Vibronic Coupling Effects Research Articles

Electronic Absorption and Circular Dichroism Spectra of One-Dimensional Bay-Substituted Chiral PDIs: Effects of Intermolecular Interactions, Vibronic Coupling, and Aggregate Size

Electronic Absorption and Circular Dichroism Spectra of One-Dimensional Bay-Substituted Chiral PDIs: Effects of Intermolecular Interactions, Vibronic Coupling, and Aggregate Size

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.

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.

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 %).

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

AbstractWe 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 %).

Inspecting molecular aggregate quadratic vibronic coupling effects using squeezed coherent states.

We present a systematic comparison of three quantum mechanical approaches describing excitation dynamics in molecular complexes using the time-dependent variational principle (TDVP) with increasing sophistication trial wavefunctions (ansatze): Davydov D2, squeezed D2 (sqD2) and a numerically exact multiple D2 (mD2) ansatz in order to characterize validity of the sqD2 ansatz. Numerical simulations of molecular aggregate absorption and fluorescence spectra with intra- and intermolecular vibrational modes, including quadratic electronic-vibrational (vibronic) coupling term, which is due to vibrational frequency shift upon pigment excitation are presented. Simulated absorption and fluorescence spectra of a J type molecular dimer with high frequency intramolecular vibrational modes obtained with D2 and sqD2 ansatze match the spectra of mD2 ansatz only in the single pigment model without quadratic vibronic coupling. In general, the use of mD2 ansatz is required to model an accurate dimer and larger aggregate's spectra. For a J dimer aggregate coupled to a low frequency intermolecular phonon bath, absorption and fluorescence spectra are qualitatively similar using all three ansatze. The quadratic vibronic coupling term in both absorption and fluorescence spectra manifests itself as a lineshape peak amplitude redistribution, static frequency shift and an additional shift, which is temperature dependent. Overall the squeezed D2 model does not result in a considerable improvement of the simulation results compared to the simplest Davydov D2 approach.

Electronic Substitution Effect on the Ground and Excited State Properties of Indole Chromophore: A Computational Study.

Indole, being the main chromophore of amino acid tryptophan and several other biologically relevant molecules like serotonin, melatonin, has prompted considerable theoretical and experimental interest. The current work focuses on the investigation of substitution effect on the ground and excited electronic states of indole using computational quantum chemistry. Having three close-lying excited electronic states, the vibronic coupling effect becomes extremely important yet challenging for the photophysics and photochemistry of indole. Here, we have evaluated the performance of time-dependent density functional theory against available experimental and ab initio results from the literature. The electronic effects on the excited states of indole and indole derivatives e. g. tryptophan, serotonin and melatonin are reported. A bathochromic shift has been observed in the absorption spectrum for the La state. The absorption wavelength increases in the order of indole<tryptophan <serotonin <melatonin. While the contribution of the in-plane small adjacent groups increases the electron density of the indole ring, the out-of-plane long substituent groups have minor effect. The absorption spectra calculated including the vibronic coupling are in good agreement with experiments. These results can be used to estimate the error in photophysical observables of indole derivatives calculated considering indole as a prototypical system.

Illuminating Ligand Field Contributions to Molecular Qubit Spin Relaxation via T1 Anisotropy.

Electron spin relaxation in paramagnetic transition metal complexes constitutes a key limitation on the growth of molecular quantum information science. However, there exist very few experimental observables for probing spin relaxation mechanisms, leading to a proliferation of inconsistent theoretical models. Here we demonstrate that spin relaxation anisotropy in pulsed electron paramagnetic resonance is a powerful spectroscopic probe for molecular spin dynamics across a library of highly coherent Cu(II) and V(IV) complexes. Neither the static spin Hamiltonian anisotropy nor contemporary computational models of spin relaxation are able to account for the experimental T1 anisotropy. Through analysis of the spin-orbit coupled wave functions, we derive an analytical theory for the T1 anisotropy that accurately reproduces the average experimental anisotropy of 2.5. Furthermore, compound-by-compound deviations from the average anisotropy provide a promising approach for observing specific ligand field and vibronic excited state coupling effects on spin relaxation. Finally, we present a simple density functional theory workflow for computationally predicting T1 anisotropy. Analysis of spin relaxation anisotropy leads to deeper fundamental understanding of spin-phonon coupling and relaxation mechanisms, promising to complement temperature-dependent relaxation rates as a key metric for understanding molecular spin qubits.

Multi-state and Multi-mode Vibronic Coupling Effects in the Photoionization Spectroscopy of Acetaldehyde.

Multi-state and multi-mode vibronic dynamics in the seven energetically low-lying (, , , , , , and ) electronic states of the acetaldehyde radical cation is theoretically studied in this article. Adiabatic energies of these electronic states are calculated by ab initio quantum chemistry methods. A vibronic coupling model of seven electronic states is constructed in a diabatic electronic basis to carry out the first-principles nuclear dynamics study. The vibronic spectrum is calculated and compared with the experimental findings reported in the literature. The progressions of vibrational modes found in the spectrum are assigned. The findings reveal that the and electronic states are energetically well-separated from the other electronic states and the remaining states ( to ) are energetically very close or even quasi-degenerate at the equilibrium geometry of the reference electronic ground state of acetaldehyde. The energetic proximity of to electronic states results in multiple multi-state conical intersections. The impact of electronic nonadiabatic interactions due to conical intersections on the vibronic structure of the photoionization band and nonradiative internal conversion dynamics is discussed.

Vibronic fine structure in the nitrogen 1s photoelectron spectra of molecules from Franck-Condon simulations: Azines

Vibronic coupling plays a pivotal role in molecular spectroscopy. We present a theoretical study on vibrationally resolved x-ray photoelectron spectra (XPS) of seven azines (${\mathrm{C}}_{x}{\mathrm{H}}_{y}{\mathrm{N}}_{z}$; pyridine, three diazines, two triazines, and one tetrazine) at the nitrogen $1s$ edge, to explore the vibronic coupling effects as influenced by consecutive replacement of the CH group with a N atom. Franck-Condon simulations were performed with the Duschinsky rotation effect included, where the electronic structure was calculated by the density functional theory. Validations on pyrimidine show good agreement with the experiment, weak functional dependence, and weak mode mixing effect. We observed an evident blue shift in binding energies with the increasing number of N atoms in this series, together with molecule-dependent vibronic fine structures. These molecules have either ${\mathrm{C}}_{\text{2v}}$ or ${\mathrm{C}}_{\text{s}}$ molecular symmetry at the optimized core-ionized geometries. Franck-Condon-active vibrational modes were identified to be low frequency (500--1650 ${\mathrm{cm}}^{\ensuremath{-}1}$), totally symmetric (${A}_{1}$ or ${A}^{\ensuremath{'}}$), in-plane ring deformation modes. Core ionization on ${\mathrm{N}}^{*}$ always leads to elongation of the ${\mathrm{N}}^{*}\ensuremath{-}\mathrm{N}$ bond length, accompanied by an increase of the $\ensuremath{\angle}\mathrm{C}\ensuremath{-}{\mathrm{N}}^{*}\ensuremath{-}X$ bond angle ($X=\mathrm{C}$, N). Our study predicts accurate theoretical reference spectra for the azine family and provides useful information on the properties of the core-ionized states as influenced by the structural change of $\mathrm{CH}\ensuremath{\leftrightarrow}\mathrm{N}$ replacement.

Vibrationally-Resolved X-ray Photoelectron Spectra of Six Polycyclic Aromatic Hydrocarbons from First-Principles Simulations.

Vibrationally resolved C 1s X-ray photoelectron spectra (XPS) of a series of six polycyclic aromatic hydrocarbons (PAHs; phenanthrene, coronene, naphthalene, anthracene, tetracene, and pentacene) were computed by combining the full core hole density functional theory and the Franck-Condon simulations with the inclusion of the Duschinsky rotation effect. Simulated spectra of phenanthrene, coronene, and naphthalene agree well with experiments both in core binding energies (BEs) and profiles, which validate the accuracy of our predictions for the rest molecules with no high-resolution experiments. We found that three types of carbons i (inner C), p (peripheral C bonded to three C atoms), and h (peripheral C bonded to an H atom) show decreasing BEs. In linear PAHs (the latter four), h-type carbons further split into h1 or h2 (on inner or edge benzene ring) subtypes with chemical shifts of ca. 0.2-0.4 eV. All major Franck-Condon-active modes are characterized to be in-plane vibrations: low-frequency (<800 cm-1) C-C ring deformation modes play an essential role in determining the peak asymmetries; and for each h-type carbon a high-frequency (ca. 3600 cm-1) C*-H stretching mode is responsible for the high-energy tail. We found that core ionization leads to reduction of all C*-C and C*-H bond lengths and ring deformation with a definite direction. Based on theoretical spectra of four linear PAHs, we found asymptotic relations and anticipated possible spectral features for even larger linear PAHs. Our calculations provide accurate reference spectra for XPS characterizations of PAHs, which are useful in understanding the vibronic coupling effects in this family.

Revealing the vibronic coupling effects in the size-dependent optical properties of cycloparaphenylene dications

We explain the visible and near-infrared optical properties of low-lying singlet excited states (S and S) of [5]-, [7]- and [9]cycloparaphenylene dications (CPPs). A narrow energy gap (<150 cm) separates these states at the Franck–Condon point of the individual molecule. The energy gap increases upon increasing the molecular size. Consequently, [5]CPP possesses highly overlapping S and S absorption bands. The overlap between these bands decreases and the resulting composite spectrum appears broader, particularly for [9]CPP. Theoretical spectra generated using quantum wavepacket calculations within the linear vibronic coupling approach match well with the experiment. Our findings reveal near-degenerate S and S minima, highlighting the relevance of both these states while assigning experimental fluorescence emission properties of CPPs.

Vibronic Coupling of Adjacent Single-Atom Co and Zn Sites for Bifunctional Electrocatalysis of Oxygen Reduction and Evolution Reactions.

With the goal of improving the activity of single-atom catalysts, in-depth investigations were performed to design adjacent single-metal sites to produce a modulation effect by using symmetry breaking as an indicator of tuning the electronic structure. A CoN4-ZnN4/C catalyst composed of adjacent Co and Zn sites anchored on nitrogen-doped graphene was predicted by first-principle calculations to exhibit promising bifunctional electrocatalytic activity for oxygen reduction and evolution reactions with an overpotential of 0.225 and 0.264 V, respectively, which is superior to CoN4/C catalysts and outperforms commercial Pt/C and IrO2 benchmarks. The impressive catalytic activity originates from the remarkable asymmetric deformation and strong pseudo-Jahn-Teller vibronic coupling effect, through which the Zn site acts as a modulator to induce the symmetry-breaking phenomenon and tune the d-band structure and binding strength between key intermediates and the Co site. It provides mechanism-based insight for applying diatomic site catalysts for catalytic reactions and further understanding of the modulation effect.

Vibronic Coupling Effect on the Vibrationally Resolved Electronic Spectra and Intersystem Crossing Rates of a TADF Emitter: 7-PhQAD.

Assessing and improving the performance of organic light-emitting diode (OLED) materials require quantitative prediction of rate coefficients for the intersystem crossing (ISC) and reverse ISC (RISC) processes, which are determined not only by the energy gap and the direct spin-orbit coupling (SOC) between the first singlet and triplet excited-states at a thermal equilibrium position of the initial electronic state but also by the non-Condon effects such as the Herzberg-Teller-like vibronic coupling (HTVC) and the spin-vibronic coupling (SVC). Here we apply the time-dependent correlation function approaches to quantitatively calculate the vibrationally resolved absorption and fluorescence spectra and ISC/RISC rates of a newly synthesized multiple-resonance-type (MR-type) thermally activated delayed fluorescence (TADF) emitter, 7-phenylquinolino[3,2,1-de]acridine-5,9-dione (7-PhQAD), with the inclusion of the Franck-Condon (FC), HTVC, and Duschinsky rotation (DR) effects. The SVC effect on the rates has also been approximately evaluated. We find that the experimentally measured ISC rates of 7-PhQAD originate predominantly from the vibronic coupling, consistent with the previous reports on other MR-type TADF emitters. The SVC effect on ISC rates is about 10 times larger than the HTVC effect, and the latter increases the ISC rates by more than 1 order of magnitude while it slightly affects the vibrationally resolved absorption and fluorescence spectra. The discrepancy between the theoretical and experimental results is attributed to inaccurately describing excited-states calculated by the time-dependent density functional theory as well as to not fully accounting for the complex experimental conditions. This work provides a demonstration of what proportion of ISC and RISC rate coefficients of a MR-type TADF emitter can be covered by the HTVC effect, and it opens design routes that go beyond the FC approximation for the future development of high-performance OLED devices.

Suppression of Eu2+ Luminescence Loss

AbstractOwing to the intriguing luminescence properties, Eu2+ is one of the most desirable activators for next‐generation lighting devices. Yet the application of Eu2+‐doped phosphors is limited because of the drawback of inferior luminescence efficiency. Understanding of this issue is generally from perspectives of frame structural rigidity and electronic band structure, while the lack of persuasiveness of this paradigm is frequently noticed. Herein, the analysis is conducted from a fresh view to investigate the outstanding luminescence properties of Eu2+‐doped SrMgP2O7 owning the narrow‐band emission and near‐unity quantum yield. The structural rigidity of materials is elaborately evaluated, and the influence of ionization on the luminescence efficiency of material is carefully discussed. Efforts are also made to assess the effect of vibronic coupling on 4f−5d transition of Eu2+ and clarify the excitation energy transfer route by using X‐ray spectroscopy. Based on these discussions, the synergy of weak electron−vibration interaction and inactive ionization causes the suppression of Eu2+ luminescence loss, which is associated with highly rigid local coordination and strong binding of Eu2+ to its valence electrons in the system, respectively. This work provides insight into the luminescence mechanism of Eu2+, which benefits the exploration of novel phosphors with superior luminescence features.

Dynamical Jahn-Teller effects on the generation of electronic ring currents by circularly polarized light

The generation of electronic ring currents in ring-shaped molecules by photo-excitation with circularly polarized laser light is considered in the presence of vibronic coupling effects. $(E\times e)$ Jahn-Teller distortions, unavoidable by symmetry in the $(E)$ subset of electronic states supporting the ring current, mix the clockwise and anti-clockwise circulation directions of the electrons and can suppress the maximum achievable current by at least one order of magnitude, already for moderate vibronic coupling strengths, as compared to the Born-Oppenheimer limit of fixed atomic positions. The circulation direction of the electrons is found to depend on the spectral region of the $(E\times e)$ Hamiltonian. This fact results in the surprising effect that the same polarization direction of the laser pulse can trigger either clockwise or anti-clockwise electronic dynamics depending on the wavelength of the photons. These findings are illustrated in a model of the triazine molecule.

Quantum vibronic effects on the electronic properties of solid and molecular carbon

We study the effect of quantum vibronic coupling on the electronic properties of carbon allotropes, including molecules and solids, by combining path integral first principles molecular dynamics (FPMD) with a colored noise thermostat. In addition to avoiding several approximations commonly adopted in calculations of electron-phonon coupling, our approach only adds a moderate computational cost to FPMD simulations and hence it is applicable to large supercells, such as those required to describe amorphous solids. We predict the effect of electron-phonon coupling on the fundamental gap of amorphous carbon, and we show that in diamond the zero-phonon renormalization of the band gap is larger than previously reported.

Excited state distribution function for probing Herzberg–Teller vibronic coupling using linear optical response theory: Application to glassy pheophytin a

The goal of the present work is to develop an excited-state distribution function that can be used to calculate electronic transition dipole moment time correlation functions at a considerably low computational cost. An additional merit of the distribution function is its capability to probe the Hertzberg-Teller vibronic coupling effect in terms of the previously reported Condon correlation functions in the literature without having to start from the equilibrium density operator to probe spectral non-Condon effects, thereby exploring Hertzberg-Teller vibronic coupling by building on the Condon regime. It is easily extendable to anharmonic systems. Model calculations are reported to show the high degree of accuracy and computational efficiency of the presented approach. Application to a photosynthetic system such as pheophytin a in triethylamine is provided.

Benzene, Toluene, and Monosubstituted Derivatives: Diabatic Nature of the Oscillator Strengths of S1 ← S0 Transitions.

For benzene, toluene, aniline, fluorobenzene, and phenol, even sophisticated treatments of electron correlation, such as MRCI and XMS-CASPT2 calculations, show oscillator strengths typically lower than experiment. Inclusion of a simple pseudo-diabatization approach to perturb the S1 state with approximate vibronic coupling to the S2 state for each molecule results in more accurate oscillator strengths. Their absolute values agree better with experiment for all molecules except aniline. When the coupling between the S1 and S2 states is strong at the S0 geometry, the simple diabatization scheme performs less well with respect to the oscillator strengths relative to the adiabatic values. However, we expect the scheme to be useful in many cases where the coupling is weak to moderate (where the maximum component of the coupling has a magnitude less than 1.5 au). Such calculations give an insight into the effects of vibronic coupling of excited states on UV/vis spectra.

Molecular conformation dependence of phosphorescence lifetime in organic aggregates

Organic bulk crystal with room-temperature phosphorescence (RTP) is normally fabricated into nanoparticles (NPs) for biological applications, accompanying with inevitable change in RTP lifetime and molecular conformation. By using molecular dynamics and quantum chemistry methods, the difluoroboron β-diketonate (BF2bdk) compound (Br-NpCzBF2) was explored to uncover the molecular conformation-dependent RTP from crystal to NPs. We proposed that from crystal to amorphous aggregates, the distorted BF2bdk group caused by the weakened intermolecular B–F⋯H–C hydrogen bonds convert the T1 from hybridized local and charge transfer to locally excited states. Such change strengthens the vibronic coupling effect on the CC stretching vibration, and enormously accelerates the nonradiative decay rate of T1→S0 by 1–2 orders of magnitude. Consequently, the RTP lifetime is shortened from 566 μs in crystal to about 10 μs in amorphous aggregates, which is consistent with the experiments. This work provides new insight into the RTP mechanism and opens a novel design avenue for designing organic RTP materials in biological fields.