Insights for an Accurate Comparison of Computational Data to Experimental Absorption and Emission Spectra: Beyond the Vertical Transition Approximation

Rational Control of Maximum EMI/CPL Intensity and Wavelength of Bora[6]helicene via Polarity and Vibronic Effects

Solvent polarity control as an efficient methodology to regulate the chiroptical properties, including spectral shape, width, intensity, wavelength, etc., has emerged as a novel frontier in optical materials design. However, the underling relationship connecting polarity to the optical property remains unclear. Herein, using state-of-the-art computations and the FC|VG model, the solvent effect on the chiroptical properties of bora[6]helicene was accurately and systematically computed to shed light on this issue. It is found that the vibronic coupling is crucial in explaining the spectral shape, width, and relative intensity of different peaks. Moreover, the intensity and position of the emission (EMI) and circularly polarized luminescence (CPL) are closely related to the polarity of the solvent. Intriguingly, we got a series of good linear relationships between polarity and EMI|CPL (|r| ≥ 0.95). Thus, this parameter can be used as a potential descriptor to estimate the intensity and position of EMI|CPL, leading to new strategies for designing fully colored fluorescent materials.

The role of microenvironments on computed vibrationally-resolved emission spectra: The case of oxazines

Oxazine dyes act as reporters of their near environment by the response of their fluorescence spectra. At the same time, their fluorescence spectra exhibit a pronounced vibrational progression. In this work, we computationally investigate the impact of near-environment models consisting of aggregated water as well as betaine molecules on the vibrational profile of fluorescence spectra of different oxazine derivatives. For aggregated betaine and a water molecule located above the plane of the dyes, we observe a distinct modification of the vibrational profile, which is more pronounced than the effect of a continuum description of a solvent environment. Our analysis shows that this effect cannot be explained by a pure change in the electronic structure, but that also vibrational degrees of freedom of the environment can be decisive for the vibrational profile and should, hence, not generally be neglected.

Experimental and Computational Evidence of a Stable RNA G-Triplex Structure at Physiological Temperature in the SARS-CoV-2 Genome

RG1 is a quadruplex-forming sequence in the SARS-CoV-2 genome proposed as possible therapeutic target for COVID-19. We demonstrate that the dominant conformation of RG1 under physiological conditions differs from the parallel quadruplex previously assumed. Through comprehensive investigations employing CD, UV, NMR, DSC, gel electrophoresis, MD simulations, in silico spectroscopy and the use of truncated RG1 sequences, we have identified this stable conformation as an RNA G-triplex composed of two G-triads. We believe this previously unreported RNA structure could serve as a novel therapeutic target. Our findings open new avenues for further studies on the presence and biological role of RNA G-triplexes in vivo.

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.

Reference CC3 Excitation Energies for Organic Chromophores: Benchmarking TD-DFT, BSE/GW, and Wave Function Methods

To expand the QUEST database of highly accurate vertical transition energies, we consider a series of large organic chromogens ubiquitous in dye chemistry, such as anthraquinone, azobenzene, BODIPY, and naphthalimide. We compute, at the CC3 level of theory, the singlet and triplet vertical transition energies associated with the low-lying excited states. This leads to a collection of more than 120 new highly accurate excitation energies. For several singlet transitions, we have been able to determine CCSDT transition energies with a compact basis set, finding minimal deviations from the CC3 values for most states. Subsequently, we employ these reference values to benchmark a series of lower-order wave function approaches, including the popular ADC(2) and CC2 schemes, as well as time-dependent density-functional theory (TD-DFT), both with and without applying the Tamm-Dancoff approximation (TDA). At the TD-DFT level, we evaluate a large panel of global, range-separated, local, and double hybrid functionals. Additionally, we assess the performance of the Bethe-Salpeter equation (BSE) formalism relying on both G0W0 and evGW quasiparticle energies evaluated from various starting points. It turns out that CC2 and ADC(2.5) are the most accurate models among those with respective O ( N 5 ) and O ( N 6 ) scalings with system size. In contrast, CCSD does not outperform CC2. The best performing exchange-correlation functionals include BMK, M06-2X, M06-SX, CAM-B3LYP, ωB97X-D, and LH20t, with average deviations of approximately 0.20 eV or slightly below. Errors on vertical excitation energies can be further reduced by considering double hybrids. Both SOS-ωB88PP86 and SOS-ωPBEPP86 exhibit particularly attractive performances with overall quality on par with CC2, whereas PBE0-DH and PBE-QIDH are only slightly less efficient. BSE/evGW calculations based on Kohn-Sham starting points have been found to be particularly effective for singlet transitions, but much less for their triplet counterparts.

The Excited State Dynamics of a Mutagenic Guanosine Etheno Adduct Investigated by Femtosecond Fluorescence Spectroscopy and Quantum Mechanical Calculations

Femtosecond fluorescence upconversion experiments were combined with CASPT2 and time dependent DFT calculations to characterize the excited state dynamics of the mutagenic etheno adduct 1,N2-etheno-2'-deoxyguanosine (ϵdG). This endogenously formed lesion is attracting great interest because of its ubiquity in human tissues and its highly mutagenic properties. The ϵdG fluorescence is strongly modified with respect to that of the canonical nucleoside dG, notably by an about 6-fold increase in fluorescence lifetime and quantum yield at neutral pH. In addition, femtosecond fluorescence upconversion experiments reveal the presence of two emission bands with maxima at 335 nm for the shorter-lived and 425 nm for the longer-lived. Quantum mechanical calculations rationalize these findings and provide absorption and fluorescence spectral shapes similar to the experimental ones. Two different bright minima are located on the potential energy surface of the lowest energy singlet excited state. One planar minimum, slightly more stable, is associated with the emission at 335 nm, whereas the other one, with a bent etheno ring, is associated with the red-shifted emission.

Explicit Modelling of Spectral Bandshapes by a Mixed Quantum-Classical Approach: Solvent Order and Temperature Effects in the Optical Spectra of Distyrylbenzene

The absorption and emission spectral shapes of a flexible organic probe, the distyrylbenzene (DSB) dye, are simulated accounting for the effect of different environments of increasing complexity, ranging from a homogeneous, low-molecular- weight solvent, to a long-chain alkane, and, eventually, a channel-forming organic matrix. Each embedding is treated explicitly, adopting a mixed quantum-classical approach, the Adiabatic Molecular Dynamics - generalized vertical Hessian (Ad-MD|gVH) model, which allows a direct simulation of the environment-induced constraining effects on the vibronic spectral shapes. In such a theoretical framework, the stiff modes of the dye are described at a quantum level within the harmonic approximation, including Duschinsky mixing effects, while flexible degrees of freedom of the solute (e. g. torsions) and those of the solvent are treated classically by means of molecular dynamics sampling. Such a setup is shown to reproduce the distinct effects exerted by the different environments in varied thermodynamic conditions. Besides allowing for a first-principles rationale on the supramolecular mechanism leading to the experimental spectral features, this result represents the first successful application of the Ad-MD|gVH method to complex embeddings and supports its potential application to other heterogeneous environments, such as for instance, pigment-protein complexes or organic dyes adsorbed into metal-organic frameworks.

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.

Two- and three-photon processes during photopolymerization in 3D laser printing

The performance of a photoinitiator is key to control efficiency and resolution in 3D laser nanoprinting. Upon light absorption, a cascade of competing photophysical processes leads to photochemical reactions toward radical formation that initiates free radical polymerization (FRP). Here, we investigate 7-diethylamino-3-thenoylcoumarin (DETC), belonging to an efficient and frequently used class of photoinitiators in 3D laser printing, and explain the molecular bases of FRP initiation upon DETC photoactivation. Depending on the presence of a co-initiator, DETC causes radical generation either upon two-photon- or three-photon excitation, but the mechanism for these processes is not well understood so far. Here, we show that the unique three-photon based radical formation by DETC, in the absence of a co-initiator, results from its excitation to highly excited triplet states. They allow a hydrogen-atom transfer reaction from the pentaerythritol triacrylate (PETA) monomer to DETC, enabling the formation of the reactive PETA alkyl radical, which initiates FRP. The formation of active DETC radicals is demonstrated to be less spontaneous. In contrast, photoinitiation in the presence of an onium salt co-initiator proceeds via intermolecular electron transfer after the photosensitization of the photoinitiator to the lowest triplet excited state. Our quantum mechanical calculations demonstrate photophysical processes upon the multiphoton activation of DETC and explain different reactions for the radical formation upon DETC photoactivation. This investigation for the first time describes possible pathways of FRP initiation in 3D laser nanoprinting and permits further rational design of efficient photoinitiators to increase the speed and sensitivity of 3D laser nanoprinting.

A DFT/MRCI Hamiltonian parameterized using only ab initio data: I. valence excited states

A new combined density functional theory and multi-reference configuration interaction (DFT/MRCI) Hamiltonian parameterized solely using the benchmark ab initio vertical excitation energies obtained from the QUEST databases is presented. This new formulation differs from all previous versions of the method in that the choice of the underlying exchange-correlation (XC) functional employed to construct the one-particle (orbital) basis is considered, and a new XC functional, QTP17, is chosen for its ability to generate a balanced description of core and valence vertical excitation energies. The ability of the new DFT/MRCI Hamiltonian, termed QE8, to furnish accurate excitation energies is confirmed using benchmark quantum chemistry computations, and a mean absolute error of 0.16 eV is determined for the wide range of electronic excitations included in the validation dataset. In particular, the QE8 Hamiltonian dramatically improves the performance of DFT/MRCI for doubly excited states. The performance of fast approximate DFT/MRCI methods, p-DFT/MRCI and DFT/MRCI(2), is also evaluated using the QE8 Hamiltonian, and they are found to yield excitation energies in quantitative agreement with the parent DFT/MRCI method, with the two methods exhibiting a mean difference of 0.01 eV with respect to DFT/MRCI over the entire benchmark set.

Axial H-Bonding Solvent Controls Inhomogeneous Spectral Broadening, While Peripheral H-Bonding Solvent Controls Vibronic Broadening: Cresyl Violet in Methanol

The dynamics of the nuclei of both a chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both force field and ab initio molecular dynamics trajectories along with the inclusion of only certain solvent molecules in the excited-state calculations, we determine that the methanol molecules axial to the chromophore are responsible for the majority of inhomogeneous broadening, with a single methanol molecule that forms an axial hydrogen bond dominating the response. The strong peripheral hydrogen bonds do not contribute to spectral broadening, as they are very stable throughout the dynamics and do not lead to increased energy-gap fluctuations. We also find that treating the strong peripheral hydrogen bonds as molecular mechanical point charges during the molecular dynamics simulation underestimates the vibronic coupling. Including these peripheral hydrogen bonding methanol molecules in the quantum-mechanical region in a geometry optimization increases the vibronic coupling, suggesting that a more advanced treatment of these strongly interacting solvent molecules during the molecular dynamics trajectory may be necessary to capture the full vibronic spectral broadening.

Photodissociation of leucine-enkephalin protonated peptide: an experimental and theoretical perspective

Understanding the competing processes that govern far ultraviolet photodissociation (FUV-PD) of biopolymers such as proteins is a challenge. Here, we report a combined experimental and theoretical investigation of FUV-PD of protonated leucine-enkephalin pentapeptide ([YGGFL + H]+) in the gas-phase. Time-dependent density functional theory (TD-DFT) calculations in combination with experiments and previous results for amino acids and shorter peptides help in rationalizing the evolution of the excited states. The results confirm that fragmentation of [YGGFL + H]+ results mainly from vibrationally excited species in the ground electronic state, populated after internal conversion. We also propose fragmentation mechanisms for specific photo-fragments such as tyrosine side chain loss (with an extra hydrogen) or hydrogen loss. In general, we observe the same mechanisms as for smaller peptides or protonated Tyr and Phe, that are not quenched by the presence of other amino acids. Nevertheless, we also found some differences, as for H loss, in part due to the fact that the charge is solvated by the peptide chain and not only by the COOH terminal group.

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.

Ag+-Mediated Folding of Long Polyguanine Strands to Double and Quadruple Helixes

Metal-mediated base pairing of DNA has been a topic of extensive research spanning over more than four decades. Precise positioning of a single metal ion by predetermining the DNA sequence, as well as improved conductivity offered by the ions, make these structures interesting candidates in the context of using DNA in nanotechnology. Here, we report the formation and characterization of conjugates of long (kilo bases) homoguanine DNA strands with silver ions. We demonstrate using atomic force microscopy (AFM) and scanning tunneling microscope (STM) that binding of silver ions leads to folding of homoguanine DNA strands in a "hairpin" fashion to yield double-helical, left-handed molecules composed of G-G base pairs each stabilized by a silver ion. Further folding of the DNA-silver conjugate yields linear molecules in which the two halves of the double helix are twisted one against the other in a right-handed fashion. Quantum mechanical calculations on smaller molecular models support the helical twist directions obtained by the high resolution STM analysis. These long guanine-based nanostructures bearing a chain of silver ions have not been synthesized and studied before and are likely to possess conductive properties that will make them attractive candidates for nanoelectronics.

The photophysics of protonated cytidine and hemiprotonated cytidine base pair: A computational study

We here study the effect that a lowering of the pH has on the excited state processes of cytidine and a cytidine/cytidine pair in solution, by integrating time-dependent density functional theory and CASSCF/CASPT2 calculations, and including solvent by a mixed discrete/continuum model. Our calculations reproduce the effect of protonation at N3 on the steady-state infrared and absorption spectra of a protonated cytidine (CH+ ), and predict that an easily accessible non-radiative deactivation route exists for the spectroscopic state, explaining its sub-ps lifetime. Indeed, an extremely small energy barrier separates the minimum of the lowest energy bright state from a crossing region with the ground electronic state, reached by out-of-plane motion of the hydrogen substituents of the CC double bond, the so-called ethylenic conical intersection typical of cytidine and other pyrimidine bases. This deactivation route is operative for the two bases forming an hemiprotonated cytidine base pair, [CH·C]+ , the building blocks of I-motif secondary structures, whereas interbase processes play a minor role. N3 protonation disfavors instead the nπ* transitions, associated with the long-living components of cytidine photoactivated dynamics.

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

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

Excited-State Proton Transfer in Luminescent Dyes: From Theoretical Insight to Experimental Evidence

The effective utilization of luminescent dyes often relies on a comprehensive understanding of their excitation and relaxation pathways. One such pathway, Excited-State Proton Transfer (ESPT), involves the tautomerization of the dye in its excited state, resulting in a new structure that exhibits distinct emission properties, such as a very large Stokes' shift or dual-emission. Although the ESPT phenomenon is well-explained theoretically, its experimental demonstration can be challenging due to the presence of numerous other phenomena that can yield similar experimental observations. In this review, we propose that an all-encompassing methodology, integrating experimental findings, computational analyses, and a thorough evaluation of diverse mechanisms, is essential for verifying the occurrence of ESPT in luminescent dyes. Investigations have offered significant understanding of the elements impacting the ESPT process and the array of approaches that can be used to validate the existence of ESPT. These discoveries hold crucial ramifications for the advancement of molecular probes, sensors, and other applications that depend on ESPT as a detection mechanism.

Molecular torsion controls the excited state relaxation pathways of multibranched tetraphenylpyrazines: effect of substitution of morpholine vs. phenoxazine

Multibranched donor-acceptor derivatives exhibiting desirable photophysical properties are efficiently used in optoelectronic devices, in which the excited state relaxation dynamics of the derivatives control the efficiency of the devices. Here, the effect of intramolecular torsion on the excited state relaxation dynamics of tetraphenylpyrazine (TPP) derivatives in non-polar (toluene) and polar (THF) solvents is investigated by substituting the electron donor of morpholine (TPP-4MOP) and phenoxazine (TPP-4PHO) leading to the planar and twisted configurations, respectively, using femtosecond and nanosecond transient absorption spectroscopy. In the steady state, TPP-4MOP showed feeble emission (ΦF ∼0.03) due to the weak donor by the delocalization of electron density supported by theoretical optimization. The TPP-4PHO exhibited strong emission (ΦF ∼0.18) in toluene compared to that in THF, in which it showed a large Stokes shift (∼9691 cm-1) with low fluorescence quantum yield (ΦF ∼0.01). The observation of large Stokes shifts, inherent nature and theoretical calculations of TPP-4PHO suggest the twisting of the dihedral angle between tetraphenylpyrazine and phenoxazine in the excited state leading to the twisted intramolecular charge transfer state (TICT). The femtosecond and nanosecond transient absorption and picosecond time-resolved emission spectra of TPP-4PHO revealed the signature of the existence of both the partial TICT and TICT states in THF leading to the triplet state. Whereas in the case of TPP-4MOP, the transient absorption spectra showed the formation of the triplet state from the local excited state without the involvement of the TICT state. Aggregation studies of TPP-4PHO in a THF and water mixture reflect the elimination of the TICT state by the restriction of intramolecular torsion in the aggregates leading to an increase of 12-fold of the fluorescence intensity along with shifting of the maximum towards the blue region. These studies revealed that the excited state relaxation pathways of the derivatives are controlled by polarity-dependent torsional motion.

The Best Models of Bodipy's Electronic Excited State: Comparing Predictions from Various DFT Functionals with Measurements from Femtosecond Stimulated Raman Spectroscopy

Density functional theory (DFT) and time-dependent DFT (TD-DFT) are pivotal approaches for modeling electronically excited states of molecules. However, choosing a DFT exchange-correlation functional (XCF) among the myriad of alternatives is an overwhelming task that can affect the interpretation of results and lead to erroneous conclusions. The performance of these XCFs to describe the excited-state properties is often addressed by comparing them with high-level wave function methods or experimentally available vertical excitation energies; however, this is a limited analysis that relies on evaluation of a single point in the excited-state potential energy surface (PES). Different strategies have been proposed but are limited by the difficulty of experimentally accessing the electronic excited-state properties. In this work, we have tested the performance of 12 different XCFs and TD-DFT to describe the excited-state potential energy surface of Bodipy (2,6-diethyl-1,3,5,7-tetramethyl-8-phenyldipyrromethene difluoroborate). We compare those results with resonance Raman spectra collected by using femtosecond stimulated Raman spectroscopy (FSRS). By simultaneously fitting the absorption spectrum, fluorescence spectrum, and all of the resonance Raman excitation profiles within the independent mode displaced harmonic oscillator (IMDHO) formalism, we can describe the PES at the Franck-Condon (FC) region and determine the solvent and intramolecular reorganization energy after relaxation. This allows a direct comparison of the TD-DFT output with experimental observables. Our analysis reveals that using vertical absorption energies might not be a good criterion to determine the best XCF for a given molecular system and that FSRS opens up a new way to benchmark the excited-state performance of XCFs of fluorescent dyes.

Tautomeric equilibrium and spectroscopic properties of 8-azaguanine revealed by quantum chemistry methods

8-azaguanine is a triazolopyrimidine nucleobase analog possessing potent antibacterial and antitumor activities, and it has been implicated as a lead molecule in cancer and malaria therapy. Its intrinsic fluorescence properties can be utilized for monitoring its interactions with biological polymers like proteins or nucleic acids. In order to better understand these interactions, it is important to know the tautomeric equilibrium of this compound. In this work, the tautomeric equilibrium of all natural neutral and anionic compound forms (except highly improbable imino-enol tautomers) as well as their methyl derivatives and ribosides was revealed by quantum chemistry methods. It was shown that, as expected, tautomers protonated at positions 1 and 9 dominate neutral forms both in gas phase and in aqueous solution. 8-azaguanines methylated at any position of the triazole ring are protonated at position 1. The computed vertical absorption and emission energies are in very good agreement with the experimental data. They confirm the validity of the assumption that replacing the proton with the methyl group does not significantly change the positions of absorption and fluorescence peaks.

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.

Shedding Light on the Photophysics and Photochemistry of I-Motifs Using Quantum Mechanical Calculations

I-motifs are non-canonical DNA structures formed by intercalated hemiprotonated (CH·C)+ pairs, i.e., formed by a cytosine (C) and a protonated cytosine (CH+), which are currently drawing great attention due to their biological relevance and promising nanotechnological properties. It is important to characterize the processes occurring in I-motifs following irradiation by UV light because they can lead to harmful consequences for genetic code and because optical spectroscopies are the most-used tools to characterize I-motifs. By using time-dependent DFT calculations, we here provide the first comprehensive picture of the photoactivated behavior of the (CH·C)+ core of I-motifs, from absorption to emission, while also considering the possible photochemical reactions. We reproduce and assign their spectral signatures, i.e., infrared, absorption, fluorescence and circular dichroism spectra, disentangling the underlying chemical-physical effects. We show that the main photophysical paths involve C and CH+ bases on adjacent steps and, using this basis, interpret the available time-resolved spectra. We propose that a photodimerization reaction can occur on an excited state with strong C→CH+ charge transfer character and examine some of the possible photoproducts. Based on the results reported, some future perspectives for the study of I-motifs are discussed.

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.

Simulation of the VUV Absorption Spectra of Oxygenates and Hydrocarbons: A Joint Theoretical-Experimental Study

Vacuum UV absorption spectroscopy is regularly used to provide unambiguous identification of a target species, insight into the electronic structure of molecules, and quantitative species concentrations. As molecules of interest have become more complex, theoretical spectra have been used in tandem with laboratory spectroscopic analysis or as a replacement when experimental data is unavailable. However, it is difficult to determine which theoretical methodologies can best simulate experiment. This study examined the performance of EOM-CCSD and 10 TD-DFT functionals (B3LYP, BH&HLYP, BMK, CAM-B3LYP, HSE, M06-2X, M11, PBE0, ωB97X-D, and X3LYP) to produce reliable vacuum UV absorption spectra for 19 small oxygenates and hydrocarbons using vertical excitation energies. The simulated spectra were analyzed against experiment using both a qualitative analysis and quantitative metrics, including cosine similarity, relative integral change, mean signed error, and mean absolute error. Based on our ranking system, it was determined that M06-2X was consistently the top performing TD-DFT method with BMK, CAM-B3LYP, and ωB97X-D also producing reliable spectra for these small combustion species.

An Expedited Route to Optical and Electronic Properties at Finite Temperature via Unsupervised Learning

Electronic properties and absorption spectra are the grounds to investigate molecular electronic states and their interactions with the environment. Modeling and computations are required for the molecular understanding and design strategies of photo-active materials and sensors. However, the interpretation of such properties demands expensive computations and dealing with the interplay of electronic excited states with the conformational freedom of the chromophores in complex matrices (i.e., solvents, biomolecules, crystals) at finite temperature. Computational protocols combining time dependent density functional theory and ab initio molecular dynamics (MD) have become very powerful in this field, although they require still a large number of computations for a detailed reproduction of electronic properties, such as band shapes. Besides the ongoing research in more traditional computational chemistry fields, data analysis and machine learning methods have been increasingly employed as complementary approaches for efficient data exploration, prediction and model development, starting from the data resulting from MD simulations and electronic structure calculations. In this work, dataset reduction capabilities by unsupervised clustering techniques applied to MD trajectories are proposed and tested for the ab initio modeling of electronic absorption spectra of two challenging case studies: a non-covalent charge-transfer dimer and a ruthenium complex in solution at room temperature. The K-medoids clustering technique is applied and is proven to be able to reduce by ∼100 times the total cost of excited state calculations on an MD sampling with no loss in the accuracy and it also provides an easier understanding of the representative structures (medoids) to be analyzed on the molecular scale.

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%.

Dibenzodipyridophenazines with Dendritic Electron Donors Exhibiting Deep-Red Emission and Thermally Activated Delayed Fluorescence

The development of deep-red thermally activated delayed fluorescence (TADF) emitters is important for applications such as organic light-emitting diodes (OLEDs) and biological imaging. Design strategies for red-shifting emission include synthesizing rigid acceptor cores to limit nonradiative decay and employing strong electron-donating groups. In this work, three novel luminescent donor-acceptor compounds based on the dibenzo[a,c]dipyrido[3,2-h:20-30-j]-phenazine-12-yl (BPPZ) acceptor were prepared using dendritic carbazole-based donors 3,3″,6,6″-tetramethoxy-9'H-9,3':6',9″-tercarbazole (TMTC), N³,N³,N⁶,N⁶-tetra-p-tolyl-9H-carbazole-3,6-diamine (TTAC), and N³,N³,N⁶,N⁶-tetrakis(4-methoxyphenyl)-9H-carbazole-3,6-diamine (TMAC). Here, dimethoxycarbazole, ditolylamine, and bis(4-methoxyphenyl)amine were introduced at the 3,6-positions of carbazole to increase the strength of these donors and induce long-wavelength emission. Substituent effects were investigated with experiments and theoretical calculations. The emission maxima of these materials in toluene were found to be 562, 658, and 680 nm for BPPZ-2TMTC, BPPZ-2TTAC, and BPPZ-2TMAC, respectively, highlighting the exceptional strength of the TMAC donor, which pushes the emission into the deep-red region of the visible spectrum as well as into the biological transparency window (650-1350 nm). Long-lived emission lifetimes were observed in each emitter due to TADF in BPPZ-2TMC and BPPZ-2TTAC, as well as room-temperature phosphorescence in BPPZ-2TMAC. Overall, this work showcases deep-red emissive dendritic donor-acceptor materials which have potential as bioimaging agents with emission in the biological transparency window.

Electronic Excitation of ortho-Fluorothiophenol

ortho-Fluorothiophenol (o-FTP) photodissociates through the well-known πσ* process. The fluorine atom of o-FTP introduces a feature in the photodissociation of o-FTP that does not occur in most other πσ* processes because the fluorine atom can form a hydrogen bond with the hydrogen atom of the SH group. Theoretical computations can serve as a good way to study these reactions because they usually proceed very quickly, and the current spectroscopies cannot probe the details of the processes as thoroughly as theory can. Here we use completely renormalized equation-of-motion coupled cluster theory with single and double excitations and a quasiperturbative treatment of connected triple excitations (CR-EOM-CCSD(T)) and quasidegenerate perturbation theory, in particular extended multistate complete-active-space second-order perturbation theory (XMS- CASPT2), to calculate the four lowest singlet states of o-FTP and hybrid density functional theory to optimize the geometries of the two lowest singlet states. We find that ten active electrons in nine active orbitals are sufficient to provide a good reference function for all four states. We find that the ground electronic state and the first excited singlet state both exhibit strongly bent hydrogen bonds. We also use density functional theory with the Tamm-Dancoff approximation and the SMD solvation model to successfully simulate the electronic spectrum of o-FTP in n-hexane solvent.

Computing the electronic circular dichroism spectrum of DNA quadruple helices of different topology: A critical test for a generalized excitonic model based on a fragment diabatization

In this study, we exploit a recently developed fragment diabatization-based excitonic model, FrDEx, to simulate the electronic circular dichroism (ECD) spectra of three guanine-rich DNA sequences arranged in guanine quadruple helices with different topologies: thrombin binding aptamer (antiparallel), c-Myc promoter (parallel), and human telomeric sequence (3+1 hybrid). Starting from time-dependent density functional theory (TD-DFT) calculations with the M052X functional, we apply our protocol to parameterize the FrDEX Hamiltonian, which accounts for electron density overlap and includes both the coupling with charge transfer transitions and the effect of the surrounding bases on the local excitation of each chromophore. The TD-DFT/M052X spectral shapes are in good agreement with the experimental ones, the main source of discrepancy being related to the intrinsic error on the computed transition energies of guanine monomer. FrDEx spectra are fairly close to the reference TD-DFT ones, allowing a significant advance with respect to a more standard excitonic Hamiltonian. We also show that the ECD spectra are sensitive to the inclusion of the inner K + $$ {}^{+} $$ cation in the calculation.

Effect of the Thermal Fluctuations of the Photophysics of GC and CG DNA Steps: A Computational Dynamical Study

Here we refine and assess two computational procedures aimed to include the effect of thermal fluctuations on the electronic spectra and the ultrafast excited state dynamics of multichromophore systems, focusing on DNA duplexes. Our approach is based on a fragment diabatization procedure that, from a given Quantum Mechanical (QM) reference method, can provide the parameters (energy and coupling) of the reference diabatic states on the basis of the isolated fragments, either for a purely electronic excitonic Hamiltonian (FrDEx) or a linear vibronic coupling Hamiltonian (FrD-LVC). After having defined the most cost-effective procedure for DNA duplexes on two smaller fragments, FrDEx is used to simulate the absorption and Electronic Circular Dichroism (ECD) spectra of (GC)₅ sequences, including the coupling with the Charge Transfer (CT) states, on a number of structures extracted from classical Molecular Dynamics (MD) simulations. The computed spectra are close to the reference TD-DFT calculations and fully consistent with the experimental ones. We then couple MD simulations and FrD-LVC to simulate the interplay between local excitations and CT transitions, both intrastrand and interstrand, in GC and CG steps when included in a oligoGC or in oligoAT DNA sequence. We predict that for both sequences a substantial part of the photoexcited population on G and C decays, within 50-100 fs, to the corresponding intrastrand CT states. This transfer is more effective for GC steps that, on average, are more closely stacked than CG ones.

Comparison among several vibronic coupling methods

A comparison of four approaches to account the vibronic coupling in photoabsorption is performed. The methods considered are nuclear ensemble (NE), direct vibronic coupling (DVC), adiabatic Hessian (AH), and vertical gradient (VG). The case study is the symmetry-forbidden [Formula: see text] [Formula: see text]A[Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text]A[Formula: see text] (n [Formula: see text] [Formula: see text]) transition in formaldehyde. Being forbidden in the equilibrium geometry, this transition is entirely induced by vibronic coupling and constitutes an appropriate case to study the performance of different methods. From DVC, it is found that mode 1 (C=O out-of-plane bending) is the most inducing, followed by mode 6 (in-plane C-H asymmetric stretching) and finally by mode 2 (in-plane C-H asymmetric bending). We were able to correlate 17 out of 20 structures obtained from NE with these modes, showing that these two methods, although different in principle, give comparable results. The simulated spectra were obtained for all methods and compared, and each one has its own advantage. In what concerns the transition studied, NE gives the best description of the spectrum, DVC is the only one that easily gives an absolute value for OOS, and AH and VG are the computationally less expensive methods. From the latter two, VG is the less demanding on computational grounds, since it does not require the excited state Hessian.

Tailored anharmonic-harmonic vibrational profiles for fluorescent biomarkers

We propose a hybrid anharmonic-harmonic scheme for vibrational broadenings, which embeds a reduced-space vibrational configuration interaction (VCI) anharmonic wave function treatment in the independent-mode displaced harmonic oscillator (IMDHO) model. The resulting systematically-improvable VCI-in-IMDHO model allows including the vibronic effects of all vibrational degrees of freedom, while focusing the effort on the important degrees of freedom with minimal extra computational effort compared to a reduced-space VCI treatment. We show for oligothiophene examples that the VCI-in-IMDHO approach can yield accurate vibrational profiles employing smaller vibrational spaces in the VCI part than the reduced-space VCI approach. By this, the VCI-in-IMDHO model enables accurate calculation of vibrational profiles of common fluorescent dyes with more than 100 vibrational degrees of freedom. We illustrate this for three examples of fluorescent biomarkers of current interest. These are the oligothiophene-based fluorescent dye called HS84, 1,4-diphenylbutadiene, and an anthracene diimide. For all examples, we assess the impact of the anharmonic treatment on the vibrational broadening, which we find to be more pronounced for the intensities than for the peak positions.

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.

Cyclo[18]carbon including zero-point motion: ground state, first singlet and triplet excitations, and hole transfer

Recent synthesis of cyclo[18]carbon has spurred increasing interest in carbon rings. We focus on a comparative inspection of ground and excited states, as well as of hole transfer properties of cumulenic and polyynic cyclo[18]carbon via Density Functional Theory (DFT), time-dependent DFT (TD-DFT) and real-time time-dependent DFT (RT-TDDFT). Zero-point vibrations are also accounted for, using a Monte Carlo sampling technique and a less exact, yet mode-resolved, quadratic approximation. The inclusion of zero-point vibrations leads to a red-shift on the HOMO-LUMO gap and the first singlet and triplet excitation energies of both conformations, correcting the values of the 'static' configurations by 9% to 24%. Next, we oxidize the molecule, creating a hole at one carbon atom. Hole transfer along polyynic cyclo[18]carbon is decreased in magnitude compared to its cumulenic counterpart and lacks the symmetric features the latter displays. Contributions by each mode to energy changes and hole transfer between diametrically opposed atoms vary, with specific bond-stretching modes being dominant.

Excited state absorption of DNA bases in the gas phase and in chloroform solution: a comparative quantum mechanical study

We study the excited state absorption (ESA) properties of the four DNA bases (thymine, cytosine, adenine, and guanine) by different single reference quantum mechanical methods, namely, equation of motion coupled cluster singles and doubles (EOM-CCSD), singles, doubles and perturbative triples (EOM-CC3), and time-dependent density functional theory (TD-DFT), with the long-range corrected CAM-B3LYP functional. Preliminary results at the Tamm-Dancoff (TDA) CAM-B3LYP level using the maximum overlap method (MOM) are reported for thymine. In the gas phase, the three methods predict similar One Photon Absorption (OPA) spectra, which are consistent with the experimental results and with the most accurate computational studies available in the literature. The ESA spectra are then computed for the ππ* states (one for pyrimidine, two for purines) associated with the lowest-energy absorption band, and for the close-lying nπ* state. The EOM-CC3, EOM-CCSD and CAM-B3LYP methods provide similar ESA spectral patterns, which are also in qualitative agreement with literature RASPT2 results. Once validated in the gas phase, TD-CAM-B3LYP has been used to compute the ESA in chloroform, including solvent effects by the polarizable continuum model (PCM). The predicted OPA and ESA spectra in chloroform are very similar to those in the gas phase, most of the bands shifting by less than 0.1 eV, with a small increase of the intensities and a moderate destabilization of the nπ* state. Finally, ESA spectra have been computed from the minima of the lowest energy ππ* state, and found in line with the available experimental transient absorption spectra of the nucleosides in solution, providing further validation of our computational approach.

A Photoreactive Iron(II) Complex Luminophore

Controlling the order and lifetimes of electronically excited states is essential to effective light-to-potential energy conversion by molecular chromophores. This work reports a luminescent and photoreactive iron(II) complex, the first performant group homologue of prototypical sensitizers of ruthenium. Double cyclometalation of a phenylphenanthroline framework at iron(II) favors the population of a triplet metal-to-ligand charge transfer (³MLCT) state as the lowest energy excited state. Near-infrared (NIR) luminescence exhibits a monoexponential decay with τ = 2.4 ns in the solid state and 1 ns in liquid phase. Lifetimes of 14 ns at 77 K are in line with a narrowing of the NIR emission band at λ_em,max = 1170-1230 nm. Featuring a ³MLCT excited-state redox potential of -2 V vs the ferrocene/ferrocenium couple, the use of the Fe(II) chromophore as a sensitizer for light-driven synthesis is exemplified by the radical cross-coupling of 4-chlorobromobenzene and benzene.

The Excited State Dynamics of a Mutagenic Cytidine Etheno Adduct Investigated by Combining Time-Resolved Spectroscopy and Quantum Mechanical Calculations

Joint femtosecond fluorescence upconversion experiments and theoretical calculations provide a hitherto unattained degree of characterization and understanding of the mutagenic etheno adduct 3,N4-etheno-2'-deoxycytidine (εdC) excited state relaxation. This endogenously formed lesion is attracting great interest because of its ubiquity in human tissues and its highly mutagenic properties. The εdC fluorescence is modified with respect to that of the canonical base dC, with a 3-fold increased lifetime and quantum yield at neutral pH. This behavior is amplified upon protonation of the etheno ring (εdCH⁺). Quantum mechanical calculations show that the lowest energy state ππ*1 is responsible for the fluorescence and that the main nonradiative decay pathway to the ground state goes through an ethene-like conical intersection, involving the out-of-plane motion of the C5 and C6 substituents. This conical intersection is lower in energy than the ππ* state (ππ*1) minimum, but a sizable energy barrier explains the increase of εdC and εdCH⁺ fluorescence lifetimes with respect to that of dC.

Assessment of time-dependent density functionals for the electronic excitation energies of organic dyes used in DSSCs

The absorption spectra modeled as the vertical excitation energies of 13 dye sensitizers used in dye-sensitized solar cells (DSSCs) are benchmarked by means of time-dependent (TD)-DFT, using 36 functionals from different DFT rungs.

The Static-Dynamic-Static Family of Methods for Strongly Correlated Electrons: Methodology and Benchmarking

A series of methods (SDSCI, SDSPT2, iCI, iCIPT2, iCISCF(2), iVI, and iCAS) is introduced to accurately describe strongly correlated systems of electrons. Born from the (restricted) static-dynamic-static (SDS) framework for designing many-electron wave functions, SDSCI is a minimal multireference (MR) configuration interaction (CI) approach that constructs and diagonalizes a [Formula: see text] matrix for [Formula: see text] states, regardless of the numbers of orbitals and electrons to be correlated. If the full molecular Hamiltonian H in the QHQ block (which describes couplings between functions of the first-order interaction space Q) of the SDSCI CI matrix is replaced with a zeroth-order Hamiltonian [Formula: see text] before the diagonalization is taken, we obtain SDSPT2, a CI-like second-order perturbation theory (PT2). Unlike most variants of MRPT2, SDSPT2 treats single and multiple states in the same way and is particularly advantageous in the presence of near degeneracy. On the other hand, if the SDSCI procedure is repeated until convergence, we will have iterative CI (iCI), which can converge quickly from the above to the exact solutions (full CI) even when starting with a poor guess. When further combined with the selection of important configurations followed by a PT2 treatment of dynamic correlation, iCI becomes iCIPT2, which is a near-exact theory for medium-sized systems. The microiterations of iCI for relaxing the coefficients of contracted many-electron functions can be generalized to an iterative vector interaction (iVI) approach for finding exterior or interior roots of a given matrix, in which the dimension of the search subspace is fixed by either the number of target roots or the user-specified energy window. Naturally, iCIPT2 can be employed as the active space solver of the complete active space (CAS) self-consistent field, leading to iCISCF(2), which can further be combined with iCAS for automated selection of active orbitals and assurance of the same CAS for all states and all geometries. The methods are calibrated by taking the Thiel set of benchmark systems as examples. Results for the corresponding cations, a new set of benchmark systems, are also reported.

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.

Electronic Circular Dichroism Spectra of DNA Quadruple Helices Studied by Molecular Dynamics Simulations and Excitonic Calculations including Charge Transfer States

We here investigate the Electronic Circular Dichroism (ECD) Spectra of two representative Guanine-rich sequences folded in a Quadruple helix (GQ), by using a recently developed fragment diabatisation based excitonic model (FrDEx). FrDEx can include charge transfer (CT) excited states and consider the effect of the surrounding monomers on the local excitations (LEs). When applied to different structures generated by molecular dynamics simulations on a fragment of the human telomeric sequence (Tel21/22), FrDEx provides spectra fully consistent with the experimental one and in good agreement with that provided by quantum mechanical (QM) method used for its parametrization, i.e., TD-M05-2X. We show that the ECD spectrum is moderately sensitive to the conformation adopted by the bases of the loops and more significantly to the thermal fluctuations of the Guanine tetrads. In particular, we show how changes in the overlap of the tetrads modulate the intensity of the ECD signal. We illustrate how this correlates with changes in the character of the excitonic states at the bottom of the La and Lb bands, with larger LE and CT involvement of bases that are more closely stacked. As an additional test, we utilised FrDEx to compute the ECD spectrum of the monomeric and dimeric forms of a GQ forming sequence T30695 (5′TGGGTGGGTGGGTGGG3′), i.e., a system containing up to 24 Guanine bases, and demonstrated the satisfactory reproduction of the experimental and QM reference results. This study provides new insights on the effects modulating the ECD spectra of GQs and, more generally, further validates FrDEx as an effective tool to predict and assign the spectra of closely stacked multichromophore systems.

Systematic improvement of molecular excited state calculations by inclusion of nuclear quantum motion: A mode-resolved picture and the effect of molecular size

The energies of molecular excited states arise as solutions to the electronic Schrödinger equation and are often compared to experiment. At the same time, nuclear quantum motion is known to be important and to induce a redshift of excited state energies. However, it is thus far unclear whether incorporating nuclear quantum motion in molecular excited state calculations leads to a systematic improvement of their predictive accuracy, making further investigation necessary. Here, we present such an investigation by employing two first-principles methods for capturing the effect of quantum fluctuations on excited state energies, which we apply to the Thiel set of organic molecules. We show that accounting for zero-point motion leads to much improved agreement with experiment, compared to "static" calculations that only account for electronic effects, and the magnitude of the redshift can become as large as 1.36 eV. Moreover, we show that the effect of nuclear quantum motion on excited state energies largely depends on the molecular size, with smaller molecules exhibiting larger redshifts. Our methodology also makes it possible to analyze the contribution of individual vibrational normal modes to the redshift of excited state energies, and in several molecules, we identify a limited number of modes dominating this effect. Overall, our study provides a foundation for systematically quantifying the shift of excited state energies due to nuclear quantum motion and for understanding this effect at a microscopic level.

Copper-Oxo Active Sites for Methane C-H Activation in Zeolites: Molecular Understanding of Impact of Methane Hydroxylation on UV-Vis Spectra

Here, we analyze changes in the optical spectra of activated copper-exchanged zeolites during methane activation with the Tamm-Dancoff time-dependent density functional theory, TDA-DFT, while using the ωB2PLYP functional. Two active sites, [Cu₂O]²⁺ and [Cu₃O₃]²⁺, were studied. For [Cu₂O]⁺, the 22 700 cm^-1 peak is associated with μ-oxo 2p → Cu 3d/4s charge transfer. Of the [Cu₂O]²⁺ methane C-H activation intermediates that we examined, only [Cu-O(H)(H)-Cu] and [Cu-O(H)(CH₃)-Cu] have spectra that match experimental observations. After methane activation, the μ-oxo 2p orbitals lose two electrons and become hybridized with methanol C 2p orbitals and/or H 1s orbitals. The frontier unoccupied orbitals become more Cu 4s/4p Rydberg-like, reducing overlap with occupied orbitals. These effects cause the disappearance of the 22 700 cm^-1 peak. For [Cu₃O₃]²⁺, the exact structures of the species formed after methane activation are unknown. Thus, we considered eight possible structures. Several of these provide a significant decrease in intensity near 23 000-38 000 cm^-1, as seen experimentally. Notably, these species involve either rebound of the separated methyl to a μ-oxo atom or its remote stabilization at a Brønsted acid site in exchange for the acidic proton. These spectral changes are caused by the same mechanism seen in [Cu₂O]²⁺ and are likely responsible for the observed reduced intensities near 23 000-38 000 cm^-1. Thus, TDA-DFT calculations with ωB2PLYP provide a molecular-level understanding of the evolution of copper-oxo active sites during methane-to-methanol conversion.

Excited States of Bromopyrimidines Probed by VUV Photoabsorption Spectroscopy and Theoretical Calculations

We report absolute photoabsorption cross sections for gas-phase 2- and 5-bromopyrimidine in the 3.7-10.8 eV energy range, in a joint theoretical and experimental study. The measurements were carried out using high-resolution vacuum ultraviolet synchrotron radiation, with quantum chemical calculations performed through the nuclear ensemble approach in combination with time-dependent density functional theory, along with additional Franck-Condon Herzberg-Teller calculations for the first absorption band (3.7-4.6 eV). The cross sections of both bromopyrimidines are very similar below 7.3 eV, deviating more substantially from each other at higher energies. In the 7.3-9.0 eV range where the maximum cross-section is found, a single and broad band is observed for 5-bromopyrimidine, while more discernible features appear in the case of 2-bromopyrimidine. Several π* ← π transitions account for the most intense bands, while weaker ones are assigned to transitions involving the nitrogen and bromine lone pairs, the antibonding σ*Br orbital, and the lower-lying Rydberg states. A detailed comparison with the available photo-absorption data of bromobenzene is also reported. We have found significant differences regarding the main absorption band, which is more peaked in bromobenzene, becoming broader and shifting to higher energies in both bromopyrimidines. In addition, there is a significant suppression of vibrational structures and of Rydberg states in the pair of isomers, most noticeably for 2-bromopyrimidine.

The molecular basis of spectral tuning in blue- and red-shifted flavin-binding fluorescent proteins

Photoactive biological systems modify the optical properties of their chromophores, known as spectral tuning. Determining the molecular origin of spectral tuning is instrumental for understanding the function and developing applications of these biomolecules. Spectral tuning in flavin-binding fluorescent proteins (FbFPs), an emerging class of fluorescent reporters, is limited by their dependency on protein-bound flavins, whose structure and hence electronic properties cannot be altered by mutation. A blue-shifted variant of the plant-derived improved light, oxygen, voltage FbFP has been created by introducing a lysine within the flavin-binding pocket, but the molecular basis of this shift remains unconfirmed. We here structurally characterize the blue-shifted improved light, oxygen, voltage variant and construct a new blue-shifted CagFbFP protein by introducing an analogous mutation. X-ray structures of both proteins reveal displacement of the lysine away from the chromophore and opening up of the structure as instrumental for the blue shift. Site saturation mutagenesis and high-throughput screening yielded a red-shifted variant, and structural analysis revealed that the lysine side chain of the blue-shifted variant is stabilized close to the flavin by a secondary mutation, accounting for the red shift. Thus, a single additional mutation in a blue-shifted variant is sufficient to generate a red-shifted FbFP. Using spectroscopy, X-ray crystallography, and quantum mechanics molecular mechanics calculations, we provide a firm structural and functional understanding of spectral tuning in FbFPs. We also show that the identified blue- and red-shifted variants allow for two-color microscopy based on spectral separation. In summary, the generated blue- and red-shifted variants represent promising new tools for application in life sciences.

Electrostatically Tuning the Photodissociation of the Irgacure 2959 Photoinitiator in the Gas Phase by Cation Binding

The low-lying electronic states of Irgacure 2959, a Norrish-type I photoinitiator, complexed with a single metal cation are investigated in the gas phase by photodissociation action spectroscopy. Analysis of the band shifts using quantum chemical calculations (TD-DFT and SCS-CC2) reveals the underlying influence of the charge on the key electronic energy levels. Since the cations (H⁺, Li⁺, Na⁺, K⁺, Zn²⁺, Ca²⁺, and Mg²⁺) bind at varying distances, the magnitude of the electric field at the center of the chromophore due to the cation is altered, and this shifts the electronic states by different amounts. Photodissociation action spectra of cation-Irg complexes show that absorption transitions to the first ¹ππ* state are red-shifted with a magnitude proportional to the electric field strength (with red shifts >1 eV), and in most cases, the cation is essentially acting as a point charge. Calculations show that a neighboring ³nπ* state, a key state for the α-cleavage pathway, is destabilized (blue-shifted) by the orientated electric field. As such, if the ¹ππ*-³nπ* energy gap is reduced, increased intersystem crossing rates are expected, resulting in higher yields of the desired radical photoproducts, and this is controlled by the orientated electric field arising from the cation.