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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 5496-5509 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A theoretical description of secondary emission from complex absorption bands of isolated polyatomic molecules is developed. The strong non-Born–Oppenheimer coupling associated with conical intersections of the multidimensional excited-state potential-energy surfaces is included in a fully microscopic manner by solving the time-dependent Schrödinger equation for appropriate model systems incorporating the most relevant electronic states and vibrational modes. The effect of the large number of remaining vibrational modes and of the weaker coupling with additional electronic states is modeled by phenomenological relaxation terms (lifetime broadening and pure dephasing) in the framework of the density-matrix formalism. Explicit eigenstate-free expressions for absorption, resonance Raman, and fluorescence spectra are derived via density-matrix perturbation theory. The computational feasibility of the resulting mixed microscopic/phenomenological theory is demonstrated for a simple three-mode model of the vibronic coupling of the S1(nπ*) and S2(ππ*) states of pyrazine. The effect of excited-state vibronic coupling and ultrafast S2→S1 internal conversion on resonance Raman and fluorescence spectra is analyzed on the basis of these model calculations.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 7184-7194 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a computer simulation of the real-time detection of ultrafast electronic decay dynamics in polyatomic molecules with femtosecond laser pulses. The intramolecular non-Born-Oppenheimer quantum dynamics is treated numerically exactly for a two-state three-mode vibronic coupling model representing the conically intersecting S1 and S2 excited states of pyrazine. The pump–probe signal is evaluated in lowest order perturbation theory with respect to the radiation–matter interaction by numerical integration over the pump and probe pulses. We discuss in some detail the dependence of the pump–probe signal on the properties of the laser pulses (frequencies and pulse durations). The calculations predict a dramatic (∼12 000 cm−1) and ultrafast (∼20 fs) red shift of the stimulated-emission signal as well as distinctive quantum beats in the pump–probe signal as a function of the delay time. Both effects are very pronounced and should therefore be relatively easily detectable experimentally. They are expected to be generic features of ultrafast internal-conversion processes in polyatomic molecules.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 69-78 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Based on a recently introduced mapping formulation [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997)], 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's) 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. © 2002 American Institute of Physics.
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 114 (2001), S. 2001-2012 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The quantum-classical Liouville formulation gives a quantum-mechanical density-matrix description of the "quantum" particles of a problem (e.g., the electrons) and a classical phase-space-density description of the "classical" particles (e.g., the nuclei). In order to employ this formulation to describe multidimensional nonadiabatic processes in complex molecular systems, this work is concerned with an efficient Monte Carlo implementation of the quantum-classical Liouville equation. Although an exact stochastic realization of this equation is in principle available, in practice one has to cope with two major complications: (i) The representation of nonlocal phase-space operators in terms of local classical trajectories and (ii) the convergence of the Monte Carlo sampling which is cumbersome due to complex-valued trajectories with rapidly oscillating phases. Several strategies to cope with these problems are discussed, including various approximations to determine the momentum shift associated with a nonadiabatic transition, the on-the-fly generation of new trajectories at curve-crossings, and the localization of trajectories after irreversible electronic transitions. Employing several multidimensional model systems describing ultrafast photoinduced electron transfer and internal conversion, detailed numerical studies are performed which are compared to exact quantum calculations as well as to the "fewest-switches" surface-hopping method. In all cases under consideration, the Liouville calculations are in good agreement with the quantum reference. In particular, the approach is shown to provide a correct quantum-classical description of the electronic coherence. © 2001 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 1085-1091 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A quantum-mechanical model description of a molecular photoswitch is developed. It takes into account (i) the electronic curve crossing arising from the cis-trans twisting of a double bond, resulting in an ultrafast internal-conversion process of the system and (ii) the coupling of the initially excited chromophore (the "system") to the remaining degrees of freedom (the "bath"), affecting a vibrational cooling of the hot photoproducts. The latter mechanism is responsible for the localization of the molecule in the cis and trans configuration, respectively, thus determining the quantum yield of the photoreaction. Following a discussion of the validity and the numerical implementation of the Redfield formulation employed, detailed numerical studies of the time-dependent dissipative photoisomerization dynamics are presented. While the short-time dynamics ((approximately-less-than)1 ps) is dominated by the coherent wave-packet motion of the system, the time evolution at larger times mainly reflects the interaction between system and bath. The quantum yield of the cis-trans forward reaction (Yc→t) and the trans-cis backward reaction (Yt→c) is shown to depend on the energy storage of the photoreaction and, in particular, on the form of the system–bath coupling. On the other hand, it is found that Yt→c=1−Yc→t, that is the population probabilities of the cis and trans configuration at long times do not depend on the initial preparation of the system. © 2002 American Institute of Physics.
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 4910-4922 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: 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 (i) the nonadiabatic cis–trans isomerization of an electronic two-state system, and (ii) the S2→S1 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. © 2000 American Institute of Physics.
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 246-254 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: It is demonstrated that photoinduced large amplitude (LA) dynamics on a picosecond time scale may result in electronic pure dephasing on a time scale of a few tens of femtoseconds. It is shown that LA photodynamics affects continuous-wave (cw) spectra (e.g., absorption and resonance-Raman) and transient spectra (e.g., photon-echo and pump–probe) in a rather different way. Calculations are presented for a two-dimensional model problem, consisting of a fast vibrational mode and a slow LA mode, which is considered as a simple model for isomerization. The spectroscopic signals for this model are compared to the results for a complementary model, where the fast vibrational mode interacts with a bath (e.g., the environment). It is shown that standard cw techniques such as absorption and resonance-Raman spectroscopy fail to clearly distinguish the two (physically rather different) model problems, as the ultrafast optical dephasing results in strong line broadening of these spectra. Time-resolved pump–probe spectroscopy, on the other hand, is not limited by electronic pure dephasing and thus allows for a clear discrimination of the two photophysical processes. Simulations of photon-echo experiments furthermore elucidate that slow intramolecular LA motion results in inhomogeneous broadening of optical spectra. Finally a novel time-resolved technique is proposed that is capable to reveal "sub-linewidth'' information on electronic transitions which are strongly broadened by homogeneous and inhomogeneous pure dephasing processes.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 6851-6860 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: New experimental and theoretical data on the resonance Raman (RR) spectroscopy of the S1 and S2 states of pyrazine are presented. Based on recent ab initio CASSCF (complete- active-space-self-consistent-field) and MRCI (multireference configuration interaction) calculations of Woywod et al. [J. Chem. Phys. 100, 1400 (1994)], we construct a vibronic coupling model of the conically intersecting S1 and S2 states of pyrazine, which includes the seven most relevant vibrational degrees of freedom of the molecule. Employing a time-dependent approach that treats the intramolecular couplings in a nonperturbative manner, we calculate RR cross sections for this model, taking explicitly into account the nonseparability of all vibrational modes. The combination of high-level ab initio calculations and multimode propagation techniques makes it possible, for the first time, to make first-principles predictions of RR spectra for vibronically coupled electronic states of an aromatic molecule. The theoretical data are compared to experimental gas-phase RR spectra which have been obtained for five different excitation wavelengths. The comparison reveals that the ab initio predictions match the experimental results in almost every detail. © 1995 American Institute of Physics.
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 3998-4011 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A general nonperturbative approach to calculate femtosecond pump-probe (PP) signals is proposed, which treats both the intramolecular couplings and the field-matter interaction (numerically) exactly. Experimentally as well as in a perturbative calculation it is straightforward to distinguish between different spectroscopic processes through the direction of the wave vector of the emitted radiation. A nonperturbative calculation, on the other hand, yields the overall polarization of the system, which is the sum of all these contributions. We present a general and practical method that allows to extract the individual spectroscopic signals, which are resolved in time, frequency, and direction of the emission, from the overall polarization. We briefly derive the basic expressions for the time- and frequency-resolved PP signals under consideration, and discuss in detail the simplifications that arise when the usual assumptions (i.e., weak laser fields, nonoverlapping pulses, slowly-varying envelope assumption and rotating-wave approximation) are invoked. The computational procedure is illustrated by nonperturbative calculations of the polarizations and PP signals for a one-dimensional shifted harmonic oscillator. To demonstrate the capability of the approach we have evaluated the polarization as well as PP signals for a three-dimensional model system with vibronically coupled potential-energy surfaces, which describes ultrafast nonadiabatic isomerization dynamics triggered by the twisting of a double bond. We consider various wavelengths and pulse durations of the laser fields and study integral and dispersed PP spectra as well as coherent photon-echo signals. It is shown that the time- and frequency-resolved PP signals reflect in real time the disappearance of the reactants and the delayed appearance of the products. © 1995 American Institute of Physics.
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 1561-1573 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A semiclassical time-dependent self-consistent-field approach for the description of dissipative quantum phenomena is proposed. The total density operator is approximated by a semiclassical ansatz, which couples the system degrees of freedom to the bath degrees of freedom in a self-consistent manner, and is thus in the spirit of a classical-path description. The capability of the approach is demonstrated by comparing semiclassical calculations for a spin–boson model with an Ohmic bath to exact path-integral calculations. It is shown that the semiclassical model nicely reproduces the complex dissipative behavior of the spin–boson model for a large range of model parameters. The validity and accuracy of the semiclassical approach is discussed in some detail. It is shown that the method is essentially based on the assumption of complete randomization of nuclear phases. In particular, the assumption of phase randomization allows one to perform the trace over the bath variables through quasiclassical sampling of the nuclear initial conditions without invoking any further approximation. © 1995 American Institute of Physics.
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