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  • 1
    Electronic Resource
    Electronic Resource
    Doubly ionized states of ethylene: Auger spectrum, potential energy surfaces and nuclear dynamics (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 1734-1753 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Theoretical investigations of the outer valence doubly ionized states of ethylene are presented using ab initio Green's function and configuration interaction methods. The vertical double ionization potentials computed by the Green's function method using the ADC(2) scheme are discussed in connection with the Auger spectrum of ethylene and found to reproduce the experimental spectrum quite accurately. Another main purpose of the present work is the investigation of the potential energy surfaces of selected states via ADC(2) and the study of the nuclear dynamics on them. It is shown that only the ground state of the dication is nonplanar with a torsional angle of 90°. The investigation of the topology of the surfaces reveals a low energy conical intersection of the dicationic ground and first excited states. The associated vibronic coupling problem turns out to include, additionally, the second excited state and thus, we encounter here a three-state problem. In the approximation of linear vibrational and vibronic coupling the static and dynamic aspects of the vibronic interaction are investigated by a model Hamiltonian comprising three nonseparable nondegenerate vibrational modes. The input data for the model are extracted from the ADC(2) results. With the aid of this Hamiltonian we have computed a hypothetical "sudden'' double ionization spectrum of ethylene whose complex structure is analyzed stepwise and by cuts through the pertinent adiabatic and diabatic surfaces. The analysis exhibits that the conical intersection of the two lower lying states dominates the vibronic dynamics and leads to strong vibronic mixing between them. This mixing is indirectly reinforced by the interaction between the intermediate and the upper states. As a consequence, strong nonadiabatic effects occur in the ethylene dication. Furthermore, two of the three surfaces involved in the conical intersection are also involved in a multidimensional avoided crossing. A more detailed analysis presented earlier has exhibited that the states belong to an interesting class where two potential energy surfaces are likely not to coincide although plenty of nuclear degrees of freedom exist, in principle, to allow for an intersection to occur.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457080
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  • 2
    Electronic Resource
    Electronic Resource
    New method for calculating wave packet dynamics: Strongly coupled surfaces and the adiabatic basis (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 345-356 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The nuclear dynamics on potential energy surfaces with a conical intersection is investigated on the basis of exact (numerical) integration of the time-dependent Schrödinger equation. The ethylene cation is chosen as a typical realistic model system. Complementing earlier work we study the dynamics also in the adiabatic basis, which will be seen to allow for a more profound understanding of the decay and dephasing processes occurring in the system. The computational effort exceeds considerably that of propagation in the diabatic basis, to which previous related studies have been confined. To solve the resulting computational problems we develop and present a special multidimensional adaptation of the finite basis set method utilizing the product structure of the basis. It allows us to calculate propagation in a general potential including three vibrational modes. For the time integration a fourth order differencing scheme is introduced which is faster than the second order differencing-scheme and predictor–corrector approaches.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459606
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  • 3
    Electronic Resource
    Electronic Resource
    Approximately diabatic states from block diagonalization of the electronic Hamiltonian (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 7367-7381 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In many cases of interest there is only a small number of electronic states which interact with each other through the nuclear motion and are well-separated energetically from the other states. The aim of this work is to find a nearly diabatic (quasidiabatic) representation for the coupled states in which their coupling becomes small. Block diagonalization of the electronic Hamiltonian can accomplish this goal. It is achieved by a unitary transformation T which is uniquely determined by a "least action principle'' which demands that T "does not do anything but block diagonalization.'' By the help of the transformation we arrive at a decoupling of the relevant states from the rest and have to deal with a small matrix Hamiltonian. We have investigated in detail this block diagonalization procedure and succeeded in calculating the matrix elements of the total Hamiltonian in the new basis in closed form, in a nonperturbative way. Qualitative criteria are given to decide in which cases the method can successfully be applied to obtain quasidiabatic states. Particular attention is paid to the derivative couplings within the block of the interacting states. We have calculated that part of these couplings present in the adiabatic basis which will be transformed away and also the residual couplings which remain in the quasidiabatic basis after the transformation. The general results are exemplified on two model examples, describing a Σ–Π coupling in a linear molecule and a pseudo-Jahn–Teller effect, respectively. In addition, we briefly discuss the applicability of the proposed method in ab initio calculations on the example of the ethylene dication.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455268
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  • 4
    Electronic Resource
    Electronic Resource
    Erratum: Gauge theory and quasidiabatic states in molecular physics [J. Chem. Phys. 91, 7057 (1989)] (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 5166-5166 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458621
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  • 5
    Electronic Resource
    Electronic Resource
    Statistical fluctuations of decay rates (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 3934-3947 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We introduce a general Hamiltonian describing two coupled subsystems, each having a finite zero-order decay probability. With use of simple statistical assumptions on the underlying states, we derive new probability distributions of individual decay rates. We analyze the cases of weak and intermediate to strong coupling, respectively. The resulting distributions often resemble a suitable χ2 distribution, but do not belong to that class of functions. An interpretation of decay rates in terms of a χ2 model thus may lead to wrong conclusions. As a concrete realization, we study a Hamiltonian describing the non-Born–Oppenheimer coupling of two electronic states via the nuclear motion. The model is applied to the calculation of absorption-type spectra of NO2 and C2H+4. We investigate statistical properties of energy levels, line intensities, and decay rates. For NO2, we find from all statistics a completely irregular behavior, consistent with random matrix predictions and demonstrating the strong mixing of zero-order states due to the nonadiabatic coupling. For C2H+4, all statistics exhibit characteristic deviations from the irregular limit that can be given a consistent interpretation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456825
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  • 6
    Electronic Resource
    Electronic Resource
    Gauge theory and quasidiabatic states in molecular physics (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 7057-7062 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Following previous works [Moody et al., Phys. Rev. Lett. 56, 893 (1986) and Zygelman, Phys. Lett. A 125, 476 (1987)], we review in some detail the gauge theoretical form of the Born–Oppenheimer description of molecules. The derivative couplings which describe nonadiabatic effects play the role of gauge potentials. Applying the gauge theoretical formalism (well known in particle physics), we rederive a theorem concerning the nonexistence of strictly diabatic states. Further we propose the Lorentz gauge condition to define quasidiabatic states. We show that the recently proposed block diagonalization method to obtain quasidiabatic states leads automatically to the Lorentz gauge locally.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457323
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  • 7
    Electronic Resource
    Electronic Resource
    Interplay of Jahn–Teller and pseudo-Jahn–Teller vibronic dynamics in the benzene cation (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 2023-2040 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The static and dynamic aspects of the vibronic interaction of the B˜ 2E2g and C˜ 2A2u electronic states of C6H+6 are analyzed. In the approximation of linear vibrational and vibronic coupling, the model Hamiltonian for this system comprises eight nonseparable vibrational modes, six of which are degenerate (two of A1g symmetry, four of E2g symmetry, and two of E2u symmetry). The coupling constants are estimated from existing ab initio SCF and semiempirical (CNDO/S) calculations. The topology of the adiabatic potential-energy surfaces of this class of model Hamiltonians is investigated. It is shown that the model exhibits a variety of conical intersections which dominate the vibronic dynamics. The dynamical problem is solved with simultanteous inclusion of six vibrational modes, four of which are degenerate (the Jahn–Teller coupling of two of the E2g modes is negligible). Hamiltonian matrices with dimensions up to 6×106 are diagonalized using the Lanczos algorithm. After some adjustments of coupling constants, the calculation reproduces well the complex structure of the overlapping B˜ 2E2g–C˜ 2A2u bands in the photoelectron spectrum of benzene. The vibronic structure of the lower-energy E2g band is dominated by a two-mode Jahn–Teller effect in the B˜ state. At higher energy, the marked diffuseness of the "C˜ 2A2u band'' is shown to be a consequence of complete vibronic mixing with the lower-lying B˜ state. Based on thenumerical solution of the full problem, the reliability of approximations (neglect of nonseparability of modes, introduction of a single effective pseudo-Jahn–Teller mode) is assessed. A time-dependent analysis reveals an ultrafast decay of the population of the C˜ state on a time scale of about 20 fs, followed by quasiperiodic recurrences which are damped on a time scale of a few hundred femtoseconds. These findings underline the importance of conical intersections and strong nonadiabatic effects also for larger molecules such as aromatic hydrocarbons. They demonstrate that nowadays a full quantum treatment is feasible also for these larger systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455100
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  • 8
    Electronic Resource
    Electronic Resource
    Dynamics on potential energy surfaces with a conical intersection: Adiabatic, intermediate, and diabatic behavior (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 1658-1669 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The nuclear dynamics on potential energy surfaces which are strongly vibronically coupled through a conical intersection is investigated by exact (numerical) integration of the time-dependent Schrödinger equation. Results for realistic model systems including three nuclear degrees of freedom are presented: C2H+4, pyrazine and NO2. It was found previously for C2H+4 that the wave packet moves after an initial decay mainly on the lower adiabatic surface. This observation could be confirmed also for pyrazine and NO2. By varying the coupling strength λ also other types of behavior could be identified. A transition from adiabatic via intermediate to a diabatic nature of the system dynamics is found upon decreasing λ. Population of diabatic and adiabatic states in the long time limit are calculated by classical phase-space statistics. Analytic relations between the population of the diabatic states and the dynamical observables, coordinates and momenta, are derived. They allow for a deeper understanding of their long time limits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459094
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  • 9
    Electronic Resource
    Electronic Resource
    Aspects of dissipative electronic and vibrational dynamics of strongly vibronically coupled systems (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 1045-1061 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The intramolecular non–Born–Oppenheimer quantum dynamics on conically intersecting potential-energy surfaces is analyzed on the basis of exact (numerical) time-dependent quantum calculations for two representative two-state three-mode vibronic-coupling models. A compact description of the time-dependent dynamics in terms of reduced density matrices of the electronic and vibrational subsystems is introduced. Results are presented for the time evolution of electronic and vibrational coherences, populations, as well as subsystem entropies. It is found that such simple two-state three-mode vibronic coupling models exhibit a rich variety of dissipative phenomena on femtosecond time scales. The numerical results reveal an interesting interplay of driven electronic surface-hopping processes and dephasing of coherent vibrational motion which is presumably a generic feature of ultrafast internal conversion processes in polyatomic molecules.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458167
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  • 10
    Electronic Resource
    Electronic Resource
    Construction scheme for regularized diabatic states (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 2377-2388 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A simple construction scheme for quasidiabatic electronic states implemented earlier for a Jahn–Teller situation [J. Chem. Phys. 110, 9371 (1999)] is extended to the case of a seam of symmetry-allowed conical intersections. It is based on the idea of removing only the singular part of the nonadiabatic coupling elements, leading to the notion of "regularized" diabatic states. Explicit working equations are given for the resulting potential energy matrix which require only information from the adiabatic potential energy surfaces alone. The approach is tested for the photodissociation of H2S and O3 and very good agreement with reference data from the literature is found. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1383986
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