Vibronic Coupling Effects Research Articles

Surface-enhanced hyper-Raman scattering of Rhodamine 6G isotopologues: Assignment of lower vibrational frequencies.

We report a comprehensive experimental and theoretical study of the lower-wavenumber vibrational modes in the surface-enhanced hyper-Raman scattering (SEHRS) of Rhodamine 6G (R6G) and its isotopologue R6G-d4. Measurements acquired on-resonance with two different electronic states, S1 and S2, are compared to the time-dependent density functional theory computations of the resonance hyper-Raman spectra and electrodynamics-quantum mechanical computations of the SEHRS spectra on-resonance with S1 and S2. After accounting for surface orientation, we find excellent agreement between experiment and theory for both R6G and its isotopologue. We then present a detailed analysis of the complex vibronic coupling effects in R6G and the importance of surface orientation for characterizing the system. This combination of theory and experiment allows, for the first time, an unambiguous assignment of lower-wavenumber vibrational modes of R6G and its isotopologue R6G-d4.

Engineering couplings for exciton transport using synthetic DNA scaffolds

Summary Control over excitons enables electronic energy to be harnessed and transported for light harvesting and molecular electronics. Such control requires nanoscale precision over the molecular components. Natural light-harvesting systems achieve this precision through sophisticated protein machinery, which is challenging to replicate synthetically. Here, we introduce a DNA-based platform that spatially organizes cyanine chromophores to construct tunable excitonic systems. We synthesized DNA-chromophore nanostructures and characterized them with ensemble ultrafast and single-molecule spectroscopy and structure-based modeling. This synthetic approach facilitated independent control over the coupling among the chromophores and between the chromophores and the environment. We demonstrated that the coupling between the chromophores and the environment could enhance exciton transport efficiency, highlighting the key role of the environment in driving exciton dynamics. Control over excitons, as reported here, offers a path toward the development of designer nanophotonic devices.

Ultrafast processes: coordination chemistry and quantum theory.

Coordination compounds, characterized by fascinating and tunable electronic properties, are capable of binding easily to proteins, polymers, wires and DNA. Upon irradiation, these molecular systems develop functions finding applications in solar cells, photocatalysis, luminescent and conformational probes, electron transfer triggers and diagnostic or therapeutic tools. The control of these functions is activated by the light wavelength, the metal/ligand cooperation and the environment within the first picoseconds (ps). After a brief summary of the theoretical background, this perspective reviews case studies, from 1st row to 3rd row transition metal complexes, that illustrate how spin-orbit, vibronic coupling and quantum effects drive the photophysics of this class of molecules at the early stage of the photoinduced elementary processes within the fs-ps time scale range.

Impact of vibronic coupling effects on light-driven charge transfer in pyrene-functionalized middle and large-sized metalloid gold nanoclusters from Ehrenfest dynamics.

Theoretical calculations are an effective strategy to complement and understand the experimental results in atomistic detail. Ehrenfest molecular dynamics simulations based on the real-time time-dependent density functional tight-binding (RT-TDDFTB) approach are performed to reveal for the first time the electron dynamics for the charge separation of pyrene-functionalized middle-sized Au70S20(PH3)16 and large-sized Au108S24(PR3)16 (R = H, CH3, C2H5, C6H5) clusters. The proposed mechanism uncovers an ultrafast and irreversible photoinduced charge transfer from the gold nanocluster (GNC) unit to the pyrene derivative in all cases. By a Fourier transform analysis of the dynamics, the effect of vibronic couplings is highlighted. The Au108S24(PPh3)15PPh2Pyr system exhibits the best performance for charge separation.

On the generation of electronic ring currents under vibronic coupling effects.

We study the generation of electronic ring currents in the presence of nonadiabatic coupling using circularly polarized light. For this, we introduce a solvable model consisting of an electron and a nucleus rotating around a common center and subject to their mutual Coulomb interaction. The simplicity of the model brings to the forefront the non-trivial properties of electronic ring currents in the presence of coupling to the nuclear coordinates and enables the characterization of various limiting situations transparently. Employing this model, we show that vibronic coupling effects play a crucial role even when a single E degenerate eigenstate of the system supports the current. The maximum current of a degenerate eigenstate depends on the strength of the nonadiabatic interactions. In the limit of large nuclear to electronic masses, in which the Born-Oppenheimer approximation becomes exact, constant ring currents and time-averaged oscillatory currents necessarily vanish.

Vibronic coupling induced by fast Rabi oscillations for kinetic energy control in free atom

Vibronic coupling effects usually manifest themselves in molecules and crystals rather than in unbound atoms. We theoretically demonstrate the existence of vibronic states in a moving two-level atom exposed to a strong electromagnetic (EM) wave. In this case, the Rabi oscillations of the electron density give rise to periodic displacements of the atomic nucleus with the Rabi frequency. The periodic displacements mix the Stark split electron levels and lead to the establishment of a channel for energy transfer in the atomic system. Such a channel paves the way for fast control of the kinetic energy of a free atom with the use of the parameters of an EM wave. Thus, the system kinetic energy can be decreased or increased if the detuning between the laser pulse frequency and the optical transition is positive or negative, respectively. For actual values of the detuning, the pulse duration should be an order of magnitude longer than the lifetime of the excited atomic level in order to complete the energy transfer process.

Theoretical and Experimental Investigations on the Aggregation‐Enhanced Emission from Dark State: Vibronic Coupling Effect

AbstractAggregation‐induced/‐enhanced emission (AIE/AEE) has aroused broad interest. The mechanism behind is understood as the aggregation restriction of the nonradiative decay from electronically excited state to the ground state, either through interconversion or through conical intersection, leaving the dipole‐allowed radiative decay channel relatively intact. Here, a report on an AEE phenomenon for 5,10‐diphenylphenazine (DPhPZ) compound is presented, for which the experiment shows to be AEE active but the lowest excited state has been long known to be “dark state,” namely with zero transition dipole with the ground state according to Kasha’s rule. The computational studies demonstrate that the optical emission stems from the “dark state” with emission intensity borrowed from higher‐lying “bright state” through Herzberg–Teller vibronic coupling, and the resultant spectra are in good agreement with the experiment in terms of both line shape and peak position. The vibronic‐coupling‐induced radiative decay and the restricted nonradiative decay synergistically bring about highly efficient luminescence of DPhPZ in the solid phase. The findings open a new avenue for the development of solid‐emissive luminophores.

Effect of Vibronic Coupling on Correlated Triplet Pair Formation in the Singlet Fission Process of Linked Tetracene Dimers.

Tetracene-based singlet fission (SF) materials show application prospects as triplet sensitizers in organic optoelectronics. SF involves internal conversion from photoexcited singlet states 1(S1S0) to correlated triplet pair states 1(T1T1). We derive an expression for the internal conversion rate on the basis of the Fermi golden rule with an artificial Lorentzian broadening. The internal conversion rate depends on the interstate vibronic couplings (VCs) and energy difference (ΔESF) between 1(S1S0) and 1(T1T1). Therefore, understanding the interplay between interstate VCs and ΔESF is necessary to reveal how the structure-property relationship affects the SF efficiency. Here, we propose a method to quantitatively analyze interstate VCs between 1(S1S0) and 1(T1T1). We apply this method to SF in ortho-, meta-, and para-bis(ethynyltetracenyl)benzene and identify an effect of interstate VCs on the 1(T1T1) formation rate. The interstate VCs of the meta dimer are remarkably weak, which reasonably explains the experimentally obtained slow 1(T1T1) formation rate. The weak VCs result from a very small overlap density between 1(S1S0) and 1(T1T1) of the meta dimer. Furthermore, we investigate structure-dependence of the 1(T1T1) formation rate of the para dimer and find that the para dimer shows large VCs and small ΔESF when the rotational angle between the two tetracene units is large, which leads to the faster 1(T1T1) formation rate than those of the ortho and meta dimers. The rotation of the tetracene units is the origin of the experimentally observed fast 1(T1T1) formation rate of the para dimer.

Spectroscopy of Vibronically Coupled and Duschinskcally Rotated Polyatomic Molecules.

Electron-vibration coupling (or vibronic coupling) of polyatomic molecules in the condensed phase has received considerable attention experimentally and theoretically using linear spectroscopy and four-wave mixing techniques in an effort to probe the structure and dynamics of the system at hand. For this reason, a detailed study of vibronic coupling in harmonic polyatomic molecules featuring a greater degree of computational efficiency is presented. A full treatment of non-Condon systems whereupon linear and nonlinear Herzberg-Teller vibronic coupling and Duschinsky mixing effects in harmonic systems taking place upon electronic excitation is provided. The utilization of an exponential function to express the nuclear dependence of the electronic transition dipole moment, thereby avoiding the finite sum and eigenstate representation that is normally used in computing a non-Condon interaction, leads to a simpler electronic transition dipole moment time correlation function with rapid convergence and better numerical stability than previously reported works. A closed-form expression is obtained for the electronic transition dipole moment time correlation function of polyatomic molecules in which linear and nonlinear Herzberg-Teller vibronic coupling and Duschinsky mixing effects are accounted for. An important numerical observation regarding dealing with branch cuts, which manifest themselves as discontinuities in the function itself or its first derivative, and are often exhibited by complex-valued correlation functions, is noted and treated using the Riemann surface approach. The resultant dipole moment correlation function is in turn employed to calculate linear absorption and hole-burning signals, accounting for the aforementioned spectroscopic effects. A link between wavelets and the electronic transition dipole moment time correlation function in multidimensional harmonic systems is made in the concluding remarks.

Generalized Kasha’s Model: T-Dependent Spectroscopy Reveals Short-Range Structures of 2D Excitonic Systems

Summary Excitonic organic materials owe their tunable optoelectronic properties to intricate microscopic configurations, challenging for conventional characterization methods to resolve. We generalize Kasha’s model by incorporating the temperature (T)-dependent absorption peak shift, in addition to the monomer-aggregate absorption peak shift that defines J- and H-aggregates, to characterize the microscopic structures. We show that the short-range interactions dominate in determining the direction of the T-dependent peak shift, which accounts for previously observed T-dependent blueshifting J-aggregates (BJ-aggregates) that were not explained and predicts the existence of redshifting H-aggregates (RH-aggregates). This defines four types of excitonic aggregates: RJ-, BH-, BJ-, and RH-aggregates, where the latter two unconventional aggregates are possible because of the two dimensionality of excitonic systems and cannot be understood with the original Kasha’s theory. Our conceptual framework is useful for elucidating structure-function relationships in molecular excitonic systems and is fully compatible with existing tools. Possible extensions to other spectroscopic observables and related systems are discussed.

Electronic Spectra of Diacetylene Cations (HC4H+) Tagged with Ar and N2

Electronic spectra of mass-selected HC4H+-Arn (n = 1-3) and HC4H+-(N2)n (n = 1-2) complexes are measured over the 290-530 nm range using resonance-enhanced photodissociation spectroscopy in a tandem mass spectrometer. Vibronic transitions in the visible region are compared with previous experimental and theoretical results for the Ã2Πu ← X̃2Πg band system of HC4H+. Hole burning experiments confirm that transitions over the 290-340 nm range involve the diacetylene cation (HC4H+). On the basis of previous experiments and comparison with spectra of isoelectronic molecules the peaks are assigned to the 22Πu ← X̃2Πg band system, with the origin transition for HC4H+-Ar occurring at 29723 cm-1. The main progression has a spacing of 906 cm-1 and is assigned to the symmetric C-C stretch vibrational mode (ν3). The assignment of additional bands is complicated by spectral congestion, the possible presence of energetically close-lying electronic states, vibronic coupling effects, and by the fact that HC4H+ possibly becomes nonlinear in the 22Πu state.

Signatures of Strong Vibronic Coupling Mediating Coherent Charge Transfer in Two-Dimensional Electronic Spectroscopy

Abstract The role of molecular vibrations for the persistence of quantum coherences, recently observed in photoinduced charge transfer reactions in both biological and artificial energy conversion systems at room temperature, is currently being intensely discussed. Experiments using two-dimensional electronic spectroscopy (2DES) suggest that vibrational motion – and its coupling to electronic degrees of freedom – may play a key role for such coherent dynamics and potentially even for device function. In organic photovoltaics materials, strong coupling of electronic and vibrational motion is predicted, especially for ubiquitous C=C stretching vibrations. The signatures of such strong vibronic couplings in 2DES are, however, debated. Here we analyse the effect of strong vibronic coupling in model simulations of 2DES spectra and dynamics for an electronic dimer coupled to a single high-frequency vibrational mode. This system represents the simplest conceivable model for a prototypical donor–acceptor interface in the active layer of organic solar cells. The vibrational mode is chosen to mimic C=C stretching vibrations with typical large vibronic couplings predicted in organic photovoltaics materials. Our results show that the decisive signatures of strong vibronic coupling mediating coherent charge transfer between donor and acceptor are not only temporally oscillating cross-peaks, but also most importantly characteristic peak splittings in the 2DES spectra. The 2DES pattern thus directly reflects the new eigenstates of the system that are formed by strong mixing of electronic states and vibrational mode.

Quantum master equation approach to singlet fission dynamics in pentacene ring-shaped aggregate models.

The quantum master equation approach is applied to the singlet fission (SF) dynamics of pentacene ring-shaped aggregate models to clarify the Frenkel excitonic (FE) coupling effects on the SF rate and correlated-triplet pair (TT) yield as well as their dependences on the aggregate structure and size. Interestingly, the smallest ring model, a ring-shaped trimer, is found to exhibit a significantly smaller SF rate and a slightly smaller TT yield than those of the dimer model with the same intermonomer interaction and to show remarkable variations in the SF dynamics with increasing the FE coupling. With increasing the size of the aggregates with FE coupling, it is found that the SF rate rapidly increases, attains the maximum at 17-mer (∼3 times enhancement compared to the non-FE-coupling case), and then decreases, approaching a stationary value around 25-mer, while the almost stationary TT yield at 25-mer remains 16% smaller than that in the non-FE-coupling case. These features are found to be in qualitative agreement with those in the corresponding linear aggregates, although the aggregate size gives a maximum SF rate, and the values of the maximum SF rate as well as of the converged TT yield are different between the ring-shaped and linear aggregates. These results are interpreted based on the relative relaxation factors between the adiabatic exciton states as well as on the vibronic coupling effects. The present results contribute to a deeper understanding of the aggregate structure and size dependences of SF dynamics and to constructing the design guidelines for highly efficient SF aggregates.

Linear and nonlinear Herzberg−Teller vibronic coupling effects. II: Hole-burning and fluorescence line narrowing spectroscopy

Part I of this series showed that Herzberg-Teller vibronic coupling manifests itself in linear spectroscopy through the breakdown of the mirror image symmetry between the absorption and emission spectra, whereby a nuclear exponential function was used to represent the molecular electronic transition dipole moment. This part tests the applicability of the framework developed in Paper I to absorption-emission asymmetry in nonlinear signals such as hole-burned and fluorescence line narrowed spectra. Model calculations of nonlinear absorption and emission spectra showing asymmetry is provided. Hole-burning and fluorescence line narrowing signals are to exemplify nonlinear absorption and emission spectra so as to reveal the anticipated asymmetry in 4-wave mixing experiments, and probe the consequent zero-phonon hole and the phonon-sideband hole. These calculations prove to be efficient and fast, exhibiting remarkable numerical stability. The observation of richer phonon-side band (PSB) in linear spectra, phono-side band hole (PSBH) in Hole-burning and fluorescence line narrowing signals, and emergence of new quantum beats over longer time scale (despite the dissipative medium) under the non-Condon regime are linked to the long quantum coherence phenomenon and stimulated photon peak shift in photosynthetic systems.

Breakdown of the Perturbative Approach to Molecular Packing Dependence of Singlet Fission Rates in Pentacene Dimer Models: A Systematic Comparison with the Quantum Master Equation Approach

We have compared the molecular packing dependences of singlet fission (SF) rates calculated by perturbative and quantum master equation approaches using slip-stacked pentacene dimer models to clarify the applicability of the perturbative treatment and the importance of vibronic coupling effects on the SF dynamics. Several significant differences between these two approaches are found in the peak positions as well as in the relative peak amplitudes on the two-dimensional map of the SF rate as a function of the longitudinal and lateral displacements of the molecular backbones. Using the relative relaxation factor analysis, these disagreements are more striking for increasing the electronic couplings between the related diabatic exciton states as well as for reducing the energy difference between the lowest adiabatic Frenkel-like and double-triplet-like exciton states to match the primary vibronic coupling frequency. These results systematically illuminate the breakdown of the perturbative approach to the pr...

A deeper look into Herzberg-Teller vibronic coupling effect and spectroscopic signature of non-Condon systems

A physical explanation with rigorous basis for the newly emerging vibrational progressions due Herzberg-Teller vibronic coupling that show up in absorption spectra and quantum beats in photon echo signals, respectively, in linearly coupled non-Condon systems besides those arising under the Condon regime, thereby leading to further broadening of the make-up of the phonon-side-band, is provided. The spectroscopic signature of non-Condon systems, whose electronic transition dipole moment depends on nuclear coordinates exponentially, with linear electron-phonon coupling seems to increase the Condon intensity or both increase the Condon intensity and give rise to new bands with different intensity of linear and nonlinear absorption spectra. Model system calculations of a single-site (homogeneous) linear absorption spectra and pump-probe signals are provided.

Linear and nonlinear Herzberg-Teller vibronic coupling effects. I: Electronic photon echo spectroscopy

The dependence of the transition dipole moment on nuclear coordinates gives rise to non-Condon interaction, signaling that the adiabatic Herzberg-Teller vibronic coupling should be considered. This coupling manifests itself in linear spectroscopy through the breakdown of the mirror image symmetry between the absorption and emission spectra. The stronger the non-Condon interaction, the more pronounced is the absorption-emission asymmetry. A nuclear exponential function is used as a simple model to represent the electronic transition dipole moment, the purpose of which is to avoid the use of eigenstate-approach, convergence issues, and finally be able to extend its applicability to nonlinear spectroscopy inexpensively while accounting for linear and nonlinear non-Condon effects (Herzberg-Teller vibronic coupling). The non-Condon effects on linear and nonlinear spectroscopic signals (e.g. 2-pulse photon echo) are examined. Closed-form expressions of the non-Condon electronic transition dipole moment time correlation functions, accounting for Herzberg-Teller vibronic coupling effects, are derived. It is shown that nonlinear optical signals in time domain such as 2-pulse photon echo signal, conspicuously reflects the degree of the non-Condon interaction (mostly constructive interference in this work) despite the inhomogeneous broadening disguising the homogeneous structural aspects of the molecular system of interest. As such, this study should be useful in relation to extracting structural and dynamical information of condensed molecular systems. Model calculations of absorption and emission spectra and 2-pulse photon echo signals of Herzberg-Teller vibronically coupled systems are presented. The method presented here seems to more efficient computationally, fast and stable compared to the methods which involve perturbation theory and eigenstate expansion.

Vibronic and spin-orbit coupling effects in the absorption spectra of pyrazine: A quantum chemical approach

Derivatives of dipole transition moments between spin?orbit coupled (SOC) multireference configuration interaction wave functions have been used in conjunction with vibrational frequencies from density functional theories to compute vibronic S1?S0 (11B3u11Ag ) and T1?S0 (13B3u?11Ag) absorption spectra in Herzberg?Teller approximation. The experimentally known spectra are well reproduced. The calculations reveal unexpectedly small spin?orbit couplings between the 13B3u (3n?*) state and nearby optically bright 1B2u (1??*) states, thus explaining the absence of the 1b1g10 (v10a10 ) fundamental in the vibrational fine-structure of the T1?S0 transition. Adiabatically, two triplet states are found below the S1 state. The out-of-plane distorted T2 minimum results from a pseudo Jahn?Teller interaction between two 3??* states of B1u and B2u symmetry. At the D2h-symmetric S0 and S1 minimum geometries, the latter states are located well above S1. The S1 and T2 potentials intersect at geometries far away from the Franck?Condon region. This explains the apparently contradictory results that the linewidth in the higher energy regime above the T1?S0 origin suddenly broadens while no trace of a second triplet state, located energetically below the S1 origin, could be identified in phosphorescence excitation spectra of the ultracold isolated pyrazine molecule.

Vacuum ultraviolet excited state dynamics of the smallest ring, cyclopropane. I. A reinterpretation of the electronic spectrum and the effect of intensity borrowing.

Cyclopropane, the smallest organic ring compound, exhibits complex spectroscopy and excited state dynamics. In Paper I, we reinterpret the vacuum ultraviolet (VUV) electronic absorption spectrum of cyclopropane via ab initio computation. The first two bands in the VUV spectrum are simulated using wavepacket propagations employing the multiconfigurational time-dependent Hartee method and a newly parameterized linear vibronic coupling Hamiltonian. The parameters of the model Hamiltonian are obtained directly from high level multireference configuration interaction calculations. An analysis of the results, with an emphasis on previously neglected vibronic coupling effects, reveals that these vibronic coupling terms must be included in order to account for strong intensity borrowing effects. This treatment dramatically changes the assignment of much of the VUV spectrum, with intensity borrowing by the optically dark (σ3p x /3p y ) and (σ3p x /3p y ) states from the E'(σ3p x /3p y ) state being found to give rise to almost all the spectral intensities below 8 eV. This is in stark contrast to previous studies, which attributed the first two bands to transitions to the E'(σ3p x /3p y ) state. This highlights the limitations of assigning spectral features based solely on calculated electronic excitation energies and oscillator strengths. Furthermore, we address the significant but infrequently discussed difficulties involved in determining the electronic character of a wavepacket produced in the pump step of ultrafast pump-probe experiments for systems exhibiting strong vibronic coupling.

Expanded Theory of H- and J-Molecular Aggregates: The Effects of Vibronic Coupling and Intermolecular Charge Transfer.

The electronic excited states of molecular aggregates and their photophysical signatures have long fascinated spectroscopists and theoreticians alike since the advent of Frenkel exciton theory almost 90 years ago. The influence of molecular packing on basic optical probes like absorption and photoluminescence was originally worked out by Kasha for aggregates dominated by Coulombic intermolecular interactions, eventually leading to the classification of J- and H-aggregates. This review outlines advances made in understanding the relationship between aggregate structure and photophysics when vibronic coupling and intermolecular charge transfer are incorporated. An assortment of packing geometries is considered from the humble molecular dimer to more exotic structures including linear and bent aggregates, two-dimensional herringbone and "HJ" aggregates, and chiral aggregates. The interplay between long-range Coulomb coupling and short-range charge-transfer-mediated coupling strongly depends on the aggregate architecture leading to a wide array of photophysical behaviors.