Vibronic Coupling Mechanism Research Articles

Electron impact electronic excitation of benzene: Theory and experiment.

We report experimental differential cross sections (DCSs) for electron impact excitation of bands I to V of benzene at incident energies of 10, 12.5, 15, and 20eV. They are compared to calculations using the Schwinger multichannel method while accounting for up to 437 open channels. For intermediate scattering angles, the calculations reveal that the most intense band (V) emerges from surprisingly similar contributions from all its underlying states (despite some preference for the dipole-allowed transitions). They further shed light on intricate multichannel couplings between the states of bands I to V and higher-lying Rydberg states. In turn, the measurements support a vibronic coupling mechanism for excitation of bands II and IV and also show an unexpected forward peak in the spin-forbidden transition accounting for band III. Overall, there is decent agreement between theory and experiment at intermediate angles and at lower energies and in terms of the relative DCSs of the five bands. Discrepancies between the present and previous experiment regarding bands IV and V draw attention to the need of additional experimental investigations. We also report measured DCSs for vibrational excitation of combined C-H stretching modes.

Revisiting the Spectrum of Co(CN)63–: The Role of Correlation, Solvation, and Vibronic and Spin–Orbit Couplings

In the present work, we revisit the spectrum of the hexacyanocobaltate(III) ion, [Co(CN)6]3-, which has been considered a prototype complex in the coordination chemistry, with modern quantum chemistry methods. The main features have been describing by revealing the role of different effects, such as vibronic coupling, solvation and spin-orbit coupling. The UV-vis spectrum is composed by two bands (1A1g → 1T1g and 1A1g → 1T2g), characterized by singlet-singlet metal-centered transitions, and a more intense third one, characterized by charge transfer transition. There is also a small band shoulder. The first two are symmetry-forbidden transitions in the Oh group. Their intensity can only be explained by a vibronic coupling mechanism. For the band shoulder, additional to vibronic coupling, spin-orbit coupling is also necessary, since the transition is characterized as singlet to triplet, 1A1g → 3T1g.

Simulation of the dispersed fluorescence spectrum of the NO[formula omitted][formula omitted] origin vibronic band

A vibronic Hamiltonian and transition dipole operator parametrized by high-level equation-of-motion coupled-cluster calculations are used as a basis for predicting the dispersed fluorescence spectrum of the B̃−X̃ origin band in the nitrate radical (NO3). The position and intensities of transitions to ground state vibrational levels observed in the photodetachment spectrum of the NO3 anion have previously been predicted to high fidelity with this Hamiltonian; it is expected that it also offers a basis for accurate prediction of the dispersed fluorescence spectrum. Comparison to experimental spectra provides considerable insight into various assignments. Significantly, this work joins a growing body of research that supports reassignment of the ground state ν3 vibrational fundamental to the region between 1050–1060 cm−1, which is more than 400 cm−1 below the feature to which it has traditionally been assigned. The in-plane vibrational levels below 2000 cm−1 are reviewed, with theory and experiment agreeing to within 25 cm−1 for all that have been observed experimentally. Finally, the various vibronic coupling mechanisms that affect the ground state energy levels of NO3 are summarized, and a discussion is provided about how the Lanczos algorithm can be used to efficiently calculate the dispersed fluorescence spectrum of the B̃−X̃ origin band.

Light Emission from Vibronic Polaritons in Coupled Metalloporphyrin-Multimode Cavity Systems.

In this study, we explore how one can use cavity polariton formation and a non-Condon vibronic coupling mechanism to form a type of hybrid light-matter state we denote as Herzberg-Teller (HT) vibronic polaritons. We use simple models to define the basic characteristics of these hybrid light-matter excitations including their dispersive energies. Experimentally, we find evidence of HT polaritons in the light emission spectra from copper(II) tetraphenylporphyrin (CuTPP) molecules strongly coupled to both single and multimode Fabry-Perot resonator structures. For specific resonator designs, we find evidence of significant enhancement of light emission from a short-lived sing-doublet state of CuTPP, which couples to a higher energy singlet state via a non-Condon vibronic mechanism. The results of a two-state model support the conclusion that this enhancement and the temperature-dependent dispersion of the light emission peak energy stem from radiative relaxation into cavity photon states dressed by collective vibrations of the molecules participating in polariton formation. These results show how researchers can leverage the complex interplay of electronic and nuclear degrees of freedom in light absorbing molecules to form a vaster array of coherent light-matter states and potentially transform platforms in optoelectronic and photocatalytic technologies.

Normal & reversed spin mobility in a diradical by electron-vibration coupling

π−conjugated radicals have great promise for use in organic spintronics, however, the mechanisms of spin relaxation and mobility related to radical structural flexibility remain unexplored. Here, we describe a dumbbell shape azobenzene diradical and correlate its solid-state flexibility with spin relaxation and mobility. We employ a combination of X-ray diffraction and Raman spectroscopy to determine the molecular changes with temperature. Heating leads to: i) a modulation of the spin distribution; and ii) a “normal” quinoidal → aromatic transformation at low temperatures driven by the intramolecular rotational vibrations of the azobenzene core and a “reversed” aromatic → quinoidal change at high temperatures activated by an azobenzene bicycle pedal motion amplified by anisotropic intermolecular interactions. Thermal excitation of these vibrational states modulates the diradical electronic and spin structures featuring vibronic coupling mechanisms that might be relevant for future design of high spin organic molecules with tunable magnetic properties for solid state spintronics.

Vibronic coupling in energy transfer dynamics and two-dimensional electronic-vibrational spectra.

We introduce a heterodimer model in which multiple mechanisms of vibronic coupling and their impact on energy transfer can be explicitly studied. We consider vibronic coupling that arises through either Franck-Condon activity in which each site in the heterodimer has a local electron-phonon coupling or Herzberg-Teller activity in which the transition dipole moment coupling the sites has an explicit vibrational mode-dependence. We have computed two-dimensional electronic-vibrational (2DEV) spectra for this model while varying the magnitude of these two effects and find that 2DEV spectra contain static and dynamic signatures of both types of vibronic coupling. Franck-Condon activity emerges through a change in the observed excitonic structure, while Herzberg-Teller activity is evident in the appearance of significant side-band transitions that mimic the lower-energy excitonic structure. A comparison of quantum beating patterns obtained from analysis of the simulated 2DEV spectra shows that this technique can report on the mechanism of energy transfer, elucidating a means of experimentally determining the role of specific vibronic coupling mechanisms in such processes.

A unified quantum model susceptible to elucidate the dissimilarity of IR spectral density of dicarboxylic acid crystals: Phthalic and terephthalic acid crystals cases

Over the last decades, several approaches have been developed for elucidating the infrared spectral density of dicarboxylic acid crystals, which has been served as prototype for determining hydrogen bonds dynamics. These approaches differ in how accurately the simulated spectra can superimpose the experimental ones. In this study, we present a superdimer quantum approach susceptible to elucidate the infrared spectral properties of some particular dicarboxylic acid crystals using a newly proposed algorithm, which favors the rule of Davydov coupling in the generation of the spectra. The approach, which is herein effectively applied to terephthalic and phthalic acid dimer crystals, ascribes the non-conventional IR spectral properties of these particular acid crystals to the existence of superdimer structure in their lattices. In this superdimer structure, a strong vibronic coupling mechanism, namely Davydov coupling, takes place between the proton stretching vibrations in the (COOH)₂ cycles. This strong coupling exciton, generated by the resonance arising in the two coupled (COOH)₂ cycles of the aromatic rings of the superdimer, in conjunction with the strong anharmonic coupling between the fast and slow modes of each hydrogen bonds provide a strong support basis for a common explanation of the physical properties of these two different crystalline systems. The numerical simulations, involving the implications of the superdimer model, are systematically correlated with the experimental spectra. A decent agreement between the evaluated spectra and the experimental bandshapes of terephthalic and phthalic dicarboxylic acid crystals was obtained using a set of physically sound parameters as inputs in the theoretical formulation. The superdimer quantum approach thereby underscore the potential of the dynamical cooperative interactions between "Davydov coupling" and "strong anharmonic coupling" mechanisms in the generation of the spectral features of terephthalic and phthalic dicarboxylic acid crystals, suggesting that the congregated effects of these two mechanisms can be considered as the most reliable source of the non-conventional IR spectral properties observed. It is therefore expected that this novel algorithm reduces the discrepancies between the simulated spectra compared to the experimental one and simplify the computation of spectra in more complex hydrogen bonded systems.

Conservation of El-Sayed's Rules in the Photolysis of Phenyl Azide: Two Independent Decomposition Doorways for Alternate Direct Formation of Triplet and Singlet Phenylnitrene.

In the present work, we demonstrate that the formation of triplet and singlet phenylnitrene, when arises from the photodissociation of phenyl azide, fulfills El-Sayed's rules or the electronic angular momentum conservation law. It is shown that the singlet-triplet inversion of phenylnitrene via the vibronic coupling mechanism is not an effective process. In contrast, it is found that there exist two independent dissociation channels that yield alternatively singlet and triplet phenylnitrene. Therefore, a proposed mechanism that violates the angular momentum low is avoided. The clue of the photoreaction lies in the conjunction (energetic and spatial) of two crossing points in a very narrow region of the multidimensional space: (i) an intersystem crossing (ISC1) and (ii) a conical intersection (CI1). The geometrical separation between these two crossing geometries is only 0.016 Å measured in Cartesian coordinates, and the respective energy difference is 2 kcal/mol. This work has been performed by application of the complete active space self-consistent field and multiconfigurational second-order perturbation method.

Generalized oscillator strengths of carbon disulfide calculated by multireference configuration interaction.

Transition energies and generalized oscillator strengths (GOSs) for transitions up to 6.3 eV of carbon disulfide were calculated at the multireference configuration interaction level. It is shown that the consideration of the vibronic coupling mechanism is essential to establish not only a quantitative but also a qualitative profile of the GOS, as a function of the momentum transferred, for the dipole forbidden transitions (Σg+1→1Σu - and Σg+1→1Δu). For the dipole allowed Σg +→Σu + transition, the calculated GOS is in good agreement with the available experimental data.

Vibrational Control of Covalency Effects Related to the Active Sites of Molybdenum Enzymes.

A multitechnique spectroscopic and theoretical study of the Cp2M(benzenedithiolato) (M = Ti, V, Mo; Cp = η5-C5H5) series provides deep insight into dithiolene electronic structure contributions to electron transfer reactivity and reduction potential modulation in pyranopterin molybdenum enzymes. This work explains the magnitude of the dithiolene folding distortion and the concomitant changes in metal-ligand covalency that are sensitive to electronic structure changes as a function of d-electron occupancy in the redox orbital. It is shown that the large fold angle differences correlate with covalency, and the fold angle distortion is due to a pseudo-Jahn-Teller (PJT) effect. The PJT effect in these and related transition metal dithiolene systems arises from the small energy differences between metal and sulfur valence molecular orbitals, which uniquely poise these systems for dramatic geometric and electronic structure changes as the oxidation state changes. Herein, we have used a combination of resonance Raman, magnetic circular dichroism, electron paramagnetic resonance, and UV photoelectron spectroscopies to explore the electronic states involved in the vibronic coupling mechanism. Comparison between the UV photoelectron spectroscopy (UPS) of the d2 M = Mo complex and the resonance Raman spectra of the d1 M = V complex reveals the power of this combined spectroscopic approach. Here, we observe that the UPS spectrum of Cp2Mo(bdt) contains an intriguing vibronic progession that is dominated by a "missing-mode" that is composed of PJT-active distortions. We discuss the relationship of the PJT distortions to facile electron transfer in molybdenum enzymes.

Identifying complex Fermi resonances in p-difluorobenzene using zero-electron-kinetic-energy (ZEKE) spectroscopy.

The vibrations of the ground state cation ( 2B2g) of para-difluorobenzene (pDFB) have been investigated using zero-electron-kinetic-energy (ZEKE) spectroscopy. A comprehensive set of ZEKE spectra were recorded via different vibrational levels of the S1 state (<00 + 1300 cm-1). The adiabatic ionization energy for pDFB was measured as 73 869 ± 5 cm-1. Use of different intermediate levels allows different cationic vibrational activity to be obtained via the modification of the Franck-Condon factors for the ionization step, allowing the wavenumbers of different vibrational levels in the cation to be established. In addition, assignment of the vibrational structure in the ZEKE spectra allowed interrogation of the assignments of the S1 ← S0 transition put forward by Knight and Kable [J. Chem. Phys. 89, 7139 (1988)]. Assignment of the vibrational structure has been aided by quantum chemical calculations. In this way, it was possible to assign seventeen of the thirty vibrational modes of the ground state pDFB+ cation. Evidence for complex Fermi resonances in the S1 state, i.e., those that involve more than two vibrations, was established. One of these was investigated using picosecond time-resolved photoelectron spectroscopy. In addition, we discuss the appearance of several symmetry-forbidden bands in the ZEKE spectra, attributing their appearance to a Rydberg state variation of an intrachannel vibronic coupling mechanism.

Chemical and conformational control of the energy gaps involved in the thermally activated delayed fluorescence mechanism

This review summarises the significant developments in our understanding and control of thermally-activated delayed fluorescence (TADF) molecules and the spin–vibronic coupling mechanism, from which we have designed new generations of emitters.

Revealing the spin-vibronic coupling mechanism of thermally activated delayed fluorescence.

Knowing the underlying photophysics of thermally activated delayed fluorescence (TADF) allows proper design of high efficiency organic light-emitting diodes. We have proposed a model to describe reverse intersystem crossing (rISC) in donor–acceptor charge transfer molecules, where spin–orbit coupling between singlet and triplet states is mediated by one of the local triplet states of the donor (or acceptor). This second order, vibronically coupled mechanism describes the basic photophysics of TADF. Through a series of measurements, whereby the energy ordering of the charge transfer (CT) excited states and the local triplet are tuned in and out of resonance, we show that TADF reaches a maximum at the resonance point, substantiating our model of rISC. Moreover, using photoinduced absorption, we show how the populations of both singlet and triplet CT states and the local triplet state change in and out of resonance. Our vibronic coupling rISC model is used to predict this behaviour and describes how rISC and TADF are affected by external perturbation.

An experimental and theoretical study of the Ã(2)A(″)Π-X̃(2)A(') band system of the jet-cooled HBBr/DBBr free radical.

The electronic spectra of the HBBr and DBBr free radicals have been studied in depth. These species were prepared in a pulsed electric discharge jet using a precursor mixture of BBr3 vapor and H2 or D2 in high pressure argon. Transitions to the electronic excited state of the jet-cooled radicals were probed with laser-induced fluorescence and the ground state energy levels were measured from the single vibronic level emission spectra. HBBr has an extensive band system in the red which involves a linear-bent transition between the two Renner-Teller components of what would be a (2)Π state at linearity. We have used high level ab initio theory to calculate potential energy surfaces for the bent (2)A' ground state and the linear Ã(2)A(″)Π excited state and we have determined the ro-vibronic energy levels variationally, including spin orbit effects. The correspondence between the computed and experimentally observed transition frequencies, upper state level symmetries, and H and B isotope shifts was used to make reliable assignments. We have shown that the ground state barriers to linearity, which range from 10 000 cm(-1) in HBF to 2700 cm(-1) in BH2, are inversely related to the energy of the first excited (2)Σ ((2)A') electronic state. This suggests that a vibronic coupling mechanism is responsible for the nonlinear equilibrium geometries of the ground states of the HBX free radicals.

Toward assessment of density functionals for vibronic coupling in two-photon absorption: A case study of 4-nitroaniline.

In this study, we predict vibronic two-photon absorption (TPA) spectra for 4-nitroaniline in vacuo. The simulations are performed using density functional theory and the approximate second-order coupled-cluster singles and doubles model CC2. Thereby we also demonstrate the possibility of simulations of vibronic TPA spectra with ab initio wavefunction methods that include electron correlation for medium-sized systems. A special focus is put on the geometric derivatives of the second-order transition moment and the dipole moment difference between the charge-transfer excited state and the ground state. The results of CC2 calculations bring new insight into the vibronic coupling mechanism in TPA spectra of 4-nitroniline and demonstrate that the mixed term is quite large and that it also exhibits a negative interference with the Franck-Condon contribution.

Probing and Exploiting the Interplay between Nuclear and Electronic Motion in Charge Transfer Processes.

The Born-Oppenheimer approximation refers to the assumption that the nuclear and electronic wave functions describing a molecular system evolve and can be determined independently. It is now well-known that this approximation often breaks down and that nuclear-electronic (vibronic) coupling contributes greatly to the ultrafast photophysics and photochemistry observed in many systems ranging from simple molecules to biological organisms. In order to probe vibronic coupling in a time-dependent manner, one must use spectroscopic tools capable of correlating the motions of electrons and nuclei on an ultrafast time scale. Recent developments in nonlinear multidimensional electronic and vibrational spectroscopies allow monitoring both electronic and structural factors with unprecedented time and spatial resolution. In this Account, we present recent studies from our group that make use of different variants of frequency-domain transient two-dimensional infrared (T-2DIR) spectroscopy, a pulse sequence combining electronic and vibrational excitations in the form of a UV-visible pump, a narrowband (12 cm(-1)) IR pump, and a broadband (400 cm(-1)) IR probe. In the first example, T-2DIR is used to directly compare vibrational dynamics in the ground and relaxed electronic excited states of Re(Cl)(CO)3(4,4'-diethylester-2,2'-bipyridine) and Ru(4,4'-diethylester-2,2'-bipyridine)2(NCS)2, prototypical charge transfer complexes used in photocatalytic CO2 reduction and electron injection in dye-sensitized solar cells. The experiments show that intramolecular vibrational redistribution (IVR) and vibrational energy transfer (VET) are up to an order of magnitude faster in the triplet charge transfer excited state than in the ground state. These results show the influence of electronic arrangement on vibrational coupling patterns, with direct implications for vibronic coupling mechanisms in charge transfer excited states. In the second example, we show unambiguously that electronic and vibrational movement are coupled in a donor-bridge-acceptor complex based on a Pt(II) trans-acetylide design motif. Time-resolved IR (TRIR) spectroscopy reveals that the rate of electron transfer (ET) is highly dependent on the amount of excess energy localized on the bridge following electronic excitation. Using an adaptation of T-2DIR, we are able to selectively perturb bridge-localized vibrational modes during charge separation, resulting in the donor-acceptor charge separation pathway being completely switched off, with all excess energy redirected toward the formation of a long-lived intraligand triplet state. A series of control experiments reveal that this effect is mode specific: it is only when the high-frequency bridging C≡C stretching mode is pumped that radical changes in photoproduct yields are observed. These experiments therefore suggest that one may perturb electronic movement by stimulating structural motion along the reaction coordinate using IR light. These studies add to a growing body of evidence suggesting that controlling the pathways and efficiency of charge transfer may be achieved through synthetic and perturbative approaches aiming to modulate vibronic coupling. Achieving such control would represent a breakthrough for charge transfer-based applications such as solar energy conversion and molecular electronics.

Long-distance inter-hydrogen bond coupling effects in the polarized IR spectra of succinic acid crystals

The spectral properties of four different crystalline succinic acid (HOOC-(CH2)2-COOH) (SAC) isotopomer systems, h6, d2, d4 and d6, were examined by means of the IR spectroscopy in polarized light aided by numerical simulations of the νO–H and νO–D band contour shapes on utilizing the “strong-coupling” model. The abnormal IR spectral properties of SAC crystals in relation to the corresponding properties of glutaric, pimelic and adipic acid crystals were ascribed to the hyperconjugation electronic effects in the acid associated molecules. A vibronic coupling mechanism involving the proton stretching vibrations in the (COOH)2 cycles and the electronic motions in the molecular skeletons, the isotopic “H/D self-organization” mechanisms and a long-distance vibrational exciton coupling between the adjacent (COOH)2 cycles in the molecular chains are mainly responsible for the generation of the temperature effects in the crystalline IR spectra.

Elucidating the Davydov-coupling mechanism in hydrogen bond dimers: Experimental and theoretical investigation of the polarized IR spectra of 3-thiopheneacetic and 3-thiopheneacrylic acid crystals.

Monocrystals of the 3-thiopheneacetic and 3-thiopheneacrylic acid dimers were investigated by polarized IR spectroscopy at 77 and 293K in the υO‒H and υO‒D band frequency ranges. We propose to elucidate the strong difference between spectra of the two individual systems, expressed by the corresponding band shapes and by the temperature effects characterizing the bands. The experimental results are compared to predictions obtained with theoretical calculations based on a model for a centrosymmetric hydrogen-bonded dimer that treats the high-frequency OH stretches harmonically and the low-frequency intermonomer stretches anharmonically. It was found that the vibronic coupling mechanism involving the hydrogen bond protons and the electrons on the π-electronic systems in the molecules determines the way in which the vibrational exciton coupling between the hydrogen bonds in the carboxylic acid dimers occurs.

Vibronic coupling in asymmetric bichromophores: experimental investigation of diphenylmethane-d₅.

Vibrationally and rotationally resolved electronic spectra of diphenylmethane-d5 (DPM-d5) are reported in the isolated-molecule environment of a supersonic expansion. While small, the asymmetry induced by deuteration of one of the aromatic rings is sufficient to cause several important effects that change the principle mechanism of vibronic coupling between the close-lying S1 and S2 states, and spectroscopic signatures such coupling produces. The splitting between S1 and S2 origins is 186 cm(-1), about 50% greater than its value in DPM-d0 (123 cm(-1)), and an amount sufficient to bring the S2 zero-point level into near-resonance with the v = 1 level in the S1 state of a low-frequency phenyl flapping mode, ν(R) = 191 cm(-1). Dispersed fluorescence spectra bear clear evidence that Δv(R) = 1 Herzberg-Teller coupling dominates the near-resonant internal mixing between the S1 and S2 manifolds. The fluorescence into each pair of Franck-Condon active ring modes shows an asymmetry that suggests incorrectly that the S1 and S2 states may be electronically localized. From rotationally resolved studies, the S0 and S1 states have been well-fit to asymmetric rotor Hamiltonians while the S2 state is perturbed and not fit. The transition dipole moment (TDM) orientation of the S1 state is nearly perpendicular to the C2 symmetry axes with 66(2)%:3(1)%:34(2)% a:b:c hybrid-type character while that of the S2 origin contains 50(10)% a:c-type (S1) and 50(10)% b-type (S2) character. A model is put forward that explains qualitatively the TDM compositions and dispersed emission patterns without the need to invoke electronic localization. The experimental data discussed here serve as a foundation for a multi-mode vibronic coupling model capable of being applied to asymmetric bichromophores, as presented in the work of B. Nebgen and L. V. Slipchenko ["Vibronic coupling in asymmetric bichromophores: Theory and application to diphenylmethane-d5," J. Chem. Phys. (submitted)].

Electronic and vibronic properties of a discotic liquid-crystal and its charge transfer complex

Discotic liquid crystalline (DLC) charge transfer (CT) complexes combine visible light absorption and rapid charge transfer characteristics, being favorable properties for photovoltaic (PV) applications. We present a detailed study of the electronic and vibrational properties of the prototypic 1:1 mixture of discotic 2,3,6,7,10,11-hexakishexyloxytriphenylene (HAT6) and 2,4,7-trinitro-9-fluorenone (TNF). It is shown that intermolecular charge transfer occurs in the ground state of the complex: a charge delocalization of about 10(-2) electron from the HAT6 core to TNF is deduced from both Raman and our previous NMR measurements [L. A. Haverkate, M. Zbiri, M. R. Johnson, B. Deme, H. J. M. de Groot, F. Lefeber, A. Kotlewski, S. J. Picken, F. M. Mulder, and G. J. Kearley, J. Phys. Chem. B 116, 13098 (2012)], implying the presence of permanent dipoles at the donor-acceptor interface. A combined analysis of density functional theory calculations, resonant Raman and UV-VIS absorption measurements indicate that fast relaxation occurs in the UV region due to intramolecular vibronic coupling of HAT6 quinoidal modes with lower lying electronic states. Relatively slower relaxation in the visible region the excited CT-band of the complex is also indicated, which likely involves motions of the TNF nitro groups. The fast quinoidal relaxation process in the hot UV band of HAT6 relates to pseudo-Jahn-Teller interactions in a single benzene unit, suggesting that the underlying vibronic coupling mechanism can be generic for polyaromatic hydrocarbons. Both the presence of ground state CT dipoles and relatively slow relaxation processes in the excited CT band can be relevant concerning the design of DLC based organic PV systems.