New tools for the systematic analysis and visualization of electronic excitations. I. Formalism

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.

Monitoring Density Redistribution at the Excited State in a Dual Emitting Molecule: An Analysis Based on Real-Time Density Functional Theory and Density Descriptors

In this work, we computed and analyzed, by means of density-based descriptors, the real-time evolution of both the locally excited (LE) and charge-transfer (CT) excited states for the planar and twisted conformations of the DMABN (4-(N,N-dimethylamino)benzonitrile) molecule using real-time time-dependent density functional theory (DFT) and three different exchange-correlation energy functionals (EXC) belonging to the same family (the PBE one). Our results based on the analysis of density-based descriptors show that the underlying EXC modifies the evolution in time of the density. In particular, comparing the frequency of density reorganization computed with the three functionals (PBE, PBE0, and LC-PBE), we found that the frequency of electronic interconversion of the individual determinants involved during the dynamics increases from PBE to PBE0 and to LC-PBE. This allows us to show that there is a correlation between the delocalization of the electronic density and the frequency of reorganization. In particular, the greater the mean hole-electron distance during the dynamics, the lower is the frequency of density reorganization.

Ab initio investigation of excited state charge transfer pathways in differently capped bithiophene cages

The electronic excitations of conformationally constrained bithiophene cage systems as previously investigated by Lewis et al. (J. Am. Chem. Soc. 143, 18548 (2021)) are revisited, employing the correlated ab initio Scaled Opposite-Spin Algebraic Diagrammatic Construction Second Order electronic structure method. Quantitative descriptors are determined to assess the extent of charge transfer between the bithiophene moieties and the capping domains, represented by either phenyl or triazine groups. The investigation substantiates intrinsic differences in the photophysical behavior of these two structural variants and reveals the presence of lower-energy excited states characterized by noteworthy charge transfer contributions in the triazine cage system. The manifestation of this charge transfer character is discernible even at the Franck-Condon geometry, persisting throughout the relaxation of the excited state. By examining isolated monomer building blocks, we confirm the existence of analogous charge transfer contributions in their excitations. Employing this methodological approach facilitates the prospective identification of potential wall/cap chromophore pairs, wherein charge transfer pathways can be accessed within the energetically favorable regime.

Why does the orientation of azulene affect the two-photon activity of a porphyrinoid-azulene system?

Attaching a dipolar molecule in a symmetric system induces a major change in the electronic structure, which may be reflected as the enhancement of the optical and charge-transfer properties of the combined system as compared to the pristine ones. Furthermore, the orientation of the dipolar molecule may also affect the said properties. This idea is explored in this work by taking porphyrinoid molecules as the pristine systems. We attached azulene, a dipolar molecule, at various positions of five porphyrinoid cores and studied the effect on charge-transfer and one- and two-photon absorption properties using the state-of-the-art RICC2 method. The attachment of azulene produces two major effects - firstly it introduces asymmetry in the system and, secondly, being dipolar, it makes the resultant molecule dipolar/quadrupolar. Porphyrin, N-confused porphyrin, sub-porphyrin, sapphyrin, and hexaphyrin are used as core porphyrinoid systems. The change in charge-transfer has been studied using the orbital analysis and charge-transfer distance parameter for the first five singlet states of the systems. The effect of orientation of azulene on the said properties is also explored. The insights gained from our observations are explored further at the dipole and transition dipole moment levels using a three-state model.

Quantum Mechanical Versus Polarizable Embedding Schemes: A Study of the Xray Absorption Spectra of Aqueous Ammonia and Ammonium

The X-ray absorption spectra of aqueous ammonia and ammonium are computed using a combination of coupled cluster singles and doubles (CCSD) with different quantum mechanical and molecular mechanical embedding schemes. Specifically, we compare frozen Hartree-Fock (HF) density embedding, polarizable embedding (PE), and polarizable density embedding (PDE). Integrating CCSD with frozen HF density embedding is possible within the CC-in-HF framework, which circumvents the conventional system-size limitations of standard coupled cluster methods. We reveal similarities between PDE and frozen HF density descriptions, while PE spectra differ significantly. By including approximate triple excitations, we also investigate the effect of improving the electronic structure theory. The spectra computed using this approach show an improved intensity ratio compared to CCSD-in-HF. Charge transfer analysis of the excitations shows the local character of the pre-edge and main-edge, while the post-edge is formed by excitations delocalized over the first solvation shell and beyond.

PyrAtes: Modular Organic Salts with Large Stokes Shifts for Fluo-rescence Microscopy

The deployment of small-molecule fluorescent agents plays an ever-growing role in medicine and drug development. Herein, we complement the portfolio of powerful fluorophores, reporting the serendipitous discovery and development of a novel class with an imidazo[1,2-a]pyridinium triflate core, which we term PyrAtes. These fluorophores are synthesized in a single step from readily available materials (>60 examples) and display Stokes shifts as large as 240 nm, while also reaching NIR-I emissions at λmax as long as 720 nm. Computational studies allow the development of a platform for the prediction of λmax and λEm. Furthermore, we demonstrate the compatibility of these novel fluorophores with live cell imaging in HEK293 cells, suggesting PyrAtes as potent intracellular markers.

Interpretation of molecular electron transport in ab initio many-electron framework incorporating zero-point nuclear motion effects

A computational methodology, founded on chemical concepts, is presented for interpreting the role of nuclear motion in the electron transport through single-molecule junctions (SMJ) using many-electron ab initio quantum chemical calculations. Within this approach the many-electron states of the system, computed at the SOS-ADC(2) level, are followed along the individual normal modes of the encapsulated molecules. The inspection of the changes in the partial charge distribution of the many-electron states allows the quantification of the electron transport and the estimation of transmission probabilities. This analysis improves the understanding of the relationship between internal motions and electron transport. Two SMJ model systems are studied for validation purposes, constructed from a conductor (BDA, benzene-1,4-diamine) and an insulator molecule (DABCO, 1,4-diazabicyclo[2.2.2]octane). The trends of the resulting transmission probabilities are in agreement with the experimental observations, demonstrating the capability of the approach to distinguish between conductor and insulator type systems, thereby offering a straightforward and cost-effective tool for such classifications via quantum chemical calculations.

Observation of a promethium complex in solution

Lanthanide rare-earth metals are ubiquitous in modern technologies1-5, but we know little about chemistry of the 61st element, promethium (Pm)6, a lanthanide that is highly radioactive and inaccessible. Despite its importance7,8, Pm has been conspicuously absent from the experimental studies of lanthanides, impeding our full comprehension of the so-called lanthanide contraction phenomenon: a fundamental aspect of the periodic table that is quoted in general chemistry textbooks. Here we demonstrate a stable chelation of the 147Pm radionuclide (half-life of 2.62 years) in aqueous solution by the newly synthesized organic diglycolamide ligand. The resulting homoleptic PmIII complex is studied using synchrotron X-ray absorption spectroscopy and quantum chemical calculations to establish the coordination structure and a bond distance of promethium. These fundamental insights allow a complete structural investigation of a full set of isostructural lanthanide complexes, ultimately capturing the lanthanide contraction in solution solely on the basis of experimental observations. Our results show accelerated shortening of bonds at the beginning of the lanthanide series, which can be correlated to the separation trends shown by diglycolamides9-11. The characterization of the radioactive PmIII complex in an aqueous environment deepens our understanding of intra-lanthanide behaviour12-15 and the chemistry and separation of the f-block elements16.

Understanding X-ray absorption in liquid water using triple excitations in multilevel coupled cluster theory

X-ray absorption (XA) spectroscopy is an essential experimental tool to investigate the local structure of liquid water. Interpretation of the experiment poses a significant challenge and requires a quantitative theoretical description. High-quality theoretical XA spectra require reliable molecular dynamics simulations and accurate electronic structure calculations. Here, we present the first successful application of coupled cluster theory to model the XA spectrum of liquid water. We overcome the computational limitations on system size by employing a multilevel coupled cluster framework for large molecular systems. Excellent agreement with the experimental spectrum is achieved by including triple excitations in the wave function and using molecular structures from state-of-the-art path-integral molecular dynamics. We demonstrate that an accurate description of the electronic structure within the first solvation shell is sufficient to successfully model the XA spectrum of liquid water within the multilevel framework. Furthermore, we present a rigorous charge transfer analysis of the XA spectrum, which is reliable due to the accuracy and robustness of the electronic structure methodology. This analysis aligns with previous studies regarding the character of the prominent features of the XA spectrum of liquid water.

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.

Chemical and Redox Noninnocence of Pentane-2,4-dione Bis(S-methylisothiosemicarbazone) in Cobalt Complexes and Their Application in Wacker-Type Oxidation

Cobalt complexes with multiproton- and multielectron-responsive ligands are of interest for challenging catalytic transformations. The chemical and redox noninnocence of pentane-2,4-dione bis(S-methylisothiosemicarbazone) (PBIT) in a series of cobalt complexes has been studied by a range of methods, including spectroscopy [UV-vis, NMR, electron paramagnetic resonance (EPR), X-ray absorption spectroscopy (XAS)], cyclic voltammetry, X-ray diffraction, and density functional theory (DFT) calculations. Two complexes [CoIII(H2LSMe)I]I and [CoIII(LSMe)I2] were found to act as precatalysts in a Wacker-type oxidation of olefins using phenylsilane, the role of which was elucidated through isotopic labeling. Insights into the mechanism of the catalytic transformation as well as the substrate scope of this selective reaction are described, and the essential role of phenylsilane and the noninnocence of PBIT are disclosed. Among the several relevant species characterized was an unprecedented Co(III) complex with a dianionic diradical PBIT ligand ([CoIII(LSMe••)I]).

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.

Contrasting the excited state properties of different conformers of trans- and cis-2,2'-bipyridine oligomers in the gas phase

In this article, we present conformation-dependent photophysical and excited state properties of trans- and cis- BPY oligomers. Oligomers up to tetramers for three conformers, namely, o-, m-, and p-, are constructed and optimized at the B3LYP-D3/def2-SVPD level. The photophysical and excited state properties are interpreted in terms of UV and CD spectra at the RI-ADC(2)/def2-TZVPD level. The UV spectra of oligomers of the m-conformer show high-intensity and red-shifted UV bands compared to o- and p-oligomers. The CD spectra of p-oligomers show intense CD bands compared to o- and p-oligomers in the case of trans-structures. In contrast, oligomers of each conformer of cis-structures show high-intensity CD bands. The excited states of (BPY)2 and (BPY)4 are also characterized by analysis of one-electron transition density matrix considering three descriptors: ωCT, dexc, and PRNTO. The ωCT values of dimers are in the range of 0.06-0.32, which indicates the excited states are mainly LE states, whereas, for (BPY)4, the ωCT values range from 0.17 to 0.53, indicating the possibility of partial CT in the excited states. These observations are also explained using the NTOs and e-h correlation plots.

Efficient and Parallel Implementation of Real and Complex Response Functions Employing the Second-Order Algebraic-Diagrammatic Construction Scheme for the Polarization Propagator

We present the implementation of an efficient matrix-folded formalism for the evaluation of complex response functions and the calculation of transition properties at the level of the second-order algebraic-diagrammatic construction (ADC(2)) scheme. The underlying algorithms, in combination with the adopted hybrid MPI/OpenMP parallelization strategy, enabled calculations of the UV/vis spectra of a guanine oligomer series ranging up to 1032 contracted basis functions, thereby utilizing vast computational resources from up to 32,768 CPU cores. Further analysis of the convergence behavior of the involved iterative subspace algorithms revealed the superiority of a frequency-separated treatment of response equations even for a large spectral window, including 101 frequencies. We demonstrate the applicability to general quantum mechanical operators by the first reported electronic circular dichroism spectrum calculated with a complex polarization propagator approach at the ADC(2) level of theory.

Comparison of Computational Strategies for the Calculation of the Electronic Coupling in Intermolecular Energy and Electron Transport Processes

Electronic couplings in intermolecular electron and energy transfer processes calculated by six different existing computational techniques are compared to nonorthogonal configuration interaction for fragments (NOCI-F) results. The paper addresses the calculation of the electronic coupling in diketopyrrolopyrol, tetracene, 5,5'-difluoroindigo, and benzene-Cl for hole and electron transport, as well as the local exciton and singlet fission coupling. NOCI-F provides a rigorous computational scheme to calculate these couplings, but its computational cost is rather elevated. The here-considered ab initio Frenkel-Davydov (AIFD), Dimer projection (DIPRO), transition dipole moment coupling, Michl-Smith, effective Hamiltonian, and Mulliken-Hush approaches are computationally less demanding, and the comparison with the NOCI-F results shows that the NOCI-F results in the couplings for hole and electron transport are rather accurately predicted by the more approximate schemes but that the NOCI-F exciton transfer and singlet fission couplings are more difficult to reproduce.

Photophysical Outcomes of Water-Solvated Heterocycles: Single-Conformation Ultraviolet and Infrared Spectroscopy of Microsolvated 2-Phenylpyrrole

The molecular chromophores within brown carbon (BrC) aerosols absorb solar radiation at visible and near-ultraviolet wavelengths. This contributes to the overall warming of the troposphere and the photochemical aging of aerosols. In this investigation, we combine a suite of experimental and theoretical methods to reveal the conformation-specific ultraviolet and infrared spectroscopy of 2-phenylpyrrole (2PhPy)─an extended π-conjugated pyrrole derivative and a model BrC chromophore─along with its water microsolvated molecular complexes (2PhPy:nH2O, n = 1-3). Using resonant two-photon ionization and double-resonance holeburning techniques alongside MP3 (ground state) and ADC(3) (excited state) torsional potential energy surfaces and discrete variable representation simulations, we characterized the ultraviolet spectra of 2PhPy and 2PhPy:1H2O. This analysis revealed evidence for Herzberg-Teller vibronic coupling along the CH wagging and NH stretching coordinates of the aromatic rings. Conformation-specific infrared spectroscopy revealed extended hydrogen-bonding networks of the 2PhPy:nH2O complexes. Upon stepwise addition of H2O solvation, the nearest H2O acceptor forms a strong, noncovalent interaction with the pyrrole NH donor, while the second and third H2O partners interface with the phenyl and pyrrole aromatic rings through growing van der Waals π/H atom stabilization. A local-mode Hamiltonian approach was employed for comparison with the experimental spectra, thus identifying the vibrational spectral signatures to specific 2PhPy:nH2O oscillators.

Resonance Raman spectra and excited state properties of methyl viologen and its radical cation from time-dependent density functional theory

Time-dependent density functional theory (TDDFT) was applied to gain insights into the electronic and vibrational spectroscopic properties of an important electron transport mediator, methyl viologen (MV2+ ). An organic dication, MV2+ has numerous applications in electrochemistry that include energy conversion and storage, environmental remediation, and chemical sensing and electrosynthesis. MV2+ is easily reduced by a single electron transfer to form a radical cation species (MV•+ ), which has an intense UV-visible absorption near 600 nm. The redox properties of the MV2+ /MV•+ couple and light-sensitivity of MV•+ have made the system appealing for photo-electrochemical energy conversion (e.g., solar hydrogen generation from water) and the study of photo-induced charge transfer processes through electronic absorption and resonance Raman spectroscopic measurements. The reported work applies leading TDDFT approaches to investigate the electronic and vibrational spectroscopic properties of MV2+ and MV•+ . Using a conventional hybrid exchange functional (B3-LYP) and a long-range corrected hybrid exchange functional (ωB97X-D3), including with a conductor-like polarizable continuum model to account for solvation, the electronic absorption and resonance Raman spectra predicted are in good agreement with experiment. Also analyzed are the charge transfer character and natural transition orbitals derived from the TDDFT vertical excitations calculated. The findings and models developed further the understanding of the electronic properties of viologens and related organic redox mediators important in renewable energy applications and serve as a reference for guiding the interpretation of electronic absorption and Raman spectra of the ions.

A comprehensive analysis of charge transfer effects on donor-pyrene (bridge)-acceptor systems using different substituents

The alternant polycyclic aromatic hydrocarbon pyrene has photophysical properties that can be tuned with different donor and acceptor substituents. Recently, a D (donor)-Pyrene (bridge)-A (acceptor) system, DPA, with the electron donor N,N-dimethylaniline (DMA), and the electron acceptor trifluoromethylphenyl (TFM), was investigated by means of time-resolved spectroscopic measurements (J. Phys. Chem. Lett. 2021, 12, 2226-2231). DPA shows great promise for potential applications in organic electronic devices. In this work, we used the ab initio second-order algebraic diagrammatic construction method ADC(2) to investigate the excited-state properties of a series of analogous DPA systems, including the originally synthesized DPAs. The additionally investigated substituents were amino, fluorine, and methoxy as donors and nitrile and nitro groups as acceptors. The focus of this work was on characterizing the lowest excited singlet states regarding charge transfer (CT) and local excitation (LE) characters. For the DMA-pyrene-TFM system, the ADC(2) calculations show two initial electronic states relevant for interpreting the photodynamics. The bright S1 state is locally excited within the pyrene moiety, and an S2 state is localized ~0.5 eV above S1 and characterized as a donor to pyrene CT state. HOMO and LUMO energies were employed to assess the efficiency of the DPA compounds for organic photovoltaics (OPVs). HOMO-LUMO and optical gaps were used to estimate power conversion and light-harvesting efficiencies for practical applications in organic solar cells. Considering the systems using smaller D/A substituents, compounds with the strong acceptor NO2 substituent group show enhanced CT and promising properties for use in OPVs. Some of the other compounds with small substituents are also found to be competitive in this regard.

Quantification of the Ionic Character of Multiconfigurational Wave Functions: The Qat Diagnostic

The complete active space self-consistent field (CASSCF) method is a cornerstone in modern excited-state quantum chemistry providing the starting point for most common multireference computations. However, CASSCF, when used with a minimal active space, can produce significant errors (>2 eV) even for the excitation energies of simple hydrocarbons if the states of interest possess ionic character. After illustrating this problem in some detail, we present a diagnostic for ionic character, denoted as Q at, that is readily computed from the transition density. A set of 11 molecules is considered to study errors in vertical excitation energies. State-averaged CASSCF obtains a mean absolute error (MAE) of 0.87 eV for the 34 singlet states considered. We highlight a strong correlation between the obtained errors and the Q at diagnostic, illustrating its power to predict problematic cases. Conversely, using multireference configuration interaction with single and double excitations and Pople's size extensivity correction (MR-CISD+P), excellent results are obtained with an MAE of 0.11 eV. Furthermore, correlations with the Q at diagnostic disappear. In summary, we hope that the presented diagnostic will facilitate reliable and user-friendly multireference computations on conjugated organic molecules.

Pitfall in simulations of vibronic TD-DFT spectra: diagnosis and assessment

In this Communication, we study the effect of spurious oscillations in the profiles of energy derivatives with respect to nuclear coordinates calculated with density functional approximations (DFAs) for formaldehyde, pyridine, and furan in their ground and electronic excited states. These spurious oscillations, which can only be removed using extensive integration grids that increase enormously the CPU cost of DFA calculations, are significant in the case of third- and fourth-order energy derivatives of the ground and excited states computed by M06-2X and ωB97X functionals. The errors in question propagate to anharmonic vibronic spectra computed under the Franck-Condon approximation, i.e., positions and intensities of vibronic transitions are affected to a large extent (shifts as significant as hundreds of cm-1 were observed). On the other hand, the LC-BLYP and CAM-B3LYP functionals show a much less pronounced effect due to spurious oscillations. Based on the results presented herein, we recommend either LC-BLYP or CAM-B3LYP with integration grids (250, 974) (or larger) for numerically stable simulations of vibronic spectra including anharmonic effects.

Earth Mover's Distance as a Metric to Evaluate the Extent of Charge Transfer in Excitations Using Discretized Real-Space Densities

This paper presents a novel theoretical measure, μEMD, based on the earth mover's distance (EMD), for quantifying the density shift caused by electronic excitations in molecules. As input, the EMD metric uses only the discretized ground- and excited-state electron densities in real space, rendering it compatible with almost all electronic structure methods used to calculate excited states. The EMD metric is compared against other popular theoretical metrics for describing the extent of electron-hole separation in a wide range of excited states (valence, Rydberg, charge transfer, etc.). The results showcase the EMD metric's effectiveness across all excitation types and suggest that it is useful as an additional tool to characterize electronic excitations. The study also reveals that μEMD can function as a promising diagnostic tool for predicting the failure of pure exchange-correlation functionals. Specifically, we show statistical relationships among the functional-driven errors, the exact exchange content within the functional, and the magnitude of μEMD values.

Polyradical character assessment using multireference calculations and comparison with density-functional derived fractional occupation number weighted density analysis

The biradicaloid character of different types of polycyclic aromatic hydrocarbons (PAHs) based on small band gaps is an important descriptor to assess their opto-electronic properties. In this work, the unpaired electron densities and numbers of unpaired electrons (NU values) calculated at the high-level multireference averaged quadratic coupled-cluster (MR-AQCC) method are used to develop a test set to assess the capabilities of different biradical descriptors based on density functional theory. A benchmark collection of 29 different compounds has been selected. The DFT descriptors contain primarily the fractional occupation number weighted electron density (FOD) based on simplified thermally-assisted-occupation density functional theory (TAO-DFT) calculations, but the singlet-triplet energy difference and other descriptors denoted as y0 and nLUNO have been considered as well. After adjustment of the literature-recommended finite temperatures, a very good, detailed agreement between unpaired density and FOD analysis is observed which is also manifested in excellent statistical correlations. The other two descriptors also show good correlations even though the absolute scaling is not satisfactory. A new linear fit of FOD data to the MR-AQCC reference values leads to an improved regression relation for determining the recommended finite temperature value in dependence of the Hartree-Fock exchange. This provides the basis for fast and reliable assessment of the biradical character of many classes of PAHs without the need for performing computationally extended MR calculations.

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.

Quantum mechanics/molecular mechanics studies on the excited-state decay mechanisms of cytidine aza-analogues: 5-azacytidine and 2'-deoxy-5-azacytidine in aqueous solution

The excited state properties and deactivation pathways of two DNA methylation inhibitors, i.e., 5-azacytidine (5ACyd) and 2'-deoxy-5-azacytidine (5AdCyd) in aqueous solution, are comprehensively explored with the QM(CASPT2//CASSCF)/MM protocol. We systematically map the feasible decay mechanisms based on the obtained excited-state decay paths involving all the identified minimum-energy structures, conical intersections, and crossing points driving the different internal conversion (IC) and intersystem crossing (ISC) routes in and between the 1ππ*, 1nπ*, 3ππ*, 3nπ*, and S0 states. Unlike the 1nπ* state below the 1ππ* state in 5ACyd, deoxyribose group substitution at the N1 position leads to the 1ππ* state becoming the S1 state in 5AdCyd. In 5ACyd and 5AdCyd, the initially populated 1ππ* state mainly deactivates to the S0 state through the direct 1ππ* → S0 IC or mediated by the 1nπ* state. The former nearly barrierless IC channel of 1ππ* → S0 occurs ultrafast via the nearby low-lying 1ππ*/S0 conical intersection. In the latter IC channel of 1ππ* → 1nπ* → S0, the initially photoexcited 1ππ* state first approaches the nearby S2/S1 conical section 1ππ*/1nπ* and then undergoes efficient IC to the 1nπ* state, followed by the further IC to the initial S0 state via the S1/S0 conical intersection 1nπ*/S0. The 1nπ*/S0 conical intersection is estimated to be located 6.0 and 4.9 kcal mol-1 above the 1nπ* state minimum in 5ACyd and 5AdCyd, respectively, at the QM(CASPT2)/MM level. In addition to the efficient singlet-mediated IC channels, the minor ISC routes would populate 1ππ* to T1(ππ*) through 1ππ* → T1 or 1ππ* → 1nπ* → T1. Relatively, the 1ππ* → 1nπ* → T1 route benefits from the spin-orbit coupling (SOC) of 1nπ*/3ππ* of 8.7 cm-1 in 5ACyd and 10.2 cm-1 in 5AdCyd, respectively. Subsequently, the T1 system will approach the nearby T1/S0 crossing point 3ππ*/S0 driving it back to the S0 state. Given the 3ππ*/S0 crossing point located above the T1 minimum and the small T1/S0 SOC, i.e., 8.4 kcal mol-1 and 2.1 cm-1 in 5ACyd and 6.8 kcal mol-1 and 1.9 cm-1 in 5AdCyd, respectively, the slow T1 → S0 would trap the system in the T1 state for a while. The present work could contribute to understanding the mechanistic photophysics and photochemistry of similar aza-nucleosides and their derivatives.

Theoretical Study of the Photochemical Mechanisms of the Electronic Quenching of NO(A2Σ+) with CH4, CH3OH, and CO2

The electronic quenching of NO(A2Σ+) with molecular partners occurs through complex non-adiabatic dynamics that occurs on multiple coupled potential energy surfaces. Moreover, the propensity for NO(A2Σ+) electronic quenching depends heavily on the strength and nature of the intermolecular interactions between NO(A2Σ+) and the molecular partner. In this paper, we explore the electronic quenching mechanisms of three systems: NO(A2Σ+) + CH4, NO(A2Σ+) + CH3OH, and NO(A2Σ+) + CO2. Using EOM-EA-CCSD calculations, we rationalize the very low electronic quenching cross-section of NO(A2Σ+) + CH4 as well as the outcomes observed in previous NO + CH4 photodissociation studies. Our analysis of NO(A2Σ+) + CH3OH suggests that it will undergo facile electronic quenching mediated by reducing the intermolecular distance and significantly stretching the O-H bond of CH3OH. For NO(A2Σ+) + CO2, intermolecular attractions lead to a series of low-energy ON-OCO conformations in which the CO2 is significantly bent. For both the NO(A2Σ+) + CH3OH and NO(A2Σ+) + CO2 systems, we see evidence of the harpoon mechanism and low-energy conical intersections between NO(A2Σ+) + M and NO(X2Π) + M. Overall, this work provides the first detailed theoretical study on the NO(A2Σ+) + M potential energy surface of each of these systems and will inform future velocity map imaging experiments.

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.

Electronic Couplings for Singlet Fission Processes Based on the Fragment Particle-Hole Densities

A new diabatization scheme is proposed to calculate the electronic couplings for the singlet fission process in multichromophoric systems. In this approach, a robust descriptor that treats single and multiple excitations on an equal footing is adopted to quantify the localization degree of the particle and hole densities of the electronic states. By maximally localizing the particles and holes in terms of predefined molecular fragments, quasi-diabatic states with well-defined characters (locally excited, charge transfer, correlated triplet pair, etc.) can be automatically constructed as the linear combinations of the adiabatic ones, and the electronic couplings can be directly obtained. This approach is very general in that it applies to electronic states with various spin multiplicities and can be combined with various kinds of preliminary electronic structure calculations. Due to the high numerical efficiency, it is able to manipulate more than 100 electronic states in diabatization. The applications to the tetracene dimer and trimer reveal that high-lying multiply excited charge transfer states have significant influences on both the formation and separation of the correlated triplet pair and can even enlarge the coupling for the latter process by 1 order of magnitude.

Functionalisation of conjugated macrocycles with type I and II concealed antiaromaticity via cross-coupling reactions

Conjugated macrocycles can exhibit concealed antiaromaticity; that is, despite not being antiaromatic, under specific circumstances, they can display properties typically observed in antiaromatic molecules due to their formal macrocyclic 4n π-electron system. Paracyclophanetetraene (PCT) and its derivatives are prime examples of macrocycles exhibiting this behaviour. In redox reactions and upon photoexcitation, they have been shown to behave like antiaromatic molecules (requiring type I and II concealed antiaromaticity, respectively), with such phenomena showing potential for use in battery electrode materials and other electronic applications. However, further exploration of PCTs has been hindered by the lack of halogenated molecular building blocks that would permit their integration into larger conjugated molecules by cross-coupling reactions. Here, we present two dibrominated PCTs, obtained as a mixture of regioisomers from a three-step synthesis, and demonstrate their functionalisation via Suzuki cross-coupling reactions. Optical, electrochemical, and theoretical studies reveal that aryl substituents can subtly tune the properties and behaviour of PCT, showing that this is a viable strategy in further exploring this promising class of materials.

Algebraic Diagrammatic Construction Theory for Simulating Charged Excited States and Photoelectron Spectra

Charged excitations are electronic transitions that involve a change in the total charge of a molecule or material. Understanding the properties and reactivity of charged species requires insights from theoretical calculations that can accurately describe orbital relaxation and electron correlation effects in open-shell electronic states. In this Review, we describe the current state of algebraic diagrammatic construction (ADC) theory for simulating charged excitations and its recent developments. We start with a short overview of ADC formalism for the one-particle Green's function, including its single- and multireference formulations and extension to periodic systems. Next, we focus on the capabilities of ADC methods and discuss recent findings about their accuracy for calculating a wide range of excited-state properties. We conclude our Review by outlining possible directions for future developments of this theoretical approach.

Excited states of ortho-nitrobenzaldehyde as a challenging case for single- and multi-reference electronic structure theory

We present a large set of vertical excitation calculations for the ortho-nitrobenzaldehyde (oNBA) molecule, which exhibits a very challenging excited-state electronic structure like other nitroaromatic compounds. The single-reference methods produce mostly consistent results up to about 5.5 eV. By contrast, the CAS second-order perturbation theory (CASPT2) results depend sensitively on the employed parameters. At the CAS self-consistent field level, the energies of the bright ππ * $$ {\pi \pi}^{\ast } $$ states are strongly overestimated while doubly excited states appear too low and mix with these ππ * $$ {\pi \pi}^{\ast } $$ states. This mixing hampers the CASPT2 step, leading to inconsistent results. Only by increasing the number of states in the state-averaging step to about 40-to cover all bright ππ * $$ {\pi \pi}^{\ast } $$ states embedded in the double excitations-and employing extended multistate CASPT2 could CASPT2 results consistent with experiment be obtained. We assign the four bands in the molecule's spectrum: The weakest band at 3.7 eV arises from the n NO 2 π * $$ {n}_{\mathrm{NO}2}{\pi}^{\ast } $$ states, the second one at 4.4 eV from the ππ * $$ {\pi \pi}^{\ast } $$ ( L b $$ {L}_b $$ ) state, the shoulder at 5.2 eV from the ππ * $$ {\pi \pi}^{\ast } $$ ( L a $$ {L}_a $$ ) state, and the maximum at 5.7 eV from the ππ * $$ {\pi \pi}^{\ast } $$ ( B a / B b $$ {B}_a/{B}_b $$ ) states. We also highlight the importance of modern wave function analysis techniques in elucidating the absorption spectrum of challenging molecules.

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin-flip DFT and Heisenberg effective Hamiltonians

Low-energy spectra of single-molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For 12 binuclear complexes with J-values ranging from -6 to -132 cm^-1 , our benchmark calculations using the short-range hybrid ωPBEh functional and 6-31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm^-1 ). For the tetranuclear SMMs, the computed J constants are within 6 cm^-1 from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

Long-range corrected fragment molecular orbital density functional tight-binding method for excited states in large molecular systems

Herein, we present a new method to efficiently calculate electronically excited states in large molecular assemblies, consisting of hundreds of molecules. For this purpose, we combine the long-range corrected tight-binding density functional fragment molecular orbital method (FMO-LC-DFTB) with an excitonic Hamiltonian, which is constructed in the basis of locally excited and charge-transfer configuration state functions calculated for embedded monomers and dimers and accounts explicitly for the electronic coupling between all types of excitons. We first evaluate both the accuracy and efficiency of our fragmentation approach for molecular dimers and aggregates by comparing it with the full LC-TD-DFTB method. The comparison of the calculated spectra of an anthracene cluster shows a very good agreement between our method and the LC-TD-DFTB reference. The effective computational scaling of our method has been explored for anthracene clusters and for perylene bisimide aggregates. We demonstrate the applicability of our method by the calculation of the excited state properties of pentacene crystal models consisting of up to 319 molecules. Furthermore, the participation ratio of the monomer fragments to the excited states is analyzed by the calculation of natural transition orbital participation numbers, which are verified by the hole and particle density for a chosen pentacene cluster. The use of our FMO-LC-TDDFTB method will allow for future studies of excitonic dynamics and charge transport to be performed on complex molecular systems consisting of thousands of atoms.

Theoretical Study of Charge Mobility in Crystal Porphine and a Computer Design of a Porphine-Based Semiconductive Discotic Liquid Mesophase

Organic semiconductors are the focus of numerous studies; they are used in electronic devices. Modern research involves the production of neuromorphic organic materials, including those based on liquid crystal materials. The purpose of this work involves the theoretical modeling of molecules (the "core with branches" type) to construct a discotic mesophase capable of performing the functions of a neuromorphic material. For this purpose, the conductivity of crystal porphine, which can act as the nucleus of a molecule of the "core with branches" type, was investigated. The Marcus theory charge mobility values for the hole and electron were 0.148 and 0.088 cm²/V·s, respectively (the MOO method for calculating transfer integrals), and 0.561 and 0.160 cm²/V·s (DIPRO method). Based on TD-HF (HF-3c level of theory) calculations, possible structures of molecules for the formation of a discotic mesophase are proposed.

Photophysics of Anionic Bis(4H-imidazolato)CuI Complexes

In this paper, the photophysical behavior of four panchromatically absorbing, homoleptic bis(4H-imidazolato)Cu^I complexes, with a systematic variation in the electron-withdrawing properties of the imidazolate ligand, were studied by wavelength-dependent time-resolved femtosecond transient absorption spectroscopy. Excitation at 400, 480, and 630 nm populates metal-to-ligand charge transfer, intraligand charge transfer, and mixed-character singlet states. The pump wavelength-dependent transient absorption data were analyzed by a recently established 2D correlation approach. Data analysis revealed that all excitation conditions yield similar excited-state dynamics. Key to the excited-state relaxation is fast, sub-picosecond pseudo-Jahn-Teller distortion, which is accompanied by the relocalization of electron density onto a single ligand from the initially delocalized state at Franck-Condon geometry. Subsequent intersystem crossing to the triplet manifold is followed by a sub-100 ps decay to the ground state. The fast, nonradiative decay is rationalized by the low triplet-state energy as found by DFT calculations, which suggest perspective treatment at the strong coupling limit of the energy gap law.

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.

Quantum-Compute Algorithm for Exact Laser-Driven Electron Dynamics in Molecules

In this work, we investigate the capability of known quantum computing algorithms for fault-tolerant quantum computing to simulate the laser-driven electron dynamics of excitation and ionization processes in small molecules such as lithium hydride, which can be benchmarked against the most accurate time-dependent full configuration interaction (TD-FCI) calculations. The conventional TD-FCI wave packet propagation is reproduced using the Jordan-Wigner transformation for wave function and operators and the Trotter product formula for expressing the propagator. In addition, the time-dependent dipole moment, as an example of a time-dependent expectation value, is calculated using the Hadamard test. To include non-Hermitian operators in the ionization dynamics, a similar approach to the quantum imaginary time evolution (QITE) algorithm is employed to translate the propagator, including a complex absorption potential, into quantum gates. The computations are executed on a quantum computer simulator. By construction, all quantum computer algorithms, except for the QITE algorithm used only for ionization but not for excitation dynamics, would scale polynomially on a quantum computer with fully entangled qubits. In contrast, TD-FCI scales exponentially. Hence, quantum computation holds promises for substantial progress in the understanding of electron dynamics of excitation processes in increasingly large molecular systems, as has already been witnessed in electronic structure theory.

Squarephaneic Tetraanhydride: A Conjugated Square-Shaped Cyclophane for the Synthesis of Porous Organic Materials

Aromatic carboxylic anhydrides are ubiquitous building blocks in organic materials chemistry and have received considerable attention in the synthesis of organic semiconductors, pigments, and battery electrode materials. Here we extend the family of aromatic carboxylic anhydrides with a unique new member, a conjugated cyclophane with four anhydride groups. The cyclophane is obtained in a three-step synthesis and can be functionalised efficiently, as shown by the conversion into tetraimides and an octacarboxylate. Crystal structures reveal the high degree of porosity achievable with the new building block. Excellent electrochemical properties and reversible reduction to the tetraanions are shown for the imides; NMR and EPR measurements confirm the global aromaticity of the dianions and evidence the global Baird aromaticity of the tetraanions. Considering the short synthesis and unique properties, we expect widespread use of the new building block in the development of organic materials.

Squarephaneic Tetraanhydride: A Conjugated Square-Shaped Cyclophane for the Synthesis of Porous Organic Materials

Aromatic carboxylic anhydrides are ubiquitous building blocks in organic materials chemistry and have received considerable attention in the synthesis of organic semiconductors, pigments, and battery electrode materials. Here we extend the family of aromatic carboxylic anhydrides with a unique new member, a conjugated cyclophane with four anhydride groups. The cyclophane is obtained in a three-step synthesis and can be functionalised efficiently, as shown by the conversion into tetraimides and an octacarboxylate. Crystal structures reveal the high degree of porosity achievable with the new building block. Excellent electrochemical properties and reversible reduction to the tetraanions are shown for the imides; NMR and EPR measurements confirm the global aromaticity of the dianions and evidence the global Baird aromaticity of the tetraanions. Considering the short synthesis and unique properties, we expect widespread use of the new building block in the development of organic materials.

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.

Using diketopyrrolopyrroles to stabilize double excitation and control internal conversion

Diketopyrrolopyrrole (DPP) is a pivotal functional group to tune the physicochemical properties of novel organic photoelectronic materials. Among multiple uses, DPP-thiophene derivatives forming a dimer through a vinyl linker were recently shown to quench the fluorescence observed in their isolated monomers. Here, we explain this fluorescence quenching using computational chemistry. The DPP-thiophene dimer has a low-lying doubly excited state that is not energetically accessible for the monomer. This state delays the fluorescence allowing internal conversion to occur first. We characterize the doubly excited state wavefunction by systematically changing the derivatives to tune the π-scaffold size and the acceptor and donor characters. The origin of this state's stabilization is related to the increase in the π-system and not to the charge-transfer features. This analysis delivers core conceptual information on the electronic properties of organic chromophores arranged symmetrically around a vinyl linker, opening new ways to control the balance between luminescence and internal conversion.

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.

Umpolung in a Pair of Cobalt(III) Terminal Imido/Imidyl Complexes

Reaction of the Co^I complex [(TIMMN^mes)Co^I](PF₆) (1) (TIMMN^mes=tris‐[2‐(3‐mesityl‐imidazolin‐2‐ylidene)‐methyl]amine) with mesityl azide yields the Co^III imide [(TIMMN^mes)Co^III(NMes)](PF₆) (2). Oxidation of 2 with [FeCp₂](PF₆) provides access to a rare Co^III imidyl [(TIMMN^mes)Co(NMes)](PF₆)₂ (3). Single‐crystal X‐ray diffractometry and EPR spectroscopy confirm the molecular structure of 3 and its S=1/2 ground state. ENDOR, X‐ray absorption spectroscopy and computational analyses indicate a ligand‐based oxidation; thus, an imidyl‐radical electronic structure for 3. Migratory insertion of one ancillary NHC to the imido ligand in 2 gives the Co^IN‐heterocyclic imine (4) within 12 h. Conversely, it takes merely 0.5 h for 3 to transform to the Co^II congener (5). The migratory insertion in 2 occurs via a nucleophilic attack of the imido ligand at the NHC to give 4, whereas in 3, a nucleophilic attack of the NHC at the electrophilic imidyl ligand yields 5. The reactivity shunt upon oxidation of 2 to 3 confirms an umpolung of the imido ligand.

Atomic Group Decomposition of Charge Transfer Excitation Global Indexes

A model for decomposing the Le Bahers, Adamo, and Ciofini Charge Transfer (CT) Excitations global indexes ( J. Chem. Theory Comput. 2011, 7, 2498-2506) into molecular subdomains contributions is presented and a software, DOCTRINE (atomic group Decomposition Of the Charge TRansfer INdExes) for the implementation of this novel model has been coded. Although our method applies to any fuzzy or to any disjoint exhaustive partitioning of the real space, it is here applied using a definition of chemically relevant molecular subdomains based on the Atoms in Molecules Bader basins. This choice has the relevant advantage of associating intra or inter subdomain contributions to rigorously defined quantum objects, yet bearing a clear chemical meaning. Our method allows for a quantitative evaluation of the subdomain contributions to the charge transfer, the charge transfer excitation length and the dipole moment change upon excitation. All these global indexes may be obtained either from the electron density increment or the electron density depletion upon excitation. However, the subdomain contributions obtained from the two distributions generally differ, therefore allowing to distinguish whether the contribution to a given property of a given subdomain is dominated by one of the two distributions or if both are playing a significant role. As a toy system for the first application of our model, a typical [D-π-A, π = conjugated bridge] compound belonging to the merocyanine dyes family is selected, and the first four excited states of this compound in a strongly polar protic solvent and in a weakly polar solvent are thoroughly investigated.