Franck-Condon and Herzberg-Teller Signatures in Molecular Absorption and Emission Spectra

Influence of Quadrupolar Molecular Transitions within Plasmonic Cavities

Optical nanocavities have revolutionized the manipulation of radiative properties of molecular and semiconductor emitters. Here, we investigate the amplified photoluminescence arising from exciting a dark transition of β-carotene molecules embedded within plasmonic nanocavities. Integrating a molecular monolayer into nanoparticle-on-mirror nanostructures unveils enhancements surpassing 4 orders of magnitude in the initially light-forbidden excitation. Such pronounced enhancements transcend conventional dipolar mechanisms, underscoring the presence of alternative enhancement pathways. Notably, Fourier-plane scattering spectroscopy shows that the photoluminescence excitation resonance aligns with a higher-order plasmonic cavity mode, which supports strong field gradients. Combining quantum chemistry calculations with electromagnetic simulations reveals an important interplay between the Franck-Condon quadrupole and Herzberg-Teller dipole contributions in governing the absorption characteristics of this dark transition. In contrast to free space, the quadrupole moment plays a significant role in photoluminescence enhancement within nanoparticle-on-mirror cavities. These findings provide an approach to access optically inactive transitions, promising advancements in spectroscopy and sensing applications.

Finite-temperature vibronic spectra from the split-operator coherence thermofield dynamics

We present a numerically exact approach for evaluating vibrationally resolved electronic spectra at finite temperatures using the coherence thermofield dynamics. In this method, which avoids implementing an algorithm for solving the von Neumann equation for coherence, the thermal vibrational ensemble is first mapped to a pure-state wavepacket in an augmented space, and this wavepacket is then propagated by solving the standard, zero-temperature Schrödinger equation with the split-operator Fourier method. We show that the finite-temperature spectra obtained with the coherence thermofield dynamics in a Morse potential agree exactly with those computed by Boltzmann-averaging the spectra of individual vibrational levels. Because the split-operator thermofield dynamics on a full tensor-product grid is restricted to low-dimensional systems, we briefly discuss how the accessible dimensionality can be increased by various techniques developed for the zero-temperature split-operator Fourier method.

A molecular descriptor of a shallow potential energy surface for the ground state to achieve narrowband thermally activated delayed fluorescence emission

Narrowband thermally activated delayed fluorescence (TADF) molecules have extensive applications in optoelectronics, biomedicine, and energy. The full-width at half-maximum (FWHM) holds significant importance in assessing the luminescence efficiency and color purity of TADF molecules. The goal is to achieve efficient and stable TADF emissions by regulating and optimizing the FWHM. However, a bridge from the basic physical parameters (such as geometric structure and reorganization energy) to the macroscopic properties (delayed fluorescence, efficiency, and color purity) is needed and it is highly necessary and urgent to explore the internal mechanisms that influence FWHM. Herein, first-principles calculations coupled with the thermal vibration correlation function (TVCF) theory were performed to study the energy consumption processes of the excited states for the three TADF molecules (2,3-POA, 2,3-DPA, and 2,3-CZ) with different donors; inner physical parameters affecting the FWHM were detected. By analyzing the basic geometric and electronic structures as well as the transition properties and reorganization energies, three main findings in modulating FWHM were obtained, namely a large local excitation (LE) proportion in the first singlet excited state is advantageous in reducing FWHM, a donor group with weak electron-donating ability is beneficial for achieving narrowband emission, and small reorganization energies for the ground state are favorable for reducing FWHM. Thus, wise molecular design strategies to achieve efficient narrowband TADF emission are theoretically proven and proposed. We hope that these results will promote an in-depth understanding of FWHM and accelerate the development of high color purity TADF emitters.

Beyond the Condon limit: Condensed phase optical spectra from atomistic simulations

While dark transitions made bright by molecular motions determine the optoelectronic properties of many materials, simulating such non-Condon effects in condensed phase spectroscopy remains a fundamental challenge. We derive a Gaussian theory to predict and analyze condensed phase optical spectra beyond the Condon limit. Our theory introduces novel quantities that encode how nuclear motions modulate the energy gap and transition dipole of electronic transitions in the form of spectral densities. By formulating the theory through a statistical framework of thermal averages and fluctuations, we circumvent the limitations of widely used microscopically harmonic theories, allowing us to tackle systems with generally anharmonic atomistic interactions and non-Condon fluctuations of arbitrary strength. We show how to calculate these spectral densities using first-principles simulations, capturing realistic molecular interactions and incorporating finite-temperature, disorder, and dynamical effects. Our theory accurately predicts the spectra of systems known to exhibit strong non-Condon effects (phenolate in various solvents) and reveals distinct mechanisms for electronic peak splitting: timescale separation of modes that tune non-Condon effects and spectral interference from correlated energy gap and transition dipole fluctuations. We further introduce analysis tools to identify how intramolecular vibrations, solute-solvent interactions, and environmental polarization effects impact dark transitions. Moreover, we prove an upper bound on the strength of cross correlated energy gap and transition dipole fluctuations, thereby elucidating a simple condition that a system must follow for our theory to accurately predict its spectrum.

The photophysical properties of sulfone-based TADF emitters in relation to their structural properties

In this work, thermally activated delayed fluorescence (TADF) of a series of emitters with sulfone-based acceptor moieties was studied by density functional theory (DFT) methods. Sulfone derivatives were shown to be high performing TADF emitters over recent years. When discussing the TADF efficiency, various properties, such as the singlet-triplet energy gap (ΔEST), spin-orbit coupling (SOC) and the nature of states, stand out due to their roles in reverse intersystem crossing (RISC). Here, we mainly focused on three important structural parameters that affect the intersystem crossing (ISC) and RISC pathways and their efficiencies. These three parameters are: (1) the effect of meta- and para-conjugation, (2) the effect of rigid acceptor moieties and (3) the effect of the phenyl bridge on photophysical properties.

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. I. Response function theory

Fluorescence-encoded infrared (FEIR) spectroscopy is an emerging technique for performing vibrational spectroscopy in solution with detection sensitivity down to single molecules. FEIR experiments use ultrashort pulses to excite a fluorescent molecule's vibrational and electronic transitions in a sequential, time-resolved manner, and are therefore sensitive to intervening vibrational dynamics on the ground state, vibronic coupling, and the relative orientation of vibrational and electronic transition dipole moments. This series of papers presents a theoretical treatment of FEIR spectroscopy that describes these phenomena and examines their manifestation in experimental data. This first paper develops a nonlinear response function description of Fourier-transform FEIR experiments for a two-level electronic system coupled to multiple vibrations, which is then applied to interpret experimental measurements in the second paper [L. Whaley-Mayda et al., J. Chem. Phys. 159, 194202 (2023)]. Vibrational coherence between pairs of modes produce oscillatory features that interfere with the vibrations' population response in a manner dependent on the relative signs of their respective Franck-Condon wavefunction overlaps, leading to time-dependent distortions in FEIR spectra. The orientational response of population and coherence contributions are analyzed and the ability of polarization-dependent experiments to extract relative transition dipole angles is discussed. Overall, this work presents a framework for understanding the full spectroscopic information content of FEIR measurements to aid data interpretation and inform optimal experimental design.

Phosphorescent Properties of Heteroleptic Ir(III) Complexes: Uncovering Their Emissive Species

In this contribution, we assess the computational machinery to calculate the phosphorescence properties of a large pool of heteroleptic [Ir(C^N)2(N^N)]+ complexes (where N^N is an ancillary ligand and C^N is a cyclometalating ligand) including their phosphorescent rates and their emission spectra. Efficient computational protocols are next proposed. Specifically, different flavors of DFT functionals were benchmarked against DLPNO-CCSD(T) for the phosphorescence energies. The transition density matrix and decomposition analysis of the emitting triplet excited state enable us to categorize the studied complexes into different cases, from predominant triplet ligand-centered (3LC) character to predominant charge-transfer (3CT) character, either of metal-to-ligand charge transfer (3MLCT), ligand-to-ligand charge transfer (3LLCT), or a combination of the two. We have also calculated the vibronically resolved phosphorescent spectra and rates. Ir(III) complexes with predominant 3CT character are characterized by less vibronically resolved bands as compared to those with predominant 3LC character. Furthermore, some of the complexes are characterized by close-lying triplet excited states so that the calculation of their phosphorescence properties poses additional challenges. In these scenarios, it is necessary to perform geometry optimizations of higher-lying triplet excited states (i.e., Tn). We demonstrate that in the latter scenarios all of the close-lying triplet species must be considered to recover the shape of the experimental emission spectra. The global analysis of computed emission energies, shape of the computed emission spectra, computed rates, etc. enable us to unambiguously pinpoint for the first time the triplet states involved in the emission process and to provide a general classification of Ir(III) complexes with regard to their phosphorescence properties.

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.

Interference between Franck-Condon and Herzberg-Teller Terms in the Condensed-Phase Molecular Spectra of Metal-Based Tetrapyrrole Derivatives

The commonly used Franck-Condon (FC) approximation is inadequate for explaining the electronic spectra of compounds that possess vibrations with substantial Herzberg-Teller (HT) couplings. Metal-based tetrapyrrole derivatives, which are ubiquitous natural pigments, often exhibit prominent HT activity. In this paper, we compare the condensed phase spectra of zinc-tetraphenylporphyrin (ZnTPP) and zinc-phthalocyanine (ZnPc), which exhibit vastly different spectral features in spite of sharing a common tetrapyrrole backbone. The absorption and emission spectra of ZnTPP are characterized by a lack of mirror symmetry and nontrivial temperature dependence. In contrast, mirror symmetry is restored, and the nontrivial temperature-dependent features disappear in ZnPc. We attribute these differences to FC-HT interference, which is less pronounced in ZnPc because of a larger FC component in the dipole moment that leads to FC-dominated transitions. A single minimalistic FC-HT vibronic model reproduces all the experimental spectral features of these molecules. These observations suggest that FC-HT interference is highly susceptible to chemical modification.