Classical description of nonadiabatic photoisomerization processes and their real‐time detection via femtosecond spectroscopy

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.

Characterizing Mode Anharmonicity and Huang-Rhys Factors Using Models of Femtosecond Coherence Spectra

Femtosecond laser pulses readily produce coherent quantum beats in transient-absorption spectra. These oscillatory signals often arise from molecular vibrations and therefore may contain information about the excited-state potential energy surface near the Franck-Condon region. Here, by fitting the measured spectra of two laser dyes to microscopic models of femtosecond coherence spectra (FCS) arising from molecular vibrations, we classify coherent quantum-beat signals as fundamentals or overtones and quantify their Huang-Rhys factors and anharmonicity values. We discuss the extracted Huang-Rhys factors in the context of quantum-chemical computations. This work solidifies the use of FCS for analysis of coherent quantum beats arising from molecular vibrations, which will aid studies of molecular aggregates and photosynthetic proteins.

Relaxation dynamics through a conical intersection: Quantum and quantum-classical studies

We study the relaxation process through a conical intersection of a photo-excited retinal chromophore model. The analysis is based on a two-electronic-state two-dimensional Hamiltonian developed by Hahn and Stock [J. Phys. Chem. B 104 1146 (2000)] to reproduce, with a minimal model, the main features of the 11-cis to all-trans isomerization of the retinal of rhodopsin. In particular, we focus on the performance of various trajectory-based schemes to nonadiabatic dynamics, and we compare quantum-classical results to the numerically exact quantum vibronic wavepacket dynamics. The purpose of this work is to investigate, by analyzing electronic and nuclear observables, how the sampling of initial conditions for the trajectories affects the subsequent dynamics.

E to Z Photoisomerization of Phytochrome Cph1Δ Exceeds the Born-Oppenheimer Adiabatic Limit

The Born-Oppenheimer adiabatic limit applies broadly in chemistry because most reactions occur on the ground electronic state. Photochemical reactions involve two or more electronic states and need not be subject to this adiabatic limit. The spectroscopic signatures of nonadiabatic processes are subtle, and therefore, experimental investigations have been limited to the few systems dominated by single photochemical outcomes. Systems with branched excited-state pathways have been neglected, despite their potential to reveal insights into photochemical reactivity. Here we present experimental evidence from coherent three-dimensional electronic spectroscopy that the E to Z photoisomerization of phytochrome Cph1 is strongly nonadiabatic, and the simulations reproduce the measured features only when the photoisomerization proceeds nonadiabatically near, but not through, a conical intersection. The results broaden the general understanding of photoisomerization mechanisms and motivate future studies of nonadiabatic processes with multiple outcomes arising from branching on excited-state potential energy surfaces.

A symmetrical quasi-classical windowing model for the molecular dynamics treatment of non-adiabatic processes involving many electronic states

In the previous work of Cotton and Miller [J. Chem. Phys. 145, 144108 (2016)], an improved symmetrical quasi-classical (SQC) windowing model for the molecular dynamics treatment of electronically non-adiabatic processes was developed in order to extend the original SQC approach to the regime of weak-coupling between the electronic states. The improved SQC model-based on triangular-shaped window functions-handled the weak-coupling limit as intended and, as a bonus, was shown to be universally superior to the original square/histogram SQC windowing model over all coupling regimes, but only for treating systems of two electronic states, as no higher-dimensional generalization was evident. This paper, therefore, provides a generalized version for treating an arbitrary number of electronic states. By construction, the benefits of the two-state triangle model-seamless treatment of weak-coupling and improved accuracy in all coupling regimes-carry over to the generalized version. Far more significant, however, is that the new model provides vastly improved windowing statistics in higher dimensions, enabling the SQC simulation of electronically non-adiabatic processes involving many more relevant electronic states than was previously practical. Capabilities are demonstrated with respect to a 24 pigment trimer model of the Fenna-Matthews-Olson light-harvesting complex, as well as treating similar 48- and 96-electronic state model problems, illustrating the scaling properties of the new method.

Coulomb Explosion Imaging for the Visualization of a Conical Intersection

Coulomb explosion imaging is proposed as a method to directly map the presence of conical intersections encountered by a propagating wave packet in a molecular system. The case of choice is the nonadiabatic coupling between two dissociative surfaces in the methyl iodide molecule, probed by Coulomb explosion with short, intense near-infrared pulses causing multiple ionization. On-the-fly multidimensional trajectory calculations with surface hopping using perturbation theory and including spin-orbit coupling are performed to visualize the dynamics through the conical intersection and compare with experimental results. The possibilities and limitations of the technique are examined and discussed.

Experimental Detection of Branching at a Conical Intersection in a Highly Fluorescent Molecule

Conical intersections are molecular configurations at which adiabatic potential-energy surfaces touch. They are predicted to be ubiquitous, yet condensed-phase experiments have focused on the few systems with clear spectroscopic signatures of negligible fluorescence, high photoactivity, or femtosecond electronic kinetics. Although rare, these signatures have become diagnostic for conical intersections. Here we detect a coherent surface-crossing event nearly two picoseconds after optical excitation in a highly fluorescent molecule that has no photoactivity and nanosecond electronic kinetics. Time-frequency analysis of high-sensitivity measurements acquired using sub-8 fs pulses reveals phase shifts of the signal due to branching of the wavepacket through a conical intersection. The time-frequency analysis methodology demonstrated here on a model compound will enable studies of conical intersections in molecules that do not exhibit their diagnostic signatures. Improving the ability to detect conical intersections will enrich the understanding of their mechanistic role in molecular photochemistry.

Classical molecular dynamics simulation of electronically non-adiabatic processes

Both classical and quantum mechanics (as well as hybrids thereof, i.e., semiclassical approaches) find widespread use in simulating dynamical processes in molecular systems. For large chemical systems, however, which involve potential energy surfaces (PES) of general/arbitrary form, it is usually the case that only classical molecular dynamics (MD) approaches are feasible, and their use is thus ubiquitous nowadays, at least for chemical processes involving dynamics on a single PES (i.e., within a single Born–Oppenheimer electronic state). This paper reviews recent developments in an approach which extends standard classical MD methods to the treatment of electronically non-adiabatic processes, i.e., those that involve transitions between different electronic states. The approach treats nuclear and electronic degrees of freedom (DOF) equivalently (i.e., by classical mechanics, thereby retaining the simplicity of standard MD), and provides “quantization” of the electronic states through a symmetrical quasi-classical (SQC) windowing model. The approach is seen to be capable of treating extreme regimes of strong and weak coupling between the electronic states, as well as accurately describing coherence effects in the electronic DOF (including the de-coherence of such effects caused by coupling to the nuclear DOF). A survey of recent applications is presented to illustrate the performance of the approach. Also described is a newly developed variation on the original SQC model (found universally superior to the original) and a general extension of the SQC model to obtain the full electronic density matrix (at no additional cost/complexity).

A coherent state approach to semiclassical nonadiabatic dynamics

A semiclassical (SC) approximation to the quantum mechanical propagator for nonadiabatic systems is derived. Our derivation starts with an exact path integral expression that uses canonical coherent states for the nuclear degrees of freedom and spin coherent states for the electronic degrees of freedom. A stationary path approximation (SPA) is then applied to the path integral to obtain the SC approximation. The SPA results in complex classical trajectories of both nuclear and electronic degrees of freedom and a double ended boundary condition. The root search problem is solved using the previously proposed "real trajectory local search" algorithm. The SC approximation is tested on three simple one dimensional two-state systems proposed by Tully [J. Chem. Phys. 93, 1061 (1990)], and the SC results are compared to Ehrenfest and surface hopping predictions. Excellent agreement with quantum results is reached when the SC trajectory is far away from caustics. We discuss the origin of caustics in this SC formalism and the strengths and weaknesses of this approach.