The nonradiative decay of the allyl radical excited B 2 A 1 state studied by picosecond time-resolved photoelectron spectroscopy An approximate theory of femtosecond spectroscopy of nonadiabatically coupled electronic states is developed. Neglecting the commutators of vibrational Hamiltonians pertaining to different diabatic electronic states, the formulation represents a generalization of the semiclassical Franck-Condon approximation to the case of nonadiabatic dynamics. Explicit expressions for various time-and frequency-resolved spectra are derived which allow for a simple interpretation of femtosecond spectroscopy of vibronically coupled molecular systems. Employing multidimensional model problems describing ͑i͒ the nonadiabatic cis-trans isomerization of an electronic two-state system, and ͑ii͒ the S 2 →S 1 internal conversion of pyrazine, exact reference data are compared to approximate calculations of transient absorbance and emission as well as time-resolved photoelectron spectra. In all cases considered, the approximation is shown to be appropriate for probe-pulse durations that are shorter than the period of the fastest relevant vibrational mode of the molecular system. Reducing the numerical costs of pump-probe simulations to the costs of a standard time-dependent wave-packet propagation, the approximate theory leads to substantial computational savings.where the time-dependent excited-state wave function ͉⌿ 0 (t d )͘ depends on its preparation by the pump pulse and the stimulated-emission projection operator P incorporates the action of the probe pulse.Assuming short probe pulses, we may evaluate the pump-probe signal within the semiclassical Franck-Condon a͒ Electronic
Articles you may be interested inVibronic coupling in asymmetric bichromophores: Theory and application to diphenylmethane-d 5Analysis of the vibronic fine structure in circularly polarized emission spectra from chiral molecular aggregates Based on a recently introduced mapping formulation ͓G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 ͑1997͔͒, a classical phase-space description of vibronically coupled molecular systems is developed. In this formulation the problem of a classical treatment of discrete quantum degrees of freedom such as electronic states is bypassed by transforming the discrete quantum variables to continuous variables. Here the mapping formalism is applied to a spin-boson-type system with a single vibrational mode, e.g., representing the situation of a photo-induced electron transfer promoted by a high-frequency vibrational mode. Studying various Poincaré surfaces-of-section, a detailed phase-space analysis of the mapped two-state problem is given, showing that the model exhibits mixed classical dynamics. Furthermore, a number of periodic orbits ͑PO's͒ of the nonadiabatic system are identified. In direct extension of the usual picture of trajectories propagating on a single Born-Oppenheimer surface, these vibronic PO's describe nuclear motion on several coupled potential-energy surfaces. A quasiclassical approximation is derived that expresses time-dependent quantities of a vibronically coupled system in terms of the PO's of the system. As an example, it is demonstrated that vibronic PO's may be used to calculate the time-dependent population probability of the initially excited electronic state. For the system under consideration, already two PO's are sufficient to qualitatively describe the short-time evolution of the nonadiabatic process.
Classical periodic orbits associated with the nonadiabatic dynamics of a spin-boson-type problem are introduced. To facilitate a classical description of spin states, the formulation employs an exact mapping of the discrete quantum variables onto continuous degrees of freedom. Adopting a one-dimensional spin-boson model, the shortest periodic orbits of the problem are identified and used to analyze the nonadiabatic quantum dynamics. The possibility of directly observing these vibronic periodic orbits in femtosecond time-resolved experiments is discussed.
Ab initio nonadiabatic quantum dynamics of cyclohexadiene/hexatriene ultrafast photoisomerization
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...
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