Nonlinear Molecular Electronic Spectroscopy via MCTDH Quantum Dynamics: From Exact to Approximate Expressions

We present an accurate and efficient approach to computing the linear and nonlinear optical spectroscopy of a closed quantum system subject to impulsive interactions with an incident electromagnetic field. It incorporates the effect of ultrafast nonadiabatic dynamics by means of explicit numerical propagation of the nuclear wave packet. The fundamental expressions for the evaluation of first- and higher-order response functions are recast in a general form that can be used with any quantum dynamics code capable of computing the overlap of nuclear wave packets evolving in different states. Here we present the evaluation of these expressions with the multiconfiguration time-dependent Hartree (MCTDH) method. Application is made to pyrene, excited to its lowest bright excited state S₂ which exhibits a sub-100-fs nonadiabatic decay to a dark state S₁. The system is described by a linear vibronic coupling Hamiltonian, parametrized with multiconfiguration electronic structure methods. We show that the ultrafast nonadiabatic dynamics can have a remarkable effect on the spectral line shapes that goes beyond simple lifetime broadening. Furthermore, a widely employed approximate expression based on the time scale separation of dephasing and population relaxation is recast in the same theoretical framework. Application to pyrene shows the range of validity of such approximations.

Steady State Photoisomerization Quantum Yield of Model Rhodopsin: Insights from Wavepacket Dynamics?

We simulate the nonequilibrium steady state cis-trans photoisomerization of retinal chromophore in rhodopsin on the basis of a two-state, two-mode model coupled to a thermal environment. By analyzing the systematic trends within an inhomogeneously broadened ensemble of systems, we find that the steady state reaction quantum yield (QY) correlates strongly with the excess energy above the crossing point of the system, in agreement with the prediction of the short-time dynamical wavepacket picture. However, the nontrivial dependence of the QY on the system-environment interaction indicates that a pure dynamical picture is insufficient and that environment-induced partial internal energy redistribution takes place before the reaction concludes. These results imply that a proper treatment of the photoisomerization reaction, particularly its high QY, must account for the redistribution and dissipation of energy beyond the dynamical wavepacket motion that is typically employed in the literature and that is appropriate only in the transient regime.

Ab Initio Quasiclassical Simulation of Femtosecond Time-Resolved Two-Dimensional Electronic Spectra of Pyrazine

Two-dimensional (2D) electronic spectroscopy is a powerful nonlinear technique which provides spectroscopic information on two frequency axes as well as dynamical information as a function of the so-called waiting time. Herein, an ab initio theoretical framework for the simulation of electronic 2D spectra has been developed. The method is based on the classical approximation to the doorway-window representation of three-pulse photon-echo signals and the description of nuclear motion by classical trajectories. Nonadiabatic effects are taken into account by a trajectory surface-hopping algorithm. 2D electronic spectra were simulated with ab initio on-the-fly trajectory calculations using the ADC(2) electronic-structure method for the pyrazine molecule, which is a benchmark system for ultrafast radiationless decay through conical intersections. It is demonstrated that 2D spectroscopy with subfemtosecond UV pulses can provide unprecedented detailed information on the ultrafast photodynamics of polyatomic molecules.

Control of Protonated Schiff Base Excited State Decay within Visual Protein Mimics: A Unified Model for Retinal Chromophores

Artificial biomimetic chromophore-protein complexes inspired by natural visual pigments can feature color tunability across the full visible spectrum. However, control of excited state dynamics of the retinal chromophore, which is of paramount importance for technological applications, is lacking due to its complex and subtle photophysics/photochemistry. Here, ultrafast transient absorption spectroscopy and quantum mechanics/molecular mechanics simulations are combined for the study of highly tunable rhodopsin mimics, as compared to retinal chromophores in solution. Conical intersections and transient fluorescent intermediates are identified with atomistic resolution, providing unambiguous assignment of their ultrafast excited state absorption features. The results point out that the electrostatic environment of the chromophore, modified by protein point mutations, affects its excited state properties allowing control of its photophysics with same power of chemical modifications of the chromophore. The complex nature of such fine control is a fundamental knowledge for the design of bio-mimetic opto-electronic and photonic devices.

Polariton induced conical intersection and berry phase

We investigate the Polariton induced conical intersection (PICI) created from coupling a diatomic molecule with the quantized photon mode inside an optical cavity, and the corresponding Berry Phase effects. We use the rigorous Pauli-Fierz Hamiltonian to describe the quantum light-matter interactions between a LiF molecule and the cavity, and use the exact quantum propagation to investigate the polariton quantum dynamics. The molecular rotations relative to the cavity polarization direction play a role as the tuning mode of the PICI, resulting in an effective CI even within a diatomic molecule. To clearly demonstrate the dynamical effects of the Berry phase, we construct two additional models that have the same Born-Oppenheimer surface, but the effects of the geometric phase are removed. We find that when the initial wavefunction is placed in the lower polaritonic surface, the Berry phase causes a π phase-shift in the wavefunction after the encirclement around the CI, indicated from the nuclear probability distribution. On the other hand, when the initial wavefunction is placed in the upper polaritonic surface, the geometric phase significantly influences the couplings between polaritonic states and therefore, the population dynamics between them. These BP effects are further demonstrated through the photo-fragment angular distribution. PICI created from the quantized radiation field has the promise to open up new possibilities to modulate photochemical reactivities.

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.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

Upper Excited State Photophysics of Malachite Green in Solution and Films

Relaxation pathways of upper excited electronic states of malachite green (MG) in ethanol and in films are studied by steady-state and time-resolved spectroscopic techniques. In contrast to ethanol, where MG emits weak short-lived spectrally well separated S₂ and S₁ fluorescence with the lifetimes ∼0.3 and ∼0.9 ps, MG films show a much stronger broadband fluorescence within 430-700 nm, revealing multiexponential kinetics with the characteristic decay times τ₁ ≈ 1 ps, τ₂ ≈ 10 ps, τ₃ ≈ 0.05-0.8 ns, and τ₄ ≈ 2-3 ns. By the analysis of spectroscopic responses of MG in ethanol and in films as well as by theoretical modeling, we demonstrate that significant increase of fluorescence lifetimes and substantial enhancement of fluorescence intensity in MG films are stipulated by the decrease of efficiency of the S₂ → S₁ and S₁ → S₀ internal conversion, which in turn is caused by hindrance of rotation of MG's phenyl rings controlling the S₂/S₁ and S₁/S₀ conical intersections. These findings indicate that MG films may become promising non-Kasha materials (with reasonable S₂ emission) with numerous photophysical and photochemical applications.

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.

Pyrene, a Test Case for Deep-Ultraviolet Molecular Photophysics

We determined the complete relaxation dynamics of pyrene in ethanol from the second bright state, employing experimental and theoretical broadband heterodyne detected transient grating and two-dimensional photon echo (2DPE) spectroscopy, using pulses with duration of 6 fs and covering a spectral range spanning from 250 to 300 nm. Multiple lifetimes are assigned to conical intersections through a cascade of electronic states, eventually leading to a rapid population of the lowest long-living excited state and subsequent slow vibrational cooling. The lineshapes in the 2DPE spectra indicate that the efficiency of the population transfer depends on the kinetic energy deposited into modes required to reach a sloped conical intersection, which mediates the decay to the lowest electronic state. The presented experimental-theoretical protocol paves the way for studies on deep-ultraviolet-absorbing biochromophores ubiquitous in genomic and proteic systems.

Two-State, Three-Mode Parametrization of the Force Field of a Retinal Chromophore Model

In recent years, the potential energy surfaces of the penta-2,4-dieniminium cation have been investigated using several electronic structure methods. The resulting pool of geometrical, electronic, and energy data provides a suitable basis for the construction of a topographically correct analytical model of the molecule force field and, therefore, for a better understanding of this class of molecules, which includes the chromophore of visual pigments. In the present contribution, we report the construction of such a model for regions of the force field that drive the photochemical and thermal isomerization of the central double bound of the cation. While previous models included only two modes, it is here shown that the proposed three-mode model and corresponding set of parameters are able to reproduce the complex topographical and electronic structure features seen in electronically correlated data obtained at the XMCQDPT2//CASSCF/6-31G* level of theory.

Two-dimensional UV spectroscopy: a new insight into the structure and dynamics of biomolecules

Two-dimensional ultraviolet spectroscopy has the potential to deliver rich structural and dynamical information on biomolecules such as DNA and proteins.