Periodic-Orbit Analysis of Coherent Electron-Transfer Femtosecond Experiments

Abstract

Femtosecond time-resolved experiments on chemical and biophysical electron-transfer systems may reveal complicated coherent beating which often cannot be simply attributed to nuclear motion on a single BornOppenheimer potential-energy surface but rather reflects electronic transitions driven by coherent nuclear motion. To facilitate an intuitive classical interpretation of these experiments, a recently proposed theoretical formulation is employed that affords an exact mapping of discrete electronic states onto continuous degrees of freedom and therefore provides a well-defined classical limit of a nonadiabatically coupled system. The formulation is used to consider the classical periodic orbits of an electron-transfer system, i.e., trajectories that describe periodic nuclear motion on several coupled potential-energy surfaces. Employing concepts of semiclassical periodic-orbit theory, it is demonstrated that transient oscillations observed in electron-transfer femtosecond experiments may be explained in terms of a few classical trajectories.With the advent of femtosecond laser pulses it has become possible to observe the nuclear motion during a chemical reaction in real time. 1 This is achieved by a pump-probe type experiment in which the molecular system is prepared at time t ) 0 by a first laser pulse (the "pump") into a nonstationary state, whose time evolution is interrogated by a second laser pulse (the "probe") at the delay time ∆t. Employing ultrashort laser pulses, the transient absorption of a polyatomic system may exhibit multiple kinetics and complex oscillation patterns, thus reflecting coherent wave packet motion on multidimensional potential-energy surfaces.In many cases, however, the interpretation of photoinduced molecular dynamics is complicated by the fact that the underlying Born-Oppenheimer assumption of noninteracting adiabatic potential-energy surfaces may break down. This becomes evident, for example, for molecules exhibiting internal conversion or photoinduced electron transfer. 2 Here, various groups have reported transient spectra showing complicated oscillations, which often cannot be simply attributed to nuclear motion on a single Born-Oppenheimer potential-energy surface but rather reflect electronic transitions driven by coherent nuclear motion. 3 To facilitate a classical interpretation of these nonadiabatic processes, we have recently proposed a bosonization formulation that affords a well-defined classical limit of a vibronically coupled system. 5 Moreover, the approach allows us to introduce the classical periodic orbits of a vibronic system. 6 Periodic orbits, i.e., solutions of the classical equation of motion that return to their initial conditions, are of particular interest, because they can be directly linked to spectral response functions via semiclassical trace formulas. 7 In favorable cases, periodic-orbit theory allows us to interpret complex absorption spectra in terms of only a few classical trajectories. 8 Considering the vibronic periodic orbits of a simple electron...

Ultrafast Photochemistry in Liquids

“…Clearly, intramolecular modes play a crucial role in ET reactions. As vibrational dephasing in the condensed phase can take several picoseconds, the possibility of observing coherent photoinduced ET processes upon ultrashort optical excitation has been investigated (91,92). Evidence of such an effect has been obtained by Hochstrasser and coworkers (12) upon direct CT excitation of a pyrene/TCNE DA complex in solution.…”

Classical Calculation of Transient Absorption Spectra Monitoring Ultrafast Electron Transfer Processes

“…With increasing time, the wave packet is seen to undergo oscillations along x with a period of ≈ 70 fs, which roughly corresponds to the vibrational frequency ω of the model. Note that the nuclear motion is directly linked to an oscillation of the electronic population; that is, the vibrational dynamics trigger electronic transitions between the two coupled states |ψ 1 〉 and |ψ 2 〉 …”

Quasiperiodic orbit analysis of nonadiabatic cis–trans photoisomerization dynamics

“…We have identified the shortest of these periodic orbits, which were also found to be most important for the interpretation of nonadiabatic quantum dynamics. [19][20][21] Adopting the adiabatic electronic representation, these vibronic periodic orbits could be characterized in a simple and physically appealing way. First, there are periodic orbits that evolve predominantly on a single ͑either the lower or the upper͒ Born-Oppenheimer surface.…”

“…With this end in mind, we have recently investigated the classical phase space of a nonadiabatically coupled system and also introduced the classical periodic orbits of such a system. [19][20][21] Periodic orbits, i.e., solutions of the classical equation of motion that return to their initial conditions, are of particular interest, because they can be directly linked to spectral response functions via semiclassical trace formulas. 22 Because periodic-orbit theory allows us to express quantum observables in terms of classical trajectories, it represents an appealing tool to analyze complicated or elusive quantum phenomena with the aid of intuitively clear classical concepts.…”

“…19 In particular, it has been demonstrated that transient oscillations observed in electron-transfer femtosecond experiments may be explained in terms of a few classical trajectories. 21 So far, we have restricted our studies to a highly idealized spin-boson-type model, i.e., to an electronic two-state system with constant interstate coupling and a single linearly shifted harmonic vibrational mode. As a first attempt to extend our investigations to multidimensional and anharmonic vibronic-coupling systems, in this work we are concerned with cis-trans photoisomerization dynamics.…”