Model Study of Coherent-Control of the Femtosecond Primary Event of Vision

Tensor-Train Split-Operator KSL (TT-SOKSL) Method for Quantum Dynamics Simulations

Numerically exact simulations of quantum reaction dynamics, including nonadiabatic effects in excited electronic states, are essential to gain fundamental insights into ultrafast chemical reactivity and rigorous interpretations of molecular spectroscopy. Here, we introduce the tensor-train split-operator KSL (TT-SOKSL) method for quantum simulations in tensor-train (TT)/matrix product state (MPS) representations. TT-SOKSL propagates the quantum state as a tensor train using the Trotter expansion of the time-evolution operator, as in the tensor-train split-operator Fourier transform (TT-SOFT) method. However, the exponential operators of the Trotter expansion are applied using a rank-adaptive TT-KSL scheme instead of using the scaling and squaring approach as in TT-SOFT. We demonstrate the accuracy and efficiency of TT-SOKSL as applied to simulations of the photoisomerization of the retinal chromophore in rhodopsin, including nonadiabatic dynamics at a conical intersection of potential energy surfaces. The quantum evolution is described in full dimensionality by a time-dependent wavepacket evolving according to a two-state 25-dimensional model Hamiltonian. We find that TT-SOKSL converges faster than TT-SOFT with respect to the maximally allowed memory requirement of the tensor-train representation and better preserves the norm of the time-evolving state. When compared to the corresponding simulations based on the TT-KSL method, TT-SOKSL has the advantage of avoiding the need to construct the matrix product state Laplacian by exploiting the linear scaling of multidimensional tensor-train Fourier transforms.

Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations

Methods for efficient simulations of multidimensional quantum dynamics are essential for theoretical studies of chemical systems where quantum effects are important, such as those involving rearrangements of protons or electronic configurations. Here, we introduce the functional tensor-train Chebyshev (FTTC) method for rigorous nuclear quantum dynamics simulations. FTTC is essentially the Chebyshev propagation scheme applied to the initial state represented in a continuous analogue tensor-train format. We demonstrate the capabilities of FTTC as applied to simulations of proton quantum dynamics in a 50-dimensional model of hydrogen-bonded DNA base pairs.

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.

On Weak-Field (One-Photon) Coherent Control of Photoisomerization

Photochemistry induced by phase-coherent laser light is an intriguing topic. The possibility of weak-field (one-photon) phase-only control of photoisomerization is controversial. Experimental studies on the weak-field coherent control of cis-trans isomerization have led to conflicting results. Here we address this issue by quantum dynamical calculations, focusing on a mechanism where different "phase-shaped" wave packets are quickly stabilized ("dumped") in the trans configuration because of prompt energy dissipation. We systematically investigate different relaxation rates with the system-bath dynamics described within the time-dependent Hartree approximation leading to a friction-type force. We find evidence for phase control of trans-isomer yields (about 5%) in this model with pure energy dissipation given sufficiently strong dampening.

Quantum and Quantum-Classical Studies of the Photoisomerization of a Retinal Chromophore Model

We report an in-depth analysis of the photo-induced isomerization of the 2-cis-penta-2,4-dieniminium cation: a minimal model of the 11-cis retinal protonated Schiff base chromophore of the dim-light photoreceptor rhodopsin. Based on recently developed three-dimensional potentials parametrized on ab initio multi-state multi-configurational second-order perturbation theory data, we perform quantum-dynamical studies. In addition, simulations based on various quantum-classical methods, among which Tully surface hopping and the coupled-trajectory approach derived from the exact factorization, allow us to validate their performance against vibronic wavepacket propagation and, therefore, a purely quantum treatment. Quantum-dynamics results uncover qualitative differences with respect to the two-dimensional Hahn-Stock potentials, widely used as model potentials for the isomerization of the same chromophore, due to the increased dimensionality and three-mode correlation. Quantum-classical simulations show, instead, that three-dimensional model potentials are capable of capturing a number of features revealed by atomistic simulations and experimental observations. In particular, a recently reported vibrational phase relationship between double-bond torsion and hydrogen-out-of-plane modes critical for rhodopsin isomerization efficiency is correctly reproduced.

Floquet Study of Quantum Control of the Cis-Trans Photoisomerization of Rhodopsin

Understanding how to control reaction dynamics of polyatomic systems by using ultrafast laser technology is a fundamental challenge of great technological interest. Here, we report a Floquet theoretical study of the effect of light-induced potentials on the ultrafast cis-trans photoisomerization dynamics of rhodopsin. The Floquet Hamiltonian involves an empirical 3-state 25-mode model with frequencies and excited-state gradients parametrized to reproduce the rhodopsin electronic vertical excitation energy, the resonance Raman spectrum, and the photoisomerization time and efficiency as probed by ultrafast spectroscopy. We simulate the excited state relaxation dynamics using the time-dependent self-consistent field method, as described by a 3-state 2-mode nuclear wavepacket coupled to a Gaussian ansatz of 23 vibronic modes. We analyze the reaction time and product yield obtained with pulses of various widths and intensity profiles, defining 'dressed states' where the perturbational effect of the pulses is naturally decoupled along the different reaction channels. We find pulses that delay the excited-state photoisomerization for hundreds of femtoseconds, and we gain insights on the underlying control mechanisms. The reported findings provide understanding of quantum control, particularly valuable for the development of ultrafast optical switches based on visual pigments.

Ultrafast dynamics in the power stroke of a molecular rotary motor

Light-driven molecular motors convert light into mechanical energy through excited-state reactions. Unidirectional rotary molecular motors based on chiral overcrowded alkenes operate through consecutive photochemical and thermal steps. The thermal (helix inverting) step has been optimized successfully through variations in molecular structure, but much less is known about the photochemical step, which provides power to the motor. Ultimately, controlling the efficiency of molecular motors requires a detailed picture of the molecular dynamics on the excited-state potential energy surface. Here, we characterize the primary events that follow photon absorption by a unidirectional molecular motor using ultrafast fluorescence up-conversion measurements with sub 50 fs time resolution. We observe an extraordinarily fast initial relaxation out of the Franck-Condon region that suggests a barrierless reaction coordinate. This fast molecular motion is shown to be accompanied by the excitation of coherent excited-state structural motion. The implications of these observations for manipulating motor efficiency are discussed.

Control of retinal isomerization in bacteriorhodopsin in the high-intensity regime

A learning algorithm was used to manipulate optical pulse shapes and optimize retinal isomerization in bacteriorhodopsin, for excitation levels up to 1.8 x 10(16) photons per square centimeter. Below 1/3 the maximum excitation level, the yield was not sensitive to pulse shape. Above this level the learning algorithm found that a Fourier-transform-limited (TL) pulse maximized the 13-cis population. For this optimal pulse the yield increases linearly with intensity well beyond the saturation of the first excited state. To understand these results we performed systematic searches varying the chirp and energy of the pump pulses while monitoring the isomerization yield. The results are interpreted including the influence of 1-photon and multiphoton transitions. The population dynamics in each intermediate conformation and the final branching ratio between the all-trans and 13-cis isomers are modified by changes in the pulse energy and duration.

Coherent Control of Quantum Dynamics with Sequences of Unitary Phase-Kick Pulses

Coherent-optical-control schemes exploit the coherence of laser pulses to change the phases of interfering dynamical pathways and manipulate dynamical processes. These active control methods are closely related to dynamical decoupling techniques, popularized in the field of quantum information. Inspired by nuclear magnetic resonance spectroscopy, dynamical decoupling methods apply sequences of unitary operations to modify the interference phenomena responsible for the system dynamics thus also belonging to the general class of coherent-control techniques. This article reviews related developments in the fields of coherent optical control and dynamical decoupling, emphasizing the control of tunneling and decoherence in general model systems. Considering recent experimental breakthroughs in the demonstration of active control of a variety of systems, we anticipate that the reviewed coherent-control scenarios and dynamical-decoupling methods should raise significant experimental interest.

Femtosecond quantum control of molecular dynamics in the condensed phase

We review the progress in controlling quantum dynamical processes in the condensed phase with femtosecond laser pulses. Due to its high particle density the condensed phase has both high relevance and appeal for chemical synthesis. Thus, in recent years different methods have been developed to manipulate the dynamics of condensed-phase systems by changing one or multiple laser pulse parameters. Single-parameter control is often achieved by variation of the excitation pulse's wavelength, its linear chirp or its temporal subpulse separation in case of pulse sequences. Multiparameter control schemes are more flexible and provide a much larger parameter space for an optimal solution. This is realized in adaptive femtosecond quantum control, in which the optimal solution is iteratively obtained through the combination of an experimental feedback signal and an automated learning algorithm. Several experiments are presented that illustrate the different control concepts and highlight their broad applicability. These fascinating achievements show the continuous progress on the way towards the control of complex quantum reactions in the condensed phase.

Coherent Control of Retinal Isomerization in Bacteriorhodopsin

Optical control of the primary step of photoisomerization of the retinal molecule in bacteriorhodopsin from the all-trans to the 13-cis state was demonstrated under weak field conditions (where only 1 of 300 retinal molecules absorbs a photon during the excitation cycle) that are relevant to understanding biological processes. By modulating the phases and amplitudes of the spectral components in the photoexcitation pulse, we showed that the absolute quantity of 13-cis retinal formed upon excitation can be enhanced or suppressed by +/-20% of the yield observed using a short transform-limited pulse having the same actinic energy. The shaped pulses were shown to be phase-sensitive at intensities too low to access different higher electronic states, and so these pulses apparently steer the isomerization through constructive and destructive interference effects, a mechanism supported by observed signatures of vibrational coherence. These results show that the wave properties of matter can be observed and even manipulated in a system as large and complex as a protein.

Matching-pursuit split-operator Fourier-transform simulations of excited-state intramolecular proton transfer in 2-(2′-hydroxyphenyl)-oxazole

The excited-state intramolecular proton-transfer dynamics associated with the keto-enolic tautomerization reaction in 2-(2(')-hydroxyphenyl)-oxazole is simulated according to a numerically exact quantum-dynamics propagation method and a full-dimensional excited-state potential energy surface, based on an ab initio reaction surface Hamiltonian. The reported simulations involve the propagation of 35-dimensional wave packets according to the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method by Wu and Batista. The underlying propagation scheme recursively applies the time-evolution operator as defined by the Trotter expansion to second order accuracy in dynamically adaptive coherent-state expansions. Computations of time-dependent survival amplitudes, photoabsorption cross sections, and time-dependent reactant(product) populations are compared to the corresponding calculations based on semiclassical approaches, including the Herman-Kluk semiclassical initial value representation method. The reported results demonstrate the capabilities of the MP/SOFT method as a valuble computational tool to study ultrafast reaction dynamics in polyatomic systems as well as to validate semiclassical simulations of complex (nonintegrable) quantum dynamics in multidimensional model systems.

Model study of coherent quantum dynamics of hole states in functionalized semiconductor nanostructures

Functionalization of semiconductor nanocrystals can be achieved by anchoring organic ligands to the surface dangling bonds. The resulting surface complexes often introduce electronic states in the semiconductor band gap. These interband states sensitize the host material for photoabsorption at frequencies characteristic of the molecular adsorbates, leading to the well-known process of photoexcitation and subsequent femtosecond interfacial electron transfer. This paper investigates the relaxation dynamics of hole states, energetically localized deep in the semiconductor band gap, after the ultrafast electron-hole pair separation due to interfacial electron transfer. Mixed quantum-classical methods, based on mean-field nuclear dynamics approximated by ab initio density functional theory molecular dynamics simulations, reveal superexchange hole tunneling between adjacent adsorbate molecules in a model study of functionalized TiO2-anatase nanostructures. It is shown that electronic coherences can persist for hundreds of picoseconds under cryogenic and vacuum conditions, despite the partial intrinsic decoherence induced by thermal ionic motion, providing results of broad theoretical and experimental interest.

Vibrational energy relaxation in proteins

An overview of theories related to vibrational energy relaxation (VER) in proteins is presented. VER of a selected mode in cytochrome c is studied by using two theoretical approaches. One approach is the equilibrium simulation approach with quantum correction factors, and the other is the reduced model approach, which describes the protein as an ensemble of normal modes interacting through nonlinear coupling elements. Both methods result in similar estimates of the VER time (subpicoseconds) for a CD stretching mode in the protein at room temperature. The theoretical predictions are in accord with previous experimental data. A perspective on directions for the detailed study of time scales and mechanisms of VER in proteins is presented.

QM/MM study of energy storage and molecular rearrangements due to the primary event in vision

The energy storage and the molecular rearrangements due to the primary photochemical event in rhodopsin are investigated by using quantum mechanics/molecular mechanics hybrid methods in conjunction with high-resolution structural data of bovine visual rhodopsin. The analysis of the reactant and product molecular structures reveals the energy storage mechanism as determined by the detailed molecular rearrangements of the retinyl chromophore, including rotation of the (C11-C12) dihedral angle from -11 degrees in the 11-cis isomer to -161 degrees in the all-trans product, where the preferential sense of rotation is determined by the steric interactions between Ala-117 and the polyene chain at the C13 position, torsion of the polyene chain due to steric constraints in the binding pocket, and stretching of the salt bridge between the protonated Schiff base and the Glu-113 counterion by reorientation of the polarized bonds that localize the net positive charge at the Schiff-base linkage. The energy storage, computed at the ONIOM electronic-embedding approach (B3LYP/6-31G*:AMBER) level of theory and the S0-->S1 electronic-excitation energies for the dark and product states, obtained at the ONIOM electronic-embedding approach (TD-B3LYP/6-31G*//B3LYP/6-31G*:AMBER) level of theory, are in very good agreement with experimental data. These results are particularly relevant to the development of a first-principles understanding of the structure-function relations in prototypical G-protein-coupled receptors.