Cost-Effective Simulations of Vibrationally-Resolved Absorption Spectra of Fluorophores with Machine-Learning-Based Inhomogeneous Broadening

Simulations of Two-Photon Absorption Spectra of Fluorescent Dyes: The Impact of Non-Condon Effects

Computer simulations play a pivotal role in interpreting experimental two-photon absorption (2PA) spectra. One of the key aspects of the simulation of these spectra is to take into account the vibrational fine structure of the bands in electronic spectra. This is typically done by employing Franck-Condon (FC) term and low-order terms in the Herzberg-Teller (HT) expansion. In this work, we present a systematic study of first-order HT effects on the vibronic structure of π → π* electronic bands in 2PA spectra of 13 common fluorophores. We begin by evaluating the performance of several density functional approximations (DFAs) against the second-order coupled cluster singles and doubles model (CC2) for reproducing two-photon transition moments and their first- and second-order derivatives with respect to normal modes of vibration on a set of six donor-acceptor molecules. Our findings reveal that most DFAs produce inaccurate values for these derivatives, with the exception of the LC-BLYP functionals with range-separation parameters of 0.33 and 0.47. Although these functionals underestimate the HT contribution to the 2PA total intensities of the π → π* electronic bands, they offer a reasonable qualitative reproduction of the HT vibrational fine structure of the reference spectra. We further explore HT effects on fluorescent chromophores, finding that HT contributions are secondary to FC effects, leading to small shifts of the wavelengths peaks, and minimal changes in the intensities. Additionally, the adiabatic Hessian, vertical Hessian, and vertical gradient vibronic models are assessed. The general agreement among these models confirms that the harmonic approximation is suitable for studying the selected fluorophores.

One- and two-photon absorption spectra of organoboron complexes: vibronic and environmental effects

We synthesized a series of four parent aza-β-ketoiminate organoboron complexes and performed spectroscopic studies using both experimental and computational techniques. We studied how benzannulation influences the vibronic structure of the UV/Vis absorption bands with a focus on the bright lowest-energy π → π* electronic excitation. Theoretical simulations, accounting for inhomogeneous broadening effects using different embedding schemes, allowed gaining in-depth insights into the observed differences in band shapes induced by structural modifications. We observed huge variations in the distributions of vibronic transitions depending on the position of benzannulation. By and large, the harmonic approximation combined with the adiabatic hessian model delivers qualitatively correct band shapes for the one-photon absorption spectra, except in one case. We also assessed the importance of non-Condon effects (accounted for by the linear term in Herzberg-Teller expansion of the dipole moment) for S0 → S1 band shapes. It turned out that non-Condon contributions have no effect on the band shape in one-photon absorption spectra. In contrast, these effects significantly change the Franck-Condon band shapes of the two-photon absorption spectra. For one of the studied organoboron complexes we also performed a preliminary exploration of mechanical anharmonicity, resulting in an increase of the intensity of the 0-0 transition, which improves the agreement with the experimental data compared to the harmonic model.

Taming the third order cumulant approximation to linear optical spectroscopy

The second order cumulant method offers a promising pathway to predicting optical properties in condensed phase systems. It allows for the computation of linear absorption spectra from excitation energy fluctuations sampled along molecular dynamics (MD) trajectories, fully accounting for vibronic effects, direct solute-solvent interactions, and environmental polarization effects. However, the second order cumulant approximation only guarantees accurate line shapes for energy gap fluctuations obeying Gaussian statistics. A third order correction has recently been derived but often yields unphysical spectra or divergent line shapes for moderately non-Gaussian fluctuations due to the neglect of higher order terms in the cumulant expansion. In this work, we develop a corrected cumulant approach, where the collective effect of neglected higher order contributions is approximately accounted for through a dampening factor applied to the third order cumulant term. We show that this dampening factor can be expressed as a function of the skewness and kurtosis of energy gap fluctuations and can be parameterized from a large set of randomly sampled model Hamiltonians for which exact spectral line shapes are known. This approach is shown to systematically remove unphysical contributions in the form of negative absorbances from cumulant spectra in both model Hamiltonians and condensed phase systems sampled from MD and dramatically improves over the second order cumulant method in describing systems exhibiting Duschinsky mode mixing effects. We successfully apply the approach to the coumarin-153 dye in toluene, obtaining excellent agreement with experiment.

How does theory compare to experiment for oscillator strengths in electronic spectra? Proposing range-separated hybrids with reliable accountability

As an important quantity in atomic and molecular spectroscopy, oscillator strength should be mentioned. Oscillator strength is linked to the transition dipole moment and consequently to the transition probability between two states, where its magnitude is directly connected to the intensity of the peaks in ultraviolet-visible spectra. However, accurately accounting for oscillator strengths still remains one of the greatest challenges in theory and experiment. Given previous efforts in the context of investigations into oscillator strengths, the related theoretical treatments are relatively limited and have proven to be challenging. In this work, the oscillator strengths in the electronic spectra of organic compounds have thoroughly been investigated with the help of optimally tuned range-separated hybrids (OT-RSHs). In particular, variants of the OT-RSHs combined with the polarizable continuum model (PCM), OT-RSHs-PCM, as well as their screened versions accounting for the screening effects by the electron correlation through the dielectric constant, OT-SRSHs-PCM, are proposed for reliable prediction of the oscillator strengths. The role of the involved ingredients in the proposed methods, namely the underlying density functional approximations, short-range and long-range Hartree-Fock (HF) exchange, as well as the range-separation parameter, has been examined in detail. It is shown that any combination of the parameters in the proposed approximations does not render the reliable oscillator strengths, but a particular compromise among them is needed to describe the experimental data well. Perusing all the results of our developed methods, the best ones are found to be the generalized gradient approximation-based OT-RSHs-PCM, coupled with the linear response theory in the non-equilibrium solvation regime, with the correct asymptotic behavior and incorporating no (low) HF exchange contributions in the short-range part. The best proposed approximations also reveal superior performances not only with respect to their standard counterparts with the default parameters but also as compared to earlier range-separated functionals. Finally, the applicability of the best approximation is also put into broader perspective, where it is used for predicting the oscillator strengths in other sets of compounds not included in the process of developing the approximations. Hopefully, our proposed method can function as an affordable alternative to the expensive wave function-based methods for both theoretical modeling and confirming the experimental observations in the field of electronic spectroscopy.

Modeling the Fluorescence Quantum Yields of Aromatic Compounds: Benchmarking the Machinery to Compute Intersystem Crossing Rates

The from-first-principles calculation of fluorescence quantum yields (FQYs) and lifetimes of organic dyes remains very challenging. In this article, we extensively test the machinery to calculate FQYs. Specifically, we perform an extensive analysis on the parameters influencing the intersystem crossing (ISC), internal conversion (IC), and fluorescence rate constants calculations. The impact of (i) the electronic structure (chosen exchange-correlation functional and spin-orbit Hamiltonian), (ii) the vibronic parameters (coordinate system, broadening function, and dipole expansion), and (iii) the excited-state kinetic models are systematically assessed for a series of seven rigid aromatic molecules. Our studies provide more insights into the choice of parameters and the expected accuracy for the computational protocols aiming to deliver FQY values. Some challenges are highlighted, such as, on the one hand, the difficulty to benchmark against the experimental nonradiative rate constants, for which the separation between the IC and ISC contributions is often not provided in the literature and, on the other hand, the need to go beyond the harmonic approximation for the calculation of the IC rates.

Elucidating the Role of Hydrogen Bonding in the Optical Spectroscopy of the Solvated Green Fluorescent Protein Chromophore: Using Machine Learning to Establish the Importance of High-Level Electronic Structure

Hydrogen bonding interactions with chromophores in chemical and biological environments play a key role in determining their electronic absorption and relaxation processes, which are manifested in their linear and multidimensional optical spectra. For chromophores in the condensed phase, the large number of atoms needed to simulate the environment has traditionally prohibited the use of high-level excited-state electronic structure methods. By leveraging transfer learning, we show how to construct machine-learned models to accurately predict the high-level excitation energies of a chromophore in solution from only 400 high-level calculations. We show that when the electronic excitations of the green fluorescent protein chromophore in water are treated using EOM-CCSD embedded in a DFT description of the solvent the optical spectrum is correctly captured and that this improvement arises from correctly treating the coupling of the electronic transition to electric fields, which leads to a larger response upon hydrogen bonding between the chromophore and water.