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  • 1
    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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  • 2
    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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  • 3
    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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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 77-88 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The unphysical flow of zero-point energy (ZPE) in classical trajectory calculations is a consequence of the fact that the classical phase-space distribution may enter regions of phase space that correspond to a violation of the uncertainty principle. To restrict the classically accessible phase space, we employ a reduced ZPE γεZP, whereby the quantum correction γ accounts for the fraction of ZPE included. This ansatz is based on the theoretical framework given in Paper I [G. Stock and U. Müller, J. Chem. Phys. 111, 65 (1999), preceding paper], which provides a general connection between the level density of a system and its relaxation behavior. In particular, the theory establishes various criteria which allows us to explicitly calculate the quantum correction γ. By construction, this strategy assures that the classical calculation attains the correct long-time values and, as a special case thereof, that the ZPE is treated properly. As a stringent test of this concept, a recently introduced classical description of nonadiabatic quantum dynamics is adopted [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997)], which facilitates a classical treatment of discrete quantum degrees of freedom through a mapping of discrete onto continuous variables. Resulting in negative population probabilities, the quasiclassical implementation of this theory significantly suffers from spurious flow of ZPE. Employing various molecular model systems including multimode models with conically intersecting potential-energy surfaces as well as several spin-boson-type models with an Ohmic bath, detailed numerical studies are presented. In particular, it is shown, that the ZPE problem indeed vanishes, if the quantum correction γ is chosen according to the criteria established in Paper I. Moreover, the complete time evolution of the classical simulations is found to be in good agreement with exact quantum-mechanical calculations. Based on these studies, the general applicability of the method, the performance of the classical description of nonadiabatic quantum dynamics, as well as various issues concerning classical and quantum ergodicity are discussed. © 1999 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 79 (1996), S. 6803-6810 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The wide rocking curves of matrix reflections of the in situ eutectic composite TaSi2–Si make wafers of this material attractive for use as wide-bandpass monochromators for synchrotron radiation, and characterization of wafers of TaSi2–Si for use with energies normally accessible at storage rings (i.e., 5–40 keV) is the focus of the present report. A wafer with [111]Si orientation and a wafer with [110]Si orientation are studied. The high degree of preferred orientation of the TaSi2 rods relative to the Si matrix is examined using synchrotron Laue patterns, and the 100TaSi2, 003TaSi2, 101TaSi2, and 102TaSi2 reflections are used to establish the orientation relationship and to determine that the spread of rod orientations is at least 5° and probably no greater than 6°. Double-axis diffractometry with Cu Kα radiation reveals matrix reflections with rocking curve widths that are about 20 times broader than those from perfect Si and with peak reflectivities approaching 20%. The rocking curves widths are found to be relatively insensitive to irradiated area, thus indicating that most of the observed width is not due to long-range bending. Triple-axis diffractometry with Cu Kα radiation reveals that considerable compressive strain exists in the matrix and that much of the width of the diffraction peak is due to mosaicity. The performance of the [111]Si TaSi2–Si wafer and a perfect [111] Si wafer as monochromators for microradiography are compared, and a gain of an order of magnitude in x-ray intensity delivered to the sample is demonstrated with the composite crystal. © 1996 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 107 (1997), S. 6230-6245 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A mixed quantum-classical description of nonadiabatic photoreactions such as internal conversion and electron transfer is outlined. In particular the validity and limitations of Tully's surface-hopping (SH) model [J. Chem. Phys. 93, 1061 (1990)] is investigated in the case of photoinduced relaxation processes which are triggered by a multidimensional conical intersection (or avoided crossing) of two potential-energy surfaces. Detailed numerical studies are presented, adopting (i) a three-mode model of the S2→S1 internal-conversion process in pyrazine, (ii) a multimode model of ultrafast intramolecular electron-transfer, (iii) a model exhibiting nonadiabatic photoisomerization dynamics, and (iv) various spin-boson-type models with an Ohmic bath for the description of electron-transfer in solution. The SH simulations are compared to exact quantum-mechanical calculations as well as to results obtained by an alternative mixed quantum-classical description, that is, the self-consistent classical-path method. In all cases, the SH data are shown to reproduce the quantum results at least qualitatively; in some cases the SH results are in quantitative agreement with the complex electronic and vibrational relaxation dynamics exhibited by the quantum calculations. Depending on the physical situation under consideration, either the SH or the self-consistent classical-path method was found to be superior. The characteristic features of a mixed quantum-classical description of photoinduced bound-state dynamics (e.g., the start of the trajectories on a diabatic electronic potential-energy surface, high chance of a trajectory undergoing multiple electronic transitions) as well as the specific problems of the SH approach are discussed in some detail. In particular, the focus is on the ability of a method to account for the branching of trajectories, to correctly describe the electronic phase coherence and the vibrational motion on coupled potential-energy surfaces, and to obey the principle of microreversibility. Furthermore, an alternative way to handle classically forbidden electronic transitions is proposed, which is shown to lead to significantly better results than the usual procedure. © 1997 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 103 (1995), S. 10015-10029 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A classical-path approach to the description of photoinduced isomerization dynamics as well as the interrelated electronic and vibrational relaxation processes is outlined. Adopting a three-mode model of photoisomerization that has been recently proposed by Seidner and Domcke (Chem. Phys. 186, 27 (1994)), we perform detailed numerical studies and compare the results of the classical simulations to available exact quantum-mechanical results. It is shown that the classical model reproduces semiquantitatively time-dependent diabatic and adiabatic electronic population probabilities, state-specific torsional wave functions, and energy contents of vibrational degrees of freedom. Furthermore it is demonstrated that the classical approach is able to simulate at least qualitatively time- and frequency-resolved pump-probe spectra of these processes. In accordance with exact quantum calculations, the classical simulations reveal the decay of the stimulated emission of the reactants and the delayed onset of the absorption of the photoproducts. To demonstrate the capability of the classical approach, the three-mode model of Seidner et al. is augmented by a hundred weakly-coupled harmonic modes. This allows to roughly simulate the relaxation dynamics of a chromophore interacting with a solvent. The simulations reveal that the time evolution of the full system within the first few hundred femtoseconds is quite similar to the case of the bare three-mode model. For later times, however, the dynamics of the three-mode model becomes quasistationary, whereas the calculations for the full system reflect the redistribution of the excess energy of the reaction mode into the bath nuclear degrees of freedom. It is found that the quantum yield of the cis-trans photoreaction depends to a large extent on the specific chromophore-solvent coupling employed, as it governs directly the competition of the various relaxation pathways. Simulations of the corresponding time- and frequency-resolved pump-probe spectra reveal that the cooling of the vibrationally hot photoproducts in the solvent is mainly reflected in a blue shift and a narrowing of the width of the absorption spectrum. © 1995 American Institute of Physics.
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 7516-7526 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A mixed quantum-classical formulation of nonadiabatic molecular processes is outlined. Based on a recently introduced mapping formalism [Stock and Thoss, Phys. Rev. Lett. 78, 578 (1997)], the formulation employs a quantum-mechanically exact mapping of discrete electronic states onto continuous variables, thus describing the dynamics of both electronic and nuclear degrees of freedom by continuous variables. It is shown that the classical evaluation of the mapping formalism results in a self-consistent description of electronic and nuclear degrees of freedom, which treats both types of dynamical variables in a completely equivalent way. The applicability of the approach is thus solely determined by the validity of the classical approximation and does not rest on additional assumptions such as the ad hoc combination of classical and quantum-mechanical theories. The observation of unrestricted flow of zero-point energy in the electronic degrees of freedom indicates the limits of the classical approximation. However, it is shown that this problem can virtually be removed by restricting the classically accessible phase-space. Adopting a multidimensional model of the internal-conversion process in the benzene cation, it is demonstrated that the classical mapping approach is able to account for the branching of classical trajectories in the presence of multiple surface crossings. The classical simulations are found to match the exact quantum-mechanical reference calculations quite accurately. The virtues and limitations of various mixed quantum-classical descriptions are discussed by comparing the mapping approach to the classical-path, the classical electron-analog, and the surface-hopping formulation, respectively. © 1998 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 111 (1999), S. 65-76 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Necessary conditions under which a classical description will give the correct quantum relaxation behavior are analyzed. Assuming a nonequilibrium preparation, it is shown that the long-time mean values of observables can be expressed in terms of the spectral density and state-specific level densities of the system. Any approximation that reproduces these quantities therefore yields the correct expectation values at long times. Apart from this rigorous condition, a weaker but more practical criterion is established, that is, to require that the total level density is well approximated in the energy range defined by the spectral density. Since the integral level density is directly proportional to the phase-space volume that is energetically accessible to the system, the latter condition means that an appropriate classical approximation should explore the same phase-space volume as the quantum description. In general, however, this is not the case. A well-known example is the unrestricted flow of zero-point energy in classical mechanics. To correct for this flaw of classical mechanics, quantum corrections are derived which result in a restriction of the classically accessible phase space. At the simplest level of the theory, these corrections are shown to correspond to the inclusion of only a fraction of the full zero-point energy into the classical calculation. Based on these considerations, a general strategy for the classical simulation of quantum relaxation dynamics is suggested. The method is (i) dynamically consistent in that it refers to the behavior of the ensemble rather than to the behavior of individual trajectories, (ii) systematic in that it provides (rigorous as well as minimal) criteria which can be checked in a practical calculation, and (iii) practical in that it retains the conceptional and computational simplicity of a standard quasiclassical calculation. Employing various model problems which allow for an analytical evaluation of the quantities of interest, the virtues and limitations of the approach are discussed. © 1999 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. 2888-2902 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A semiclassical time-dependent self-consistent-field (TDSCF) formulation is developed for the description of internal conversion (IC) processes in polyatomic molecules. The total density operator is approximated by a semiclassical ansatz, which couples the electronic degrees of freedom to the nuclear degrees of freedom in a self-consistent manner, whereby the vibrational density operator is described in terms of Gaussian wave packets. The resulting TDSCF formulation represents a generalization of familiar classical-path theories, and is particularly useful to make contact to quantum-mechanical formulations. To avoid problems associated with spurious phase factors, we assume rapid randomization of the nuclear phases and a single vibrational density operator for all electronic states. Classically, the latter approximation corresponds to a single trajectory propagating along a "mean path'' instead of several state-specific trajectories, which may become a critical assumption for the description of IC processes. The validity and the limitations of the mean-path approximation are discussed in detail, including both theoretical as well as numerical studies. It is shown that for constant diabatic coupling elements Vkk′ the mean-path approximation should be appropriate in many cases, whereas in the case of coordinate-dependent coupling Vkk′(x) the approximation is found to lead to an underestimation of the overall relaxation rate.As a remedy for this inadequacy of the mean-path approximation, we employ dynamical corrections to the off-diagonal elements of the electronic density operator, as has been suggested by Meyer and Miller [J. Chem. Phys. 70, 3214 (1979)]. We present detailed numerical studies, adopting (i) a two-state three-mode model of the S1−S2 conical intersection in pyrazine, and (ii) a three-state five-mode and a five-state sixteen-mode model of the C˜→B˜→X˜ IC process in the benzene cation. The comparison with exact basis-set calculations for the two smaller model systems and the possible predictions for larger systems demonstrate the capability of the semiclassical model for the description of ultrafast IC processes. © 1995 American Institute of Physics.
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