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Two-dimensional electronic spectroscopy (2DES) is a powerful experimental technique, as it directly probes the nonlinear (third-order) response function of the system, providing key insights into ultrafast energy transfer and relaxation processes. However, 2DES experiments are generally difficult to interpret, often relying on simulations in order to associate observed spectral features with specific underlying system dynamics. For this reason, the development of robust, computationally inexpensive theoretical methods for modeling these experiments remains an active area of research. We have recently derived such an approach for computing the exact finite-temperature nonlinear response function for harmonic Hamiltonians within the Condon approximation, assuming that the transition dipole moment is independent of nuclear coordinates. In this work, we extend our formalism to exactly account for non-Condon/Herzberg−Teller (HT) type contributions to the nonlinear response function, which are known to be crucial for accurately describing linear optical spectra in a wide range of molecular systems. We highlight the key insights that can be gained from our new method, named FC2DES+HT, by simulating the 2DES signals of two molecules with known non-Condon behavior, the phenolate anion and free-base porphyrin. The results demonstrate that Herzberg−Teller couplings substantially impact energy relaxation dynamics in these systems. 

Two-dimensional electronic spectroscopy (2DES) can provide detailed insight into the energy transfer and relaxation dynamics of chromophores by directly measuring the nonlinear response function of the system. However, experiments are often difficult to interpret, and the development of computationally affordable approaches to simulate experimental signals is desirable. For linear spectroscopy, optical spectra of small to medium-sized molecules can be efficiently calculated in the Franck-Condon approach. Approximating the nuclear degrees of freedom as harmonic around the ground- and excited-state minima, closed-form expressions for the exact finite-temperature linear response function can be derived using known solutions for the propagation operator between normal mode coordinate sets, fully accounting for Duschinsky mode-mixing effects. In the present work, we demonstrate that a similar approach can be utilized to yield analogous closed-form expression for the finite-temperature nonlinear (third-order) response function of harmonic nuclear Hamiltonians. The resulting approach, named FC2DES, is implemented on graphics processing units (GPUs), allowing efficient computations of 2DES signals for medium-sized molecules containing hundreds of normal modes. Benchmark comparisons against the widely used cumulant method for computing 2DES signals are performed on small model systems, as well as the nile red molecule. We highlight the advantages of the FC2DES approach, especially in systems with moderate Duschinsky mode mixing and for long delay times in the nonlinear response function, where low-order cumulant approximations are shown to fail. 

Singlet fission (SF) is a charge carrier multiplication process that has potential for improving the performance of (opto)electronic devices from the conversion of one singlet exciton S1 into two triplet excitons T1 via a spin-entangled triplet pair state 1(TT). This process depends highly on molecular packing and morphology, both for the generation and dissociation of 1(TT) states. Many benchmark SF materials, such as acenes, are also prone to photodegradation reactions, such as endoperoxide (EPO) formation and photodimerization, which inhibit realization of SF devices. In this paper, we compare functionalized tetracenes R–Tc with two packing motifs: “slip-stack” packing in R = TES, TMS, and tBu and “gamma” packing in R = TBDMS to determine the effects of morphology on SF as well as on photodegradation using a combination of temperature and magnetic field dependent spectroscopy, kinetic modeling, and time-dependent density functional theory. We find that both “slip-stack” and “gamma” packing support SF with high T1 yield at room temperature (up to 191% and 181%, respectively), but “slip-stack” is considerably more advantageous at low temperatures (<150 K). In addition, each packing structure has a distinct emissive relaxation pathway competitive to SF, while the states involved in the SF itself are dark. The “gamma” packing has superior photostability, both in regards to EPO formation and photodimerization. The results indicate that the trade-off between SF efficiency and photostability can be overcome with material design, emphasize the importance of considering both photophysical and photochemical properties, and inform efforts to develop optimal SF materials for (opto)electronic applications. 

Accurately modeling absorption and fluorescence spectra for molecules in solution poses a challenge due to the need to incorporate both vibronic and environmental effects, as well as the necessity of accurate excited state electronic structure calculations. Nuclear ensemble approaches capture explicit environmental effects, Franck–Condon methods capture vibronic effects, and recently introduced ensemble-Franck–Condon approaches combine the advantages of both methods. In this study, we present and analyze simulated absorption and fluorescence spectra generated with combined ensemble-Franck–Condon approaches for three chromophore–solvent systems and compare them to standard ensemble and Franck–Condon spectra, as well as to the experiment. Employing configurations obtained from ground and excited state ab initio molecular dynamics, three combined ensemble-Franck–Condon approaches are directly compared to each other to assess the accuracy and relative computational time. We find that the approach employing an average finite-temperature Franck–Condon line shape generates spectra nearly identical to the direct summation of an ensemble of Franck–Condon spectra at one-fourth of the computational cost. We analyze how the spectral simulation method, as well as the level of electronic structure theory, affects spectral line shapes and associated Stokes shifts for 7-nitrobenz-2-oxa-1,3-diazol-4-yl and Nile red in dimethyl sulfoxide and 7-methoxy coumarin-4-acetic acid in methanol. For the first time, our studies show the capability of combined ensemble-Franck–Condon methods for both absorption and fluorescence spectroscopy and provide a powerful tool for simulating linear optical spectra. 

Including both environmental and vibronic effects is important for accurate simulation of optical spectra, but combining these effects remains computationally challenging. We outline two approaches that consider both the explicit atomistic environment and the vibronic transitions. Both phenomena are responsible for spectral shapes in linear spectroscopy and the electronic evolution measured in nonlinear spectroscopy. The first approach utilizes snapshots of chromophore-environment configurations for which chromophore normal modes are determined. We outline various approximations for this static approach that assumes harmonic potentials and ignores dynamic system-environment coupling. The second approach obtains excitation energies for a series of time-correlated snapshots. This dynamic approach relies on the accurate truncation of the cumulant expansion but treats the dynamics of the chromophore and the environment on equal footing. Both approaches show significant potential for making strides toward more accurate optical spectroscopy simulations of complex condensed phase systems.