOS and the fragment-projected TCM. We have used time-dependent density-functional theory (TDDFT), as implemented in ADF software, and the Bethe-Salpeter equation, as provided by MolGW package, for the description of the electronic excited states. This suite of postprocessing tools also provides the time evolution of the electronic states of the system of interest. To illustrate the usefulness of these postprocessing tools, excited-state populations have been computed for HBDI (the chromophore of GFP) and DNQDI molecules interacting with a sequence of two pulses. Time-resolved descriptors have been applied to study the time-resolved electron dynamics of HBDI, DNQDI, LiCN (being a model system for dipole switching upon highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) electronic excitation), and Ag22. The computational analysis tools presented in this article can be employed to help the interpretation of fast and ultrafast spectroscopies on molecular, supramolecular, and composite systems.

Optical and Electronic Properties of Organic NIR-II Fluorophores by Time-Dependent Density Functional Theory and Many-Body Perturbation Theory: GW-BSE Approaches

Organic-molecule fluorophores with emission wavelengths in the second near-infrared window (NIR-II, 1000-1700 nm) have attracted substantial attention in the life sciences and in biomedical applications because of their excellent resolution and sensitivity. However, adequate theoretical levels to provide efficient and accurate estimations of the optical and electronic properties of organic NIR-II fluorophores are lacking. The standard approach for these calculations has been time-dependent density functional theory (TDDFT). However, the size and large excitonic energies of these compounds pose challenges with respect to computational cost and time. In this study, we used the GW approximation combined with the Bethe-Salpeter equation (GW-BSE) implemented in many-body perturbation theory approaches based on density functional theory. This method was used to perform calculations of the excited states of two NIR molecular fluorophores (BTC980 and BTC1070), going beyond TDDFT. In this study, the optical absorption spectra and frontier molecular orbitals of these compounds were compared using TDDFT and GW-BSE calculations. The GW-BSE estimates showed excellent agreement with previously reported experimental results.

Simple Protocol for Capturing Both Linear-Response and State-Specific Effects in Excited-State Calculations with Continuum Solvation Models

We present an effective computational protocol (cLR²) to describe both solvatochromism and fluorosolvatochromism. This protocol, which couples the polarizable continuum model to time-dependent density functional theory, simultaneously accounts for both linear-response and state-specific solvation effects. A series of test cases, including solvatochromic and fluorosolvatochromic compounds and excited-state intramolecular proton transfers, are used to highlight that cLR² is especially beneficial for modeling bright excitations possessing a significant charge-transfer character, as well as cases in which an accurate balance between states of various polarities should be restored.

LayerPCM: An implicit scheme for dielectric screening from layered substrates

We present LayerPCM, an extension of the polarizable-continuum model coupled to real-time time-dependent density-functional theory, for an efficient and accurate description of the electrostatic interactions between molecules and multilayered dielectric substrates on which they are physisorbed. The former are modeled quantum-mechanically, while the latter are treated as polarizable continua characterized by their dielectric constants. The proposed approach is purposely designed to simulate complex hybrid heterostructures with nano-engineered substrates including a stack of anisotropic layers. LayerPCM is suitable for describing the polarization-induced renormalization of frontier energy levels of the adsorbates in the static regime. Moreover, it can be reliably applied to simulating laser-induced ultrafast dynamics of molecules through the inclusion of electric fields generated by Fresnel-reflection at the substrate. Depending on the complexity of the underlying layer structure, such reflected fields can assume non-trivial shapes and profoundly affect the dynamics of the photo-excited charge carriers in the molecule. In particular, the interaction with the substrate can give rise to strong delayed fields, which lead to interference effects resembling those of multi-pulse-based spectroscopy. The robustness of the implementation and the above-mentioned features are demonstrated with a number of examples, ranging from intuitive models to realistic systems.

Strongly Bound Excitons in Metal-Organic Framework MOF-5: A Many-Body Perturbation Theory Study

During the past years, one of the most iconic metal-organic frameworks (MOFs), MOF-5, has been characterized as a semiconductor by theory and experiments. Here we employ the GW many-body perturbation theory in conjunction with the Bethe-Salpeter equation to compute the electronic structure and optical properties of this MOF. The GW calculations show that MOF-5 is a wide-band-gap insulator with a fundamental gap of ∼8 eV. The strong excitonic effects, arising from highly localized states and low screening, result in an optical gap of 4.5 eV and in an optical absorption spectrum in excellent agreement with experiments. The origin of the incorrect conclusion reported by past studies and the implication of this result are also discussed.

A polarizable three-layer frozen density embedding/molecular mechanics approach

We present a novel multilayer polarizable embedding approach in which the system is divided into three portions, two of which are treated using density functional theory and their interaction is based on frozen density embedding (FDE) theory, and both also mutually interact with a polarizable classical layer described using an atomistic model based on fluctuating charges (FQ). The efficacy of the model is demonstrated by extending the formalism to linear response properties and applying it to the simulation of the excitation energies of organic molecules in aqueous solution, where the solute and the first solvation shell are treated using FDE, while the rest of the solvent is modeled using FQ charges.

Subsystem-Based GW/Bethe-Salpeter Equation

Subsystem Density-Functional Theory and its extension to excited states, namely, subsystem Time-Dependent Density-Functional Theory, have been proven to be efficient and accurate fragmentation approaches for ground and excited states. In the present study we extend this approach to the subsystem-based description of total systems by means of GW and the Bethe-Salpeter equation (BSE). For this, we derive the working equations starting from a subsystem-based partitioning of the screened-Coulomb interaction for an arbitrary number of subsystems. Making use of certain approximations, we develop a parameter-free approach in which environmental screening contributions are effectively included for each subsystem. We demonstrate the applicability of these approximations by comparing quasi-particle energies and excitation energies from subsystem-based GW/BSE calculations to the supermolecular reference. Furthermore, we demonstrate the computational efficiency and the usefulness of this method for the description of photoinduced processes in complex chemical environments.

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.

Methine-Quinoidal Fragment Induces Significant Bathochromic Shifts in Organic Dyes

Bathochromical shifts in the UV-vis absorption (and emission) spectra and reduced molecular sizes are two desirable features of organic dyes in many applications, i.e., live-cell fluorescence imaging and solar cells. Yet, these two features are often viewed as contradictory requirements as expanding the π-conjugation is one of the most widely used methods for prompting this redshift. Interestingly, it has been reported that linking a methine-quinoidal unit can result in a significant redshift in the UV-vis absorption spectra in comparison with the methine-benzenoidal constitutional isomers (by 61 nm in dioxane). Herein, using comprehensive quantum chemical calculations with various functionals and solvent formalisms in 10 solvents with different polarities, we demonstrated that the formation of the quinoidal moiety plays a decisive role in this redshift. We further showed that the inclusion of a quinoidal unit without increasing the molecular size represents a general design strategy for the bathochromic shifts of many organic dyes.

Combining multilevel Hartree–Fock and multilevel coupled cluster approaches with molecular mechanics: a study of electronic excitations in solutions

We present the coupling of different quantum-embedding approaches with a third molecular-mechanics layer, which can be either polarizable or non-polarizable.

Simulating Absorption Spectra of Flavonoids in Aqueous Solution: A Polarizable QM/MM Study

We present a detailed computational study of the UV/Vis spectra of four relevant flavonoids in aqueous solution, namely luteolin, kaempferol, quercetin, and myricetin. The absorption spectra are simulated by exploiting a fully polarizable quantum mechanical (QM)/molecular mechanics (MM) model, based on the fluctuating charge (FQ) force field. Such a model is coupled with configurational sampling obtained by performing classical molecular dynamics (MD) simulations. The calculated QM/FQ spectra are compared with the experiments. We show that an accurate reproduction of the UV/Vis spectra of the selected flavonoids can be obtained by appropriately taking into account the role of configurational sampling, polarization, and hydrogen bonding interactions.

TD-DFT and CC2 insights into the dual-emissive behaviour of 2-(2'-hydroxyphenyl)oxazoles core and their derivatives

Two efficient excited state intramolecular proton transfer (ESIPT) dyes based on the hydroxyphenyl-oxazole core and containing one or two triphenylamine donor groups are explored with theoretical tools. These compounds are known to show clear experimental dual emission behaviour, leading to nearly pure white-light emission for one derivative. To probe the excited state properties, we use both Time Dependent Density Functional Theory (TD-DFT) and post Hartree-Fock methods [ADC(2) and CC2] coupled to different solvent models to describe polarisation effects. After validating our theoretical protocol on the two known systems, we design 14 new derivatives with different substitution patterns to quantify the impact of electron accepting and donating groups on the fluorescence spectrum and the ESIPT mechanism. We show that the selected protocol delivers accurate spectroscopic values for the two experimentally-characterised structures, and more importantly, that the relative stabilisation of the keto tautomer depends on the substitution side. Adding donor or acceptor groups to the ESIPT donor moiety favours the formation of the keto form, whereas when placed on the ESIPT accepting side, they tend to preclude ESIPT. Moreover, combining two donor or acceptor substituents generally results in similar ESIPT behaviour as single substitution on one of the two sides: simple additive rules do not apply.

Orientation dependent molecular electrostatics drives efficient charge generation in homojunction organic solar cells

Organic solar cells usually utilise a heterojunction between electron-donating (D) and electron-accepting (A) materials to split excitons into charges. However, the use of D-A blends intrinsically limits the photovoltage and introduces morphological instability. Here, we demonstrate that polycrystalline films of chemically identical molecules offer a promising alternative and show that photoexcitation of α-sexithiophene (α-6T) films results in efficient charge generation. This leads to α-6T based homojunction organic solar cells with an external quantum efficiency reaching up to 44% and an open-circuit voltage of 1.61 V. Morphological, photoemission, and modelling studies show that boundaries between α-6T crystalline domains with different orientations generate an electrostatic landscape with an interfacial energy offset of 0.4 eV, which promotes the formation of hybridised exciton/charge-transfer states at the interface, dissociating efficiently into free charges. Our findings open new avenues for organic solar cell design where material energetics are tuned through molecular electrostatic engineering and mesoscale structural control.

The Bethe-Salpeter Equation Formalism: From Physics to Chemistry

The Bethe-Salpeter equation (BSE) formalism is steadily asserting itself as a new efficient and accurate tool in the ensemble of computational methods available to chemists in order to predict optical excitations in molecular systems. In particular, the combination of the so-called GW approximation, giving access to reliable ionization energies and electron affinities, and the BSE formalism, able to model UV/vis spectra, has shown to provide accurate singlet excitation energies with a typical error of 0.1-0.3 eV. With a similar computational cost as time-dependent density-functional theory (TD-DFT), BSE is able to provide an accuracy on par with the most accurate global and range-separated hybrid functionals without the unsettling choice of the exchange-correlation functional, resolving further known issues (e.g., charge-transfer excitations). In this Perspective, we provide a historical overview of BSE, with a particular focus on its condensed-matter roots. We also propose a critical review of its strengths and weaknesses in different chemical situations.

Antiadiabatic View of Fast Environmental Effects on Optical Spectra

An antiadiabatic approach is proposed to model how the refractive index of the surrounding medium affects optical spectra of molecular systems in condensed phases. The approach solves some of the issues affecting current implementations of continuum solvation models and more generally of effective models where a classical description is adopted for the molecular environment.

Dual fluorescence in strap ESIPT systems: a theoretical study

Alkylamine-strapped chromophores based on a dithienylpyrrole core, and in which the Excited State Intramolecular Proton Transfer (ESIPT) process yields a zwitterionic structure rather than a keto tautomer have been reported recently (Suzuki et al., Angew. Chem. Int. Ed., 2014, 53, 8231), and are known to exhibit large Stokes shifts. Using Time-Dependent Density Functional Theory (TD-DFT) we investigate the ESIPT mechanism in this family of chromophores considering various substituents and two solvents (cyclohexane and acetone). In order to model the solvent effects, three polarisation models have been applied: the linear response (LR), the corrected linear-response (cLR), and the combination of these two formalisms (LR + cLR). The selected protocol is shown to be effective for a series of compounds with known experimental behaviors, and is then applied to novel derivatives with various donor and acceptor groups and heteroatoms. We determine the absorption and emission wavelengths as well as the energies of the different states that play a role in the ESIPT process. We show that the introduction of electron-withdrawing and electron-donating groups plays an important role in achieving redshifted emission from the ESIPT state.

Electronic transitions for a fully polarizable QM/MM approach based on fluctuating charges and fluctuating dipoles: Linear and corrected linear response regimes

The fully polarizable Quantum Mechanics/Molecular Mechanics (QM/MM) approach based on fluctuating charges and fluctuating dipoles, named QM/FQFμ [T. Giovannini et al., J. Chem. Theory Comput. 15, 2233 (2019)], is extended to the calculation of vertical excitation energies of solvated molecular systems. Excitation energies are defined within two different solvation regimes, i.e., linear response (LR), where the response of the MM portion is adjusted to the QM transition density, and corrected-Linear Response (cLR) in which the MM response is adjusted to the relaxed QM density, thus being able to account for charge equilibration in the excited state. The model, which is specified in terms of three physical parameters (electronegativity, chemical hardness, and polarizability) is applied to vacuo-to-water solvatochromic shifts of aqueous solutions of para-nitroaniline, pyridine, and pyrimidine. The results show a good agreement with their experimental counterparts, thus highlighting the potentialities of this approach.

Quantum Confinement Effects on Solvatochromic Shifts of Molecular Solutes

We demonstrate the pivotal role of quantum mechanics density confinement effects on solvatochromic shifts. In particular, by resorting to a quantum mechanics/molecular mechanics (QM/MM) approach capable of accounting for confinement effects we successfully reproduce vacuo-to-water solvatochromic shifts for dark n → π* and bright π → π* transitions of acrolein and dark n → π* transitions of pyridine and pyrimidine without the need of including explicit water molecules in the QM portion. Remarkably, our approach is also able to dissect the effects of the single forces acting on the solute-solvent couple and allows for a rationalization of the experimental findings in terms of physicochemical quantities.

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.

The role of solvation models on the computed absorption and emission spectra: the case of fireflies oxyluciferin

Absorption and emission energies calculation covering both implicit and explicit solvation models using oxyluciferin as the case of study.

First-principles investigation of the double ESIPT process in a thiophene-based dye

Explanation of the experimental triple emission with theoretical tools requires advanced solvent models.