A classical time-frequency theory of transient absorption 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.

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.

Ab Initio Surface-Hopping Simulation of Femtosecond Transient-Absorption Pump-Probe Signals of Nonadiabatic Excited-State Dynamics Using the Doorway-Window Representation

An ab initio theoretical framework for the simulation of femtosecond time-resolved transient absorption (TA) pump-probe (PP) spectra with quasi-classical trajectories is presented. The simulations are based on the classical approximation to the doorway-window (DW) representation of third-order four-wave-mixing signals. The DW formula accounts for the finite duration and spectral shape of the pump and probe pulses. In the classical DW formalism, classical trajectories are stochastically sampled from a positive definite doorway distribution, and the signals are evaluated by averaging over a positive definite window distribution. Nonadiabatic excited-state dynamics is described by a stochastic surface-hopping algorithm. The method has been implemented for the pyrazine molecule with the second-order algebraic-diagrammatic construction (ADC(2)) ab initio electronic-structure method. The methodology is illustrated by ab initio simulations of the ground-state bleach, stimulated emission, and excited-state absorption contributions to the TA PP spectrum of gas-phase pyrazine.

Optical N-wave-mixing spectroscopy with strong and temporally well-separated pulses: the doorway-window representation

We have extended the doorway-window representation of optical pump-probe spectroscopy with weak pulses toward N-wave-mixing spectroscopy with temporally well-separated pulses of arbitrary strength. The expressions for the signals in the strong-pulse doorway-window representation are derived in the framework of the nonperturbative theory of N-wave-mixing spectroscopy. The strong-pulse doorway-window representation is complementary to the equation-of-motion phase-matching approach. The latter fully accounts for pulse-overlap effects in signals induced by weak pulses but is computationally more expensive. The performance of the doorway-window approximation for temporally well-separated strong pulses is illustrated for an electronic two-level system with an underdamped Condon-active vibrational mode.

Role of Molecular Anchor Groups in Molecule-to-Semiconductor Electron Transfer

The dynamics of heterogeneous electron transfer (ET) from the polycyclic aromatic chromophore perylene to nanostructured TiO2 anatase was investigated for two different anchor groups with transient absorption spectroscopy in an ultrahigh vacuum. Data from ultraviolet photoelectron spectroscopy and from linear absorption spectroscopy showed that the donor state of the chromophore was located around 900 meV above the lower edge of the conduction band. With the wide band limit fulfilled the rate of the heterogeneous ET reaction was only controlled by the strength of the electronic coupling and not reduced by Franck-Condon factors. Two different time constants for the electron transfer, i.e., 13 and 28 fs, were measured with carboxylic acid and phosphonic acid as the respective anchor groups. The difference in the ET time constants was explained with the different extension of the donor orbital onto the respective anchor group to reach the empty electronic states of the semiconductor. The time constants were extracted by means of a simple rate equation model. The validity of applying this model on this ultrafast time scale was verified by comparing the rate equation model with an optical Bloch equation model.

Transient Phenomena in Time- and Frequency-Gated Spontaneous Emission

The effect of overlapping pump and gate pulses on time- and frequency-gated spontaneous emission spectra is explored for a model of material dynamics that accounts for strong nonadiabatic and electron-vibrational coupling effects, vibrational relaxation, and optical dephasing, thus representing characteristic features of photoinduced excited-state dynamics in large molecules in the gas phase or in condensed phases. The behaviors of the sequential, coherent, and doorway-window contributions to the spontaneous emission spectrum are studied separately. The interrelation between the sequential and coherent contributions is demonstrated to be sensitive to the carrier frequencies of the pump and gate pulses and also to the optical dephasing rate, opening the possibility of an experimental determination of the latter. The coherent contribution is shown to dominate the spectrum at specific emission frequencies.