Protic Processes in an Extended Pyrazinacene: The Case of Dihydrotetradecaazaheptacene

Pyrazinacenes are linearly fused heteroaromatic rings, with N atoms replacing all apical CH moieties. Component rings may exist in a reduced state, having NH groups instead of N, causing cross-conjugation. These compounds have interesting optical and electronic properties, including strong fluorescence in the near-infrared region and photocatalytic properties, leading to diverse possible applications in bio-imaging and organic synthesis, as well as obvious molecular electronic uses. In this study, we investigated the behavior of seven-ring pyrazinacene 2,3,11,12-tetraphenyl-7,16-dihydro-1,4,5,6,7,8,9,12,13,14,15,16,17,18-tetradecaazaheptacene (Ph4H2N14HEPT), with an emphasis on protic processes, including oxidation, tautomerism, deprotonation, and protonation, and the species resulting from those processes. We used computational methods to optimize the structures of the different species and generate/compare molecular orbital structures. The aromaticity of the species generated by the different processes was assessed using the nucleus-independent chemical shifts, and trends in the values were associated with the different transformations of the pyrazinacene core. The computational data were compared with experimental data obtained from synthetic samples of the molecule tBu8Ph4H2N14HEPT.

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.

2,3-Dichloroanthracene crystal, a new rigid matrix for single molecule optical investigations

Absorption and emission spectra of single crystals of 2,3-dichloroathracene (23DCA) and 23DCA dispersed in n-nonane matrix were studied at 5 K. Singlet and triplet excitonic bands in the crystal were estimated to be at about 415 nm and at wavelengths shorter than 700 nm, respectively. Thus, from the spectroscopic point of view, these crystals satisfy all criteria for a transparent and rigid matrix for low temperature optical studies of single molecules of dibenzoterrylene, which have their purely electronic S0→S1 transition at around 785 nm. Quantum-chemistry calculations were used to analyze the spectra.

Size Isn't Everything: Geometric Tuning in Polycyclic Aromatic Hydrocarbons and Its Implications for Carbon Nanodots

Recent developments in light-emitting carbon nanodots and molecular organic semiconductors have seen renewed interest in the properties of polycyclic aromatic hydrocarbons (PAHs) as a family. The networks of delocalized π electrons in sp2-hybridized carbon grant PAHs light-emissive properties right across the visible spectrum. However, the mechanistic understanding of their emission energy has been limited due to the ground state-focused methods of determination. This computational chemistry work, therefore, seeks to validate existing rules and elucidate new features and characteristics of PAHs that influence their emissions. Predictions based on (time-dependent) density functional theory account for the full 3-dimensional electronic structure of ground and excited states and reveal that twisting and near-degeneracies strongly influence emission spectra and may therefore be used to tune the color of PAHs and, hence, carbon nanodots. We particularly note that the influence of twisting goes beyond torsional destabilization of the ground-state and geometric relaxation of the excited state, with a third contribution associated with the electric transition dipole. Symmetries and peri-condensation may also have an effect, but this could not be statistically confirmed. In pursuing this goal, we demonstrate that with minimal changes to molecular size, the entire visible spectrum may be spanned by geometric modification alone; we have also provided a first estimate of emission energy for 35 molecules currently lacking published emission spectra as well as clear guidelines for when more sophisticated computational techniques are required to predict the properties of PAHs accurately.

Isolated Dimers Versus Solid-State Dimers of N-Heteropolycycles: Matrix-Isolation Spectroscopy in Concert with Quantum Chemistry

In this work, matrix-isolation spectroscopy and quantum-chemical calculations are used together to analyse the structure and properties of weakly bound dimers of the two isomers benzo[a]acridine and benzo[c]acridine. Our measured experimental electronic absorbance spectra agree with simulated spectra calculated for the equilibrium structures of the dimers in gas-phase, but in contrast, disagree with the simulated spectra calculated for the structures obtained by optimising the experimental solid-state structures. This highlights the sensitivity of the electronic excitations with respect to the dimer structures. The comparison between the solid-state and gas-phase dimers shows how far the intermolecular interactions could change the geometric and electronic structure in a disordered bulk material or at device interfaces, imposing consequences for exciton and charge mobility and other material properties.

Description of Solvatochromism of Peak Broadening in Absorption Spectra in Solution Using the Reference Interaction Site Model Self-Consistent Fields Spatial Electron Density Distribution

We quantified and subsequently analyzed bandwidth of ultraviolet and visible photoabsorption spectral lines in solution by applying time-dependent first-order perturbation theory using the Born-Oppenheimer adiabatic potential calculated using the multistate extended-multi-configurational quasi-degenerated second-order perturbation theory (MS-XMCQDPT2) coupled with the reference interaction site model self-consistent field spatial electron density distribution (RISM-SCF-cSED). The proposed method was implemented for 2-thiocytosine in solution, and solvatochromism of the bandwidth of the πSπ* transition was clearly observed. The standard deviation of a characteristic electronic excitation was decomposed into the contributions of the characteristic vibrational mode of 2-thiocytosine. The main vibrational modes contributing to peak broadening were found to be for acetonitrile, methanol, and the aqueous phase. We concluded that the mechanism for peak broadening is qualitatively different for phases of protic and aprotic solvents because of the structural variation in 2-thiocytosine driven by the breakage of the resonance structures.

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Tautomerism and Rotamerism of Favipiravir and Halogenated Analogues in Solution and in the Solid State

Favipiravir is an important selective antiviral against RNA-based viruses, and currently, it is being repurposed as a potential drug for the treatment of COVID-19. This type of chemical system presents different carboxamide-rotameric and hydroxyl-tautomeric states, which could be essential for interpreting its selective antiviral activity. Herein, the tautomeric 3-hydroxypyrazine/3-pyrazinone pair of favipiravir and its 6-substituted analogues, 6-Cl, 6-Br, 6-I, and 6-H, were fully investigated in solution and in the solid state through ultraviolet-visible, 1H nuclear magnetic resonance, infrared spectroscopy, and X-ray diffraction techniques. Also, a study of the gas phase was performed using density functional theory calculations. In general, the keto-enol balance in these 3-hydroxy-2-pyrazinecarboxamides is finely modulated by external and internal electrical variations via changes in solvent polarity or by replacement of substituents at position 6. The enol tautomer was prevalent in an apolar environment, whereas an increase in the level of the keto tautomer was favored by an increase in solvent polarity and, even moreso, with a strong hydrogen-donor solvent. Keto tautomerization was favored either in solution or in the solid state with a decrease in 6-substituent electronegativity as follows: H ≫ I ≈ Br > Cl ≥ F. Specific rotameric states based on carboxamide, "cisoide" and "transoide", were identified for the enol and keto tautomer, respectively; their rotamerism is dependent on the tautomerism and not the aggregation state.

Photon energy dependence of the photoelectron spectra of the anthracene anion: On the influence of autodetaching states

Vibrationally resolved photoelectron spectra of anthracene anions have been measured for photon energies between 1.13 and 4.96 eV. In this energy range, photoemission mostly occurs via autodetaching electronically excited states of the anion, which strongly modifies the vibrational excitation of the neutral molecule after electron emission. Based on the observed vibrational patterns, eight different excited states could be identified, seven of which are resonances known from absorption spectroscopy. Distinctly different photon energy dependencies of vibrational excitations have been obtained for different excited states, hinting at strongly different photoemission lifetimes. Unexpectedly, some resonances seem to exhibit bimodal distributions of emission lifetimes, possibly due to electronic relaxation processes induced by the excitation of specific vibrational modes.

Photogrammetry of Ultrafast Excited-State Intramolecular Proton Transfer Pathways in the Fungal Pigment Draconin Red

Proton transfer processes of organic molecules are key to charge transport and photoprotection in biological systems. Among them, excited-state intramolecular proton transfer (ESIPT) reactions are characterized by quick and efficient charge transfer within a molecule, resulting in ultrafast proton motions. The ESIPT-facilitated interconversion between two tautomers (PS and PA) comprising the tree fungal pigment Draconin Red in solution was investigated using a combination of targeted femtosecond transient absorption (fs-TA) and excited-state femtosecond stimulated Raman spectroscopy (ES-FSRS) measurements. Transient intensity (population and polarizability) and frequency (structural and cooling) dynamics of -COH rocking and -C=C, -C=O stretching modes following directed stimulation of each tautomer elucidate the excitation-dependent relaxation pathways, particularly the bidirectional ESIPT progression out of the Franck-Condon region to the lower-lying excited state, of the intrinsically heterogeneous chromophore in dichloromethane solvent. A characteristic overall excited-state PS-to-PA transition on the picosecond timescale leads to a unique "W"-shaped excited-state Raman intensity pattern due to dynamic resonance enhancement with the Raman pump-probe pulse pair. The ability to utilize quantum mechanics calculations in conjunction with steady-state electronic absorption and emission spectra to induce disparate excited-state populations in an inhomogeneous mixture of similar tautomers has broad implications for the modeling of potential energy surfaces and delineation of reaction mechanisms in naturally occurring chromophores. Such fundamental insights afforded by in-depth analysis of ultrafast spectroscopic datasets are also beneficial for future development of sustainable materials and optoelectronics.

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.

Efficient implementation of time-dependent auxiliary density functional theory

The random phase approximation of time-dependent auxiliary density functional theory (TDADFT) is rederived from auxiliary density perturbation theory. Our exhaustive validation of TDADFT reveals an upshift of the excitation energies by ∼0.1 eV with respect to standard time-dependent density functional theory. For the computationally efficient implementation of TDADFT, floating point operation optimized three-center electron repulsion integral recurrence relations and their double asymptotic expansions are implemented into the Davidson solver. The computational efficiency of TDADFT is benchmarked with four sets of molecules comprising alkanes, fullerenes, DNA fragments, and zeolites. The results show that TDADFT has a computational scaling between 1.3 and 1.9 with respect to the number of basis functions, which is lower than the scaling of standard time-dependent density functional theory. Due to its computational simplifications, TDADFT is particularly well suited for Born-Oppenheimer molecular dynamics simulations. As illustrative examples, we present the temperature effects on the gas-phase absorption spectra of benzene, naphthalene, and anthracene.

Dispersion Effect of Molecular Crowding on Ligand-Protein Surface Binding Sites of Escherichia coli RNase HI

The molecular crowding effect on ligand-protein interactions, which plays several crucial roles in life processes, has been investigated using various models by adding crowding agents to mimic the intracellular environment. Several studies evaluating this effect have focused on the ligand-protein binding reaction of well-structured binding sites with rigid conformations. However, the crowding effect on flexible binding sites is not well-understood, especially in terms of the conformations. In this work, to elucidate the detailed molecular mechanism underlying the ligand-protein interactions with flexible binding sites on a protein surface, we studied the interaction between the basic protrusion of Escherichia coli ribonuclease HI (RNase HI) and 8-anilinonaphthalene-1-sulfonic acid (ANS). The RNase HI concentration-dependent measurement of ANS fluorescence combined with the multivariate analysis and the fluorescence vibronic structure analysis revealed an increase in the heterogeneous species with an increase in the protein concentration, which is a different behavior from that of proteins with rigid binding sites. This result indicates that ANS molecules bind to the additional binding sites because of the destabilization of the main sites by the excluded volume effect in a crowded environment. The fluorescence vibronic structure analysis yields a detailed molecular picture, indicating that the main species of ANS can have a distorted structure. On the other hand, some ANS molecules move to the minor binding sites of a different microenvironment to secure a stabilized structure. These spectroscopic analyses may show a hypothesis, suggesting that the decrease in the ΔG difference between the main and minor sites due to destabilization of the main binding site could lower the potential barrier between them, inducing the dispersion of binding pathways.

Peri-Decoration of a Tetraazaperylene with Urea Units: Chiral Octaazaperopyrenedioxides (OAPPDOs) and Their Optical and Chiroptical Properties

Octaazaperopyrenedioxides (OAPPDOs) are a new class of fluorescent polycyclic aromatic hydrocarbons based on a tetraazaperylene core that is formally condensed with N-substituted urea units in the two opposite peri positions. Here, we report the synthesis of series of substituted OAPPDO derivatives with different N-substitution patterns (H, alkyl, benzyl) in the peri positions, including bay-chlorinated OAPPDOs. Starting from the latter, a series of bay-arylated OAPPDOs was synthesized by Suzuki cross coupling, which resulted in the formation of helically chiral OAPPDO derivatives. The electrochemical and photophysical properties were investigated by UV/Vis and fluorescence spectroscopy as well as cyclic voltammetry. The P and M enantiomers of a phenylated OAPPDO were separated by semipreparative HPLC and further analyzed by CD spectroscopy. The frontier orbital energies, the mechanism of the isomerization, the electronic excitation and the CD spectrum (TD-DFT) were computed and compared to the experimental data. The reversible 1e^- oxidation of the OAPPDOs generates the corresponding radical cations, one of which was characterized by EPR spectroscopy. The reversible oxidation process was also systematically investigated by spectro-electrochemistry.

Modeling the Electronic Absorption Spectra of the Indocarbocyanine Cy3

Accurate modeling of optical spectra requires careful treatment of the molecular structures and vibronic, environmental, and thermal contributions. The accuracy of the computational methods used to simulate absorption spectra is limited by their ability to account for all the factors that affect the spectral shapes and energetics. The ensemble-based approaches are widely used to model the absorption spectra of molecules in the condensed-phase, and their performance is system dependent. The Franck–Condon approach is suitable for simulating high resolution spectra of rigid systems, and its accuracy is limited mainly by the harmonic approximation. In this work, the absorption spectrum of the widely used cyanine Cy3 is simulated using the ensemble approach via classical and quantum sampling, as well as, the Franck–Condon approach. The factors limiting the ensemble approaches, including the sampling and force field effects, are tested, while the vertical and adiabatic harmonic approximations of the Franck–Condon approach are also systematically examined. Our results show that all the vertical methods, including the ensemble approach, are not suitable to model the absorption spectrum of Cy3, and recommend the adiabatic methods as suitable approaches for the modeling of spectra with strong vibronic contributions. We find that the thermal effects, the low frequency modes, and the simultaneous vibrational excitations have prominent contributions to the Cy3 spectrum. The inclusion of the solvent stabilizes the energetics significantly, while its negligible effect on the spectral shapes aligns well with the experimental observations.

On the Importance of Well-Defined Thermal Correlation Functions in Simulating Vibronic Spectra

Two difficulties associated with the computations of thermal vibrational correlation functions are discussed. The first one is the lack of a well-behaved expression that is valid at both high-temperature and T → 0 K limits. Specifically, if the partition function and the propagator are considered separately, then thermal vibrational correlation functions may have an indeterminate form 0/0 in the limit T → 0 K. This difficulty is resolved when the partition function and the propagator are jointly considered in the harmonic approximation, which allows a problematic term that emanates from the zero-point energy to be canceled out, thereby producing a thermal correlation function with a determinate form in the T → 0 K limit. The second difficulty is related to the multivaluedness of the vibrational correlation function. We show numerically that an improper selection of branch leads to discontinuities in the computed correlation function and incorrect vibronic spectra. We propose a phase tracking procedure that ensures continuity of both real and imaginary parts of the correlation function to recover the correct spectra. We support our findings by simulating the UV-vis absorption spectra of pentacene at 4 K and benzene at 298 K. Both are found to be in good agreement with their experimental counterparts.

Applicability of the Thawed Gaussian Wavepacket Dynamics to the Calculation of Vibronic Spectra of Molecules with Double-Well Potential Energy Surfaces

Simulating vibrationally resolved electronic spectra of anharmonic systems, especially those involving double-well potential energy surfaces, often requires expensive quantum dynamics methods. Here, we explore the applicability and limitations of the recently proposed single-Hessian thawed Gaussian approximation for the simulation of spectra of systems with double-well potentials, including 1,2,4,5-tetrafluorobenzene, ammonia, phosphine, and arsine. This semiclassical wavepacket approach is shown to be more robust and to provide more accurate spectra than the conventional harmonic approximation. Specifically, we identify two cases in which the Gaussian wavepacket method is especially useful due to the breakdown of the harmonic approximation: (i) when the nuclear wavepacket is initially at the top of the potential barrier but delocalized over both wells, e.g., along a low-frequency mode, and (ii) when the wavepacket has enough energy to classically go over the low potential energy barrier connecting the two wells. The method is efficient and requires only a single classical ab initio molecular dynamics trajectory, in addition to the data required to compute the harmonic spectra. We also present an improved algorithm for computing the wavepacket autocorrelation function, which guarantees that the evaluated correlation function is continuous for arbitrary size of the time step.

Cooperation of σ-π and σ*-π* Conjugation in the UV/Vis and Fluorescence Spectra of 9,10-Disilylanthracene

In 1996, we reported that silyl groups of 9,10-disilylanthracenes significantly affect the UV/Vis and fluorescence spectra. Although the results indicate that the silyl groups have strong electronic effects on anthracene, the details of the mechanisms responsible for this have not yet been clarified. This article describes the analysis of the UV/Vis and fluorescence spectra of 9,10-bis(diisopropylsilyl)anthracene by theoretical calculations. This study reveals that π conjugation of anthracene is extended by cooperation of σ-π and σ*-π* conjugation between the silyl groups and anthracene. This effect increases the transition moment of the π-π* transition of anthracene. As a result, the molecular extinction coefficient of the ¹L_a band and the fluorescence quantum yield are increased.

Active Learning Configuration Interaction for Excited-State Calculations of Polycyclic Aromatic Hydrocarbons

We present the active learning configuration interaction (ALCI) method for multiconfigurational calculations based on large active spaces. ALCI leverages the use of an active learning procedure to find important electronic configurations among the full configurational space generated within an active space. We tested it for the calculation of singlet-singlet excited states of acenes and pyrene using different machine learning algorithms. The ALCI method yields excitation energies within 0.2-0.3 eV from those obtained by traditional complete active-space configuration interaction (CASCI) calculations (affordable for active spaces up to 16 electrons in 16 orbitals) by including only a small fraction of the CASCI configuration space in the calculations. For larger active spaces (we tested up to 26 electrons in 26 orbitals), not affordable with traditional CI methods, ALCI captures the trends of experimental excitation energies. Overall, ALCI provides satisfactory approximations to large active-space wave functions with up to 10 orders of magnitude fewer determinants for the systems presented here. These ALCI wave functions are promising and affordable starting points for the subsequent second-order perturbation theory or pair-density functional theory calculations.

Laser-Induced Electronic and Vibronic Dynamics in the Pyrene Molecule and Its Cation

Among polycyclic aromatic hydrocarbons, pyrene is widely used as an optical probe thanks to its peculiar ultraviolet absorption and infrared emission features. Interestingly, this molecule is also an abundant component of the interstellar medium, where it is detected via its unique spectral fingerprints. In this work, we present a comprehensive first-principles study on the electronic and vibrational response of pyrene and its cation to ultrafast, coherent pulses in resonance with their optically active excitations in the ultraviolet region. The analysis of molecular symmetries, electronic structure, and linear optical spectra is used to interpret transient absorption spectra and kinetic energy spectral densities computed for the systems excited by ultrashort laser fields. By disentangling the effects of the electronic and vibrational dynamics via ad hoc simulations with stationary and moving ions, and, in specific cases, with the aid of auxiliary model systems, we rationalize that the nuclear motion is mainly harmonic in the neutral species, while strong anharmonic oscillations emerge in the cation, driven by electronic coherence. Our results provide additional insights into the ultrafast vibronic dynamics of pyrene and related compounds and set the stage for future investigations on more complex carbon-conjugated molecules.

Mono-/Bimetallic Neutral Iridium(III) Complexes Bearing Diketopyrrolopyrrole-Substituted N-Heterocyclic Carbene Ligands: Synthesis and Photophysics

The synthesis and photophysics (UV-vis absorption, emission, and transient absorption) of four neutral heteroleptic cyclometalated iridium(III) complexes (Ir-1-Ir-4) incorporating thiophene/selenophene-diketopyrrolopyrrole (DPP)-substituted N-heterocyclic carbene (NHC) ancillary ligands are reported. The effects of thiophene versus selenophene substitution on DPP and bis- versus monoiridium(III) complexation on the photophysics of these complexes were systematically investigated via spectroscopic techniques and density functional theory calculations. All complexes exhibited strong vibronically resolved absorption in the regions of 500-700 nm and fluorescence at 600-770 nm, and both are predominantly originated from the DPP-NHC ligand. Complexation induced a pronounced red shift of this low-energy absorption band and the fluorescence band with respect to their corresponding ligands due to the improved planarity and extended π-conjugation in the DPP-NHC ligand. Replacing the thiophene units by selenophenes and/or biscomplexation led to the red-shifted absorption and fluorescence spectra, accompanied by the reduced fluorescence lifetime and quantum yield and enhanced population of the triplet excited states, as reflected by the stronger triplet excited-state absorption and singlet oxygen generation.

How to Predict Excited State Geometry by Using Empirical Parameters Obtained from Franck-Condon Analysis of Optical Spectrum

Excited state geometries of molecules can be calculated with highly reliable wavefunction schemes. Most of such schemes, however, are applicable to small molecules and can hardly be viewed as error-free for excited state geometries. In this study, a theoretical approach is presented in which the excited state geometries of molecules can be predicted by using vibrationally resolved experimental absorption spectrum in combination with the theoretical modelling of vibrational pattern based on Franck-Condon approximation. Huang-Rhys factors have been empirically determined and used as input for revealing the structural changes occurring between the ground and the excited state geometries upon photoexcitation. Naphthalene molecule has been chosen as a test case to show the robustness of the proposed theoretical approach. Predicted 1B_2u excited state geometry of the naphthalene has similar but slightly different bond length alternation pattern when compared with the geometries calculated with CIS, B3LYP, and CC2 methods. Excited state geometries of perylene and pyrene molecules are also determined with the presented theoretical approach. This powerful method can be applied to other molecules and specifically to relatively large molecules rather easily as long as vibrationally resolved experimental spectra are available to use.

The Pyrazinacenes

Pyrazinacenes are a class of nitrogen-containing heteroacene molecules composed of linearly fused pyrazine units, which might also include dihydropyrazine groups leading to different reduced states of the compounds. While they are structurally similar to hydrocarbon acenes (e.g., pentacene) the presence of increasing numbers of N-heteroatoms introduces several different additional features of the compounds so that they can be considered for investigations beyond those suggested for acenes (i.e., organic field-effect transistors, solar cell components). Pyrazinacenes are in several ways complementary to C-H-only acenes based on the increasing stability of reduced states of the compounds with increasing numbers of fused pyrazine rings, although an acene-like electronic structure persists in the compounds so far studied. However, the introduction of multiple N atoms leads to properties that depart from C-H-only acenes. In particular, the compounds exhibit a delocalization of NH protons in extended reduced compounds and oxidation state switchability in solution and at interfaces. The presence of NH groups also allows an easy introduction of solubilizing groups at the pyrazinacene chromophore. In this Account, we will describe the preparation of extended pyrazinacenes from dipyrazino[2,3-b:2',3'-e]pyrazine (1,4,5,8,9,10-hexaazaanthracene; N6) derivatives up to 1,4,5,6,7,8,9,12,13,14,15,16,17,18-tetradecaazaheptacene (N14) and also assess structures of the relevant compounds based on X-ray crystallographic studies. Emergent properties of the molecules include highly unusual linear tautomeric processes based on a delocalization of protons (and the corresponding formation of orbitals based on multiple adjacent N lone electron pair interactions), which suggest special transport properties based on molecular protonics. Molecules such as decazapentacene (N10) exhibit multistability of oxidation state, and this is predicted to promote the redox catalytic properties of the compounds. The oxidation-state switching of on-surface processes is also described and has been investigated using scanning tunneling microscopy. The longest known pyrazinacene chromophore (N14) exhibits amphiprotism with its state of protonation being strongly coupled to its fluorescence emission properties in the near-infrared region indicating possible uses in pH-coupled bioimaging applications. The synthesis of the pyrazinacenes is flexible and allows the preparation of symmetrically or unsymmetrically substituted derivatives for the development of more complex molecules and for control of the electronic structure of the acene unit. Overall, the pyrazinacenes represent an emerging class of highly nitrogenous heteroacenes with unique properties and excellent potential for development in different applications based on their special supramolecular properties including guest binding or interactions in biological systems.

Reliable TDDFT Protocol Based on a Local Hybrid Functional for the Prediction of Vibronic Phosphorescence Spectra Applied to Tris(2,2'-bipyridine)-Metal Complexes

An efficient computational protocol for the prediction of vibrationally resolved phosphorescence spectra is developed and validated for five tris(2,2'-bipyridine)-metal complexes ([M(bpy)₃]ⁿ⁺, where M = Zn, Ru, Rh, Os, Ir). The outstanding feature of this protocol is the use of full linear-response time-dependent density functional theory (TDDFT) for the excited-state triplet calculation, i.e., the commonly seen strategies employing the Tamm-Dancoff approximation (TDA) or unrestricted density functional theory (DFT) calculations for the T₁ state are not needed. This is achieved by the use of a local hybrid functional (LH12ct-SsirPW92) that features a real-space dependent admixture of exact exchange governed by a local mixing function. The excellent performance of this LH for triplet excitation energies known from previous studies transfers to a remarkable mean absolute error of 0.06 eV for the phosphorescence 0-0 energies investigated herein, while the popular B3PW91 functional gives an error of 0.27 eV in TDDFT and 0.09 eV in unrestricted DFT calculations, respectively. The advantages of the local hybrid are particularly apparent for excited states with a mixed-valence character. The influence of spin-orbit coupling was found to be significant for [Os(bpy)₃]²⁺ red-shifting the 0-0 energy for phosphorescence by 0.17 eV, while the effect is negligible for the other complexes (<0.03 eV). The influence of the basis-set and integration-grid sizes is evaluated, and a computationally lighter protocol is validated that leads to drastic savings in computation time with negligible loss in accuracy.

Elucidating an Atmospheric Brown Carbon Species-Toward Supplanting Chemical Intuition with Exhaustive Enumeration and Machine Learning

Brown carbon (BrC) is involved in atmospheric light absorption and climate forcing and can cause adverse health effects. Understanding the formation mechanisms and molecular structure of BrC is of key importance in developing strategies to control its environment and health impact. Structure determination of BrC is challenging, due to the lack of experiments providing molecular fingerprints and the sheer number of molecular candidates with identical mass. Suggestions based on chemical intuition are prone to errors due to the inherent bias. We present an unbiased algorithm, using graph-based molecule generation and machine learning, which can identify all molecular structures of compounds involved in biomass burning and the composition of BrC. We apply this algorithm to C₁₂H₁₂O₇, a light-absorbing "test case" molecule identified in chamber experiments on the aqueous photo-oxidation of syringol, a prevalent marker in wood smoke. Of the 260 million molecular graphs, the algorithm leaves only 36,518 (0.01%) as viable candidates matching the spectrum. Although no unique molecular structure is obtained from only a chemical formula and a UV/vis absorption spectrum, we discuss further reduction strategies and their efficacy. With additional data, the method can potentially more rapidly identify isomers extracted from lab and field aerosol particles without introducing human bias.

Multiconfigurational Quantum Chemistry Determinations of Absorption Cross Sections (σ) in the Gas Phase and Molar Extinction Coefficients (ε) in Aqueous Solution and Air-Water Interface

Theoretical determinations of absorption cross sections (σ) in the gas phase and molar extinction coefficients (ε) in condensed phases (water solution, interfaces or surfaces, protein or nucleic acids embeddings, etc.) are of interest when rates of photochemical processes, J = ∫ ϕ(λ) σ(λ) I(λ) dλ, are needed, where ϕ(λ) and I(λ) are the quantum yield of the process and the irradiance of the light source, respectively, as functions of the wavelength λ. Efficient computational strategies based on single-reference quantum-chemistry methods have been developed enabling determinations of line shapes or, in some cases, achieving rovibrational resolution. Developments are however lacking for strongly correlated problems, with many excited states, high-order excitations, and/or near degeneracies between states of the same and different spin multiplicities. In this work, we define and compare the performance of distinct computational strategies using multiconfigurational quantum chemistry, nuclear sampling of the chromophore (by means of molecular dynamics, ab initio molecular dynamics, or Wigner sampling), and conformational and statistical sampling of the environment (by means of molecular dynamics). A new mathematical approach revisiting previous absolute orientation algorithms is also developed to improve alignments of geometries. These approaches are benchmarked through the nπ* band of acrolein not only in the gas phase and water solution but also in a gas-phase/water interface, a common situation for instance in atmospheric chemistry. Subsequently, the best strategy is used to compute the absorption band for the adduct formed upon addition of an OH radical to the C6 position of uracil and compared with the available experimental data. Overall, quantum Wigner sampling of the chromophore with molecular dynamics sampling of the environment with CASPT2 electronic-structure determinations arise as a powerful methodology to predict meaningful σ(λ) and ε(λ) band line shapes with accurate absolute intensities.

Symmetry-Breaking Enhanced Herzberg-Teller Effect with Brominated Polyacenes

Molecular symmetry is vital to the selection rule of vibrationally resolved electronic transition, particularly when the nuclear dependence of electronic wave function is explicitly treated by including Franck-Condon (FC) factor, Franck-Condon/Herzberg-Teller (FC/HT) interference, and Herzberg-Teller (HT) coupling. Our present study investigated the light absorption spectra of highly symmetric tetracene, pentacene, and hexacene molecules of point-group D_2h, as well as their monobrominated derivatives with a lower C_s symmetry. It was found that the symmetry-breaking monobromination allows more vibrational normal modes and their pairs to contribute to FC/HT interference and HT coupling, respectively. Through a projection of a molecule's vibrational normal modes to its irreducible representations, a linear relationship between the FC/HT intensity to the polyacene's size was deduced alongside a quadratic dependence of the HT intensity. Both theoretically derived correlations were well justified by our numerical simulations, which also demonstrated an approximately 20% improvement on the agreement with experimental line shape if the HT theory is adopted to replace the FC approximation. Moreover, for these low-symmetry monobrominated polyacenes, the FC intensity was even weaker than its FC/HT and HT counterparts at some excitation energies, making the HT theory imperative to decipher vibronic coupling, a fundamental driving force behind numerous chemical, biological, and photophysical processes.

Charge transfer induced by electronic state mixing in a symmetric X-Y-X-type multi-chromophore system

Charge transfer (CT) from electron donor (D) to acceptor (A) plays an important role in photoelectric or electrochemical devices and is a useful concept for a molecule with D and A well distinguishable. Here, we report our finding that even in a molecule with D and A not resolvable, CT can be induced by electronic state mixing (ESM) in a symmetric multi-chromophore system (MCS), namely 1,4-di(1-pyrenyl)benzene (Py-Benz-Py). Unlike Py and Py-Benz, Py-Benz-Py exhibits unique photophysical properties attributable to the reduction of the energy gap between two electronic states induced by ESM. The ESM for Py-Benz-Py is due to the extended π-conjugation owing to the further introduction of Py into Py-Benz, and consequently leads to the favorable intramolecular CT, followed by the planarization due to the twisting motion between Py and phenyl moieties. Time-resolved spectroscopic data demonstrate that the twisting process of the Py moiety in acetonitrile occurs with two unequal time constants, suggesting the localized CT state and the asynchronous twisting dynamics of two Py moieties unlike the delocalized CT state in nonpolar and low-polarity solvents leading to the synchronous twisting of two Py moieties. This means that the symmetry-breaking CT in MCSs can induce an asynchronous twisting motion. The results reported here support that a molecule without CT can be turned into another molecule with CT induced by ESM and demonstrate that the excited-state relaxation dynamics can be regulated through the ESM induced by introducing the substituents or changing the environmental factors such as solvent polarities.

Simulation of vibrationally resolved absorption spectra of neutral and cationic polyaromatic hydrocarbons

The identification of the carriers of the absorption features associated with the diffuse interstellar bands (DIBs) is a long-standing problem in astronomical spectroscopy. Computational simulations can contribute to the assignment of the carriers of DIBs since variations in molecular structure and charge state can be studied more readily than through experimental measurements. Polyaromatic hydrocarbons have been proposed as potential carriers of these bands, and it is shown that simulations based upon density functional theory and time-dependent density functional theory calculations can describe the vibrational structure observed in experiment for neutral and cationic naphthalene and pyrene. The vibrational structure arises from a small number of vibrational modes involving in-plane atomic motions, and the Franck–Condon–Herzberg–Teller approximation improves the predicted spectra in comparison with the Franck–Condon approximation. The study also highlights the challenges for the calculations to enable the assignment in the absence of experimental data, namely prediction of the energy separation between the different electronic states to a sufficient level of accuracy and performing vibrational analysis for higher-lying electronic states.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Semiclassical Approach to Photophysics Beyond Kasha's Rule and Vibronic Spectroscopy Beyond the Condon Approximation. The Case of Azulene

Azulene is a prototypical molecule with an anomalous fluorescence from the second excited electronic state, thus violating Kasha's rule, and with an emission spectrum that cannot be understood within the Condon approximation. To better understand the photophysics and spectroscopy of azulene and other nonconventional molecules, we developed a systematic, general, and efficient computational approach combining the semiclassical dynamics of nuclei with ab initio electronic structure. First, to analyze the nonadiabatic effects, we complement the standard population dynamics by a rigorous measure of adiabaticity, estimated with the multiple-surface dephasing representation. Second, we propose a new semiclassical method for simulating non-Condon spectra, which combines the extended thawed Gaussian approximation with the efficient single-Hessian approach. S₁ ← S₀ and S₂ ← S₀ absorption and S₂ → S₀ emission spectra of azulene, recorded in a new set of experiments, agree very well with our calculations. We find that accuracy of the evaluated spectra requires the treatment of anharmonicity, Herzberg-Teller, and mode-mixing effects.

Calculation of vibrationally resolved absorption and fluorescence spectra of the rylenes

A generating function method was used to simulate the vibrationally resolved absorption and emission spectra of perylene, terrylene and quaterrylene. This method operates on the basis of adiabatic excitation energies and electronic ground and excited state vibrational frequencies. These parameters were calculated using density functional theory with the PBE0 functional for perylene and terrylene and with the BH-LYP functional for quaterrylene. The vertical excitation energies of the lower excited states were calculated using functionals with differing amounts of Hartree-Fock exchange. The optimal functional for each molecule was chosen by comparing these energies to literature excitation energies. Using this technique the calculated absorption spectra and the calculated emission spectrum of perylene were found to be in excellent agreement with the literature experimental spectra after introducing a shift and a scaling factor. The most prominent bands of the absorption spectra were assigned to their respective vibronic transitions.

Benchmarking the Performance of Time-Dependent Density Functional Theory Methods on Biochromophores

Quantum chemical calculations are important for elucidating light-capturing mechanisms in photobiological systems. The time-dependent density functional theory (TDDFT) has become a popular methodology because of its balance between accuracy and computational scaling, despite its problems in describing, for example, charge transfer states. As a step toward systematically understanding the performance of TDDFT calculations on biomolecular systems, we study here 17 commonly used density functionals, including seven long-range separated functionals, and compare the obtained results with excitation energies calculated at the approximate second order coupled-cluster theory level (CC2). The benchmarking set includes the first five singlet excited states of 11 chemical analogues of biochromophores from the green fluorescent protein, rhodopsin/bacteriorhodopsin (Rh/bR), and the photoactive yellow protein. We find that commonly used pure density functionals such as BP86, PBE, M11-L, and hybrid functionals with 20-25% of Hartree-Fock (HF) exchange (B3LYP, PBE0) have a tendency to consistently underestimate vertical excitation energies (VEEs) relative to the CC2 values, whereas hybrid density functionals with around 50% HF exchange such as BHLYP, PBE50, and M06-2X and long-range corrected functionals such as CAM-B3LYP, ωPBE, ωPBEh, ωB97X, ωB97XD, BNL, and M11 overestimate the VEEs. We observe that calculations using the CAM-B3LYP and ωPBEh functionals with 65% and 100% long-range HF exchange, respectively, lead to an overestimation of the VEEs by 0.2-0.3 eV for the benchmarking set. To reduce the systematic error, we introduce here two new empirical functionals, CAMh-B3LYP and ωhPBE0, for which we adjusted the long-range HF exchange to 50%. The introduced parameterization reduces the mean signed average (MSA) deviation to 0.07 eV and the root mean square (rms) deviation to 0.17 eV as compared to the CC2 values. In the present study, TDDFT calculations using the aug-def2-TZVP basis sets, the best performing functionals relative to CC2 are ωhPBE0 (rms = 0.17, MSA = 0.06 eV); CAMh-B3LYP (rms = 0.16, MSA = 0.07 eV); and PBE0 (rms = 0.23, MSA = -0.14 eV). For the popular range-separated CAM-B3LYP functional, we obtain an rms value of 0.31 eV and an MSA value of 0.25 eV, which can be compared with the rms and MSA values of 0.37 and -0.31 eV, respectively, as obtained at the B3LYP level.

Generating Function Approach to Single Vibronic Level Fluorescence Spectra

An efficient time-dependent generating function method to compute vibronic emission and absorption spectra arising from transitions from a singly excited vibrational initial state is presented. In contrast to existing finite temperature approaches that intrinsically contain these transitions weighted by a Boltzmann factor, the current approach allows one to calculate these transitions individually. Using vibrational frequencies and normal modes computed by the second-order approximate coupled cluster (CC2) method, this formalism is used to compute the single vibronic level (SVL) fluorescence spectra of anthracene. Calculated spectra are in excellent agreement with spectra measured in jet-cooled expansion experiments. Duschinsky mixing is necessary to explain intensities of certain peaks. In a few cases, CC2, however, underestimates Duschinsky mixing, leading to too low peak intensities. An empirical correction of the Duschinsky matrix is presented. The presented method has the potential to facilitate the assignment and interpretation of SVL fluorescence spectra.