General Time Dependent Approach to Vibronic Spectroscopy Including Franck-Condon, Herzberg-Teller, and Duschinsky Effects

LIF spectrum for the localised S0 → S1(ππ*) excitation in the H-bonded anthranilic acid dimer: Symmetry breaking or coupling of vibrations

This study aims to investigate the impact of the π → π* excitation localised in one monomer on the equilibrium geometry and oscillations of the AA dimer. Several low-frequency vibrations appear in pairs in the LIF spectrum because oscillations involving intermolecular hydrogen bonds are coupled, generating approximately symmetric and antisymmetric combinations (especially the COOH rocking modes, LIF: 295 and 301 cm-1). Furthermore, quantitative evaluation based on the TDDFT(B3LYP) results indicates that a dozen among 90 intramolecular oscillations are strongly coupled. In contrast, most vibrations are decoupled or weakly coupled, since they involve remote parts of the monomers. This makes several single vibrations active in the LIF spectrum (including the bending mode of the NH···O intramolecular hydrogen bond associated the strongest vibronic band 442 cm-1), while the other in each pair remains inactive. The reason for decoupling of oscillations and symmetry breaking is that the π → π* electronic excitation is entirely localised within one of the monomers, which makes them no longer equivalent in terms of geometry and dynamics. Additionally, the excitation of one monomer induces strengthening and shortening by 6 pm of only one intermolecular hydrogen bond linking the carboxylic groups of both molecules. This causes the 1.7° in-plane distortion of the dimer and lowering of its symmetry to Cs group (from C2h for the S0 state). The distortion induces the activity of two low-frequency in-plane intermolecular vibrations, i.e. the geared oscillation (LIF: 58 cm-1) and the shearing motion (99 cm-1) of the monomers.

Origin of Intersystem Crossing in Red-Light Absorbing Bodipy Derivatives: Time-Resolved Transient Optical and Electron Paramagnetic Resonance Spectral Studies with Twisted and Planar Compounds

We studied the intersystem crossing (ISC) property of red-light absorbing heavy atom-free dihydronaphtho[b]-fused Bodipy derivatives (with phenyl group attached at the lower rim via ethylene bridge, taking constrained geometry, i.e., BDP-1 and the half-oxidized product BDP-2) and dispiroflourene[b]-fused Bodipy (BDP-3) that have a twisted π-conjugated framework. BDP-1 and BDP-3 show strong and sharp absorption bands (i.e., ε = 2.0 × 105 M-1 cm-1 at 639 nm, fwhm ∼491 cm-1 for BDP-3). BDP-1 is significantly twisted (φ = 21.6°), while upon mono-oxidation, BDP-2 becomes nearly planar on the oxidized side (φ = 3.5°). Interestingly, BDP-2 showed efficient ISC (triplet state quantum yield, ΦT = 40%) due to S1/T2 state energy matching. Long-lived triplet excited state was observed (τT = 212 μs in solution and 2.4 ms in polymer matrix), and ISC takes 4.0 ns. Differently, twisted BDP-1 gives weak ISC only 5%, ISC takes 7.7 ns, and the triplet state is populated only with addition of ethyl iodide. Time-resolved electron paramagnetic resonance spectra of BDP-1 revealed the coexistence of two triplet states, with drastically different zero-field splitting D parameters of -2047 MHz and -1370 MHz, respectively, along with varying sublevel population ratios. We demonstrate that the ISC is not necessarily enhanced by torsion of the π-conjugation framework; instead, S1/Tn state energy matching is more efficient to induce ISC even in compounds that have planar molecular structures.

Toward the improvement of vibronic spectra and non-radiative rate constants using the vertical Hessian method

For the computation of vibrationally resolved electronic spectra, various approaches can be employed. Adiabatic approaches simulate vibronic transitions using harmonic potentials of the initial and final states, while vertical approaches extrapolate the final state potential from the gradients and Hessian at the Franck-Condon point, avoiding a full exploration of the potential energy surface of the final state. Our implementation of the vertical Hessian (VH) method has been validated with a benchmark set of four small molecules, each presenting unique challenges, such as complex topologies, problematic low-frequency vibrations, or significant geometrical changes upon electronic excitation. We assess the quality of both adiabatic and vertical approaches for simulating vibronic transitions. For two types of donor-acceptor compounds with promising thermally activated delayed fluorescence properties, our computations confirm that the vertical approaches outperform the adiabatic ones. The VH method significantly reduces computational costs and yields meaningful emission spectra, where adiabatic models fail. More importantly, we pioneer the use of the VH method for the computation of rate constants for non-radiative processes, such as intersystem crossing and reverse intersystem crossing along a relaxed interpolated pathway of a donor-acceptor compound. This study highlights the potential of the VH method to advance computational vibronic spectroscopy by providing meaningful simulations of intricate decay pathway mechanisms in complex molecular systems.

Predicting Emission Spectra of Heteroleptic Iridium Complexes Using Artificial Chemical Intelligence

We report a deep learning-based approach to accurately predict the emission spectra of phosphorescent heteroleptic [Ir(C ∧ N ${{\rm{C}}^\wedge {\rm{N}}}$ )2(N ∧ N ${{\rm{N}}^\wedge {\rm{N}}}$ )]+ complexes, enabling the rapid discovery of novel Ir(III) chromophores for diverse applications including organic light-emitting diodes and solar fuel cells. The deep learning models utilize graph neural networks and other chemical features in architectures that reflect the inherent structure of the heteroleptic complexes, composed ofC ∧ N ${{\rm{C}}^\wedge {\rm{N}}}$ andN ∧ N ${{\rm{N}}^\wedge {\rm{N}}}$ ligands, and are thus geared towards efficient training over the dataset. By leveraging experimental emission data, our models reliably predict the full emission spectra of these complexes across various emission profiles, surpassing the accuracy of conventional DFT and correlated wavefunction methods, while simultaneously achieving robustness to the presence of imperfect (noisy, low-quality) training spectra. We showcase the potential applications for these and related models for in silico prediction of complexes with tailored emission properties, as well as in "design of experiment" contexts to reduce the synthetic burden of high-throughput screening. In the latter case, we demonstrate that the models allow us to exploit a limited amount of experimental data to explore a wide range of chemical space, thus leveraging a modest synthetic effort.

Quantum chemical package Jaguar: A survey of recent developments and unique features

This paper is dedicated to the quantum chemical package Jaguar, which is commercial software developed and distributed by Schrödinger, Inc. We discuss Jaguar's scientific features that are relevant to chemical research as well as describe those aspects of the program that are pertinent to the user interface, the organization of the computer code, and its maintenance and testing. Among the scientific topics that feature prominently in this paper are the quantum chemical methods grounded in the pseudospectral approach. A number of multistep workflows dependent on Jaguar are covered: prediction of protonation equilibria in aqueous solutions (particularly calculations of tautomeric stability and pKa), reactivity predictions based on automated transition state search, assembly of Boltzmann-averaged spectra such as vibrational and electronic circular dichroism, as well as nuclear magnetic resonance. Discussed also are quantum chemical calculations that are oriented toward materials science applications, in particular, prediction of properties of optoelectronic materials and organic semiconductors, and molecular catalyst design. The topic of treatment of conformations inevitably comes up in real world research projects and is considered as part of all the workflows mentioned above. In addition, we examine the role of machine learning methods in quantum chemical calculations performed by Jaguar, from auxiliary functions that return the approximate calculation runtime in a user interface, to prediction of actual molecular properties. The current work is second in a series of reviews of Jaguar, the first having been published more than ten years ago. Thus, this paper serves as a rare milestone on the path that is being traversed by Jaguar's development in more than thirty years of its existence.

Calculating absorption and fluorescence spectra for chromophores in solution with ensemble Franck-Condon methods

Accurately modeling absorption and fluorescence spectra for molecules in solution poses a challenge due to the need to incorporate both vibronic and environmental effects, as well as the necessity of accurate excited state electronic structure calculations. Nuclear ensemble approaches capture explicit environmental effects, Franck-Condon methods capture vibronic effects, and recently introduced ensemble-Franck-Condon approaches combine the advantages of both methods. In this study, we present and analyze simulated absorption and fluorescence spectra generated with combined ensemble-Franck-Condon approaches for three chromophore-solvent systems and compare them to standard ensemble and Franck-Condon spectra, as well as to the experiment. Employing configurations obtained from ground and excited state ab initio molecular dynamics, three combined ensemble-Franck-Condon approaches are directly compared to each other to assess the accuracy and relative computational time. We find that the approach employing an average finite-temperature Franck-Condon line shape generates spectra nearly identical to the direct summation of an ensemble of Franck-Condon spectra at one-fourth of the computational cost. We analyze how the spectral simulation method, as well as the level of electronic structure theory, affects spectral line shapes and associated Stokes shifts for 7-nitrobenz-2-oxa-1,3-diazol-4-yl and Nile red in dimethyl sulfoxide and 7-methoxy coumarin-4-acetic acid in methanol. For the first time, our studies show the capability of combined ensemble-Franck-Condon methods for both absorption and fluorescence spectroscopy and provide a powerful tool for simulating linear optical spectra.

Deciphering the doublet luminescence mechanism in neutral organic radicals: spin-exchange coupling, reversed-quartet mechanism, excited-state dynamics

Neutral organic radical molecules have recently attracted considerable attention as promising luminescent and quantum-information materials. However, the presence of a radical often shortens their excited-state lifetime and results in fluorescence quenching due to enhanced intersystem crossing (EISC). Recently, an experimental report introduced an efficient luminescent radical molecule, tris(2,4,6-trichlorophenyl)methyl-carbazole-anthracene (TTM-1Cz-An). In this study, we systematically performed quantum theoretical calculations combined with the path integral approach to quantitatively calculate the excited-state dynamics processes and spectral characteristics. Our theoretical findings suggest that the sing-doublet D1 state, originating from the anthracene excited singlet state, is quickly converted to the doublet (trip-doublet) state via EISC, facilitated by a significant nonequivalence exchange interaction, with ΔJ ST = 0.174 cm-1. The formation of the quartet state (Q1, trip-quartet) was predominantly dependent on the exchange coupling 3/2J TR = 0.086 cm-1 between the triplet spin electrons of anthracene and the TTM-1Cz radical. Direct spin-orbit coupling ISC to the Q1 state was minimal due to the nearly identical spatial wavefunctions of the and Q1 levels. The effective occurrence of reverse intersystem crossing (RISC) from the Q1 to D1 state is a critical step in controlling the luminescence of TTM-1Cz-An. The calculated RISC rate k RISC, including the Herzberg-Teller effect, was 3.64 × 105 s-1 at 298 K, significantly exceeding the phosphorescence and nonradiative rates of the Q1 state, thus enabling the D1 repopulation. Subsequently, a strong electronic coupling of 37.4 meV was observed between the D1 and D2 states, along with a dense manifold of doublet states near the D1 state energy, resulting in a larger reverse internal conversion rate k RIC of 9.26 × 1010 s-1. Distributed to the D2 state, the obtained emission rate of k f = 2.98-3.18 × 107 s-1 was in quite good agreement with the experimental value of 1.28 × 107 s-1, and its temperature effect was not remarkable. Our study not only provides strong support for the experimental findings but also offers valuable insights for the molecular design of high-efficiency radical emitters.

Photophysics and photochemistry of thermally activated delayed fluorescence emitters based on the multiple resonance effect: transient optical and electron paramagnetic resonance studies

The photochemistry of two representative thermally activated delayed fluorescence (TADF) emitters based on the multiple resonance effect (MRE) (DABNA-1 and DtBuCzB) was studied. No significant TADF was observed in fluid solution, although the compounds have a long-lived triplet state (ca. 30 μs). We found that these planar boron molecules bind with Lewis bases, e.g., 4-dimethylaminopyridine (DMAP) or an N-heterocyclic carbene (NHC). A new blue-shifted absorption band centered at 368 nm was observed for DtBuCzB upon formation of the adduct; however, the fluorescence of the adduct is the same as that of the free DtBuCzB. We propose that photo-dissociation occurs for the DtBuCzB-DMAP adduct, which is confirmed by femtosecond transient absorption spectra, implying that fluorescence originates from DtBuCzB produced by photo-dissociation; the subsequent in situ re-binding was observed with nanosecdon transient absorption spectroscopy. No photo-dissociation was observed for the NHC adduct. Time-resolved electron paramagnetic resonance (TREPR) spectra show that the triplet states of DABNA-1 and DtBuCzB have similar zero field splitting (ZFS) parameters (D = 1450 MHz). Theoretical studies show that the slow ISC is due to small SOC and weak Herzberg-Teller coupling, although the S1/T1 energy gap is small (0.14 eV), which rationalizes the lack of TADF.

First-Principles Modeling of the Absorption Spectrum of Crystal Violet in Solution: The Importance of Environmentally Driven Symmetry Breaking

Theoretical spectroscopy plays a crucial role in understanding the properties of the materials and molecules. One of the most promising methods for computing optical spectra of chromophores embedded in complex environments from the first principles is the cumulant approach, where both (generally anharmonic) vibrational degrees of freedom and environmental interactions are explicitly accounted for. In this work, we verify the capabilities of the cumulant approach in describing the effect of complex environmental interactions on linear absorption spectra by studying Crystal Violet (CV) in different solvents. The experimental absorption spectrum of CV strongly depends on the nature of the solvent, indicating strong coupling to the condensed-phase environment. We demonstrate that these changes in absorption line shape are driven by an increased splitting between absorption bands of two low-lying excited states that is caused by a breaking of the D3 symmetry of the molecule and that in polar solvents, this symmetry breaking is mainly driven by electrostatic interactions with the condensed-phase environment rather than distortion of the structure of the molecule, in contrast with conclusions reached in a number of previous studies. Our results reveal the importance of explicitly including a counterion in the calculations in nonpolar solvents due to electrostatic interactions between CV and the ion. In polar solvents, these interactions are strongly reduced due to solvent screening effects, thus minimizing the symmetry breaking. Computed spectra in methanol are found to be in reasonable agreement with the experiment, demonstrating the strengths of the outlined approach in modeling strong environmental interactions.

Simulating Vibronic Spectra by Direct Application of Doktorov Formulas on a Superconducting Quantum Simulator

In this work, a direct quantum implementation of the Doktorov formulas for calculating the vibronic spectrum of molecules under the harmonic approximation is presented. It is applied to the three-atom molecules H2O, SO2, ClO2, HS2, and ZnOH. The method solves the classically hard problem of estimating the Franck-Condon (FC) factors by using the Duschinsky matrices as the only input via the Doktorov quantum circuit. This has the advantage of avoiding basis changes, artificial squeezing parameters, and symmetry dependencies. In other words, it is a general method for three-atom molecules that can easily be generalized to bigger molecules. The results are compared with other quantum algorithms and classical anharmonic algorithms. Furthermore, the circuit requirements are studied in order to estimate its applicability on real superconducting quantum hardware.

Theoretical and computational methods for tip- and surface-enhanced Raman scattering

Raman spectroscopy is a versatile tool for acquiring molecular structure information. The incorporation of plasmonic fields has significantly enhanced the sensitivity and resolution of surface-enhanced Raman scattering (SERS) and tip-enhanced Raman spectroscopy (TERS). The strong spatial confinement effect of plasmonic fields has challenged the conventional Raman theory, in which a plane wave approximation for the light has been adopted. In this review, we comprehensively survey the progress of a generalized theory for SERS and TERS in the framework of effective field Hamiltonian (EFH). With this approach, all characteristics of localized plasmonic fields can be well taken into account. By employing EFH, quantitative simulations at the first-principles level for state-of-the-art experimental observations have been achieved, revealing the underlying intrinsic physics in the measurements. The predictive power of EFH is demonstrated by several new phenomena generated from the intrinsic spatial, momentum, time, and energy structures of the localized plasmonic field. The corresponding experimental verifications are also carried out briefly. A comprehensive computational package for modeling of SERS and TERS at the first-principles level is introduced. Finally, we provide an outlook on the future developments of theory and experiments for SERS and TERS.

Delocalized, asynchronous, closed-loop discovery of organic laser emitters

Contemporary materials discovery requires intricate sequences of synthesis, formulation, and characterization that often span multiple locations with specialized expertise or instrumentation. To accelerate these workflows, we present a cloud-based strategy that enabled delocalized and asynchronous design-make-test-analyze cycles. We showcased this approach through the exploration of molecular gain materials for organic solid-state lasers as a frontier application in molecular optoelectronics. Distributed robotic synthesis and in-line property characterization, orchestrated by a cloud-based artificial intelligence experiment planner, resulted in the discovery of 21 new state-of-the-art materials. Gram-scale synthesis ultimately allowed for the verification of best-in-class stimulated emission in a thin-film device. Demonstrating the asynchronous integration of five laboratories across the globe, this workflow provides a blueprint for delocalizing-and democratizing-scientific discovery.

Environmentally Driven Symmetry Breaking Quenches Dual Fluorescence in Proflavine

Nonadiabatic couplings between several electronic excited states are ubiquitous in many organic chromophores and can significantly influence optical properties. A recent experimental study demonstrated that the proflavine molecule exhibits surprising dual fluorescence in the gas phase, which is suppressed in polar solvent environments. Here, we uncover the origin of this phenomenon by parametrizing a linear-vibronic coupling Hamiltonian from spectral densities of system-bath coupling constructed along molecular dynamics trajectories, fully accounting for interactions with the condensed-phase environment. The finite-temperature absorption, steady-state emission, and time-resolved emission spectra are then computed using powerful, numerically exact tensor network approaches. We find that the dual fluorescence in vacuum is driven by a single well-defined coupling mode but is quenched in solution due to dynamic solvent-driven symmetry breaking that mixes the two low-lying electronic states. We expect the computational framework developed here to be widely applicable to the study of non-Condon effects in complex condensed-phase environments.

TD-DFT analysis of excitation of the closed-form spironaphthopyran in methanol solution: The contribution of vibronic transitions and intermolecular hydrogen bonds

A set of forty hybrid functionals, combined with a 6-31++G(d,p) basis set and an IEFPCM solvent description, was applied to calculate the S0→S1 excitation of the spironaphthopyran (SNP) photochromic compound. None of the hybrid functionals resulted in Cspiro-O bond cleavage upon optimization of the S1 excited state of the SNP, in contrast to the spiropyran BIPS which we studied earlier. At the same time, the deformations of the SNP during excitation turned out to be very small (in contrast to those for BIPS) which made it possible to calculate its vibronic absorption spectrum. The best agreement between the calculated and experimental absorption bands was demonstrated by the SOGGA11X functional. The main result of this work is confirmation of the vibration participation in the breaking of the Cspiro-O bond in the S1 excited state of the SNP. This assumption based on experimental data was previously put forward by other authors. Strong H-bonds between the SNP and two methanol molecules enhance the photoinduced distortions of the latter and are slightly weakened upon excitation.

Assessing the accuracy of TD-DFT excited-state geometries through optimal tuning with GW energy levels

We study the accuracy of excited state (ES) geometries using optimally tuned LC-PBE functionals with tuning based on GW quasiparticle energies. We compare the results obtained with the PBE, PBE0, non-tuned, and tuned LC-PBE functionals with available high-level CC reference values as well as experimental data. First, we compare ES geometrical parameters obtained for three different types of systems: molecules composed of a few atoms, 4-(dimethylamino)benzonitrile (DMABN), and conjugated dyes. To this end, we used wave-function results as benchmarks. Next, we evaluate the accuracy of the theoretically simulated spectra as compared to the experimental ones for five large dyes. Our results show that, besides small compact molecules for which tuning LC-PBE does not allow obtaining geometries more accurate than those computed with standard functionals, tuned range-separated functionals are clearly to be favored, not only for ES geometries but also for 0-0 energies, band shapes, and intensities for absorption and emission spectra. In particular, the results indicate that GW-tuned LC-PBE functionals provide improved matching with experimental spectra as compared to conventionally tuned functionals. It is an open question whether TD-DFT with GW-tuned functionals can qualitatively mimic the actual many-body Bethe-Salpeter (BSE/GW) formalism for which analytic ionic gradients remain to be developed.

Spectroscopic approaches for studies of site-specific DNA base and backbone 'breathing' using exciton-coupled dimer-labeled DNA

DNA regulation and repair processes require direct interactions between proteins and DNA at specific sites. Local fluctuations of the sugar-phosphate backbones and bases of DNA (a form of DNA 'breathing') play a central role in such processes. Here we review the development and application of novel spectroscopic methods and analyses - both at the ensemble and single-molecule levels - to study structural and dynamic properties of exciton-coupled cyanine and fluorescent nucleobase analogue dimer-labeled DNA constructs at key positions involved in protein-DNA complex assembly and function. The exciton-coupled dimer probes act as 'sensors' of the local conformations adopted by the sugar-phosphate backbones and bases immediately surrounding the dimer probes. These methods can be used to study the mechanisms of protein binding and function at these sites.

Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].

Finite-temperature vibronic spectra from the split-operator coherence thermofield dynamics

We present a numerically exact approach for evaluating vibrationally resolved electronic spectra at finite temperatures using the coherence thermofield dynamics. In this method, which avoids implementing an algorithm for solving the von Neumann equation for coherence, the thermal vibrational ensemble is first mapped to a pure-state wavepacket in an augmented space, and this wavepacket is then propagated by solving the standard, zero-temperature Schrödinger equation with the split-operator Fourier method. We show that the finite-temperature spectra obtained with the coherence thermofield dynamics in a Morse potential agree exactly with those computed by Boltzmann-averaging the spectra of individual vibrational levels. Because the split-operator thermofield dynamics on a full tensor-product grid is restricted to low-dimensional systems, we briefly discuss how the accessible dimensionality can be increased by various techniques developed for the zero-temperature split-operator Fourier method.

Taming the third order cumulant approximation to linear optical spectroscopy

The second order cumulant method offers a promising pathway to predicting optical properties in condensed phase systems. It allows for the computation of linear absorption spectra from excitation energy fluctuations sampled along molecular dynamics (MD) trajectories, fully accounting for vibronic effects, direct solute-solvent interactions, and environmental polarization effects. However, the second order cumulant approximation only guarantees accurate line shapes for energy gap fluctuations obeying Gaussian statistics. A third order correction has recently been derived but often yields unphysical spectra or divergent line shapes for moderately non-Gaussian fluctuations due to the neglect of higher order terms in the cumulant expansion. In this work, we develop a corrected cumulant approach, where the collective effect of neglected higher order contributions is approximately accounted for through a dampening factor applied to the third order cumulant term. We show that this dampening factor can be expressed as a function of the skewness and kurtosis of energy gap fluctuations and can be parameterized from a large set of randomly sampled model Hamiltonians for which exact spectral line shapes are known. This approach is shown to systematically remove unphysical contributions in the form of negative absorbances from cumulant spectra in both model Hamiltonians and condensed phase systems sampled from MD and dramatically improves over the second order cumulant method in describing systems exhibiting Duschinsky mode mixing effects. We successfully apply the approach to the coumarin-153 dye in toluene, obtaining excellent agreement with experiment.

Luminescence Properties of Al2O3:Ti in the Blue and Red Regions: A Combined Theoretical and Experimental Study

Using jointly experimental results and first-principles calculations, we unambiguously assign the underlying mechanisms behind two commonly observed luminescence bands for the Al2O3 material. Indeed, we show that the red band is associated with a Ti3+ d-d transition as expected, while the blue band is the combination of the Ti3+ + O- → Ti4+ + O2- and VO•+e- → VO× de-excitation processes. Thanks to our recent developments, which take into account the vibrational contributions to the electronic transitions in solids, we were able to simulate the luminescence spectra for the different signatures. The excellent agreement with the experiment demonstrates that it should be possible to predict the color of the material with a CIE chromaticity diagram. We also anticipated the luminescence signature of Al2O3:Ti,Ca and Al2O3:Ti,Be that were confirmed by experiment.

The ultraviolet and vacuum ultraviolet absorption spectrum of gamma-pyrone; the singlet states studied by configuration interaction and density functional calculations

A synchrotron based vacuum ultraviolet absorption spectrum for γ-pyrone has been interpreted in terms of singlet excited electronic states using a variety of coupled cluster, configuration interaction, and density functional calculations. The extremely weak spectral onset at 3.557 eV shows eight vibrational peaks, which following previous analyses, are attributed to a forbidden 1A2 state. A contrasting broad peak with a maximum at 5.381 eV has a relatively high cross-section of 30 Mb; this arises from three overlapping states, where a 1A1 state dominates over progressively weaker 1B2 and 1B1 states. After fitting the second band to a polynomial Gaussian function and plotting the regular residuals over 20 vibrational peaks, we have had limited success in analyzing this fine structure. However, the small separation between these three states clearly shows that their vibrational satellites must overlap. Singlet valence and Rydberg state vibrational profiles were determined by configuration interaction using the CAM-B3LYP density functional. Vibrational analysis using both the Franck-Condon and Herzberg-Teller procedures showed that both procedures contributed to the profiles. Theoretical Rydberg states were evaluated by a highly focused CI procedure. The superposition of the lowest photoelectron spectral band on the vacuum ultraviolet spectrum near 6.4 eV shows that the 3s and 3p Rydberg states based on the 2B2 ionic state are present; those based on the other low-lying ionic state (X2B1) are destroyed by broadening; this is a dramatic extension of the broadening previously witnessed in our studies of halogenobenzenes.

Unraveling the mystery of solvation-dependent fluorescence of fluorescein dianion using computational study

Fluorescein, one of the brightest fluorescent dye molecules, is a widely used fluorophore for various applications from biomedicine to industry. The dianionic form of fluorescein is responsible for its high fluorescence quantum yield. Interestingly, the molecule was found to be nonfluorescent in the gas phase. This characteristic is attributed to the photodetachment process, which out-competes the fluorescence emission in the gas phase. In this work, we show that the calculated vertical and adiabatic detachment energies of fluorescein dianion in the gas and solvent phases account for the drastic differences observed in their fluorescence characteristics. The functional dependence of these detachment energies on the dianion's microsolvation was systematically investigated. The performance of different solvent models was also assessed. The higher thermodynamic stability of fluorescein dianion over the monoanion doublet in the solvent phase plays a crucial role in quenching photodetachment and activating the radiative channel with a high fluorescence quantum yield.

Spin-Vibronic Coupling Controls the Intersystem Crossing of Iodine-Substituted BODIPY Triplet Chromophores

4,4-Difluoro-4-borata-3a-azonia-4a-aza-s-indacene (BODIPY) dyes are extensively used in various applications of their triplet states, ranging from photoredox catalysis, through triplet sensitization to photodynamic therapy. However, the rational design of BODIPY triplet chromophores by ab initio modelling is limited by their strong interactions of spin, electronic and vibrational dynamics. In particular, spin-vibronic coupling is often overlooked when estimating intersystem crossing (ISC) rates. In this study, a combined experimental and theoretical approach using spin-vibronic coupling to correctly describe ISC in BODIPY dyes was developed. For this purpose, seven π-extended BODIPY derivatives with iodine atoms in different positions were examined. It was found that the heavy-atom effect of iodine atoms is site specific, causing high triplet yields in only some positions. This site-specific ISC was explained by El-Sayed rules, so both the contribution and character of the molecular orbitals involved in the excitation must be considered when predicting the ISC rates. Overall, the rational design of BODIPY triplet chromophores requires using (i) the high-quality electronic structure theory, including both static and dynamical correlations; and (ii) the two-component wave function Hamiltonian, and rationalizing; and (iii) ISC based on the character of the molecular orbitals of heavy atoms involved in the excitation, expanding El-Sayed rules beyond their traditional applications.

Two-photon excitation two-dimensional fluorescence spectroscopy (2PE-2DFS) of the fluorescent nucleobase 6-MI

Base stacking is fundamentally important to the stability of double-stranded DNA. However, few experiments can directly probe the local conformations and conformational fluctuations of the DNA bases. Here we report a new spectroscopic approach to study the local conformations of DNA bases using the UV-absorbing fluorescent guanine analogue, 6-methyl isoxanthopterin (6-MI), which can be used as a site-specific probe to label DNA. In these experiments, we apply a two-photon excitation (2PE) approach to two-dimensional fluorescence spectroscopy (2DFS), which is a fluorescence-detected nonlinear Fourier transform spectroscopy. In 2DFS, a repeating sequence of four collinear laser pulses (with center wavelength ~ 675 nm and relative phases swept at radio frequencies) is used to excite the lowest energy electronic-vibrational (vibronic) transitions of 6-MI (with center wavelength ~ 340 nm). The ensuing low flux fluorescence is phase-synchronously detected at the level of individual photons and as a function of inter-pulse delay. The 2PE transition pathways that give rise to electronically excited state populations include optical coherences between electronic ground and excited states and non-resonant (one-photon-excited) virtual states. Our results indicate that 2PE-2DFS experiments can provide information about the electronic-vibrational spectrum of the 6-MI monomer, in addition to the conformation-dependent exciton coupling between adjacent 6-MI monomers within a (6-MI)2 dimer. In principle, this approach can be used to determine the local base-stacking conformations of (6-MI)2 dimer-substituted DNA constructs.

Beyond the Condon limit: Condensed phase optical spectra from atomistic simulations

While dark transitions made bright by molecular motions determine the optoelectronic properties of many materials, simulating such non-Condon effects in condensed phase spectroscopy remains a fundamental challenge. We derive a Gaussian theory to predict and analyze condensed phase optical spectra beyond the Condon limit. Our theory introduces novel quantities that encode how nuclear motions modulate the energy gap and transition dipole of electronic transitions in the form of spectral densities. By formulating the theory through a statistical framework of thermal averages and fluctuations, we circumvent the limitations of widely used microscopically harmonic theories, allowing us to tackle systems with generally anharmonic atomistic interactions and non-Condon fluctuations of arbitrary strength. We show how to calculate these spectral densities using first-principles simulations, capturing realistic molecular interactions and incorporating finite-temperature, disorder, and dynamical effects. Our theory accurately predicts the spectra of systems known to exhibit strong non-Condon effects (phenolate in various solvents) and reveals distinct mechanisms for electronic peak splitting: timescale separation of modes that tune non-Condon effects and spectral interference from correlated energy gap and transition dipole fluctuations. We further introduce analysis tools to identify how intramolecular vibrations, solute-solvent interactions, and environmental polarization effects impact dark transitions. Moreover, we prove an upper bound on the strength of cross correlated energy gap and transition dipole fluctuations, thereby elucidating a simple condition that a system must follow for our theory to accurately predict its spectrum.

How is the Observation of High-Order Overtones and Combinations Elucidated by the Charge-Transfer Mechanism in SERS?

The charge-transfer chemical mechanism is responsible for altering the molecular spectral pattern and providing valuable insights into the properties of adsorbates. The impact of charge transfer becomes more pronounced in SERS spectra when CT states can gain intensity through vibronic coupling with high-intensity excitations. Experimental SERS spectra of diamino molecules, such as 4,4'-diaminostilbene (DAS) and 4,4'-diaminotolane (DAT), featuring bright CT transitions, have been compared to dipyridyl compounds, such as 1,2-bis(4-pyridyl) ethylene (BPE) and 1,2-di(4-pyridyl) acetylene (DPA), characterized by nearly dark CT excitations. This comparison aims to elucidate the effect of CT transitions on the presence of overtones and combination bands. We explain this distinction using Albrecht's formalism for resonance Raman spectroscopy within the framework of path integral time-dependent density functional theory considering the Herzberg-Teller corrections. It is worth noting that the energy gap between the highest occupied metallic orbital and the lowest unoccupied molecular orbital in diamino derivatives is noticeably smaller than in compounds featuring two pyridyl rings. The high-intensity SERS-CT spectra for diamino derivatives, primarily driven by the Albrecht A term, were acquired and used to elucidate the experimental observation of high-order modes with a significant Huang-Rhys factor. Conversely, the absolute intensity of SERS-CT for dipyridyl compounds is at least 106 times smaller than that for diamines, and the C term makes a significant contribution, explaining the silent overtones.

Prediction of fluorescence quantum yields using the extended thawed Gaussian approximation

Spontaneous emission and internal conversion rates are calculated within harmonic approximations and compared to the results obtained within the semi-classical extended thawed Gaussian approximation (ETGA). This is the first application of the ETGA in the calculation of internal conversion and emission rates for real molecular systems, namely, formaldehyde, fluorobenzene, azulene, and a dicyano-squaraine dye. The viability of the models as black-box tools for prediction of spontaneous emission and internal conversion rates is assessed. All calculations were done using a consistent protocol in order to investigate how different methods perform without previous experimental knowledge using density functional theory (DFT) and time-dependent DFT (TD-DFT) with B3LYP, PBE0, ωB97XD, and CAM-B3LYP functionals. Contrasting the results with experimental data shows that there are further improvements required before theoretical predictions of emission and internal conversion rates can be used as reliable indicators for the photo-luminescence properties of molecules. We find that the ETGA performs rather similar to the vertical harmonical model. Including anharmonicities in the calculation of internal conversion rates has a moderate effect on the quantitative results in the studied systems. The emission rates are fairly stable with respect to computational parameters, but the internal conversion rate reveals itself to be highly dependent on the choice of the spectral line shape function, particularly the width of the Lorentzian function, associated with homogeneous broadening.

First-Principles Calculations of Excited-State Decay Rate Constants in Organic Fluorophores

In this Perspective, we discuss recent advances made to evaluate from first-principles the excited-state decay rate constants of organic fluorophores, focusing on the so-called static strategy. In this strategy, one essentially takes advantage of Fermi's golden rule (FGR) to evaluate rate constants at key points of the potential energy surfaces, a procedure that can be refined in a variety of ways. In this way, the radiative rate constant can be straightforwardly obtained by integrating the fluorescence line shape, itself determined from vibronic calculations. Likewise, FGR allows for a consistent calculation of the internal conversion (related to the non-adiabatic couplings) in the weak-coupling regime and intersystem crossing rates, therefore giving access to estimates of the emission yields when no complex photophysical phenomenon is at play. Beyond outlining the underlying theories, we summarize here the results of benchmarks performed for various types of rates, highlighting that both the quality of the vibronic calculations and the accuracy of the relative energies are crucial to reaching semiquantitative estimates. Finally, we illustrate the successes and challenges in determining the fluorescence quantum yields using a series of organic fluorophores.

Theoretical Insight into the Effect of Phosphorus Oxygenation on Nonradiative Decays: Comparative Analysis of P-Bridged Stilbene Analogs

Incorporation of the phosphorus element into a π-conjugated skeleton offers valuable prospects for adjusting the electronic structure of the resulting functional π-electron systems. Trivalent phosphorus has the potential to decrease the LUMO level through σ*-π* interaction, which is further enhanced by its oxygenation to the pentavalent P center. This study shows that utilizing our computational analysis to examine excited-state dynamics based on radiative/nonradiative rate constants and fluorescence quantum yield (ΦF) is effective for analyzing the photophysical properties of P-containing organic dyes. We theoretically investigate how the trivalent phosphanyl group and pentavalent phosphine oxide moieties affect radiative and nonradiative decay processes. We evaluate four variations of P-bridged stilbene analogs. Our analysis reveals that the primary decay pathway for photoexcited bis-phosphanyl-bridged stilbene is the intersystem crossing (ISC) to the triplet state and nonradiative. The oxidation of the phosphine moiety, however, suppresses the ISC due to the relative destabilization of the triplet states. The calculated rate constants match an increase in experimental ΦF from 0.07 to 0.98, as simulated from 0.23 to 0.94. The reduced HOMO-LUMO gap supports a red shift in the fluorescence spectra relative to the phosphine analog. The thiophene-fused variant with the nonoxidized trivalent P center exhibits intense emission with a high ΦF, 0.95. Our prediction indicates that the ISC transfer is obstructed owing to the relatively destabilized triplet state induced by the thiophene substitution. Conversely, the thiophene-fused analog with the phosphine oxide moieties triggers a high-rate internal conversion mediated by conical intersection, leading to a decreased ΦF.

Unravelling the Origin of the Vibronic Spectral Signatures in an Excitonically Coupled Indocarbocyanine Cy3 Dimer

The indocarbocyanine Cy3 dye is widely used to probe the dynamics of proteins and DNA. Excitonically coupled Cy3 dimers exhibit very unique spectral signatures that depend on the interchromophoric geometrical orientation induced by the environment, making them powerful tools to infer the dynamics of their surroundings. Understanding the origin of the dimeric spectral signatures is a necessity for an accurate interpretation of the experimental results. In this work, we simulate the vibronic spectrum of an experimentally well-studied Cy3 dimer, and we explain the origin of the experimental signatures present in its linear absorption spectrum. The Franck-Condon harmonic approximations, among other tests, are used to probe the factors contributing to the spectrum. It is found that the first peak in the absorption spectrum originates from the lower energy excitonic state, while the next two peaks are vibrational progressions of the higher energy excitonic state. The polar solvent plays a crucial role in the appearance of the spectrum, being responsible for the localized S1 minimum, which results in an increased intensity of the first peak.

Dye-Derived Red-Emitting Carbon Dots for Lasing and Solid-State Lighting

Carbon dots are carbon-based nanoparticles renowned for their intense light-emitting capabilities covering the whole visible light range. Achieving carbon dots emitting in the red region with high efficiency is extremely relevant due to their huge potential in biological applications and in optoelectronics. Currently, photoluminescence in such an energy interval is often associated with polyheterocyclic molecular domains forming during the synthesis that, however, present low emission efficiency and issues in controlling the optical features. Here, we overcome these problems by solvothermally synthesizing carbon dots starting from Neutral Red, a common red-emitting dye, as a molecular precursor. As a result of the synthesis, such molecular fluorophore is incorporated into a carbonaceous core while retaining its original optical properties. The obtained nanoparticles are highly luminescent in the red region, with a quantum yield comparable to that of the starting dye. Most importantly, the nanoparticle carbogenic matrix protects the Neutral Red molecules from photobleaching under ultraviolet excitation while preventing aggregation-induced quenching, thus allowing solid-state emission. These advantages have been exploited to develop a fluorescence-based color conversion layer by fabricating polymer-based highly concentrated solid-state carbon dot nanocomposites. Finally, the dye-based carbon dots demonstrate both stable Fabry-Perot lasing and efficient random lasing emission in the red region.

Fantastical excited state optimized structures and where to find them

The quantum chemistry community has developed analytic forces for approximate electronic excited states to enable walking on excited state potential energy surfaces (PES). One can thereby computationally characterize excited state minima and saddle points. Always implicit in using this machinery is the fact that an excited state PES only exists within the realm of the Born-Oppenheimer approximation, where the nuclear and electronic degrees of freedom separate. This work demonstrates through ab initio calculations and simple nonadiabatic dynamics that some excited state minimum structures are fantastical: they appear to exist as stable configurations only as a consequence of the PES construct, rather than being physically observable. Each fantastical structure exhibits an unphysically high predicted harmonic frequency and associated force constant. This fact can serve as a valuable diagnostic of when an optimized excited state structure is non-observable. The origin of this phenomenon can be attributed to the coupling between different electronic states. As PESs approach one another, the upper surface can form a minimum that is very close to a near-touching point. The force constant, evaluated at this minimum, relates to the strength of the electronic coupling rather than to any characteristic excited state vibration. Nonadiabatic dynamics results using a Landau-Zener model illustrate that fantastical excited state structures have extremely short lifetimes on the order of a few femtoseconds. Their appearance in a calculation signals the presence of a nearby conical intersection through which the system will rapidly cross to a lower surface.

Reassignment of the Photoelectron Spectrum of Methylketene Using a Hybrid Model of Harmonic and Anharmonic Oscillators to Compute Franck-Condon Factors

We constructed a hybrid model of harmonic and anharmonic oscillators to compute Franck-Condon factors and interpret the photoelectron spectrum of methylketene. The equilibrium structures of methylketene and its cation were optimized, and then, the harmonic and anharmonic vibrational frequencies were computed using the B3LYP, PBE0, APFD, and ωB97XD approaches of the density functional theory. The photoelectron spectrum of methylketene was simulated by computing the Franck-Condon factors with both the harmonic and hybrid models. The adiabatic ionization energy of methylketene was computed by using the CCSD(T) approach extrapolating to the complete basis set limit. The simulated photoelectron spectra are consistent with those from the experiment for both the harmonic and hybrid models. However, the error in band positions is reduced by using the hybrid model. The computed adiabatic ionization energies of methylketene are in agreement with the experiment, with the smallest error being 0.017 eV. Our interpretation based on the theoretical spectrum led to the reassignment of the experimental photoelectron spectrum of methylketene.

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.

Isotope Effects on the Electronic Spectra of Ammonia from Ab Initio Semiclassical Dynamics

Despite its simplicity, the single-trajectory thawed Gaussian approximation has proven useful for calculating the vibrationally resolved electronic spectra of molecules with weakly anharmonic potential energy surfaces. Here, we show that the thawed Gaussian approximation can capture surprisingly well even more subtle observables, such as the isotope effects in the absorption spectra, and we demonstrate it on the four isotopologues of ammonia (NH3, NDH2, ND2H, and ND3). The differences in their computed spectra are due to the differences in the semiclassical trajectories followed by the four isotopologues, and the isotope effects─narrowing of the transition band and reduction of the peak spacing─are accurately described by this semiclassical method. In contrast, the adiabatic harmonic model shows a double progression instead of the single progression seen in the experimental spectra. The vertical harmonic model correctly shows only a single progression but fails to describe the anharmonic peak spacing. Analysis of the normal-mode activation upon excitation provides insight into the elusiveness of the symmetric stretching progression in the spectra.

Phosphorescent Properties of Heteroleptic Ir(III) Complexes: Uncovering Their Emissive Species

In this contribution, we assess the computational machinery to calculate the phosphorescence properties of a large pool of heteroleptic [Ir(C^N)2(N^N)]+ complexes (where N^N is an ancillary ligand and C^N is a cyclometalating ligand) including their phosphorescent rates and their emission spectra. Efficient computational protocols are next proposed. Specifically, different flavors of DFT functionals were benchmarked against DLPNO-CCSD(T) for the phosphorescence energies. The transition density matrix and decomposition analysis of the emitting triplet excited state enable us to categorize the studied complexes into different cases, from predominant triplet ligand-centered (3LC) character to predominant charge-transfer (3CT) character, either of metal-to-ligand charge transfer (3MLCT), ligand-to-ligand charge transfer (3LLCT), or a combination of the two. We have also calculated the vibronically resolved phosphorescent spectra and rates. Ir(III) complexes with predominant 3CT character are characterized by less vibronically resolved bands as compared to those with predominant 3LC character. Furthermore, some of the complexes are characterized by close-lying triplet excited states so that the calculation of their phosphorescence properties poses additional challenges. In these scenarios, it is necessary to perform geometry optimizations of higher-lying triplet excited states (i.e., Tn). We demonstrate that in the latter scenarios all of the close-lying triplet species must be considered to recover the shape of the experimental emission spectra. The global analysis of computed emission energies, shape of the computed emission spectra, computed rates, etc. enable us to unambiguously pinpoint for the first time the triplet states involved in the emission process and to provide a general classification of Ir(III) complexes with regard to their phosphorescence properties.

Extensive Analysis of the Parameters Influencing Radiative Rates Obtained through Vibronic Calculations

Defining a theoretical model systematically delivering accurate ab initio predictions of the fluorescence quantum yields of organic dyes is highly desirable for designing improved fluorophores in a systematic rather than trial-and-error way. To this end, the first required step is to obtain reliable radiative rates (kr), as low kr typically precludes effective emission. In the present contribution, using a series of 10 substituted phenyls with known experimental kr, we analyze the impact of the computational protocol on the kr determined through the thermal vibration correlation function (TVCF) approach on the basis of time-dependent density functional theory (TD-DFT) calculations of the energies, structures, and vibrational parameters. Both the electronic structure (selected exchange-correlation functional, application or not of the Tamm-Dancoff approximation) and the vibronic parameters (line-shape formalism, coordinate system, potential energy surface model, and dipole expansion) are tackled. Considering all possible combinations yields more than 3500 cases, allowing to extract statistically-relevant information regarding the impact of each computational parameter on the magnitude of the estimated kr. It turns out that the selected vibronic model can have a significant impact on the computed kr, especially the potential energy surface model. This effect is of the same order of magnitude as the difference noted between B3LYP and CAM-B3LYP estimates. For the treated compounds, all evaluated functionals do deliver reasonable trends, fitting the experimental values.

Intramolecular hole-transfer in protonated anthracene

Excitation spectra of protonated and deuteronated anthracene are obtained by triple-resonance dissociation spectroscopy. Very cold cations, protonated/deuteronated exclusively at the 9-position, are generated from two-colour two-photon threshold ionisation of 9-dihydroanthracenyl radicals (C₁₄H₁₁). The excitation spectra reveal rich structure, not resolved in previous studies, that is assigned based on anharmonic and Herzberg-Teller coupling calculations. This work reveals that the excitation of protonated anthracene induces a symmetry-breaking intramolecular charge-transfer process along a Marcus-Hush coordinate, where the positively charged hole hops from the central bridging sp² carbon, onto one of the aromatic rings. Signatures of this charge-transfer event are observed in the excitation spectrum, through active Herzberg-Teller progressions.

High-level studies of the singlet states of quadricyclane, including analysis of a new experimental vacuum ultraviolet absorption spectrum by configuration interaction and density functional calculations

A synchrotron-based vacuum ultraviolet absorption spectrum (VUV) of quadricyclane (QC) is reported with energies up to 10.8 eV. Extensive vibrational structure has been extracted from the broad maxima by fitting short energy ranges of the VUV spectrum to high level polynomial functions and processing the regular residuals. Comparison of these data with our recent high-resolution photoelectron spectral of QC showed that this structure must be attributed to Rydberg states (RS). Several of these appear before the valence states at higher energies. Both types of states have been calculated by configuration interaction, including symmetry-adapted cluster studies (SAC-CI) and time dependent density functional theoretical methods (TDDFT). There is a close correlation between the SAC-CI vertical excitation energies (VEE) and both Becke 3-parameter hybrid functional (B3LYP), especially Coulomb-attenuating method-B3LYP determined ones. The VEE for several low-lying s-, p, d-, and f-RS have been determined by SAC-CI and adiabatic excitation energies by TDDFT methods. Searches for equilibrium structures for 11,3A2 and 11B1 states for QC led to rearrangement to a norbornadiene structure. Determination of the experimental 00 band positions, which show extremely low cross-sections, has been assisted by matching features in the spectra with Franck-Condon (FC) fits. Herzberg-Teller (HT) vibrational profiles for the RS are more intense than the FC ones, but only at high energy, and are attributed to up to ten quanta. The vibrational fine structure of the RS calculated by both FC and HT procedures gives an easy route to generating HT profiles for ionic states, which usually require non-standard procedures.

Vibronic and Cationic Features of 2-Fluorobenzonitrile and 3-Fluorobenzonitrile Studied by REMPI and MATI Spectroscopy and Franck-Condon Simulations

Fluorinated organic compounds have superior physicochemical properties than general organic compounds due to the strong C-F single bond; they are widely used in medicine, biology, pesticides, and materials science. In order to gain a deeper understanding of the physicochemical properties of fluorinated organic compounds, fluorinated aromatic compounds have been investigated by various spectroscopic techniques. 2-fluorobenzonitrile and 3-fluorobenzonitrile are important fine chemical intermediates and their excited state S₁ and cationic ground state D₀ vibrational features remain unknown. In this paper, we used two-color resonance two photon ionization (2-color REMPI) and mass analyzed threshold ionization (MATI) spectroscopy to study S₁ and D₀ state vibrational features of 2-fluorobenzonitrile and 3-fluorobenzonitrile. The precise excitation energy (band origin) and adiabatic ionization energy were determined to be 36,028 ± 2 cm^-1 and 78,650 ± 5 cm^-1 for 2-fluorobenzonitrile and 35,989 ± 2 cm^-1 and 78,873 ± 5 cm^-1 for 3-fluorobenzonitrile, respectively. The density functional theory (DFT) at the levels of RB3LYP/aug-cc-pvtz, TD-B3LYP/aug-cc-pvtz, and UB3LYP/aug-cc-pvtz were used to calculate the stable structures and vibrational frequencies for the ground state S₀, excited state S₁, and cationic ground state D₀, respectively. Franck-Condon spectral simulations for transitions of S₁ ← S₀ and D₀ ← S₁ were performed based on the above DFT calculations. The theoretical and experimental results were in good agreement. The observed vibrational features in S₁ and D₀ states were assigned according to the simulated spectra and the comparison with structurally similar molecules. Several experimental findings and molecular features were discussed in detail.

Origin of intersystem crossing in highly distorted organic molecules: a case study with red light-absorbing N,N,O,O-boron-chelated Bodipys

To explore the relationship between the twisted π-conjugation framework of aromatic chromophores and the efficacy of intersystem crossing (ISC), we have studied a N,N,O,O-boron-chelated Bodipy derivative possessing a severely distorted molecular structure. Surprisingly, this chromophore is highly fluorescent, showing inefficient ISC (singlet oxygen quantum yield, Φ_Δ = 12%). These features differ from those of helical aromatic hydrocarbons, where the twisted framework promotes ISC. We attribute the inefficient ISC to a large singlet-triplet energy gap (ΔE_S1/T1 = 0.61 eV). This postulate is tested by critical examination of a distorted Bodipy having an anthryl unit at the meso-position, for which Φ_Δ is increased to 40%. The improved ISC yield is rationalized by the presence of a T₂ state, localized on the anthryl unit, with energy close to that of the S₁ state. The electron spin polarization phase pattern of the triplet state is (e, e, e, a, a, a), with the T_z sublevel of the T₁ state overpopulated. The small zero-field splitting D parameter (-1470 MHz) indicates that the electron spin density is delocalized over the twisted framework. It is concluded that twisting of π-conjugation framework does not necessarily induce ISC, but S₁/T_n energy matching may be a generic feature for increasing ISC for a new-generation of heavy atom-free triplet photosensitizers.

Non-Phenomenological Description of the Time-Resolved Emission in Solution with Quantum-Classical Vibronic Approaches-Application to Coumarin C153 in Methanol

We report a joint experimental and theoretical work on the steady-state spectroscopy and time-resolved emission of the coumarin C153 dye in methanol. The lowest energy excited state of this molecule is characterized by an intramolecular charge transfer thus leading to remarkable shifts of the time-resolved emission spectra, dictated by the methanol reorganization dynamics. We selected this system as a prototypical test case for the first application of a novel computational protocol aimed at the prediction of transient emission spectral shapes, including both vibronic and solvent effects, without applying any phenomenological broadening. It combines a recently developed quantum-classical approach, the adiabatic molecular dynamics generalized vertical Hessian method (Ad-MD|gVH), with nonequilibrium molecular dynamics simulations. For the steady-state spectra we show that the Ad-MD|gVH approach is able to reproduce quite accurately the spectral shapes and the Stokes shift, while a ∼0.15 eV error is found on the prediction of the solvent shift going from gas phase to methanol. The spectral shape of the time-resolved emission signals is, overall, well reproduced, although the simulated spectra are slightly too broad and asymmetric at low energies with respect to experiments. As far as the spectral shift is concerned, the calculated spectra from 4 ps to 100 ps are in excellent agreement with experiments, correctly predicting the end of the solvent reorganization after about 20 ps. On the other hand, before 4 ps solvent dynamics is predicted to be too fast in the simulations and, in the sub-ps timescale, the uncertainty due to the experimental time resolution (300 fs) makes the comparison less straightforward. Finally, analysis of the reorganization of the first solvation shell surrounding the excited solute, based on atomic radial distribution functions and orientational correlations, indicates a fast solvent response (≈100 fs) characterized by the strengthening of the carbonyl-methanol hydrogen bond interactions, followed by the solvent reorientation, occurring on the ps timescale, to maximize local dipolar interactions.

Cost-Effective Simulations of Vibrationally-Resolved Absorption Spectra of Fluorophores with Machine-Learning-Based Inhomogeneous Broadening

The results of electronic and vibrational structure simulations are an invaluable support for interpreting experimental absorption/emission spectra, which stimulates the development of reliable and cost-effective computational protocols. In this work, we contribute to these efforts and propose an efficient first-principle protocol for simulating vibrationally-resolved absorption spectra, including nonempirical estimations of the inhomogeneous broadening. To this end, we analyze three key aspects: (i) a metric-based selection of density functional approximation (DFA) so to benefit from the computational efficiency of time-dependent density function theory (TD-DFT) while safeguarding the accuracy of the vibrationally-resolved spectra, (ii) an assessment of two vibrational structure schemes (vertical gradient and adiabatic Hessian) to compute the Franck-Condon factors, and (iii) the use of machine learning to speed up nonempirical estimations of the inhomogeneous broadening. In more detail, we predict the absorption band shapes for a set of 20 medium-sized fluorescent dyes, focusing on the bright ππ^★ S₀ → S₁ transition and using experimental results as references. We demonstrate that, for the studied 20-dye set which includes structures with large structural variability, the preselection of DFAs based on an easily accessible metric ensures accurate band shapes with respect to the reference approach and that range-separated functionals show the best performance when combined with the vertical gradient model. As far as band widths are concerned, we propose a new machine-learning-based approach for determining the inhomogeneous broadening induced by the solvent microenvironment. This approach is shown to be very robust offering inhomogeneous broadenings with errors as small as 2 cm^-1 with respect to genuine electronic-structure calculations, with a total CPU time reduced by 98%.

Photophysics of uracil: an explicit time-dependent generating function-based method combining both nonadiabatic and spin-orbit coupling effects

We present a composite framework for calculating the rates of non-radiative deactivation processes, namely internal conversion (IC) and intersystem crossing (ISC), on an equal footing by explicitly computing the non-adiabatic coupling (NAC) and spin-orbit coupling (SOC) constants, respectively. The stationary-state approach uses a time-dependent generating function based on Fermi's golden rule. We validate the applicability of the framework by computing the rate of IC for azulene, obtaining comparable rates to experimental and previous theoretical results. Next, we investigate the photophysics associated with the complex photodynamics of the uracil molecule. Interestingly, our simulated rates corroborate experimental observations. Detailed analyses using Duschinsky rotation matrices, displacement vectors and NAC matrix elements are presented to interpret the findings alongside testing the suitability of the approach for such molecular systems. The suitability of the Fermi's golden rule based method is explained qualitatively in terms of single-mode potential energy surfaces.

Cavity Ring-Down Spectroscopy of Anthracene, 9-Methylanthracene, and 2-Methylanthracene in Supersonic Expansion

The S₀-S₁ absorption spectra of anthracene (C₁₄H₁₀), 9-methylanthracene (C₁₅H₁₂), and 2-methylanthracene (C₁₅H₁₂) are measured in the ultraviolet region between 330 and 375 nm (26,666 to 30,303 cm^-1) with cavity ring-down spectroscopy in supersonic free-jet expansions of argon. The associated vibronic band systems and their spectroscopic assignments are discussed and compared to previous studies performed using fluorescence excitation and dispersed fluorescence techniques. Density functional theory (DFT) calculations were carried out to study the structures and evaluate the vibrational transitions of the ground and excited states. Time-dependent DFT calculations of the first electronic excited states and Franck-Condon factor calculations were carried out to assist in the assignment of the experimentally measured vibronic bands. The vibronic spectra obtained in absorption agree well with fluorescence excitation spectra in terms of peak positions but exhibit different relative band intensities. We find a very good match between experimentally obtained vibronic line positions and the peak positions of the quantum chemically calculated Franck-Condon excitation lines.

Vibrationally resolved two-photon electronic spectra including vibrational pre-excitation: Theory and application to VIPER spectroscopy with two-photon excitation

Following up on our previous work on vibrationally resolved electronic absorption spectra including the effect of vibrational pre-excitation [von Cosel et al., J. Chem. Phys. 147, 164116 (2017)], we present a combined theoretical and experimental study of two-photon-induced vibronic transitions in polyatomic molecules that are probed in the VIbrationally Promoted Electronic Resonance experiment using two-photon excitation (2P-VIPER). In order to compute vibronic spectra, we employ time-independent and time-dependent methods based on the evaluation of Franck-Condon overlap integrals and Fourier transformations of time-domain correlation functions, respectively. The time-independent approach uses a generalized version of the FCclasses method, while the time-dependent approach relies on the analytical evaluation of Gaussian moments within the harmonic approximation, including Duschinsky rotation effects. For the Coumarin 6 dye, two-dimensional 2P-VIPER experiments involving excitation to the lowest-lying singlet excited state (S₁) are presented and compared with corresponding one-photon VIPER spectra. In both cases, coumarin ring modes and a CO stretch mode show VIPER activity, albeit with different relative intensities. Selective pre-excitation of these modes leads to a pronounced redshift of the low-frequency edge of the electronic absorption spectrum, which is a prerequisite for the VIPER experiment. Theoretical analysis underscores the role of interference between Franck-Condon and Herzberg-Teller effects in the two-photon experiment, which is at the root of the observed intensity distribution.

Unraveling the contributions to the spectral shape of flexible dyes in solution: insights on the absorption spectrum of an oxyluciferin analogue

We present a computational investigation of the absorption spectrum in water of 5,5-spirocyclopropyl-oxyluciferin (5,5-CprOxyLH), an analogue of the emitter compound responsible for the bioluminescence in fireflies. Several factors participate in determining the 5,5-CprOxyLH's spectral shape: (i) the contribution of the four close-energy excited states, which show significant non-adiabatic couplings, (ii) the flexible molecular structure and (iii) the specific interactions established with the surrounding environment, which strongly couple the protic solvent dynamics with the dye's spectral response. To tackle the challenge to capture and dissect the role of all these effects we preliminarily investigate the role of non-adiabatic couplings with quantum dynamics simulations and a linear vibronic coupling model in the gas phase. Then, we account for both the molecular flexibility and solvent interactions by resorting to a mixed quantum classical protocol, named Adiabatic Molecular Dynamics generalized Vertical Gradient (Ad-MD|gVG), which is built on a method recently proposed by some of us. It is rooted in the partition between stiff degrees of freedom of the dye, accounted for at the vibronic level within the harmonic approximation, and flexible degrees of freedom of the solute (and of the solvent), described classically through a sampling based on Molecular Dynamics (MD). Ad-MD|gVG avoids spurious effects arising in the excited state Hessians due to non-adiabatic couplings, and can therefore be applied to account for the contributions of the first four excited states to the 5,5-CprOxyLH absorption spectrum. The final simulated spectrum is in very good agreement with the experiment, especially when the MD is driven by a refined quantum-mechanically derived force-field. More importantly, the origin of each separate contribution to the spectral shape is appropriately accounted for, paving the way to future applications of the method to more complex systems or alternative spectroscopies, as emission or circular dichroism.

XPS and quantum chemical analysis of 4Me-BODIPY derivatives

The results of a X-ray photoelectron spectroscopy (XPS) and steady-state absorption spectroscopy study of the electronic structure, and cationic and excited states of a series of 1,3,5,7-tetramethyl-substituted BODIPYs (4Me,2R-BODIPYs) are presented. The experimental data were interpreted using high-level ab initio quantum chemical computations, including the algebraic diagrammatic construction method for the polarization propagator of the second order (ADC(2)), the outer-valence Green's function (OVGF) method, the density functional (DFT) approach, and the time-dependent DFT (TD-DFT) approach. Substitution effects on the XPS and absorption spectra were determined for 2,6-positions of 4Me,2R-BODIPY pyrrole nuclei (R = H, Br, Bu, benzyl). A very satisfactory performance of the DFT Koopmans theorem analogue was demonstrated with respect to the energy intervals between the electronic levels of 4Me,2R-BODIPY above 13 eV (BHHLYP functional) and the values of the HOMO-LUMO energy gap (ωB97X functional).

FCclasses3: Vibrationally-resolved spectra simulated at the edge of the harmonic approximation

We introduce FCclasses3, a code to carry out vibronic simulations of electronic spectra and nonradiative rates, based on the harmonic approximation. Key new features are: implementation of the full family of vertical and adiabatic harmonic models, vibrational analysis in curvilinear coordinates, extension to several electronic spectroscopies and implementation of time-dependent approaches. The use of curvilinear valence internal coordinates allows the adoption of quadratic model potential energy surfaces (PES) of the initial and final states expanded at arbitrary configurations. Moreover, the implementation of suitable projectors provides a robust framework for defining reduced-dimensionality models by sorting flexible coordinates out of the harmonic subset, so that they can then be treated at anharmonic level, or with mixed quantum classical approaches. A set of tools to facilitate input preparation and output analysis is also provided. We show the program at work in the simulation of different spectra (one and two-photon absorption, emission and resonance Raman) and internal conversion rate of a typical rigid molecule, anthracene. Then, we focus on absorption and emission spectra of a series of flexible polyphenyl molecules, highlighting the relevance of some of the newly implemented features. The code is freely available at http://www.iccom.cnr.it/en/fcclasses/.

A Materials Acceleration Platform for Organic Laser Discovery

Conventional materials discovery is a laborious and time-consuming process that can take decades from initial conception of the material to commercialization. Recent developments in materials acceleration platforms promise to accelerate materials discovery using automation of experiments coupled with machine learning. However, most of the automation efforts in chemistry focus on synthesis and compound identification, with integrated target property characterization receiving less attention. In this work, an automated platform is introduced for the discovery of molecules as gain mediums for organic semiconductor lasers, a problem that has been challenging for conventional approaches. This platform encompasses automated lego-like synthesis, product identification, and optical characterization that can be executed in a fully integrated end-to-end fashion. Using this workflow to screen organic laser candidates, discovered eight potential candidates for organic lasers is discovered. The lasing threshold of four molecules in thin-film devices and find two molecules with state-of-the-art performance is tested. These promising results show the potential of automated synthesis and screening for accelerated materials development.