Two-dimensional electronic spectroscopy of anharmonic molecular potentials

The Influence of Electronic Polarization on Nonlinear Optical Spectroscopy

The environment surrounding a chromophore can dramatically affect the energy absorption and relaxation process, as manifested in optical spectra. Simulations of nonlinear optical spectroscopy, such as two-dimensional electronic spectroscopy (2DES) and transient absorption (TA), will be influenced by the computational model of the environment. We here compare a fixed point charge molecular mechanics model and a quantum mechanical (QM) model of the environment in computed 2DES and TA spectra of Nile red in water and the chromophore of photoactive yellow protein (PYP) in water and protein environments. In addition to simulating these nonlinear optical spectra, we directly juxtapose the computed excitation energy correlation function to the dynamic Stokes shift function often used to analyze environment dynamics. Overall, we find that for the three systems studied here the mutual electronic polarization provided by the QM environment manifests in broader 2DES signals, as well as a larger reorganization energy and a larger static Stokes shift due to stronger coupling between the chromophore and the environment.

Vibronic and Environmental Effects in Simulations of Optical Spectroscopy

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.

Finite-Temperature, Anharmonicity, and Duschinsky Effects on the Two-Dimensional Electronic Spectra from Ab Initio Thermo-Field Gaussian Wavepacket Dynamics

Accurate description of finite-temperature vibrational dynamics is indispensable in the computation of two-dimensional electronic spectra. Such simulations are often based on the density matrix evolution, statistical averaging of initial vibrational states, or approximate classical or semiclassical limits. While many practical approaches exist, they are often of limited accuracy and difficult to interpret. Here, we use the concept of thermo-field dynamics to derive an exact finite-temperature expression that lends itself to an intuitive wavepacket-based interpretation. Furthermore, an efficient method for computing finite-temperature two-dimensional spectra is obtained by combining the exact thermo-field dynamics approach with the thawed Gaussian approximation for the wavepacket dynamics, which is exact for any displaced, distorted, and Duschinsky-rotated harmonic potential but also accounts partially for anharmonicity effects in general potentials. Using this new method, we directly relate a symmetry breaking of the two-dimensional signal to the deviation from the conventional Brownian oscillator picture.

Two-dimensional spectroscopy beyond the perturbative limit: The influence of finite pulses and detection modes

Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular, two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems, which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However, in both techniques, it can be difficult to unambiguously identify the pathways that dominate the signal. Therefore, the use of numerically modeling of 2DES is vitally important, which, in turn, requires approximating the pulsing scheme to some degree. Here, we employ non-perturbative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so, we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artifacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and in which limits more sophisticated approaches are required.

Explicit environmental and vibronic effects in simulations of linear and nonlinear optical spectroscopy

Accurately simulating the linear and nonlinear electronic spectra of condensed phase systems and accounting for all physical phenomena contributing to spectral line shapes presents a significant challenge. Vibronic transitions can be captured through a harmonic model generated from the normal modes of a chromophore, but it is challenging to also include the effects of specific chromophore-environment interactions within such a model. We work to overcome this limitation by combining approaches to account for both explicit environment interactions and vibronic couplings for simulating both linear and nonlinear optical spectra. We present and show results for three approaches of varying computational cost for combining ensemble sampling of chromophore-environment configurations with Franck-Condon line shapes for simulating linear spectra. We present two analogous approaches for nonlinear spectra. Simulated absorption spectra and two-dimensional electronic spectra (2DES) are presented for the Nile red chromophore in different solvent environments. Employing an average Franck-Condon or 2DES line shape appears to be a promising method for simulating linear and nonlinear spectroscopy for a chromophore in the condensed phase.

Nonlinear spectroscopy in the condensed phase: The role of Duschinsky rotations and third order cumulant contributions

First-principles modeling of nonlinear optical spectra in the condensed phase is highly challenging because both environment and vibronic interactions can play a large role in determining spectral shapes and excited state dynamics. Here, we compute two dimensional electronic spectroscopy (2DES) signals based on a cumulant expansion of the energy gap fluctuation operator, with specific focus on analyzing mode mixing effects introduced by the Duschinsky rotation and the role of the third order term in the cumulant expansion for both model and realistic condensed phase systems. We show that for a harmonic model system, the third order cumulant correction captures effects introduced by a mismatch in curvatures of ground and excited state potential energy surfaces, as well as effects of mode mixing. We also demonstrate that 2DES signals can be accurately reconstructed from purely classical correlation functions using quantum correction factors. We then compute nonlinear optical spectra for the Nile red and methylene blue chromophores in solution, assessing the third order cumulant contribution for realistic systems. We show that the third order cumulant correction is strongly dependent on the treatment of the solvent environment, revealing the interplay between environmental polarization and the electronic-vibrational coupling.

Quantum dissipative systems beyond the standard harmonic model: Features of linear absorption and dynamics

Current simulations of ultraviolet-visible absorption lineshapes and dynamics of condensed phase systems largely adopt a harmonic description to model vibrations. Often, this involves a model of displaced harmonic oscillators that have the same curvature. Although convenient, for many realistic molecular systems, this approximation no longer suffices. We elucidate nonstandard harmonic and anharmonic effects on linear absorption and dynamics using a stochastic Schrödinger equation approach to account for the environment. First, a harmonic oscillator model with ground and excited potentials that differ in curvature is utilized. Using this model, it is shown that curvature difference gives rise to an additional substructure in the vibronic progression of absorption spectra. This effect is explained and subsequently quantified via a derived expression for the Franck-Condon coefficients. Subsequently, anharmonic features in dissipative systems are studied, using a Morse potential and parameters that correspond to the diatomic molecule H₂ for differing displacements and environment interaction. Finally, using a model potential, the population dynamics and absorption spectra for the stiff-stilbene photoswitch are presented and features are explained by a combination of curvature difference and anharmonicity in the form of potential energy barriers on the excited potential.

One- to Two-Exciton Transitions in Perylene Bisimide Dimer Revealed by Two-Dimensional Electronic Spectroscopy

The excited-state energy levels of molecular dimers and aggregates play a critical role in their photophysical behavior and an understanding of the photodynamics in such structures is important for developing applications such as photovoltaics and optoelectronic devices. Here, exciton transitions in two different covalently bound PBI dimers are studied by two-dimensional electronic spectroscopy (2DES), a powerful spectroscopic method, providing the most complete picture of vibronic transitions in molecular systems. The data are accurately reproduced using the equation of motion-phase matching approach. The unambiguous presence of one-exciton to two-exciton transitions are captured in our results and described in terms of a molecular exciton energy level scheme based on the Kasha model. Furthermore, the results are supported by comparative measurements with the PBI monomer and another dimer in which the interchromophore distance is increased.

Coherent multidimensional spectroscopy of dilute gas-phase nanosystems

Two-dimensional electronic spectroscopy (2DES) is one of the most powerful spectroscopic techniques with unique sensitivity to couplings, coherence properties and real-time dynamics of a quantum system. While successfully applied to a variety of condensed phase samples, high precision experiments on isolated systems in the gas phase have been so far precluded by insufficient sensitivity. However, such experiments are essential for a precise understanding of fundamental mechanisms and to avoid misinterpretations. Here, we solve this issue by extending 2DES to isolated nanosystems in the gas phase prepared by helium nanodroplet isolation in a molecular beam-type experiment. This approach uniquely provides high flexibility in synthesizing tailored, quantum state-selected model systems of single and many-body character. In a model study of weakly-bound Rb₂ and Rb₃ molecules we demonstrate the method's unique capacity to elucidate interactions and dynamics in tailored quantum systems, thereby also bridging the gap to experiments in ultracold quantum science.