Herzberg-Teller Effects Research Articles

Electron Spin Dynamics of the Intersystem Crossing in Aminoanthraquinone Derivatives: The Spectral Telltale of Short Triplet Excited States.

We studied the excited state dynamics of two bis-amino substituted anthraquinone (AQ) derivatives, with absorption in the visible spectral region, which results from the attachment of a electron-donating group to the electron-deficient AQ chromophore. Femtosecond transient absorption spectra show that intersystem crossing (ISC) takes place in 190-320 ps, and nanosecond transient absorption spectra demonstrated an unusually short triplet state lifetime (2.06-5.43 μs) for the two AQ derivatives. Pulsed laser-excited time-resolved electron paramagnetic resonance (TREPR) spectra show an inversion of the electron spin polarization (ESP) phase pattern of the triplet state at a longer delay time after laser flash. Spectral simulations show faster decay of the Ty sublevel than the other two sublevels (τx = 15.0 μs, τy = 1.50 μs, τz = 15.0 μs); theoretical computation predicts initial overpopulation of the Ty sublevel, and rationalizes the short T1 state lifetime and the ESP inversion. Theoretical computations taking into account the electron-vibrational coupling, i.e., the Herzberg-Teller effect, successfully rationalize the TREPR experimental observations.

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.

Deciphering the doublet luminescence mechanism in neutral organic radicals: spin-exchange coupling, reversed-quartet mechanism, excited-state dynamics.

Neutral organic radical molecules have recently attracted considerable attention as promising luminescent and quantum-information materials. However, the presence of a radical often shortens their excited-state lifetime and results in fluorescence quenching due to enhanced intersystem crossing (EISC). Recently, an experimental report introduced an efficient luminescent radical molecule, tris(2,4,6-trichlorophenyl)methyl-carbazole-anthracene (TTM-1Cz-An). In this study, we systematically performed quantum theoretical calculations combined with the path integral approach to quantitatively calculate the excited-state dynamics processes and spectral characteristics. Our theoretical findings suggest that the sing-doublet D1 state, originating from the anthracene excited singlet state, is quickly converted to the doublet (trip-doublet) state via EISC, facilitated by a significant nonequivalence exchange interaction, with ΔJ ST = 0.174 cm-1. The formation of the quartet state (Q1, trip-quartet) was predominantly dependent on the exchange coupling 3/2J TR = 0.086 cm-1 between the triplet spin electrons of anthracene and the TTM-1Cz radical. Direct spin-orbit coupling ISC to the Q1 state was minimal due to the nearly identical spatial wavefunctions of the and Q1 levels. The effective occurrence of reverse intersystem crossing (RISC) from the Q1 to D1 state is a critical step in controlling the luminescence of TTM-1Cz-An. The calculated RISC rate k RISC, including the Herzberg-Teller effect, was 3.64 × 105 s-1 at 298 K, significantly exceeding the phosphorescence and nonradiative rates of the Q1 state, thus enabling the D1 repopulation. Subsequently, a strong electronic coupling of 37.4 meV was observed between the D1 and D2 states, along with a dense manifold of doublet states near the D1 state energy, resulting in a larger reverse internal conversion rate k RIC of 9.26 × 1010 s-1. Distributed to the D2 state, the obtained emission rate of k f = 2.98-3.18 × 107 s-1 was in quite good agreement with the experimental value of 1.28 × 107 s-1, and its temperature effect was not remarkable. Our study not only provides strong support for the experimental findings but also offers valuable insights for the molecular design of high-efficiency radical emitters.

The anisotropic nature of singlet fission in single crystalline organic semiconductors

The escalating global energy predicament implores for a revolutionary resolution—one that converts sunlight into electricity—holding the key to supreme conversion efficiency. This comprehensive review embarks on the exploration of the principle of generating multiple excitons per absorbed photon, a captivating concept that possesses the potential to redefine the fundamental confines of conversion efficiency, albeit its application remains limited in photovoltaic devices. At the nucleus of this phenomenon are two principal processes: multiple exciton generation (MEG) within quantum-confined environments, and singlet fission (SF) inside molecular crystals. The process of SF, characterized by the cleavage of a single photogenerated singlet exciton into two triplet excitons, holds promise to potentially amplify photon-to-electron conversion efficiency twofold, thereby laying the groundwork to challenge the detailed balance limit of solar cell efficiency. Our discourse primarily dissects the complex nature of SF in crystalline organic semiconductors, laying special emphasis on the anisotropic behavior of SF and the diffusion of the subsequent triplet excitons in single-crystalline polyacene organic semiconductors. We initiate this journey of discovery by elucidating the principles of MEG and SF, tracing their historical genesis, and scrutinizing the anisotropy of SF and the impact of quantum decoherence within the purview of functional mode electron transfer theory. We present an overview of prominent techniques deployed in investigating anisotropic SF in organic semiconductors, including femtosecond transient absorption microscopy and imaging as well as stimulated Raman scattering microscopies, and highlight recent breakthroughs linked with the anisotropic dimensions of Davydov splitting, Herzberg–Teller effects, SF, and triplet transport operations in single-crystalline polyacenes. Through this comprehensive analysis, our objective is to interweave the fundamental principles of anisotropic SF and triplet transport with the current frontiers of scientific discovery, providing inspiration and facilitating future ventures to harness the anisotropic attributes of organic semiconductor crystals in the design of pioneering photovoltaic and photonic devices.

Combination of resonance and non-resonance chiral Raman scattering in a cobalt(III) complex.

Resonance Raman optical activity (RROA) spectra with high sensitivity reveal details on molecular structure, chirality, and excited electronic properties. Despite the difficulty of the measurements, the recorded data for the Co(III) complex with S,S-N,N-ethylenediaminedisuccinic acid are of exceptional quality and, coupled with the theory, spectacularly document the molecular behavior in resonance. This includes a huge enhancement of the chiral scattering, contribution of the antisymmetric polarizabilities to the signal, and the Herzberg-Teller effect significantly shaping the spectra. The chiral component is by about one order of magnitude bigger than for an analogous aluminum complex. The band assignment and intensity profile were confirmed by simulations based on density functional and vibronic theories. The resonance was attributed to the S0®S3 transition, with the strongest signal enhancement of Raman and ROA spectral bands below about 800 cm-1. For higher wavenumbers, other excited electronic states contribute to the scattering in a less resonant way. RROA spectroscopy thus appears as a unique tool to study the structure and electronic states of absorbing molecules in analytical chemistry, biology, and material science.

Vibrationally resolved two-photon electronic spectra including vibrational pre-excitation: Theory and application to VIPER spectroscopy with two-photon excitation.

Following up on our previous work on vibrationally resolved electronic absorption spectra including the effect of vibrational pre-excitation [von Cosel et al., J. Chem. Phys. 147, 164116 (2017)], we present a combined theoretical and experimental study of two-photon-induced vibronic transitions in polyatomic molecules that are probed in the VIbrationally Promoted Electronic Resonance experiment using two-photon excitation (2P-VIPER). In order to compute vibronic spectra, we employ time-independent and time-dependent methods based on the evaluation of Franck-Condon overlap integrals and Fourier transformations of time-domain correlation functions, respectively. The time-independent approach uses a generalized version of the FCclasses method, while the time-dependent approach relies on the analytical evaluation of Gaussian moments within the harmonic approximation, including Duschinsky rotation effects. For the Coumarin 6 dye, two-dimensional 2P-VIPER experiments involving excitation to the lowest-lying singlet excited state (S1) are presented and compared with corresponding one-photon VIPER spectra. In both cases, coumarin ring modes and a CO stretch mode show VIPER activity, albeit with different relative intensities. Selective pre-excitation of these modes leads to a pronounced redshift of the low-frequency edge of the electronic absorption spectrum, which is a prerequisite for the VIPER experiment. Theoretical analysis underscores the role of interference between Franck-Condon and Herzberg-Teller effects in the two-photon experiment, which is at the root of the observed intensity distribution.

Internal conversion rate constant calculations considering Duschinsky, anharmonic and Herzberg-Teller effects.

A novel method for calculating rate constants for internal conversion (kIC) that simultaneously accounts for Duschinsky, anharmonic and Herzberg-Teller effects has been developed and implemented. This method has been applied to robust planar molecules like tetraoxa[8]circulene (4B), free-base porphyrin (H2P) and pyrometene (PM567) with small Duschinsky rotation (i.e. with almost identical normal coordinates in the ground and excited states) and to poly[n]fluorenes (P[n]F) (n = 2-14) with a substantial Duschinsky rotation. The obtained results show that the Duschinsky effect is large in the harmonic approximation, whereas it is in general much smaller in the anharmonic approximation. The Duschinsky effect is found to be large for high frequency vibrational modes with energies of ∼3300 cm-1 such as the X-H (X = C, N and O) stretching modes that mix in the S1 → S0 electronic transition. However, even in this case, the increase in kIC due to the Duschinsky effect does not exceed one order of magnitude. The calculations show that anharmonic contributions to kIC are larger than Herzberg-Teller contributions which in turn are larger than contributions from the Duschinsky effect ANH > HT > Du. We also show that an approximation, where only X-H bonds are considered in the kIC calculation, is accurate even for P[n]F (n = 2-14).

Vibronic Emission Spectra of Dithiophene and Terthiophene and Their Complexes with H2S and (H2S)2

In this work, the vibronic emission spectra of dithiophene (T2) and terthiophene (T3) molecules and their complexes with hydrogen sulfide and its dimmer were calculated at the TD-DFT / CAM-B3LYP / 6-31G(d) theory level. The solvent was taken into account within the PCM model. Vibronic spectra were calculated considering both the Herzberg-Teller and Duschinsky effects. Good agreement between the computed and experimental spectra was obtained. The vibration promoting modes forming vibronic progressions were found. Vibronic bands for bithiophene and terthiophene were formed by their low-frequency modes (≤370 cm–1), combinations of low-frequency modes with high-frequency modes (1497 and 1672 cm–1 for T2 and 1516 and 1573 cm–1 for T3), and with their composite high-frequency modes. The intensities of vibronic lines for the emission spectra of T2∙∙∙H2S, T3∙∙∙H2S and T2∙∙∙(H2S)2, T3∙∙∙(H2S)2 complexes were shown to decrease 3.7, 2.6 and 5.5, 3.6 times compared to T2 and T3, respectively. The bathochromic shifts of the vibronic bands of dithiophene and terthiophene complexes with H2S and (H2S)2 did not exceed 130 cm–1 for all bands.

The dominant nature of Herzberg–Teller terms in the photophysical description of naphthalene compared to anthracene and tetracene

The first order and second order corrected photoluminescence quantum yields are computed and compared to experiment for naphthalene in this manuscript discussing negative results. Results for anthracene and tetracene are recalled from previous work (Manian et al. in J Chem Phys 155:054108, 2021), and the results for all three polyacenes are juxtaposed to each other. While at the Franck–Condon point, each of the three noted polyacenes were found to possess a quantum yield near unity. Following the consideration of Herzberg–Teller effects, quantum yields stabilised for anthracene and tetracene to 0.19 and 0.08, respectively. Conversely, the second order corrected quantum yield for naphthalene was found to be 0.91. Analysis of this result showed that while the predicted non-radiative pathways correlate well with what should be expected, the approximation used to calculate second order corrected fluorescence, which yielded very positive results for many other molecular systems, here is unable to account for strong second order contributions, resulting in a grossly overestimated rate of fluorescence. However, substitution of an experimental radiative rate results in a quantum yield of 0.33. This work extols the importance of Herzberg–Teller terms in photophysical descriptions of chromophores, and highlights those cases in which a treatment beyond the above approximation is required.

Franck-Condon spectra of unbound and imaginary-frequency vibrations via correlation functions: A branch-cut free, numerically stable derivation.

Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both real and imaginary harmonic frequencies. The derivation rests on Lie algebra techniques that map otherwise complicated exponential operator arithmetic to simpler matrix formulas. The expressions for the zero- and finite-temperature harmonic auto-correlation functions have been carefully structured both to be free of branch-cut discontinuities and to remain numerically stable with finite-precision arithmetic. Simple extensions correct the harmonic Franck-Condon approximation for the lowest-order anharmonic and Herzberg-Teller effects. Quantitative simulations are shown for several examples, including the electronic absorption spectra of F2, HOCl, CH2NH, and NO2.

Intrinsic Analysis of Thermally Activated Delayed Fluorescence (TADF) for Ag(I) Complex Based on the Path Integral Approach: Origin of the Effective Spin-Flipping Channel and Vibrational Spin-Orbit Coupling Effect.

In order to design new Ag(I)-based materials for thermally activated delayed fluorescence (TADF), it is vital to develop a detailed understanding of the current best performing materials. The quantitative predictions of the photophysical processes of the Ag(dmp)(P2-nCB) TADF complex are calculated using time-dependent density functional theory (TD-DFT) combined with the path integral approach for dynamics including the Herzberg-Teller effects. All calculated results are in good agreement with the experimentally available data, demonstrating the validity of our applied theoretical approach. Analysis of ETS-NOCV (extended transition state natural orbital for chemical valence) shows that there is a weak bond interaction dominated by electrostatic interactions and accompanied by some covalent components between Ag(I) and dmp ligands due to the introduction of the strongly electron-donating negatively charged P2-nCB ligand, thus giving a small energy separation between the lowest singlet S1 and triplet T1 states of ΔE(S1 - T1) ≈ 532 cm-1. The SOC strongly depends on the geometrical alteration caused by the molecular "promotion" vibrations. Our study has revealed that a few "promotion" vibrational modes, that is, ω46 and ω227, effectively induce the strong SOC between S1 and T1 and speed up the reverse intersystem crossing (RISC) process dramatically. The computed kRISC value is 1.19 × 107 s-1 for the solid phase at 300 K, which are about 5 orders of magnitude larger than the mean phosphorescence rate, kP = 9.56 × 102 s-1, and it is also far larger than ISC k0ISC = 7.84 × 102 s-1 rates from T1 to S0. The S1 state thus can be an efficient thermal repopulation from the T1 state by the RISC pathway. Finally, we also note that the diabatic vibration coupling triplet pair T1/T2 will also be important for efficient and practical RISC. Our investigation will be of great utility toward designing and improving the Ag(I)-based TADF complexes.

Doubly Resonant Sum-Frequency Vibrational Spectroscopy of 1,1'-Bi-2-naphthol Chiral Solutions Due to the Nonadiabatic Effect.

Second-order nonlinear spectroscopy is a powerful tool in exploring significant physical and chemical characteristics at various interfaces and on chiral systems. We present a method of computing the nonadiabatic couplings between the different excited electronic states with time-dependent density functional theory and then study doubly resonant sum-frequency vibrational spectroscopy (SFVS) of chiral solutions due to the nonadiabatic, Franck-Condon, and Herzberg-Teller (HT) effects. The calculations for R-1,1'-bi-2-naphthol show that the theoretical spectra agree with experiment, and the nonadiabatic corrections are comparable with the HT terms or even larger for some vibrational modes, which is different from the mechanism of SFVS off electronic resonance. Doubly resonant SFVS may be a useful method of studying the nonradiative transition and nonadiabatic effect between the excited electronic states.

Sum-over-state expressions including second-order Herzberg-Teller effects for the calculation of absorption and resonance Raman intensities.

The sum-over-state expressions are derived to calculate the second-order Herzberg-Teller (HT) effects in absorption and resonance Raman spectroscopies. These effects depend on the second derivatives of the transition dipole moment with respect to the vibrational coordinates. The method is applied to the molecule of 1,3-butadiene using density functional theory calculations. It is found that the second-order HT effects are significant for both absorption and resonance Raman intensities, and that the calculated spectra are in good agreement with the experimental data. The second-order HT effects originate from diagonal elements of the second derivatives matrix, whereas non-diagonal elements have a negligible impact on the intensities of 1,3-butadiene.

Symmetry-Breaking Enhanced Herzberg-Teller Effect with Brominated Polyacenes.

Molecular symmetry is vital to the selection rule of vibrationally resolved electronic transition, particularly when the nuclear dependence of electronic wave function is explicitly treated by including Franck-Condon (FC) factor, Franck-Condon/Herzberg-Teller (FC/HT) interference, and Herzberg-Teller (HT) coupling. Our present study investigated the light absorption spectra of highly symmetric tetracene, pentacene, and hexacene molecules of point-group D2h, as well as their monobrominated derivatives with a lower Cs symmetry. It was found that the symmetry-breaking monobromination allows more vibrational normal modes and their pairs to contribute to FC/HT interference and HT coupling, respectively. Through a projection of a molecule's vibrational normal modes to its irreducible representations, a linear relationship between the FC/HT intensity to the polyacene's size was deduced alongside a quadratic dependence of the HT intensity. Both theoretically derived correlations were well justified by our numerical simulations, which also demonstrated an approximately 20% improvement on the agreement with experimental line shape if the HT theory is adopted to replace the FC approximation. Moreover, for these low-symmetry monobrominated polyacenes, the FC intensity was even weaker than its FC/HT and HT counterparts at some excitation energies, making the HT theory imperative to decipher vibronic coupling, a fundamental driving force behind numerous chemical, biological, and photophysical processes.

The spectral-shapes of absorption, emission, ECD and CPL of a fluorene-fused [7]helicene: Vibronic effect and solvent inhomogenous broadening

We compute the line shapes of absorption (ABS), emission (EMI), electronic circular dichroism (ECD), and circularly polarized luminescence (CPL) of a fluorene-fused [7]helicene. To elucidate different physico-chemical factors responsible for the spectral shapes, we account for Franck-Condon (FC) contribution, Herzberg-Teller (HT) effect and Duschinsky rotation, as well as the solvent inhomogenous broadening. The latter is connected to the solvent reorganization energy which is calculated with the state-specific (SS) implementation of Polarizable Continuum Model (PCM). To understand the relative importance of different effects of equilibrium geometry displacements, frequencies changes, and Duschinsky mixing, we carefully compare and discuss the results of Adiabatic Hessian (AH), Adiabatic Shift and Frequencies (ASF), and Adiabatic Shift (AS) models in details. Our results agree with the experimental spectra very well. They show that FC contribution dominates the spectral shapes and HT effect leads to the break of mirror images between absorptive (ABS + ECD) and emissive (EMI + CPL) spectra.

Herzberg-Teller Effect on the Vibrationally Resolved Absorption Spectra of Single-Crystalline Pentacene at Finite Temperatures.

The line shape of an electronic spectrum conveys the coupling between electronic and vibrational degrees of freedom. In the present study, the light absorption spectra of single-crystalline pentacene were measured by polarized UV-vis microscopy at 77, 185, and 293 K. The vibronic coupling encoded in each spectrum was resolved by the Herzberg-Teller theory that considers the contributions from the Franck-Condon (FC) factor, Franck-Condo/Herzberg-Teller (FC/HT) interference, and Herzberg-Teller (HT) coupling. Specifically, excitation energies, electronic transition dipole moments, and their nuclear gradients were evaluated by the GW method to ensure numerical accuracy, while the computationally efficient density function theory was employed to determine the optimized structures and vibrational normal modes. For every pair of electronic transition and normal mode that gives rise to a strong vibronic transition intensity, we examined their spatial characteristics by projecting them onto the three crystal axes. It was found that all normal modes strongly coupled to the lowest-lying a-polarized electronic transitions oscillate along axis a, whereas none of their counterparts for the lowest-lying b-polarized electronic transitions is predominantly along axis b. This notable difference on the alignment between the electronic transition and molecular vibration could help the directional control of charge dissociation and/or spin separation. Moreover, a significant variance of the destructive FC/HT interference was discovered with increasing temperatures that can well explain the a-polarized fading tableland near 650 nm. Finally, the importance of HT coupling was corroborated by comparing its intensity with those of FC factor and FC/HT interference. Taken all together, the vibrational dependence of the electronic wave function is critical to resolve the light absorption spectra of single-crystalline pentacene and its temperature effects, facilitating the systematic design of functional optical materials based on pentacene and its derivatives.

Herzberg-Teller Effect Predominates in Sum-Frequency Vibrational Spectroscopy of Limonene Chiral Liquids.

We theoretically study the bulk sum-frequency vibrational spectroscopy of chiral liquids under the influence of the Franck-Condon, Herzberg-Teller, and nonadiabatic effects. With quantum chemistry computations we calculate the chiral spectra for the R-limonene molecule. When we compare the theoretical and experimental spectra, we find that the Herzberg-Teller effect under the Born-Oppenheimer approximation, instead of the nonadiabatic effect, predominates in the chiral spectra.

On-the-fly ab initio semiclassical evaluation of vibronic spectra at finite temperature.

To compute and analyze vibrationally resolved electronic spectra at zero temperature, we have recently implemented the on-the-fly ab initio extended thawed Gaussian approximation [A. Patoz et al., J. Phys. Chem. Lett. 9, 2367 (2018)], which accounts for anharmonicity, mode-mode coupling, and Herzberg-Teller effects. Here, we generalize this method in order to evaluate spectra at non-zero temperature. In line with thermo-field dynamics, we transform the von Neumann evolution of the coherence component of the density matrix to the Schrödinger evolution of a wavefunction in an augmented space with twice as many degrees of freedom. Due to the efficiency of the extended thawed Gaussian approximation, this increase in the number of coordinates results in nearly no additional computational cost. More specifically, compared to the original, zero-temperature approach, the finite-temperature method requires no additional ab initio electronic structure calculations. At the same time, the new approach allows for a clear distinction among finite-temperature, anharmonicity, and Herzberg-Teller effects on spectra. We show, on a model Morse system, the advantages of the finite-temperature thawed Gaussian approximation over the commonly used global harmonic methods and apply it to evaluate the symmetry-forbidden absorption spectrum of benzene, where all of the aforementioned effects contribute.

Efficient simulation of overtones and combination bands in resonant Raman spectra.

In this work, we describe how Resonant Raman (RR) spectra can be predicted with good accuracy using the path integral formulation for the harmonic oscillator, including the Herzberg-Teller and Duschinsky rotation effects. In particular, we will focus on approximations to make these calculations more efficient and expand the current methodology to include overtones and combination bands in the final prediction. After outlining the theory, we explain how it can be made into a black-box method and discuss the approximations that rely on its intrinsic parameters. It is shown that the latter can improve the efficiency by orders of magnitude, without substantial loss in accuracy. We will also show that the predicted RR spectra are in good agreement with experiment for both the intensity and position of spectral peaks, even for higher order vibronic excitations. Thus, the method proposed here can be used as a computational aid to experiments to improve the quality of analysis and theoretical understanding of RR.

On the simulation of vibrationally resolved electronic spectra of medium-size molecules: the case of styryl substituted BODIPYs.

BODIPY dyes are used in a variety of applications because of their peculiar spectroscopic and photo-physical properties that vary depending on the stereochemistry of the functional groups attached to the boron-dipyrromethene core structure. In this work, we have applied several computational methods, adapted for semi-rigid molecules based on the Franck-Condon principle, for the study of the optical properties of BODIPY systems and for the understanding of the influence of functional groups on their spectroscopic features. We have analyzed the electronic spectra of two styryl substituted BODIPY molecules of technological interest, properly taking into account the vibronic contribution. For comparison with recently recorded experimental data in methanol, the vibrationally resolved electronic spectra of these systems were computed using both Time-Independent (TI) and Time-Dependent (TD) formalisms. The first step toward the analysis of optical properties of the styryl modified BODIPYs was a benchmark of several density functionals, to select the most appropriate one. We have found that all benchmarked functionals provide good results in terms of band shape but some of them show strong discrepancies in terms of band position. Beyond the issue of the electronic structure calculation method, different levels of sophistication can be adopted for the calculation of vibronic transitions. In this study, the effect of mode couplings and the influence of the Herzberg-Teller terms on the theoretical spectra has been investigated. It has been found that all levels of theory considered give reproducible results for the investigated systems: band positions and shapes are similar at all levels and little improvements have been found in terms of band shape with the inclusion of Herzberg-Teller effect. Inclusion of temperature effects proved to be challenging due to the important impact of large amplitude motions. Better agreement can be achieved by adopting a suitable set of coordinates coupled with a reduced-dimensionality scheme.