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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 5566-5577 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The use of a time-dependent basis set for solving the time-dependent Schrödinger equation is proposed. The basis set is a generalization of the harmonic oscillator functions. The proposed method is similar to the approaches formulated by Lee and Heller and by Coalson and Karplus. However, in the present method the time dependence of the basis functions is determined differently. Numerical studies on the quartic oscillator and on the Morse potential are carried out to investigate the performance of the various methods.
    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 117 (2002), S. 2657-2671 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The multistate vibronic dynamics in the X˜ 2E1g-E˜ 2B2u electronic states of the benzene radical cation is investigated theoretically by an ab initio quantum-dynamical approach. The vibronic coupling scheme and the ab initio values of the system parameters are adopted from the previous Paper I. Vibronic line spectra are obtained with the Lanczos procedure. Extensive calculations on wave-packet propagation have been performed with the aid of the multiconfiguration time-dependent Hartree method. Up to five coupled electronic potential energy surfaces and 13 vibrational degrees of freedom have been included in these calculations. As a result, the impact of a third electronic state (X˜ or B˜) on a strongly coupled manifold (B˜-C˜ or D˜-E˜ states) is quantitatively assessed. It leads to a restructuring of the spectral envelope which is stronger for the B˜-D˜-E˜ than for the X˜-B˜-C˜ system. The internal conversion dynamics is characterized by a stepwise transfer of electronic population to the lowest electronic state on a time scale of ∼100 fs, if the system is prepared initially on the highest potential energy surface. Companion calculations have also been performed for the case when the system is prepared in the intermediate state at t=0; they show a branching of the electronic populations. These are all novel findings which are discussed in terms of a series of conical intersections between the various potential energy surfaces. The importance of such multistate vibronic interactions for the photophysics and photochemistry of medium-sized systems is pointed out. © 2002 American Institute of Physics.
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  • 3
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The ground state and the first excited electronic states of the octa-atomic butatriene cation (C4H4+) exhibit a multidimensional conical intersection. This intersection is energetically low lying and is located in the vicinity of the Franck–Condon region of the neutral molecule's ground state. The conical intersection thus dominates the nuclear dynamics in ionization processes of this molecule. This is a particularly interesting example of vibronic coupling, introducing what appears to be a new, structured band into the energy spectrum. In this work, the potential energy surfaces and their intersection are investigated by ab initio methods. A diabatic model Hamiltonian including all possible linear, quadratic and bilinear vibronic coupling terms is introduced, with coupling constants determined by a fit to the ab initio data. The nuclear dynamics of all 18 vibrational modes is then evaluated by propagating the wave packet using the multi-configuration time-dependent Hartree method. Finally, the photoelectron spectrum of butatriene is computed and compared with the experimental one. © 2001 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. 8759-8772 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The multiconfiguration time-dependent Hartree (MCTDH) method is formulated for density operators and applied to their numerical propagation. We introduce two types of MCTDH density operators which are expanded in different kinds of so-called single-particle density operators. The latter may either be hermitian, or else represent ket–bra products of so-called single-particle functions. For both types of MCTDH expansions of density operators we derive equations of motion employing the Dirac–Frenkel/MacLachlan variational principle. Further an alternative set of equations of motion for the second type of density operators is proposed, which is not based on a variational principle but derived by taking partial traces. We thus obtain three sensible approaches within the framework of the MCTDH method which differ in their performance and properties. We investigate these approaches and their properties analytically and numerically. Our numerical results refer to a model of vibronic-coupling dynamics in the pyrazine molecule representing coupled electronic states with four vibrational modes and two and three electronic states respectively. We analyze the closed-system dynamics for this model with temperature-dependent initial states. The influence of temperature on state populations, on correlation functions and on absorption spectra is discussed. We assess the numerical performance of two of the three approaches and find that both can be very efficiently applied to investigate the type of systems studied here. © 1999 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1417-1430 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new approximation for solving the time-dependent Schrödinger equation is proposed. It improves the time-dependent Hartree approximation by including time-dependent unitary operators acting on the Hartree product. This allows for the approximate description of the correlation between the various degrees of freedom. The mathematical structure of the new approach is analyzed and an alternative Lie algebraic derivation is presented. By adopting two different time-dependent variational principles two different sets of equations are obtained. Differences between the two resulting methods are discussed.
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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. 10718-10729 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A numerical study based on the multiconfiguration time-dependent Hartree (MCTDH) method for the propagation of density operators is presented. Within the MCTDH framework, there exist two types of expansions of the density operator which employ different kinds of so-called single-particle density operators. The latter may either represent Hermitian operators (type I), or else ket-bra products of so-called single-particle functions (type II). The performance of these two types of representations is tested on three models for closed and open system dynamics. The open dynamics is induced for each system by Lindblad-type dissipation operators. We find that the MCTDH representation of type I is most efficient if the coupling between the degrees of freedom is weak, but if the temperature of the initial state and/or the strength of the dissipation is moderate. On the other hand, for strong coupling between the degrees of freedom, but for lower temperatures and for weak dissipation type II is more efficient. Furthermore, considering the open dynamics of the systems both types of MCTDH density operators can be very efficiently used to calculate absorption spectra. The Lindblad-type dissipation operator is shown, however, to capture only partially the effects of a real environment. © 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 109 (1998), S. 3730-3741 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present an extension of the filter-diagonalization (FD) approach which allows the extraction of accurate bound-state spectra from a time-dependent wave function determined by an approximate propagation scheme. To investigate the method, an approximate wave function is generated by a wave packet propagation on a two-dimensional potential energy surface for the LiCN molecule, employing a second-order differencing integrator with large step size. When applied to this inaccurate wave function, our formulation of the FD technique is capable of yielding eigenenergies considerably more precise than those obtained with the original FD method, while the effort is almost the same. The present FD scheme contains some additional refinements that increase the method's efficiency, accuracy, and practicability. We demonstrate that the accuracy of the FD procedure can be improved by using cosinetype filters. The quality of different variational principles employed to determine the eigenenergies is examined. These variational principles can also be utilized to estimate the error of the energies and intensities inexpensively and reliably. © 1998 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 109 (1998), S. 3772-3779 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An efficient method was recently introduced [J. Chem. Phys. 102, 5605 (1995); 104, 7974 (1996)] to represent multidimensional potential energy surfaces as a linear combination of products of one-dimensional functions, so-called natural potentials. Weight functions were shown to be easily implemented in the product representation scheme as long as they are separable, i.e., defined as a product of one-dimensional weight functions. Here the constraint imposed by the special product form of the separable weights is removed. Nonseparable weights are emulated by dividing the potential energy surface in arbitrary regions of minor and major physical relevance and by utilizing a so-called relevant region iteration procedure. Maintaining the advantageous computational scaling properties of the product representation scheme, this relevant region iteration procedure allows the stepwise improvement of the surface representation in the regions of major relevance. The quality of the product representation in the regions of minor relevance remains nevertheless acceptable. As a consequence, the number of potential expansion coefficients can be reduced substantially. The product representation of potential energy surfaces is especially well suited to be employed within the framework of the multiconfiguration time-dependent Hartree (MCTDH) approximation. To check the performance of the proposed method the Liu–Siegbahn–Truhlar–Horowitz (LSTH) surface is represented in Jacobian coordinates, and initial-state selected reaction probabilities for the H+H2(ν=j=0)→H2+H exchange reaction are computed. © 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 105 (1996), S. 1409-1419 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The reflection and transmission properties of different complex absorbing potentials (CAPs) are studied using WKB and scaling procedures which make the results transferable to any mass and kinetic energy. Explicit formulas are obtained which describe the reflection and transmission properties of monomial CAPs −iηxn with high accuracy. These properties are now well understood. The approximate results are compared to exact analytical results available for quadratic CAPs, and to numerical results obtained by wave packet propagation followed by an energy resolved analysis. The approximate, but accurate, description of the action of the CAP is finally used to determine optimal CAP parameters. CAP length, strength, and order can now be chosen in such a way that the sum of reflection and transmission is minimized. Optimal parameters are compiled for different energies and energy intervals. © 1996 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 104 (1996), S. 8433-8441 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Numerical studies of resonant scattering of electrons by diatomic molecules with full account of the nonlocal level shift and resonance width operators are carried out with emphasis on the various approximations of the nonlocal potentials. The Schwinger–Lanczos approach proposed recently by Meyer, Horácek and Cederbaum [Phys. Rev. A 43, 3587 (1991)] is applied and its performance is investigated. The efficiency of the method is further improved by introducing a new local complex potential. Very accurate values of the dissociative attachment cross sections for a d-wave resonance model are reported. © 1996 American Institute of Physics.
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