New tools for the systematic analysis and visualization of electronic excitations. II. Applications

Coupled-cluster treatment of complex open-shell systems: the case of single-molecule magnets

We investigate the reliability of two cost-effective coupled-cluster methods for computing spin-state energetics and spin-related properties of a set of open-shell transition-metal complexes. Specifically, we employ the second-order approximate coupled-cluster singles and doubles (CC2) method and projection-based embedding that combines equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) with density functional theory (DFT). The performance of CC2 and EOM-CCSD-in-DFT is assessed against EOM-CCSD. The chosen test set includes two hexaaqua transition-metal complexes containing Fe(II) and Fe(III), and a large Co(II)-based single-molecule magnet with a non-aufbau ground state. We find that CC2 describes the excited states more accurately, reproducing EOM-CCSD excitation energies within 0.05 eV. However, EOM-CCSD-in-DFT excels in describing transition orbital angular momenta and spin-orbit couplings. Moreover, for the Co(II) molecular magnet, using EOM-CCSD-in-DFT eigenstates and spin-orbit couplings, we compute spin-reversal energy barriers, as well as temperature-dependent and field-dependent magnetizations and magnetic susceptibilities that closely match experimental values within spectroscopic accuracy. These results underscore the efficiency of CC2 in computing state energies of multi-configurational, open-shell systems and highlight the utility of the more cost-efficient EOM-CCSD-in-DFT for computing spin-orbit couplings and magnetic properties of complex and large molecular magnets.

Facilitating Electron Transfer by Resizing Cyclocarbon Acceptor from C18 to C16

Recent advances in synthetic methods, combined with tip-induced on-surface chemistry, have enabled the formation of numerous cyclocarbon molecules. Here, we investigate computationally the experimentally studied C16 and C18 molecules as well as their van der Waals (vdW) complexes with several typical donor and acceptor molecules. Our results demonstrate a remarkable electron-withdrawing ability of cyclocarbon molecules. The vdW complexes of C16 and C18 exhibit a thermodynamically favorable photoinduced electron transfer (ET) from the donor partner to the cyclocarbons that occurs on a picosecond time scale. The lower reorganization energy of C16 compared to C18 leads to a significant acceleration of the ET reactions.

Two- and one-photon absorption spectra of aqueous thiocyanate anion highlight the role of symmetry in the condensed phase

We present the two-photon absorption (2PA) spectrum of aqueous thiocyanate calculated using high-level quantum-chemistry methods. The 2PA spectrum is compared to the one-photon absorption (1PA) spectrum computed using the same computational protocol. Although the two spectra probe the same set of electronic states, the intensity patterns are different, leading to an apparent red-shift of the 2PA spectrum relative to the 1PA spectrum. The presented analysis explains the intensity patterns and attributes the differences between the 1PA and 2PA spectra to the native symmetry of isolated SCN  - , which influences the spectra in the low-symmetry solvated environment. The native symmetry also manifests itself in variations of the polarization ratio (e.g., parallel vs. perpendicular cross sections) across the spectrum. The presented results highlight the potential of 2PA spectroscopy and high-level quantum-chemistry methods in studies of condensed-phase phenomena.

Multiexcitonic and optically bright states in subunits of pentacene crystals: A hybrid DFT/MRCI and molecular mechanics study

A hybrid quantum mechanics/molecular mechanics setup was used to model electronically excited pentacene in the crystal phase. Particularly interesting in the context of singlet fission (SF) is the energetic location of the antiferromagnetically coupled multiexcitonic singlet state, 1(TT), and the ferromagnetically coupled analog in relation to the optically bright singlet state. To provide photophysical properties of the accessible spin manifold, combined density functional theory and multi-reference configuration interaction calculations were performed on pentacene dimers and a trimer, electrostatically embedded in the crystal. The likelihood of a quintet intermediate in the SF process was estimated by computing singlet-quintet electron spin-spin couplings employing the Breit-Pauli Hamiltonian. The performance of the applied methods was assessed on the pentacene monomer. The character of the optically bright state and the energetic location of the 1(TT) state depend strongly on the relative orientation of the pentacene units. In the V-shaped dimers and in the trimer, the optically bright state is dominated by local and charge transfer (CT) excitations, with admixtures of doubly excited configurations. The CT excitations gain weight upon geometry relaxation, thus supporting a CT-mediated SF mechanism as the primary step of the SF process. For the slip-stacked dimer, the energetic order of the bright and the 1(TT) states swaps upon geometry relaxation, indicating strong nonadiabatic coupling close to the Franck-Condon region-a prerequisite for a coherent SF process. The multiexcitonic singlet, triplet, and quintet states are energetically too far apart and their spin-spin couplings are too small to bring about a noteworthy multiplicity mixing.

Revisiting the benzene excimer using [2,2] paracyclophane model system: Experiment and theory

We report high-level calculations of the excited states of [2,2]-paracyclophane (PCP), which was recently investigated experimentally by ultrafast pump-probe experiments on oriented single crystals [Haggag et al., ChemPhotoChem 6 e202200181 (2022)]. PCP, in which the orientation of the two benzene rings and their range of motion are constrained, serves as a model for studying benzene excimer formation. The character of the excimer state and the state responsible for the brightest transition are similar to those of the benzene dimer. The constrained structure of PCP allows one to focus on the most important degree of freedom, the inter-ring distance. The calculations explain the main features of the transient absorption spectral evolution. This brightest transition of the excimer is polarized along the inter-fragment axis. The absorption of the light polarized in the plane of the rings reveals the presence of other absorbing states of Rydberg character, with much weaker intensities. We also report new transient absorption data obtained by a broadband 8 fs pump, which time-resolve strong modulations of the excimer absorption. The combination of theory and experiment provides a detailed picture of the evolution of the electronic structure of the PCP excimer in the course of a single molecular vibration.

Performance of Density Functionals for Excited-State Properties of Isolated Chromophores and Exciplexes: Emission Spectra, Solvatochromic Shifts, and Charge-Transfer Character

This study assesses the performance of various meta-generalized gradient approximation (meta-GGA), global hybrid, and range-separated hybrid (RSH) density functionals in capturing the excited-state properties of organic chromophores and their excited-state complexes (exciplexes). Motivated by their uses in solar energy harvesting and photoredox CO2 reduction, we use oligo-(p-phenylenes) and their excited-state complexes with triethylamine as model systems. We focus on the fluorescence properties of these systems, specifically emission energies. We also consider solvatochromic shifts and wave function characteristics. The latter is described by using reduced quantities such as natural transition orbitals (NTOs) and exciton descriptors. The functionals are benchmarked against the experimental fluorescence spectra and the equation-of-motion coupled-cluster method with single and double excitations. Both in isolated chromophores and in exciplexes, meta-GGA functionals drastically underestimate the emission energies and exhibit significant exciton delocalization and anticorrelation between electron and hole motion. The performance of global hybrid functionals is strongly dependent on the percentage of exact exchange. Our study identifies RSH GGAs as the best-performing functionals, with ωPBE demonstrating the best agreement with experimental results. RSH meta-GGAs often overestimate emission energies in exciplexes and yield larger hole NTOs. Their performance can be improved by optimally tuning the range-separation parameter.

Predictions of photophysical properties of phosphorescent platinum(II) complexes based on ensemble machine learning approach

Cyclometalated Pt(II) complexes are popular phosphorescent emitters with color-tunable emissions. To render their practical applications as organic light-emitting diodes emitters, it is required to develop Pt(II) complexes with high radiative decay rate constant and photoluminescence (PL) quantum yield. Here, a general protocol is developed for accurate predictions of emission wavelength, radiative decay rate constant, and PL quantum yield based on the combination of first-principles quantum mechanical method, machine learning, and experimental calibration. A new dataset concerning phosphorescent Pt(II) emitters is constructed, with more than 200 samples collected from the literature. Features containing pertinent electronic properties of the complexes are chosen and ensemble learning models combined with stacking-based approaches exhibit the best performance, where the values of squared correlation coefficients are 0.96, 0.81, and 0.67 for the predictions of emission wavelength, PL quantum yield and radiative decay rate constant, respectively. The accuracy of the protocol is further confirmed using 24 recently reported Pt(II) complexes, which demonstrates its reliability for a broad palette of Pt(II) emitters.

Electrochemical Diselenation of BODIPY Fluorophores for Bioimaging Applications and Sensitization of 1 O2

We report a rapid, efficient, and scope-extensive approach for the late-stage electrochemical diselenation of BODIPYs. Photophysical analyses reveal red-shifted absorption - corroborated by TD-DFT and DLPNO-STEOM-CCSD computations - and color-tunable emission with large Stokes shifts in the selenium-containing derivatives compared to their precursors. In addition, due to the presence of the heavy Se atoms, competitive ISC generates triplet states which sensitize 1 O2 and display phosphorescence in PMMA films at RT and in a frozen glass matrix at 77 K. Importantly, the selenium-containing BODIPYs demonstrate the ability to selectively stain lipid droplets, exhibiting distinct fluorescence in both green and red channels. This work highlights the potential of electrochemistry as an efficient method for synthesizing unique emission-tunable fluorophores with broad-ranging applications in bioimaging and related fields.

Visualizing and characterizing excited states from time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) is the most widely-used electronic structure method for excited states, due to a favorable combination of low cost and semi-quantitative accuracy in many contexts, even if there are well recognized limitations. This Perspective describes various ways in which excited states from TD-DFT calculations can be visualized and analyzed, both qualitatively and quantitatively. This includes not just orbitals and densities but also well-defined statistical measures of electron-hole separation and of Frenkel-type exciton delocalization. Emphasis is placed on mathematical connections between methods that have often been discussed separately. Particular attention is paid to charge-transfer diagnostics, which provide indicators of when TD-DFT may not be trustworthy due to its categorical failure to describe long-range electron transfer. Measures of exciton size and charge separation that are directly connected to the underlying transition density are recommended over more ad hoc metrics for quantifying charge-transfer character.

Density-functional theory (DFT) and time-dependent DFT study of the chemical and physical origins of key photoproperties of end-group derivatives of a nonfullerene acceptor molecule for bulk heterojunction organic solar cells

As emphasized in a recent review article (Chem. Rev. 2022, 122, 14180), organic solar cell (OSC) photoconversion efficiency has been rapidly evolving with results increasingly comparable to those of traditional inorganic solar cells. Historically, OSC performance improvement focused first on the morphology of P3HT:PC 61 BM solar cells then went through different stages to shift lately interest towards nonfullerene acceptors (NFAs) as a replacement ofPC 61 BM acceptor (ACC) molecule. Here, we use density-functional theory (DFT) and time-dependent DFT to investigate four novel NFAs of A-D-A (acceptor-donor-acceptor) form derived from the recently synthesized IDIC-4Cl (Dyes Pigm. 2019, 166, 196). Our level of theory is carefully evaluated for IDIC-4Cl and then applied to the four novel NFAs in order to understand how chemical modifications lead to physical changes in cyclic voltammetry (CV) frontier molecular orbital energies and absorption spectra in solution. Finally we design and apply a new type of Scharber plot for NFAs based upon some simple but we think reasonable assumptions. Unlike the original Scharber plots where a larger DON band gap favors a larger PCE, our modified Scharber plot reflects the fact that a smaller ACC band gap may favor PCE by filling in gaps in the DON acceptor spectrum. We predict that only the candidate molecule with the least good acceptor A, with the highest frontier molecular orbital energies, and one of the larger CV lowest unoccupied molecular orbital (LUMO) - highest unoccupied molecular orbital (HOMO) gaps, will yield a PM6:ACC PCE exceeding that of the parent IDIC-4Cl ACC. This candidate also shows the largest oscillator strength for the primary1 (HOMO, LUMO) charge- transfer transition and the largest degree of delocalization of charge transfer of any of the ACC molecules investigated here.

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics

When molecules are coupled to an optical cavity, new light-matter hybrid states, so-called polaritons, are formed due to quantum light-matter interactions. With the experimental demonstrations of modifying chemical reactivities by forming polaritons under strong light-matter interactions, theorists have been encouraged to develop new methods to simulate these systems and discover new strategies to tune and control reactions. This review summarizes some of these exciting theoretical advances in polariton chemistry, in methods ranging from the fundamental framework to computational techniques and applications spanning from photochemistry to vibrational strong coupling. Even though the theory of quantum light-matter interactions goes back to the midtwentieth century, the gaps in the knowledge of molecular quantum electrodynamics (QED) have only recently been filled. We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their connections to various quantum optics models. Then, we review recently developed ab initio QED approaches which can accurately describe polariton states in a realistic molecule-cavity hybrid system. We then discuss applications using these method advancements. We review advancements in polariton photochemistry where the cavity is made resonant to electronic transitions to control molecular nonadiabatic excited state dynamics and enable new photochemical reactivities. When the cavity resonance is tuned to the molecular vibrations instead, ground-state chemical reaction modifications have been demonstrated experimentally, though its mechanistic principle remains unclear. We present some recent theoretical progress in resolving this mystery. Finally, we review the recent advances in understanding the collective coupling regime between light and matter, where many molecules can collectively couple to a single cavity mode or many cavity modes. We also lay out the current challenges in theory to explain the observed experimental results. We hope that this review will serve as a useful document for anyone who wants to become familiar with the context of polariton chemistry and molecular cavity QED and thus significantly benefit the entire community.

Natural orbitals and two-particle correlators as tools for the analysis of effective exchange couplings in solids

Using generalizations of spin-averaged natural orbitals and two-particle charge correlators for solids, we investigate the electronic structure of antiferromagnetic transition-metal oxides with a fully self-consistent, imaginary-time GW method. Our findings disagree with the Goodenough-Kanamori (GK) rules that are commonly used for the qualitative interpretation of such solids. First, we found a strong dependence of the natural orbital occupancies on momenta, contradicting GK assumptions. Second, along the momentum path, the character of natural orbitals changes. In particular, the contributions of oxygen 2s orbitals are important, which has not been considered in the GK rules. To analyze the influence of the electronic correlation on the values of effective exchange coupling constants, we use both natural orbitals and two-particle correlators and show that electronic screening modulates the degree of superexchange by stabilizing the charge-transfer contributions, which greatly affects these coupling constants. Finally, we give a set of predictions and recommendations regarding the use of density functional, Green's function, and wave-function methods for evaluating effective magnetic couplings in molecules and solids.

The inverted singlet-triplet gap: a vanishing myth?

Molecules with an inverted singlet-triplet gap (STG) between the first excited singlet and triplet states, for example, heptazine, have recently been reported and gained substantial attention since they violate the famous Hund's rule. Utilizing state-of-the-art high-level ab initio methods, the singlet-triplet gap vanishes and approaches zero from below whatever is improved in the theoretical description of the molecules: the basis set or the level of electron correlation. Seemingly, the phenomenon of inverted singlet-triplet gaps tends to vanish the closer we observe.

On the Cooperative Origin of Solvent-Enhanced Symmetry-Breaking Charge Transfer in a Covalently Bound Tetracene Dimer Leading to Singlet Fission

Singlet fission in covalently bound acene dimers in solution is driven by the interplay of excitonic and singlet correlated triplet ¹(TT) states with intermediate charge-transfer states, a process which depends sensitively on the solvent environment. We use high-level electronic structure methods to explore this singlet fission process in a linked tetracene dimer, with emphasis on the symmetry-breaking mechanism for the charge-transfer (CT) states induced by low-frequency antisymmetric vibrations and polar/polarizable solvents. A combination of the second-order algebraic diagrammatic construction (ADC(2)) and density functional theory/multireference configuration interaction (DFT/MRCI) methods are employed, along with a state-specific conductor-like screening model (COSMO) solvation model in the former case. This work quantifies, for the first time, an earlier mechanistic proposal [Alvertis et al., J. Am. Chem. Soc. 2019, 141, 17558] according to which solvent-induced symmetry breaking leads to a high-energy CT state which interacts with the correlated triplet state, resulting in singlet fission. An approximate assessment of the nonadiabatic interactions between the different electronic states underscores that the CT states are essential in facilitating the transition from the bright excitonic state to the ¹(TT) state leading to singlet fission. We show that several types of symmetry-breaking inter- and intra-fragment vibrations play a crucial role in a concerted mechanism with the solvent environment and with the symmetric inter-fragment torsion, which tunes the admixture of excitonic and CT states. This offers a new perspective on how solvent-induced symmetry-breaking CT can be understood and how it cooperates with intramolecular mechanisms in singlet fission.

Either Accurate Singlet-Triplet Gaps or Excited-State Structures: Testing and Understanding the Performance of TD-DFT for TADF Emitters

The energy gap between the lowest singlet and triplet excited states (ΔE_ST) is a key property of thermally activated delayed fluorescence (TADF) emitters, where these states are dominated by charge-transfer (CT) character. Despite its well-known shortcomings concerning CT states, time-dependent density functional theory (TD-DFT) is widely used to predict this gap and study TADF. Moreover, polar CT states exhibit a strong interaction with their molecular environment, which further complicates their computational description. Addressing these two major challenges, this work studies the performance of Tamm-Dancoff-approximated TD-DFT (TDA-DFT) on the recent STGABS27 benchmark set,¹ exploring different strategies to include orbital and structural relaxation, as well as dielectric embedding. The results show that the best-performing strategy is to calculate ΔE_ST at the ground-state structure using functionals with a surprisingly small amount of Fock exchange of ≈10% and without a (complete) solvent model. However, as this approach heavily relies on error cancellation to mimic dielectric relaxation, it is not robust and exhibits large systematic deviations in excited state energies, state characters, and structures. More rigorous approaches, including state-specific solvation, do not share these systematic deviations, but their predicted ΔE_ST values exhibit larger statistical errors. We thus conclude that for the description of CT states in dielectric environments, none of the tested TDA-DFT methods is competitive with the recently presented ROKS/PCM approach regarding robustness, accuracy, and computational efficiency.

A posteriori localization of many-body excited states through simultaneous diagonalization

In this paper we propose a numerical method to localize many-electron excited states. To characterize the electronic structure of the electronic excited states of a system, quantum chemistry methods typically yield a delocalized description of the excitations. Some a priori localization methods have been developed to provide an intuitive local picture of the excited states. They typically require a good strategy to separate the system of interest from its environment, or a set of a priori localized orbitals, that may reduce their computational accuracy. Here, we introduce an a posteriori method to localize delocalized many-body excited states directly obtained from quantum chemistry calculations. A localization metric for the excited states is defined from their representation as electron-hole pairs, which is encoded in the transition density matrix. This novel a posteriori strategy thus allows to localize excitons within a volume around selected fragments of a complex molecular system without tempering with its quantum chemical treatment. The method is tested on π-stacked oligomers of phenanthrenes and pyrenes. It is found to efficiently localize and separate the excitons according to their character while preserving the information about delocalized many-body states at a low computational cost.

Cherry-Picking Resolvents: Recovering the Valence Contribution in X-ray Two-Photon Absorption within the Core-Valence-Separated Equation-of-Motion Coupled-Cluster Response Theory

Calculations of first-order response wave functions in the X-ray regime often diverge within correlated frameworks such as equation-of-motion coupled-cluster singles and doubles (EOM-CCSD), a consequence of the coupling with the valence ionization continuum. Here, we extend our strategy of introducing a hierarchy of approximations to the EOM-EE-CCSD resolvent (or, inversely, the model Hamiltonian) involved in the response equations for the calculation of X-ray two-photon absorption (X2PA) cross sections. We exploit the frozen-core core-valence separation (fc-CVS) scheme to first decouple the core and valence Fock spaces, followed by a separate approximate treatment of the valence resolvent. We demonstrate the robust convergence of X-ray response calculations within this framework and compare X2PA spectra of small benchmark molecules with the previously reported density functional theory results.

Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges

Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin–orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm–Dancoff approximation to TDDFT, spin–flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine–Ag20 complex), we emphasize that caution is needed to properly account for system–environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.

Exploring the accuracy and usefulness of semi-empirically scaled ADC schemes by blending second and third order terms

Different approaches to mixed-order algebraic-diagrammatic construction (ADC) schemes are investigated. The performance of two different strategies for scaling third-order contributions to the ADC secular matrix is evaluated. Both considered schemes employ a single tuning parameter and conserve general properties inherent to all ADC methods such as hermiticity and size-consistency.The first approach, scaled-matrix ADC[(2)+x(3)], scales all contributions first occurring in ADC(3) equally and leads to an improvement of the accuracy of excitation energies compared to ADC(3) for x=0.4-0.5. However, with respect to excited state dipole moments this method provides lower accuracy than ADC(3). The second scaling approach, MP[(1)+x(2)]-ISR(3), scales the second order contributions of the ground-state wavefunction and derives a rigorous ADC scheme via the intermediate state representation (ISR) formalism. Although the error in excitation energies is not improved, this method provides insight into the relevance of the individual terms of the ADC(3) matrix and indicates, that the MP(2) wavefunction is indeed the optimal reference wavefunction for deriving a third-order single-reference ADC scheme.

Effects of Heterocyclic Ring Fusion and Chain Elongation on Chiroptical Properties of Polyaza[9]helicene: A Computational Study

In the present work, the effect of lateral and helical extensions on the physical and chiroptical properties of azahelicenes is reported. Starting with the experimentally reported polyaza[9]helicene (9Ha), three derivatives, two with laterally fused electron-withdrawing rings and the third with larger helical length, are designed. For the excited-state properties such as UV-vis and CD spectra, performances of different DFT functionals are evaluated by comparing the energies and characters of the excited states against the ADC(2) results. CPL properties are calculated at DFT level. Among the three designed systems, pyrazine-based 9HaP shows an improved g_CPL value compared to that for parent 9Ha. However, quinoxaline-based 9HaQ is found to be the worst CPL emitter with the lowest dissymmetry factor. The helically extended derivative, 11Ha, shows good CPL results, but g_CPL remains smaller than that for the parent system. The CPL results are analyzed in terms of electric dipole transition moment (EDTM) and magnetic dipole transition moment (MDTM) vectors, and angles between these two vectors.

Design of Bis(1,10-phenanthroline) Copper(I)-Based Mechanochromic Indicators

In the growing field of single-molecule mechanochromism, the potential of transition metal complexes is yet to be examined. In this work, we have synthesized a series of [Cu(phen)₂]⁺ complexes: bis-Cu(I)-phenanthroline, bis-Cu(I)-phenanthroline-2-amine, and bis-Cu(I)-phenanthroline-2-acetamide. After that, we characterized the complexes by UV-vis spectroscopy and employed density functional theory (DFT) calculations to investigate the changes in UV-vis upon mechanical pulling via force calculations. The results of our examination of time-dependent (TD)-DFT-calculated UV-vis suggests that the bis-Cu(I)-phenanthroline-2-acetamide complex is predicted to have an observable shift of the metal-to-ligand charge transfer band upon pulling from 0 to 0.6 nN in the visible region. We have demonstrated the ability to synthesize and characterize bis-Cu(I)-phenanthroline-2-acetamide. In addition, the TD-DFT calculations predict an observable shift in the visible region of the UV-vis spectrum. This indicates that transition metal complexes are feasible candidates as mechanophores and are worthy of further exploration as to their potential role in a new subclass of mechanochromic indicators.

Lack of the ESIPT band of aromatic ortho-aminoaldehyde derivatives triggered by N-H vibration

The excited state intramolecular proton transfer (ESIPT) reactions and the fluorescence emission spectra of o-aminoaldehyde and o-aminoketone derivatives were systematically studied with density functional theory (DFT) and time-dependent density functional theory (TDDFT). The results suggest that the ESIPT process can be characterized as an ultra-fast process and that N-H vibration plays an important role in fluorescence emissions. The minimum energy pathways (MEP) on the excited states along the proton transfer coordinates (N-H vibration) were constructed for both o-aminoaldehyde and o-aminoketone derivatives, respectively, which showed a small barrier between the normal and tautomer (ESIPT) structures. By comparing the proton transfer barriers (E_b) and the N-H reorganization energies (λeleNH), we find that λeleNH is less than E_b in o-aminoketone derivatives, while λeleNH is greater than E_b in o-aminoaldehyde derivatives. It is clear that protons could move freely in o-aminoaldehyde derivatives, and thus only one normal emission band could be observed. Subsequently, the fluorescence emission spectra upon introduction of the N-H vibration effect can further confirm this mechanism, and the simulated spectra are in good agreement with the experimental observations, in which the o-aminoaldehyde derivatives have only one normal emission band while the o-aminoketone derivatives have two emission bands corresponding to the normal and tautomer structures. Consequently, this work can elucidate the lack of the ESIPT band in o-aminoaldehyde derivatives and also offer new insight into ESIPT by considering the vibronic effect.

Energy Landscape of State-Specific Electronic Structure Theory

State-specific approximations can provide a more accurate representation of challenging electronic excitations by enabling relaxation of the electron density. While state-specific wave functions are known to be local minima or saddle points of the approximate energy, the global structure of the exact electronic energy remains largely unexplored. In this contribution, a geometric perspective on the exact electronic energy landscape is introduced. On the exact energy landscape, ground and excited states form stationary points constrained to the surface of a hypersphere, and the corresponding Hessian index increases at each excitation level. The connectivity between exact stationary points is investigated, and the square-magnitude of the exact energy gradient is shown to be directly proportional to the Hamiltonian variance. The minimal basis Hartree-Fock and excited-state mean-field representations of singlet H₂ (STO-3G) are then used to explore how the exact energy landscape controls the existence and properties of state-specific approximations. In particular, approximate excited states correspond to constrained stationary points on the exact energy landscape, and their Hessian index also increases for higher energies. Finally, the properties of the exact energy are used to derive the structure of the variance optimization landscape and elucidate the challenges faced by variance optimization algorithms, including the presence of unphysical saddle points or maxima of the variance.

A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Bicyclic Systems

Pursuing our efforts to define highly accurate estimates of the relative energies of excited states in organic molecules, we investigate, with coupled-cluster methods including iterative triples (CC3 and CCSDT), the vertical excitation energies of 10 bicyclic molecules (azulene, benzoxadiazole, benzothiadiazole, diketopyrrolopyrrole, furofuran, phthalazine, pyrrolopyrrole, quinoxaline, tetrathiafulvalene, and thienothiophene). In total, we provide aug-cc-pVTZ reference vertical excitation energies for 91 excited states of these relatively large systems. We use these reference values to benchmark various wave function methods, i.e., CIS(D), EOM-MP2, CC2, CCSD, STEOM-CCSD, CCSD(T)(a)*, CCSDR(3), CCSDT-3, ADC(2), ADC(2.5), and ADC(3), as well as some spin-scaled variants of both CC2 and ADC(2). These results are compared to those obtained previously on smaller molecules. It turns out that while the accuracy of some methods is almost unaffected by system size, e.g., CIS(D) and CC3, the performance of others can significantly deteriorate as the systems grow, e.g., EOM-MP2 and CCSD, whereas others, e.g., ADC(2) and CC2, become more accurate for larger derivatives.

Exciton maps for thermally activated delayed fluorescence active/inactive carbazole benzonitrile derivatives

The all-electron first-principles GW+Bethe-Salpeter method was applied to six carbazole benzonitrile (CzBN) derivatives, which were recently reported to be both thermally activated delayed fluorescence (TADF) active and inactive despite their singlet-triplet splittings being commonly around 0.2 eV. The present method successfully reproduced very similar photoabsorption spectra as experiments from the viewpoint of the peak positions and relative peak heights. We also performed exciton analysis with the exciton wave functions for several lowest singlet and triplet exciton states to reveal the details of the optical properties. We applied this to not only the present six CzBN derivatives but also 18 other TADF molecules and proposed a new exciton map to classify the molecules as the TADF active/inactive by using the exciton binding energy in the vertical axis and the ratio of electron and hole delocalization in the horizontal axis. Our results suggest two possible TADF mechanisms: spatially less localized hole states than the electron states where the exciton binding energy is proportional to the ratio of hole and electron delocalization and spatially more localized hole states than the electron states where the exciton binding energy should be large.

Photoinduced electron transfer in non-covalent complexes of C60 and phosphangulene oxide derivatives

Investigation of photoinduced electron transfer (PET) in a series of experimentally reported complexes of fullerene with phosphangulene oxides shows that the replacement of O atoms in the bridge of phosphangulene with S atoms promotes efficient and ultrafast ET from phosphangulene oxide to fullerene in PGOOSS⊃C60 and PGOSSS⊃C60 complexes. The results obtained can be useful for the development of photovoltaic devices based on phosphangulenes.

Unexpected Charge Effects Strengthen π-Stacking Pancake Bonding

Phenalenyls (PLYs) are important synthons in many functional and electronic materials, which often display favorable molecule-to-molecule overlap for electron or hole transport. They also serve as a prototype for π-stacking pancake bonding based on two-electron multicenter bonding (2e/mc). Unexpected near-doubling of the binding energy is obtained for the positively charged PLY2 + dimer with an effect similar to that seen for the positively charged olympicenyl (OPY) radical dimer. This charge effect is reversed for the perfluorinated (PF) dimers, and the negatively charged perfluorinated (PF) dimers PF-PLY2 - and PF-OPY2 - become strongly bound. Long-range interactions reflect these differences. Also surprising is that in this case the pancake bonding corresponds to single-electron (1e/mc) or a three-electron (3e/mc) multicenter bonding in contrast to the 2e/mc bonding that occurs for the neutral radical dimers. The strong preference for a large intermolecular overlap is maintained in these charged dimers. Importantly, the preference for π-bonding in the charged dimers compared to σ-bonding is strongly enhanced relative to the neutral PLY dimers.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Analytical gradients for core-excited states in the algebraic diagrammatic construction (ADC) framework

Expressions for analytical molecular gradients of core-excited states have been derived and implemented for the hierarchy of algebraic diagrammatic construction (ADC) methods up to extended second-order within the core-valence separation (CVS) approximation. We illustrate the use of CVS-ADC gradients by determining relaxed core-excited state potential energy surfaces and optimized geometries for water, formic acid, and benzene. For water, our results show that in the dissociative lowest core-excited state, a linear configuration is preferred. For formic acid, we find that the O K-edge lowest core-excited state is non-planar, a fact that is not captured by the equivalent core approximation where the core-excited atom with its hole is replaced by the "Z + 1" neighboring atom in the periodic table. For benzene, the core-excited state gradients are presented along the Jahn-Teller distorted geometry of the 1s → π* excited state. Our development may pave a new path to studying the dynamics of molecules in their core-excited states.

Three States Involving Vibronic Resonance is a Key to Enhancing Reverse Intersystem Crossing Dynamics of an Organoboron-Based Ultrapure Blue Emitter

The recently developed narrow-band blue-emitting organoboron chromophores based on the multiple-resonance (MR) effect have now become one of the most important components for constructing efficient organic light emitting diodes (OLEDs). While they basically emit through fluorescence, they are also known for showing substantial thermally activated delayed fluorescence (TADF) even with a relatively large singlet-triplet gap (ΔE _ST). Indeed, understanding the reverse intersystem crossing (RISC) dynamics behind this peculiar TADF will allow judicious molecular designs toward achieving better performing OLEDs. Explaining the underlying nonadiabatic spin-flip mechanism, however, has often been equivocal, and how the sufficiently fast RISC takes place even with the sizable ΔE _ST and vanishingly small spin-orbit coupling is not well understood. Here, we show that a vibronic resonance, namely the frequency matching condition between the vibration and the electronic energy gap, orchestrates three electronic states together and this effect plays a major role in enhancing RISC in a typical organoboron emitter. Interestingly, the mediating upper electronic state is quite high in energy to an extent that its thermal population is vanishingly small. Through semiclassical quantum dynamics simulations, we further show that the geometry dependent non-Condon coupling to the upper triplet state that oscillates with the frequency ΔE _ST/ℏ is the main driving force behind the peculiar resonance enhancement. The existence of an array of vibrational modes with strong vibronic rate enhancements provides the ability to sustain efficient RISC over a range of ΔE _ST in defiance of the energy gap law, which can render the MR-emitters peculiar in comparison with more conventional donor-acceptor type emitters. Our investigation may provide a new guide for future blue emitting molecule developments.

How Do Defects in Carbon Nanostructures Regulate the Photoinduced Electron Transfer Processes? The Case of Phenine Nanotubes

Photoinduced electron transfer is studied in a series of inclusion complexes of structurally modified phenine nanotubes (pNT) with C70 using the TD-DFT method. Analysis of electronic properties of the complexes shows that the electron transfer is infeasible in pNT_4d⊃C70 built on the tetrameric array of [6]cyclo-meta-phenylene ([6]CMP) units. However, replacing one or more [6]CMP units with a coronene moiety enables electron transfer from pNT to C70 . The generation of the charge separated states from the lowest locally excited states occurs on a sub-nanosecond time scale. Depending on the number of the [6]CMP units, the charge recombination rate varies from 1.8 ⋅ 107 to 3.1 ⋅ 102  s-1 , i. e., five orders of magnitude.

[10]CPP-Based Inclusion Complexes of Charged Fulleropyrrolidines. Effect of the Charge Location on the Photoinduced Electron Transfer

A number of non-covalently bound donor-acceptor dyads, consisting of C₆₀ as the electron acceptor and cycloparaphenylene (CPP) as the electron donor, have been reported. A hypsochromic shift of the charge transfer (CT) band in polar medium has been found in [10]CPP⊃Li⁺ @C₆₀ . To explore this anomalous effect, we study inclusion complexes [10]CPP⊃Li⁺ @C₆₀ -MP, [10]CPP⊃C₆₀ -MPH⁺ , and [10]CPP⊃C₆₀ -PPyMe⁺ formed by fulleropyrrolidine derivatives and [10]CPP using the DFT/TDDFT approach. We show that the introduction of a positively charged fragment into fullerene stabilizes CT states that become the lowest-lying excited states. These charge-separated states can be generated by the decay of locally excited states on a nanosecond to picosecond time scale. The distance of the charged fragment to the center of the fullerenic cage and its accessibility to the solvent determine the strength of the hypsochromic shift.

2,6-diaminopurine promotes repair of DNA lesions under prebiotic conditions

High-yielding and selective prebiotic syntheses of RNA and DNA nucleotides involve UV irradiation to promote the key reaction steps and eradicate biologically irrelevant isomers. While these syntheses were likely enabled by UV-rich prebiotic environment, UV-induced formation of photodamages in polymeric nucleic acids, such as cyclobutane pyrimidine dimers (CPDs), remains the key unresolved issue for the origins of RNA and DNA on Earth. Here, we demonstrate that substitution of adenine with 2,6-diaminopurine enables repair of CPDs with yields reaching 92%. This substantial self-repairing activity originates from excellent electron donating properties of 2,6-diaminopurine in nucleic acid strands. We also show that the deoxyribonucleosides of 2,6-diaminopurine and adenine can be formed under the same prebiotic conditions. Considering that 2,6-diaminopurine was previously shown to increase the rate of nonenzymatic RNA replication, this nucleobase could have played critical roles in the formation of functional and photostable RNA/DNA oligomers in UV-rich prebiotic environments.

UV-induced photodamage that likely occurred during the prebiotic synthesis of DNA and RNA is still an untackled issue for their origin on early Earth. Here, the authors show that substitution of 2,6-diaminopurine for adenine enables repair of cyclobutane pyrimidine dimers with high yields, and demonstrate that both 2,6-diaminopurine and adenine nucleosides can be formed under the same prebiotic conditions.

The orbital picture of the first dipole hyperpolarizability from many-body response theory

We present an approach for obtaining a molecular orbital picture of the first dipole hyperpolarizability (β) from correlated many-body electronic structure methods. Ab initio calculations of β rely on quadratic response theory, which recasts the sum-over-all-states expression of β into a closed-form expression by calculating a handful of first- and second-order response states; for resonantly enhanced β, damped response theory is used. These response states are then used to construct second-order response reduced one-particle density matrices (1PDMs), which, upon visualization in terms of natural orbitals (NOs), facilitate a rigorous and black-box mapping of the underlying electronic structure with β. We explain the interpretation of different components of the response 1PDMs and the corresponding NOs within both the undamped and damped response theory framework. We illustrate the utility of this new tool by deconstructing β for cis-difluoroethene, para-nitroaniline, and hemibonded OH^· + H₂O complex, computed within the framework of coupled-cluster singles and doubles response theory, in terms of the underlying response 1PDMs and NOs for a range of frequencies.

Deciphering excited state properties utilizing algebraic diagrammatic construction schemes of decreasing order

Excited state properties are difficult to trace back to the common molecular orbital picture when the excited state wavefunction is a linear combination of two or more Slater determinants. Here, a theoretical methodology is introduced based on the algebraic diagrammatic construction scheme for the polarization propagator (ADC(n)) that allows to make this connection and to eventually derive structure-function relationships. The usefulness of this approach is demonstrated by an analysis of the transition dipole moments of the low-lying 1B_3u and 2B_3u states of anthracene and (1,4,5,8)-tetraazaanthracene.

Embelin's Versatile Photochemistry Makes It a Potent Photosensitizer for Photodynamic Therapy

Embelin, a natural product isolated from Embelia ribes, is a promising small-molecular drug for photodynamic anticancer therapy. Using modern quantum chemical methodology, embelin is shown to possess a versatile photochemistry comprising the capability of singlet oxygen generation, excited-state proton transfer, and oxidation. In particular, the detailed molecular mechanisms of singlet oxygen generation and proton transfer upon excitation are studied in great detail. While excited-state proton transfer can damage the protein itself, it also mediates intersystem crossing along its reaction pathway, thus facilitating singlet oxygen generation. When embelin is bound to proteins, all these processes can lead to protein damage and the desired phototoxicity.

Equation-of-motion coupled-cluster method with double electron-attaching operators: Theory, implementation, and benchmarks

We report a production-level implementation of the equation-of-motion (EOM) coupled-cluster (CC) method with double electron-attaching (DEA) EOM operators of 2p and 3p1h types, EOM-DEA-CCSD. This ansatz, suitable for treating electronic structure patterns that can be described as two-electrons-in-many orbitals, represents a useful addition to the EOM-CC family of methods. We analyze the performance of EOM-DEA-CCSD for energy differences and molecular properties. By considering reduced quantities, such as state and transition one-particle density matrices, we compare EOM-DEA-CCSD wave functions with wave functions computed by other EOM-CCSD methods. The benchmarks illustrate that EOM-DEA-CCSD is capable of treating diradicals, bond-breaking, and some types of conical intersections.

Influence of the Environment on Shaping the Absorption of Monomeric Infrared Fluorescent Proteins

Infrared fluorescent proteins (iRFPs) are potential candidates for deep-tissue in vivo imaging. Here, we provide molecular-level insights into the role of the protein environment in the structural stability of the chromophore within the protein binding pocket through the flexible hydrogen-bonding network using molecular dynamics simulation. Furthermore, we present systematic excited-state analysis to characterize the nature of the first two excited states and the role of the environment in shaping the nature of the chromophore's excited states within the hybrid quantum mechanics/molecular mechanics framework. Our results reveal that the environment red-shifts the absorption of the chromophore by about 0.32 eV compared to the isolated counterpart, and besides the structural stability, the protein environment does not alter the nature of the excited state of the chromophore significantly. Our study contributes to the fundamental understanding of the excited-state processes of iRFPs in a complex environment and provides a design principle for developing iRFPs with desired spectral properties.

An assessment of different electronic structure approaches for modeling time-resolved x-ray absorption spectroscopy

We assess the performance of different protocols for simulating excited-state x-ray absorption spectra. We consider three different protocols based on equation-of-motion coupled-cluster singles and doubles, two of them combined with the maximum overlap method. The three protocols differ in the choice of a reference configuration used to compute target states. Maximum-overlap-method time-dependent density functional theory is also considered. The performance of the different approaches is illustrated using uracil, thymine, and acetylacetone as benchmark systems. The results provide guidance for selecting an electronic structure method for modeling time-resolved x-ray absorption spectroscopy.

From Incident Light to Persistent and Regenerable Radicals of Urea-Assembled Benzophenone Frameworks: A Structural Investigation

Herein we probe the effects of crystalline structure and geometry on benzophenone photophysics, self-quenching, and the regenerable formation of persistent triplet radical pairs at room temperature. Radical pairs are not observed in solution but appear via an emergent pathway within the solid-state assembly. Single crystal X-ray diffraction (SC-XRD) of two sets of constitutional isomers, benzophenone bis-urea macrocycles, and methylene urea-tethered dibenzophenones are compared. Upon irradiation with 365 nm light-emitting diodes (LEDs), each forms photogenerated radicals as monitored by electron paramagnetic resonance (EPR). Once generated, the radicals exhibit half-lives from 2 to 60 days before returning to starting material without degradation. Re-exposure to light regenerates the radicals with similar efficiency. Subtle differences in the structure of the crystalline frameworks modulates the maximum concentration of photogenerated radicals, phosphorescence quantum efficiency (φ), and n-type self-quenching as observed using laser flash photolysis (LFP). These studies along with the electronic structure analysis based on the time-dependent density functional theory (TD-DFT) suggest the microenvironment surrounding benzophenone largely dictates the favorability of self-quenching or radical formation and affords insights into structure/function correlations. Advances in understanding how structure determines the excited state pathway solid-state materials undertake will aid in the design of new radical initiators, components of OLEDs, and NMR polarizing agents.

Deciphering the Electronic Transitions of Thiophene-Based Donor-Acceptor-Donor Pentameric Ligands Utilized for Multimodal Fluorescence Microscopy of Protein Aggregates

Anionic pentameric thiophene acetates can be used for fluorescence detection and diagnosis of protein amyloid aggregates. Replacing the central thiophene unit by benzothiadiazole (BTD) or quinoxaline (QX) leads to large emission shifts and basic spectral features have been reported [Chem. Eur. J. 2015, 21, 15133‐13137]. Here we present new detailed experimental results of solvent effects, time‐resolved fluorescence and examples employing multi‐photon microscopy and lifetime imaging. Quantum chemical response calculations elucidate how the introduction of the BTD/QX groups changes the electronic states and emissions. The dramatic red‐shift follows an increased conjugation and quinoid character of the π‐electrons of the thiophene backbone. An efficient charge transfer in the excited states S₁ and S₂ compared to the all‐thiophene analogue makes these more sensitive to the polarity and quenching by the solvent. Taken together, the results guide in the interpretation of images of stained Alzheimer disease brain sections employing advanced fluorescence microscopy and lifetime imaging, and can aid in optimizing future fluorescent ligand development.

Photoinduced electron transfer in nano-Saturn complexes of fullerene

The photoinduced electron transfer is studied computationally in several Saturn-shaped inclusion complexes of carbo-aromatic rings and C60 fullerene - C72⊃C60, C96⊃C60, C120⊃C60, and C168⊃C60. Analysis of their structural and electronic properties shows that the charge separation process is efficient in C120⊃C60 and C168⊃C60 where the host molecule resembles the conjugated [24]circulene unit. In contrast, the electron transfer is not feasible in the complexes of the oligophenylene-based rings C72⊃C60 and C96⊃C60.

Assessing the Performance of DFT Functionals for Excited-State Properties of Pyridine-Thiophene Oligomers

In this article, we have examined the accuracy of various density functional theory (DFT) functionals to reproduce the absorption and CD spectra of pyridine-thiophene oligomers. The performance of different levels of approximations in DFT functionals is discussed with reference to the ADC(2) results. Starting from a linear system, like monomer, calculations are carried out at ADC(2) and DFT levels till a helical system, like pentamer, is formed. For vertical excitation energies, results obtained with functionals, like CAM-B3LYP, ωB97XD, and M06-2X, are closer to the ADC(2) results. However, analysis of excited-state properties shows that the state ordering patterns or results regarding natural transition orbitals from these DFT functionals sometimes differ from the ADC(2) results. Global hybrid functionals like B3LYP and PBE0 produce excitation energies which are far away from the ADC(2) benchmark results. Similarly, pure functionals and their long-range corrected versions produce either redshifted or blueshifted energies. For the CD spectra, the above three mentioned functionals, CAM-B3LYP, ωB97XD, and M06-2X, again produce spectra closer to the benchmark spectra.