Vibronic Effects Research Articles

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.

Theoretical Study on Vibrationally Resolved Electronic Spectra of Chiral Nanographenes.

Nanographenes are of increasing importance owing to their potential applications in the photoelectronic field. Meanwhile, recent studies have primarily focused on the pure electronic spectra of nanographenes, which have been found to be inadequate for describing the experimental spectra that contain vibronic progressions. In this study, we focused on the vibronic effect on the electronic transition of a range of chiral nanographenes, especially in the low-energy regions with distinct vibronic progressions, using theoretical calculations. All the calculations were performed at the PBE0-D3(BJ)/def2-TZVP level of theory, adopting both time-dependent and time-independent approaches with Franck-Condon approximation. The resulting calculated curves exhibited good alignment with the experimental data. Notably, for the nanographenes incorporating helicene units, owing to the increasing π-extension, the major vibronic modes in the vibrationally resolved spectra differed significantly from those of the primitive helicenes. This investigation suggests that calculations that account for the vibronic effect could have better reproducibility compared with calculations based solely on pure electronic transitions. We anticipate that this study could pave the way for further investigations into optical and chiroptical properties, with a deeper understanding of the vibronic effect, thereby providing theoretical explanations with higher precision on more sophisticated nanographenes.

Frequency-Dependent Vibronic Effects in Steady State Energy Transport.

The interplay between electronic and intramolecular high-frequency vibrational degrees of freedom is ubiquitous in natural light-harvesting systems. Recent studies have indicated that an intramolecular vibrational donor-acceptor frequency difference can enhance energy transport. Here, we analyze the extent to which different intramolecular donor-acceptor vibrational frequencies affect excitation energy transport in the natural nonequilibrium steady state configuration. Comments are included on the less physical equilibrium case for comparison with the literature. It is found that for constant Huang-Rhys factors, whereas the acceptor population increases in the equilibrium case when the intramolecular vibrational frequency of the acceptor exceeds that of the donor, this increase is negligible for the nonequilibrium steady state. Therefore, these changes in acceptor population do not significantly enhance energy transport in the nonequilibrium steady state for the natural scenario of incoherent light excitation with biologically relevant parameters of typical photosynthetic complexes. Insight about a potential mechanism to optimize energy transfer in the nonequilibrium steady state based on increasing the harvesting time at the reaction center is analyzed.

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 abinitio 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.

Inverse Optically-Induced Ring Currents in Ring-Shaped Molecules.

Permanent electronic ring currents are supported within manifolds of ΓE degenerate excited electronic states as E± = Ex ± iEy excitations. In [ Phys. Rev. Res. 2021, 3, L042003] we showed the existence of inverse-current manifolds, where the direction of the electronic ring current in each degenerate state E± is opposite to the circular polarization of the generating light fields. This vibronic effect is caused by the exchange of orbital angular momentum between the electrons and the vibrational modes with the required symmetry. Here we consider the case of fixed nuclei and find that ring-shaped molecular systems possess inverse-current manifolds on a purely electronic-structure basis, i.e., without intervention of vibronic coupling. The effect is explained first on a tight-binding model with cyclic symmetry and then considering the ab initio electronic structure of benzene and sym-triazine. A framework for discriminating regular- and inverse-current ΓE manifolds in molecules using quantum chemistry calculations is provided.

Molecules with Spin and Vibronic Coupling Effects: A Computational Perspective

While fundamental to molecular quantum mechanics, limitations of the Born-Oppenheimer Approximation (BOA) have long been known. Nonetheless, calculations that include molecular interactions, such as vibronic coupling and electron spin effects, that violate the BOA have remained a challenge due to their large demand on computational resources. The purpose of this paper is to describe two complementary software programs, SOCJT and XSIM, designed for efficient calculations that include these interactions. The programs are sufficiently general and user friendly that they can be readily applied to a variety of molecules of different symmetries, state degeneracies, and interaction strengths. The programs can typically produce spin-vibronic eigenvalues and eigenvectors with sufficient accuracy for the analysis and interpretation of molecular spectra with features attributable to violations of the BOA. The two programs utilize different matrix representations of the molecular Hamiltonian, with XSIM being Cartesian based and SOCJT being cylindrically based, and their advantages/disadvantages are discussed. Several algorithms can be chosen to obtain the Hamiltonian’s eigenvalues and eigenvectors and their speed and memory usage are compared. Examples of application of SOCJT and XSIM to explain spectral observations for particular molecules are briefly reviewed.

Significance of Vibronic Coupling that Shapes Circularly Polarized Luminescence of Double Helicenes

AbstractThe circularly polarized luminescence (CPL) spectra of S‐ and X‐shaped double helicenes exhibit distinct vibrational structures and overall shape variations. In this study, we conducted an in‐depth investigation into the vibronic effects influencing the CPL spectra of two double helicenes, namely DPC and DNH. Employing state‐of‐the‐art computations utilizing the FC‐HT1|VH model at the CAM−B3LYP/def2‐TZVP level, we unveiled the paramount impact of Franck–Condon (FC), Herzberg‐Teller (HT), and Duschinsky effects on their chiroptical responses. Our research underscores the pivotal role of structural deformations associated with the S1‐to‐S0 electronic transition in molding CPL spectra and wavelength‐dependent dissymmetry (g) factor values, as well as the significance of HT effects in shaping and enhancing CPL responses. This extensive investigation not only advances our comprehension of the vibronic characteristics in configurationally distinct double helicenes but also offers valuable insights for the design of chiral molecules featuring controllable or finely‐tunable CPL responses.

Significance of Vibronic Coupling that Shapes Circularly Polarized Luminescence of Double Helicenes.

The circularly polarized luminescence (CPL) spectra of S- and X-shaped double helicenes exhibit distinct vibrational structures and overall shape variations. In this study, we conducted an in-depth investigation into the vibronic effects influencing the CPL spectra of two double helicenes, namely DPC and DNH. Employing state-of-the-art computations utilizing the FC-HT1|VH model at the CAM-B3LYP/def2-TZVP level, we unveiled the paramount impact of Franck-Condon (FC), Herzberg-Teller (HT), and Duschinsky effects on their chiroptical responses. Our research underscores the pivotal role of structural deformations associated with the S1-to-S0 electronic transition in molding CPL spectra and wavelength-dependent dissymmetry (g) factor values, as well as the significance of HT effects in shaping and enhancing CPL responses. This extensive investigation not only advances our comprehension of the vibronic characteristics in configurationally distinct double helicenes but also offers valuable insights for the design of chiral molecules featuring controllable or finely-tunable CPL responses.

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.

Vibronic effect study of 1A2 state of H2O and D2O

The generalized oscillator strengths of the dipole-forbidden excitations of the 1A2 of H2O and D2O were calculated with the time dependent density functional theory, by taking into account the vibronic effect. It is found that the vibronic effect converts the dipole-forbidden excitation of the 1A2 into a dipole-allowed one, which enhances the intensities of the corresponding generalized oscillator strength in the small squared momentum transfer region. The present investigation shows that the vibronic effect of H2O is slightly stronger than that of D2O, which exhibits a clear isotopic effect.

Two-dimensional electronic spectroscopy from first principles

The recent development of multidimensional ultrafast spectroscopy techniques calls for the introduction of computational schemes that allow for the simulation of such experiments and the interpretation of the corresponding results from a microscopic point of view. In this work, we present a general and efficient first-principles scheme to compute two-dimensional electronic spectroscopy maps based on real-time time-dependent density-functional theory. The interface of this approach with the Ehrenfest scheme for molecular dynamics enables the inclusion of vibronic effects in the calculations based on a classical treatment of the nuclei. The computational complexity of the simulations is reduced by the application of numerical advances such as branching techniques, undersampling, and a novel reduced phase cycling scheme, applicable for systems with inversion symmetry. We demonstrate the effectiveness of this method by applying it to prototypical molecules such as benzene, pyridine, and pyrene. We discuss the role of the approximations that inevitably enter the adopted theoretical framework and set the stage for further extensions of the proposed method to more realistic systems.

Quantum Vibronic Effects on the Excitation Energies of the Nitrogen-Vacancy Center in Diamond.

We investigated the impact of quantum vibronic coupling on the electronic properties of solid-state spin defects using stochastic methods and first-principles molecular dynamics with a quantum thermostat. Focusing on the negatively charged nitrogen-vacancy center in diamond as an exemplary case, we found a significant dynamic Jahn-Teller splitting of the doubly degenerate single-particle levels within the diamond's band gap, even at 0 K, with a magnitude exceeding 180 meV. This pronounced splitting leads to substantial renormalizations of these levels and, subsequently, of the vertical excitation energies of the doubly degenerate singlet and triplet excited states. Our findings underscore the pressing need to incorporate quantum vibronic effects into first-principles calculations, particularly when comparing computed vertical excitation energies with experimental data. Our study also reveals the efficiency of stochastic thermal line sampling for studying phonon renormalizations of solid-state spin defects.

Visualizing nanoscale heterogeneity in perylene thin films via tip-enhanced photoluminescence with unsupervised machine learning.

We investigate the properties of ultrathin 3,4,9,10-perylenetetracarboxylic diimide (PTCDI) films using a combination of tip-enhanced photoluminescence and unsupervised machine learning. We expose nanoscale spectral heterogeneities that can be understood on the basis of the interplay between vibronic effects, intermolecular excitons, and intramolecular excitons in PTDCI films.

One- and two-photon absorption spectra of organoboron complexes: vibronic and environmental effects.

We synthesized a series of four parent aza-β-ketoiminate organoboron complexes and performed spectroscopic studies using both experimental and computational techniques. We studied how benzannulation influences the vibronic structure of the UV/Vis absorption bands with a focus on the bright lowest-energy π → π* electronic excitation. Theoretical simulations, accounting for inhomogeneous broadening effects using different embedding schemes, allowed gaining in-depth insights into the observed differences in band shapes induced by structural modifications. We observed huge variations in the distributions of vibronic transitions depending on the position of benzannulation. By and large, the harmonic approximation combined with the adiabatic hessian model delivers qualitatively correct band shapes for the one-photon absorption spectra, except in one case. We also assessed the importance of non-Condon effects (accounted for by the linear term in Herzberg-Teller expansion of the dipole moment) for S0 → S1 band shapes. It turned out that non-Condon contributions have no effect on the band shape in one-photon absorption spectra. In contrast, these effects significantly change the Franck-Condon band shapes of the two-photon absorption spectra. For one of the studied organoboron complexes we also performed a preliminary exploration of mechanical anharmonicity, resulting in an increase of the intensity of the 0-0 transition, which improves the agreement with the experimental data compared to the harmonic model.

Quantum-Classical Protocol for Efficient Characterization of Absorption Lineshape and Fluorescence Quenching upon Aggregation: The Case of Zinc Phthalocyanine Dyes.

A quantum-classical protocol that incorporates Jahn-Teller vibronic coupling effects and cluster analysis of molecular dynamics simulations is reported, providing a tool for simulations of absorption spectra and ultrafast nonadiabatic dynamics in large molecular photosystems undergoing aggregation in solution. Employing zinc phthalocyanine dyes as target systems, we demonstrated that the proposed protocol provided fundamental information on vibronic, electronic couplings and thermal dynamical effects that mostly contribute to the absorption spectra lineshape and the fluorescence quenching processes upon dye aggregation. Decomposing the various effects arising upon dimer formation, the structure-property relations associated with their optical responses have been deciphered at atomistic resolution.

Spin-vibronic coherence drives singlet-triplet conversion.

Design-specific control over the transitions between excited electronic states with different spin multiplicities is of the utmost importance in molecular and materials chemistry1-3. Previous studies have indicated that the combination of spin-orbit and vibronic effects, collectively termed the spin-vibronic effect, can accelerate quantum-mechanically forbidden transitions at non-adiabatic crossings4,5. However, it has been difficult to identify precise experimental manifestations of the spin-vibronic mechanism. Here we present coherence spectroscopy experiments that reveal the interplay between the spin, electronic and vibrational degrees of freedom that drive efficient singlet-triplet conversion in four structurally related dinuclear Pt(II) metal-metal-to-ligand charge-transfer (MMLCT) complexes. Photoexcitation activates the formation of a Pt-Pt bond, launching a stretching vibrational wavepacket. The molecular-structure-dependent decoherence and recoherence dynamics of this wavepacket resolve the spin-vibronic mechanism. We find that vectorial motion along the Pt-Pt stretching coordinates tunes the singlet and intermediate-state energy gap irreversibly towards the conical intersection and subsequently drives formation of the lowest stable triplet state in a ratcheting fashion. This work demonstrates the viability of using vibronic coherences as probes6-9 to clarify the interplay among spin, electronic and nuclear dynamics in spin-conversion processes, and this could inspire new modular designs to tailor the properties of excited states.

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.

A BF2 Chelate Exhibiting Excimer-like Fluorescence with an Unusually Large Stokes Shift in the Crystalline Phase.

The target mono-BF2 complex is weakly emissive in fluid solution because radiationless decay of the excited-singlet state is promoted through an intramolecular N⋅⋅⋅H-N hydrogen bond. The lack of mirror symmetry for this compound is attributed to vibronic effects, as reported previously for the bis-BF2 complex (BOPHY). Red-shifted fluorescence is observed from single crystals, the emission quantum yield approaching 30 % with a fluorescence lifetime of 2 ns. The large Stokes shift of 5,700 cm-1 helps minimize self-absorption. Crystallography indicates that the internal fold and twist angles are increased substantially in the crystal, but the hydrogen bond is weakened relative to solution. The crystal structure is compiled from pairs of head-to-tail molecules having a shift of ca. 4.1 Å and closest approach of ca. 3.5 Å. These molecular pairs are arranged in columns, which, in turn, assemble into sheets. The proximity favors excitonic coupling between individual molecules, with the coupling strength obtained by analysis of the absorption spectrum reaching ca. 1,000 cm-1 . Both the ideal dipole approximation and the extended dipole methodology seriously overestimate the coupling strength, but the atomic transition charge density procedure leads to good agreement with experiment. Emission is attributed to the closely coupled molecular pair functioning in an excimer-like manner with the exciton trapped in a local minimum. Increasing temperature causes a slight blue shift and loss of fluorescence.

Theoretical approach to the one-step versus two-step spin transitions in Hofmann-like FeII SCO metal-organic frameworks

Guest molecules in the 3D Hofmann-type FeII spin-crossover (SCO) metal-organic frameworks modulate the magnetic properties of the host, modifying the spin state, transition temperature, width of the hysteresis loop and are responsible for the occurrence of a single-step or multistep spin transition. In this work we explore the guest-dependent SCO properties of the Hofmann-like FeII SCO clathrates with formula {Fe(bpb)[Pt(CN)4]}⋅2G. We use a computational strategy based on DFT periodic calculations on the whole system, CASSCF/NEVPT2 calculations on single metal fragments and plots of the reduced density gradients to identify and quantify the dominant effects governing the occurrence of one-step or two-step spin transitions in these systems. Our results inform about the strength of the ligand field around Fe sites, the relative stability of the different spin states, the amplitude and nature of the host-guest and guest-guest interactions, and the role of the vibronic effects on the SCO properties of Hofmann-type FeII clathrates.

Thermodynamic Control of Intramolecular Singlet Fission and Exciton Transport in Linear Tetracene Oligomers.

We newly synthesized a series of homo- and hetero-tetracene (Tc) oligomers to propose a molecular design strategy for the efficient exciton transport in linear oligomers by promoting correlated triplet pair (TT) dissociation and controlling sequential exciton trapping process of individual doubled triplet excitons (T+T) by intramolecular singlet fission. First, entropic gain effects on the number of Tc units are examined by comparing Tc-homo-oligomers [(Tc)n : n=2, 4, 6]. Then, a comparison of (Tc)n and Tc-hetero-oligomer [TcF3 -(Tc)4 -TcF3 ] reveals the vibronic coupling effect for entropic gain. Observed entropic effects on the T+T formation indicated that the exciton migration is rationalized by number of possible TT states increased both by increasing the number of Tc units and by the vibronic levels at the terminal TcF3 units. Finally, we successfully observed high-yield exciton trapping process (trapped triplet yield: ΦTrT =176 %).