Impact of Vibrational Coherence on the Quantum Yield at a Conical Intersection

Intramolecular charge transfer and the function of vibronic excitons in photosynthetic light harvesting

A widely discussed explanation for the prevalence of pairs or clusters of closely spaced electronic chromophores in photosynthetic light-harvesting proteins is the presence of ultrafast and highly directional excitation energy transfer pathways mediated by vibronic excitons, the delocalized optical excitations derived from mixing of the electronic and vibrational states of the chromophores. We discuss herein the hypothesis that internal conversion processes between exciton states on the <100 fs timescale are possible when the excitonic potential energy surfaces are controlled by the vibrational modes that induce charge transfer character in a strongly coupled system of chromophores. We discuss two examples, the peridinin-chlorophyll protein from marine dinoflagellates and the intact phycobilisome from cyanobacteria, in which the intramolecular charge-transfer (ICT) character arising from out-of-plane distortion of the conjugation of carotenoid or bilin chromophores also results in localization of the initially delocalized optical excitation on the vibrational timescale. Tuning of the ground state conformations of the chromophores to manipulate their ICT character provides a natural photoregulatory mechanism, which would control the overall quantum yield of excitation energy transfer by turning on and off the delocalized character of the optical excitations.

Coherent Ultrafast Stimulated X-Ray Raman Spectroscopy of Dissipative Conical Intersections

The quantum coherent dynamics of a vibronic wave packet in a molecule passing through a conical intersection can be revealed using attosecond transient coherent Raman spectroscopy. In particular, the time evolution of the electronic coherence can be monitored in the presence of vibrational dynamics. So far, the technique has been investigated without including environmental quantum noise. Here, we employ the numerically exact hierarchy equation of motion approach to show that the transient coherent Raman signals are robust and accessible on times of up to a few hundred femtoseconds with respect to electonic and vibrational dephasing.

Coherent control from quantum commitment probabilities

We introduce a general definition of a quantum committor in order to clarify reaction mechanisms and facilitate control in processes where coherent effects are important. With a quantum committor, we generalize the notion of a transition state to quantum superpositions and quantify the effect of interference on the progress of the reaction. The formalism is applicable to any linear quantum master equation supporting metastability for which absorbing boundary conditions designating the reactant and product states can be applied. We use this formalism to determine the dependence of the quantum transition state on coherences in a polaritonic system and optimize the initialization state of a conical intersection model to control reactive outcomes, achieving yields of the desired state approaching 100%. In addition to providing a practical tool, the quantum committor provides a conceptual framework for understanding reactions in cases when classical intuitions fail.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Analysis of molecular photomechanical performance using a one-dimensional harmonic model

The photochemical reaction of a molecule leads to a change in the position of its nuclei that can be harnessed to perform mechanical work. Photomechanical materials use this effect to act as light-powered actuators. In this paper, a one-dimensional model based on coupled harmonic potential energy surfaces is developed to describe the photomechanical response of a molecule. This model generates predictions that are qualitatively consistent with standard mechanochemistry models for ground state rate reactions. To analyze the photomechanical process, excited state dynamics like photon absorption and relaxation are included. The model allows us to derive analytical expressions for the work output, blocking force, and absorbed photon-to-work efficiency. The effects of nonadiabatic electronic coupling, unequal frequency potentials, and the cycling efficiency are also analyzed. If the starting state is the stable (lower energy) isomer, it is possible to attain photon-to-work efficiencies up to 55.4%. If initial state is higher in energy, for example a metastable isomer, then one-way efficiencies > 100% are possible due to the release of stored potential energy. Photomechanical materials can be competitive with photovoltaic–piezoelectric combinations in terms of efficiency, but current materials will require substantial improvement before they can approach the theoretical limits.

Graphical abstract

A systematic model study quantifying how conical intersection topography modulates photochemical reactions

Despite their important role in photochemistry and expected presence in most polyatomic molecules, conical intersections have been thoroughly characterized in a comparatively small number of systems. Conical intersections can confer molecular photoreactivity or photostability, often with remarkable efficacy, due to their unique structure: at a conical intersection, the adiabatic potential energy surfaces of two or more electronic states are degenerate, enabling ultrafast decay from an excited state without radiative emission, known as nonadiabatic transfer. Furthermore, the precise conical intersection topography determines fundamental properties of photochemical processes, including excited-state decay rate, efficacy, and molecular products that are formed. However, these relationships have yet to be defined comprehensively. In this article, we use an adaptable computational model to investigate a variety of conical intersection topographies, simulate resulting nonadiabatic dynamics, and calculate key photochemical observables. We varied the vibrational mode frequencies to modify conical intersection topography systematically in four primary classes of conical intersections and quantified the resulting rate, total yield, and product yield of nonadiabatic decay. The results reveal that higher vibrational mode frequencies reduce nonadiabatic transfer, but increase the transfer rate and resulting photoproduct formation. These trends can inform progress toward experimental control of photochemical reactions or tuning of molecules' photochemical properties based on conical intersections and their topography.

Uncovering the Functional Role of Coherent Phonons during the Photoinduced Phase Transition in a Molecular Crystal

The atomic motions that make up phonons and molecular vibrations in molecular crystals influence their photophysical and electronic properties, including polaron formation, carrier mobility, and phase transitions. Discriminating between spectator and driving motions is a significant challenge hindering optimization. Unlocking this information and developing fine-tuned controls over actively participating phonon modes would not only lead to a stronger understanding of photochemistry but also provide a significant new tool in controlling solid state chemistry. We present a strategy using rationally designed double pulses to unveil the unique function of specific excited state phonon modes. Using ultrafast spectroscopy, we identified 50 and 90 cm^-1 phonons involved in modulating the photoinduced spin-Peierls melting of potassium tetracyanoquinodimethane crystals. We show that the 50 cm^-1 phonon specifically corresponds to the coherent nuclear wavepacket involved in the charge transfer component of the overall spin-Peierls phase melting process, while the 90 cm^-1 phonon facilitates the phase transition component.

Mapping of Wave Packet Dynamics at Conical Intersections by Time- and Frequency-Resolved Fluorescence Spectroscopy: A Computational Study

Monitoring of wave packet dynamics at conical intersections by time- and frequency-resolved fluorescence spectroscopy has been investigated theoretically for a three-state two-mode model of a conical intersection coupled to a dissipative environment. The ideal and the actually measurable time- and frequency-gated fluorescence spectra are accurately and efficiently simulated by combining the hierarchy equations-of-motion method for dissipative quantum dynamics with the methodology of the equation-of-motion phase-matching approach for the calculation of spectroscopic signals. It is shown that time- and frequency-resolved fluorescence spectra reveal essential aspects of the wave packet dynamics at conical intersections and the effects of environment-induced dissipation. The results of the present work indicate that fluorescence up-conversion spectroscopy with femtosecond time resolution is an efficient tool for the characterization of ultrafast dynamics at conical intersections.

High Magnetic Field Detunes Vibronic Resonances in Photosynthetic Light Harvesting

The origin and role of oscillatory features detected in recent femtosecond spectroscopy experiments of photosynthetic complexes remain elusive. A key hypothesis underneath of these observations relies on electronic-vibrational resonance, where vibrational levels of an acceptor chromophore match the donor-acceptor electronic gap, accelerating the downhill energy transfer. Here we identify and detune such vibronic resonances using a high magnetic field that exclusively shifts molecular exciton states. We implemented ultrafast pump-probe spectroscopy into a specialized 25 T magnetic field facility and studied the light-harvesting complex PC645 from a cryptophyte algae where strongly coupled chromophores form molecular exciton states. We detected a change in high-frequency coherent oscillations when the field was engaged. Quantum chemical calculations coupled with a vibronic model explain the experiment as a magnetic field-induced shift of the exciton states, which in turn affects the electronic-vibrational resonance between pigments within the protein. Our results demonstrate the delicate sensitivity of interpigment coherent oscillations of vibronic origin to electronic-vibrational resonance interactions in light-harvesting complexes.

Ultrafast Dynamics in Light-Driven Molecular Rotary Motors Probed by Femtosecond Stimulated Raman Spectroscopy

Photochemical isomerization in sterically crowded chiral alkenes is the driving force for molecular rotary motors in nanoscale machines. Here the excited-state dynamics and structural evolution of the prototypical light-driven rotary motor are followed on the ultrafast time scale by femtosecond stimulated Raman spectroscopy (FSRS) and transient absorption (TA). TA reveals a sub-100-fs blue shift and decay of the Franck-Condon bright state arising from relaxation along the reactive potential energy surface. The decay is accompanied by coherently excited vibrational dynamics which survive the excited-state structural evolution. The ultrafast Franck-Condon bright state relaxes to a dark excited state, which FSRS reveals to have a rich spectrum compared to the electronic ground state, with the most intense Raman-active modes shifted to significantly lower wavenumber. This is discussed in terms of a reduced bond order of the central bridging bond and overall weakening of bonds in the dark state, which is supported by electronic structure calculations. The observed evolution in the FSRS spectrum is assigned to vibrational cooling accompanied by partitioning of the dark state between the product isomer and the original ground state. Formation of the product isomer is observed in real time by FSRS. It is formed vibrationally hot and cools over several picoseconds, completing the characterization of the light-driven half of the photocycle.

Atomistic Analysis of Room Temperature Quantum Coherence in Two-Dimensional CdSe Nanostructures

Recent experiments on CdSe nanoplatelets synthesized with precisely controlled thickness that eliminates ensemble disorder have allowed accurate measurement of quantum coherence at room temperature. Matching exactly the CdSe cores of the experimentally studied particles and considering several defects, we establish the atomistic origins of the loss of coherence between heavy and light hole excitations in two-dimensional CdSe and CdSe/CdZnS core/shell structures. The coherence times obtained using molecular dynamics based on tight-binding density functional theory are in excellent agreement with the measured values. We show that a long coherence time is a consequence of both small fluctuations in the energy gap between the excited state pair, which is much less than thermal energy, and a slow decay of correlation between the energies of the two states. Anionic defects at the core/shell interface have little effect on the coherence lifetime, while cationic defects strongly perturb the electronic structure, destroying the experimentally observed coherence. By coupling to the same phonon modes, the heavy and light holes synchronize their energy fluctuations, facilitating long-lived coherence. We further demonstrate that the electronic excitations are localized close to the surface of these narrow nanoscale systems, and therefore, they couple most strongly to surface acoustic phonons. The established features of electron-phonon coupling and the influence of defects, surfaces, and core/shell interfaces provide important insights into quantum coherence in nanoscale materials in general.