Inspecting molecular aggregate quadratic vibronic coupling effects using squeezed coherent states.

We present a systematic comparison of three quantum mechanical approaches describing excitation dynamics in molecular complexes using the time-dependent variational principle (TDVP) with increasing sophistication trial wavefunctions (ansatze): Davydov D2, squeezed D2 (sqD2) and a numerically exact multiple D2 (mD2) ansatz in order to characterize validity of the sqD2 ansatz. Numerical simulations of molecular aggregate absorption and fluorescence spectra with intra- and intermolecular vibrational modes, including quadratic electronic-vibrational (vibronic) coupling term, which is due to vibrational frequency shift upon pigment excitation are presented. Simulated absorption and fluorescence spectra of a J type molecular dimer with high frequency intramolecular vibrational modes obtained with D2 and sqD2 ansatze match the spectra of mD2 ansatz only in the single pigment model without quadratic vibronic coupling. In general, the use of mD2 ansatz is required to model an accurate dimer and larger aggregate's spectra. For a J dimer aggregate coupled to a low frequency intermolecular phonon bath, absorption and fluorescence spectra are qualitatively similar using all three ansatze. The quadratic vibronic coupling term in both absorption and fluorescence spectra manifests itself as a lineshape peak amplitude redistribution, static frequency shift and an additional shift, which is temperature dependent. Overall the squeezed D2 model does not result in a considerable improvement of the simulation results compared to the simplest Davydov D2 approach.

Two phases of trans-stilbene in a polystyrene matrix.

Variability in the spectral properties of solid conformations of stilbene under various external conditions still remains obscure. The photophysical properties of trans-stilbene solution in solid polystyrene glass have been studied by absorption and time-resolved fluorescence. Concentration-induced quenching has been observed for small concentrations of stilbene. At large concentrations, the spectroscopic characteristics become split between the two phases of the sample: single-molecule properties are responsible for absorption, while the micro-crystalline phase dominates in fluorescence. Ab initio and molecular dynamics analyses suggest permanent twisting of the stilbene molecular structure upon crystallization, which supports spectroscopic phase separation.

Extracting the excitonic Hamiltonian of a chlorophyll dimer from broadband two-dimensional electronic spectroscopy.

We apply Frenkel exciton theory to model the entire Q-band of a tightly bound chlorophyll dimer inspired by the photosynthetic reaction center of photosystem II. The potential of broadband two-dimensional electronic spectroscopy experiment spanning the Qx and Qy regions to extract the parameters of the model dimer Hamiltonian is examined through theoretical simulations of the experiment. We find that the local nature of Qx excitation enables identification of molecular properties of the delocalized Qy excitons. Specifically, we demonstrate that the cross-peak region, where excitation energy is resonant with Qy while detection is at Qx, contains specific spectral signatures that can reveal the full real-space molecular Hamiltonian, a task that is impossible by considering the Qy transitions alone. System-bath coupling and site energy disorder in realistic systems may limit the resolution of these spectral signatures due to spectral congestion.

Modeling molecular J and H aggregates using multiple-Davydov D2 ansatz.

The linear absorption spectrum of J and H molecular aggregates is studied using the time-dependent Dirac-Frenkel variational principle (TDVP) with the multi-Davydov D2 (mD2) trial wavefunction (Ansatz). Both the electronic and vibrational molecular degrees of freedom (DOF) are considered. By inspecting and comparing the absorption spectrum of both open and closed chain aggregates over a range of electrostatic nearest neighbor coupling and temperature values, we find that the mD2 Ansatz is necessary for obtaining an accurate aggregate absorption spectrum in all parameter regimes considered, while the regular Davydov D2 Ansatz is not sufficient. Establishing a relationship between the model parameters and the depth of the mD2 Ansatz is the main focus of this study. Molecular aggregate wavepacket dynamics, during excitation by an external field, is also studied. We find the wavepacket to exhibit an out-of-phase oscillatory behavior along the coordinate and momentum axes and an overall wavepacket broadening, implying the electron-vibrational (vibronic) eigenstates of an aggregate to reside on non-parabolic energy surfaces.

Simulation of Ab Initio Optical Absorption Spectrum of ß-Carotene with Fully Resolved S0 and S2 Vibrational Normal Modes.

The electronic absorption spectrum of ß-carotene (ß-Car) is studied using quantum chemistry and quantum dynamics simulations. Vibrational normal modes were computed in optimized geometries of the electronic ground state S0 and the optically bright excited S2 state using the time-dependent density functional theory. By expressing the S2-state normal modes in terms of the ground-state modes, we find that no one-to-one correspondence between the ground- and excited-state vibrational modes exists. Using the ab initio results, we simulated the ß-Car absorption spectrum with all 282 vibrational modes in a model solvent at 300 K using the time-dependent Dirac-Frenkel variational principle and are able to qualitatively reproduce the full absorption line shape. By comparing the 282-mode model with the prominent 2-mode model, widely used to interpret carotenoid experiments, we find that the full 282-mode model better describes the high-frequency progression of carotenoid absorption spectra; hence, vibrational modes become highly mixed during the S0 → S2 optical excitation. The obtained results suggest that electronic energy dissipation is mediated by numerous vibrational modes.

Second harmonic generation theory for a helical macromolecule with high sensitivity to structural disorder.

Microscopic theory for the second harmonic generation in a helical molecular system is developed in the minimal coupling representation including non-local interaction effects. At the second order to the field we find a compact expression which combines dipolar, quadrupolar and magnetic contributions. A detailed derivation of the response is performed to specifically isolate the quadratic coupling terms, which we denote as the K coupling. Applying the theory to a helical macromolecule we find that the dipolar and quadrupolar contributions reflect the symmetry properties of the system and its homogeneity, while the K coupling contribution reveals inhomogeneities of the system.

Unusual temperature dependence of the fluorescence decay in heterostructured stilbene.

Fluorescence spectra as well as the fluorescence decay kinetics of hot-pressed and sublimated films of stilbene have been studied in a wide temperature range, from 15 K up to room temperature. The fluorescence decay kinetics demonstrate unusual elongation of the excitation lifetime with a temperature increase. This is in contrast to the corresponding data of stilbene solutions in chloroform and in a polystyrene (PS) matrix. It is well known that the excitation dynamics of stilbene in solution and in a PS matrix is controlled by the molecular isomerization/twisting process of separate molecules. The data analysis and quantum chemistry calculations of stilbene aggregates suggest that the temperature dependence of the fluorescence kinetics of bulk stilbene solids can be explained by fast exciton diffusion, which yields a thermalized exciton distribution in a relatively small number of fluorescence centres. The temperature dependence of the distribution can thus explain the observed fluorescence decay lifetimes.

Vibration-mediated energy transport in bacterial reaction center: Simulation study.

Exciton energy relaxation in a bacterial Reaction Center (bRC) pigment-protein aggregate presumably involves emission of high energy vibrational quanta to cover wide energy gaps between excitons. Here, we assess this hypothesis utilizing vibronic two-particle theory in modeling of the excitation relaxation process in bRC. Specific high frequency molecular vibrational modes are included explicitly one at a time in order to check which high frequency vibrations are involved in the excitation relaxation process. The low frequency bath modes are treated perturbatively within Redfield relaxation theory. The analysis of the population relaxation rate data indicates energy flow pathways in bRC and suggests that specific vibrations may be responsible for the excitation relaxation process.

Modeling irreversible molecular internal conversion using the time-dependent variational approach with sD2 ansatz.

Effects of non-linear coupling between the system and the bath vibrational modes on the system internal conversion dynamics are investigated using the Dirac-Frenkel variational approach with a newly defined sD2 ansatz. It explicitly accounts for the entangled system electron-vibrational states, while the bath quantum harmonic oscillator states are expanded in a superposition of quantum coherent states. Using a non-adiabatically coupled three-level model, we show that efficient irreversible internal conversion due to quadratic vibrational-bath coupling occurs when the initially populated system vibrational levels are in resonance with the vibrational levels of a lower energy electronic state, also, a non-Gaussian bath wavepacket representation is required. The quadratic system-bath couplings result in broadened and asymmetrically squeezed bath quantum harmonic oscillator wavepackets in the coordinate-momentum phase space.

Two-dimensional electronic Stark spectroscopy of a photosynthetic dimer.

Stark spectroscopy, which measures changes in the linear absorption of a sample in the presence of an external DC electric field, is a powerful experimental tool for probing the existence of charge-transfer (CT) states in photosynthetic systems. CT states often have small transition dipole moments, making them insensitive to other spectroscopic methods, but are particularly sensitive to Stark spectroscopy due to their large permanent dipole moment. In a previous study, we demonstrated a new experimental method, two-dimensional electronic Stark spectroscopy (2DESS), which combines two-dimensional electronic spectroscopy (2DES) and Stark spectroscopy. In order to understand how the presence of CT states manifest in 2DESS, here, we perform computational modeling and calculations of 2DESS as well as 2DES and Stark spectra, studying a photosynthetic dimer inspired by the photosystem II reaction center. We identify specific cases where qualitatively different sets of system parameters produce similar Stark and 2DES spectra but significantly different 2DESS spectra, showing the potential for 2DESS to aid in identifying CT states and their coupling to excitonic states.

Effects of tunable excitation in carotenoids explained by the vibrational energy relaxation approach.

Carotenoids are fundamental building blocks of natural light harvesters with convoluted and ultrafast energy deactivation networks. In order to disentangle such complex relaxation dynamics, several studies focused on transient absorption measurements and their dependence on the pump wavelength. However, such findings are inconclusive and sometimes contradictory. In this study, we compare internal conversion dynamics in [Formula: see text]-carotene, pumped at the first, second, and third vibronic progression peak. Instead of employing data fitting algorithms based on global analysis of the transient absorption spectra, we apply a fully quantum mechanical model to treat the high-frequency symmetric carbon-carbon (C=C and C-C) stretching modes explicitly. This model successfully describes observed population dynamics as well as spectral line shapes in their time-dependence and allows us to reach two conclusions: Firstly, the broadening of the induced absorption upon excess excitation is an effect of vibrational cooling in the first excited state ([Formula: see text]). Secondly, the internal conversion rate between the second excited state ([Formula: see text]) and [Formula: see text] crucially depends on the relative curve displacement. The latter point serves as a new perspective on solvent- and excitation wavelength-dependent experiments and lifts contradictions between several studies found in literature.

Two-dimensional electronic spectroscopy of anharmonic molecular potentials.

Two-dimensional electronic spectroscopy (2DES) is a powerful tool in the study of coupled electron-phonon dynamics, yet very little is known about how nonlinearities in the electron-phonon coupling, arising from anharmonicities in the nuclear potentials, affect the spectra. These become especially relevant when the coupling is strong. From the linear spectroscopies, anharmonicities are known to give structure to the zero-phonon line and to break mirror-symmetry between absorption and emission, but the 2D analogues of these effects have not been identified. Using a simple two-level model where the electronic states are described by (displaced) harmonic oscillators with differing curvatures or displaced Morse oscillators, we find that the zero-phonon line shape is essentially transferred to the diagonal in 2DES spectra, and that anharmonicities break a horizontal mirror-symmetry in the infinite waiting time limit. We also identify anharmonic effects that are only present in 2DES spectra: twisting of cross-peaks stemming from stimulated emission signals; and oscillation period mismatch between ground state bleach and stimulated emission (for harmonic oscillators with differing curvatures), or inherently chaotic oscillations (for Morse oscillators). Our findings will facilitate an improved understanding of 2DES spectra and aid the interpretation of signals that are more realistic than those arising from simple models.

Tracing feed-back driven exciton dynamics in molecular aggregates.

Perturbative treatment of excitation dynamics in molecular systems with respect to external interactions with a dissipative environment is extensively used for the description of excitation energy transfer and relaxation. However the simulated dynamics becomes sensitive to a specific representation basis set, which makes the conclusions obscure and questionable. We revisit questions of excitation creation patterns, coherent dynamics, relaxation and detection from a theoretical viewpoint, and demonstrate that a mixture of specific requirements should be met to observe coherent phenomena and incoherent decay processes. We discuss how intermixing of coherent components in relaxation phenomena is related to a non-perturbative regime of dynamics leading to nonlinear feed-back effects where bath relaxation also affects excitation wavepackets. We also discuss how bath equilibration causes local heating effects which is often neglected in numerical simulations. The parameters reflecting the complexity of the processes are related to excitation delocalization patterns in various basis representations. While these seem to be auxiliary nonobservable features, their evaluation allows better investigation of the physical behavior of quantum relaxation processes in molecular aggregate systems.

Ultrafast energy transfer within the photosystem II core complex.

We report 2D electronic spectroscopy on the photosystem II core complex (PSII CC) at 77 K under different polarization conditions. A global analysis of the high time-resolution 2D data shows rapid, sub-100 fs energy transfer within the PSII CC. It also reveals the 2D spectral signatures of slower energy equilibration processes occurring on several to hundreds of picosecond time scales that are consistent with previous work. Using a recent structure-based model of the PSII CC [Y. Shibata, S. Nishi, K. Kawakami, J. R. Shen and T. Renger, J. Am. Chem. Soc., 2013, 135, 6903], we simulate the energy transfer in the PSII CC by calculating auxiliary time-resolved fluorescence spectra. We obtain the observed sub-100 fs evolution, even though the calculated electronic energy shows almost no dynamics at early times. On the other hand, the electronic-vibrational interaction energy increases considerably over the same time period. We conclude that interactions with vibrational degrees of freedom not only induce population transfer between the excitonic states in the PSII CC, but also reshape the energy landscape of the system. We suggest that the experimentally observed ultrafast energy transfer is a signature of excitonic-polaron formation.

Temporal dynamics of excitonic states with nonlinear electron-vibrational coupling.

A straightforward extension to the stochastic time-dependent variational approach allows the introduction of higher-order interaction effects to the Hamiltonian of an electronic-vibrational system. This is done using an Ansatz for the global wavefunction, describing vibrational wavepackets as squeezed coherent states (a generalized version of Davydov Ansatz). The approach allows quantum dynamics simulation and simulation of spectroscopic signals on anharmonic molecular potential surfaces. We calculate electronic and vibrational dynamics for a number of model systems, showing some results attributed to nonlinearities in spectroscopy experiments (such as breaking of mirror symmetry between absorption and fluorescence signals) and analyzing the influence of nonlinear effects on electronic energy transfer in multi-site aggregates.

Spectroscopic properties of photosystem II reaction center revisited.

Photosystem II (PSII) is the only biological system capable of splitting water to molecular oxygen. Its reaction center (RC) is responsible for the primary charge separation that drives the water oxidation reaction. In this work, we revisit the spectroscopic properties of the PSII RC using the complex time-dependent Redfield (ctR) theory for optical lineshapes [A. Gelzinis et al., J. Chem. Phys. 142, 154107 (2015)]. We obtain the PSII RC model parameters (site energies, disorder, and reorganization energies) from the fits of several spectra and then further validate the model by calculating additional independent spectra. We obtain good to excellent agreement between theory and calculations. We find that overall our model is similar to some of the previous asymmetric exciton models of the PSII RC. On the other hand, our model displays differences from previous work based on the modified Redfield theory. We extend the ctR theory to describe the Stark spectrum and use its fit to obtain the parameters of a single charge transfer state included in our model. Our results suggest that ChlD1+PheoD1- is most likely the primary charge transfer state, but that the Stark spectrum of the PSII RC is probably also influenced by other states.

Mapping energy transfer channels in fucoxanthin-chlorophyll protein complex.

Fucoxanthin-chlorophyll protein (FCP) is the key molecular complex performing the light-harvesting function in diatoms, which, being a major group of algae, are responsible for up to one quarter of the total primary production on Earth. These photosynthetic organisms contain an unusually large amount of the carotenoid fucoxanthin, which absorbs the light in the blue-green spectral region and transfers the captured excitation energy to the FCP-bound chlorophylls. Due to the large number of fucoxanthins, the excitation energy transfer cascades in these complexes are particularly tangled. In this work we present the two-color two-dimensional electronic spectroscopy experiments on FCP. Analysis of the data using the modified decay associated spectra permits a detailed mapping of the excitation frequency dependent energy transfer flow with a femtosecond time resolution.

Role of coherent vibrations in energy transfer and conversion in photosynthetic pigment-protein complexes.

Oscillatory features of two-dimensional spectra of photosynthetic pigment-protein complexes during few picoseconds after electronic excitations of chlorophylls in various pigment-proteins were recently related to the coherent nuclear vibrations. It has been also speculated that the vibrations may assist the excitonic energy transfer and charge separation, hence contributing to energy transport and energy conversion efficiency. Here, we consider three theoretical approaches usually used for characterization of the excitation dynamics and charge separation, namely Redfield, Förster, and Marcus model descriptions, regarding this question. We show that two out of the three mechanisms require explicit resonances of excitonic splittings and the nuclear vibration frequencies. However, the third one related to the electron transfer is in principle off resonant.

Polaronic effects at finite temperatures in the B850 ring of the LH2 complex.

Energy transfer and relaxation dynamics in the B850 ring of LH2 molecular aggregates are described, taking into account the polaronic effects, by a stochastic time-dependent variational approach. We explicitly include the finite temperature effects in the model by sampling the initial conditions of the vibrational states randomly. This is in contrast to previous applications of the variational approach, which consider only the zero-temperature case. The method allows us to obtain both the microscopic dynamics at the single-wavefunction level and the thermally averaged picture of excitation relaxation over a wide range of temperatures. Spectroscopic observables such as temperature dependent absorption and time-resolved fluorescence spectra are calculated. Microscopic wavefunction evolution is quantified by introducing the exciton participation (localization) length and the exciton coherence length. Their asymptotic temperature dependence demonstrates that the environmental polaronic effects range from exciton self-trapping and excitonic polaron formation at low temperatures to thermally induced state delocalization and decoherence at high temperatures. While the transition towards the polaronic state can be observed on the wavefunction level, it does not produce a discernible effect on the calculated spectroscopic observables.

Vibronic energy relaxation approach highlighting deactivation pathways in carotenoids.

Energy relaxation between two electronic states of a molecule is mediated by a set of relevant vibrational states. We describe this fundamental process in a fully quantum mechanical framework based on first principles. This approach explains population transfer rates as well as describes the entire transient absorption signal as vibronic transitions between electronic states. By applying this vibronic energy relaxation approach to carotenoids, we show that ß-carotene's transient absorption signal can be understood without invoking the intensely debated S* electronic state. For a carotenoid with longer chain length, we find that vibronic energy relaxation does not suffice to explain all features in the transient absorption spectra, which we relate to an increased ground state structural inhomogeneity. Our modeling approach is generally applicable to photophysical deactivation processes in molecules. As such, it represents a well-founded alternative to data fitting techniques such as global target analysis.