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  • 1
    Electronic Resource
    Electronic Resource
    Complex quasiprobability for atoms trapped on surfaces: A novel application of the complex coordinate method (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 5864-5870 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A novel concept of complex quasiprobability Q(x) is proposed for atoms selectively trapped on a static, corrugated surface. The real part of Q(x) is the probability that the position vector of a trapped atom will have a projection x on the nominal surface plane, while Im[Q(x)]/||Q(x)−1|| is a local measure of the strength of the coupling between different diffraction channels, which leads to desorption of the trapped atoms from the surface. A method of calculating Q(x), based on the complex coordinate method, is presented and discussed. Applying this method to a model atom–surface potential which includes one-dimensional steps, it is shown that while the probability to find a trapped atom is enhanced around the top of a step, desorption is most likely to occur from the middle of the terraces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454549
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  • 2
    Electronic Resource
    Electronic Resource
    A theory of He diffraction and resonance scattering from Cu(115) by the complex coordinate method (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 1636-1642 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Our method for computing specular elastic scattering intensities of atomic beams from a periodically corrugated solid surface, is generalized to include nonspecular diffraction intensities, and is applied to the scattering of a helium beam from the Cu(115) surface for resonance as well as off-resonance incident angles. Using a simple corrugated Morse potential with a one-dimensional corrugation function and reasonable values of its parameters, a remarkable agreement with the experimental resonance line shapes over the entire angular range is obtained for both the specular and a nonspecular diffraction channel. The line shapes are found to be extremely sensitive to the corrugation strength parameter, but quite insensitive to the shape of the surface corrugation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459967
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Resonance positions and widths by a similarity transformation of a Hermitian Hamiltonian matrix (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 227-230 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The resonances obtained by a method, which is based on the original work of Datta and Chu [Chem. Phys. Lett. 87, 357 (1982)] and of Schneider [Chem. Phys. Lett. 31, 237 (1975); Phys. Rev. A 11, 1957 (1975)], are studied for a one-dimensional model, for a two-dimensional model suggested by Chu, describing rotational predissociation in van der Waals complexes, and for the variational predissociation of Ne–ICl in the adiabatic approximation for a potential surface given by Delgado-Barrio and Villarreal (to be published). The resonance positions and widths are associated with the complex eigenvalues of a complex matrix obtained by a product of three matrices St H S, where H is the Hermitian Hamiltonian matrix, and S is an overlap matrix between complex scaled and unscaled basis functions. The method has the advantage of being applicable to potentials given numerically on the real axis. It also avoids the need to construct a new complex Hamiltonian matrix for each scaling angle, as is the case in the complex coordinate method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458467
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  • 4
    Electronic Resource
    Electronic Resource
    Resonance transition probabilities by the complex Lanczos recursion method (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 6836-6840 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Resonance transition probabilities are obtained without the need to compute eigenvectors of the complex scaled Hamiltonian matrix. The new computational approach is a combination of the complex Lanczos recursion method, the complex coordinate method, and the extension of the Wyatt and Scott modified QL algorithm to complex matrices. To illustrate the method, the coupling strength between a resonance state and different scattering channels of HD from a flat Ag surface are calculated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455357
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  • 5
    Electronic Resource
    Electronic Resource
    Determination of tunneling rates in bound systems using the complex coordinate method (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 6246-6253 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Up to now tunneling rates in bound systems have been obtained primarily by semiclassical or wave packet calculations. A new accurate quantum time-independent method is presented. Those irregular eigenfunctions of bound systems which diverge asymptotically, but upon complex scaling of coordinates X→X exp(iaitch-theta) become square integrable functions and are associated with complex eigenvalues are found to describe barrier penetration processes. The imaginary part of each of the complex eigenvalues of the complex scaled Hamiltonian contains the tunneling decay rate provided that the Balslev–Combes rotation angle is large enough. The appearance of a critical value aitch-thetac as the rotational angle aitch-theta is varied, at which a sharp transition from a real energy spectrum of the bound system to a complex eigenvalue spectrum is an indication of an exponential decay through the potential barrier. Tunneling in multiple barrier problems is important in several areas of physics and chemistry, including isomerization reactions, Josephson junction superconductors, electron tunneling from a 1D metallic lattice under the influence of a uniform electric field (field emission), and tunneling in the EF 1Σg state of molecular hydrogen. Several representative numerical examples are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457391
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  • 6
    Electronic Resource
    Electronic Resource
    Application of the complex rotation method to the study of resonance states of atoms at a corrugated surface (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 86 (1987), S. 1048-1054 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The complex rotation method is applied to the calculation of complex poles of the scattering matrix for atoms selectively trapped at a corrugated, static surface. The method is found to be extremely efficient and accurate even for highly corrugated surfaces, for which the use of more conventional methods is known to be in trouble. The method also provides insight into the trapping processes, revealing that for a simple harmonic corrugation there is a critical value of the corrugation amplitude, below which the trapping process is dominated by the coupling between adjacent diffraction channels, while above this critical value the coupling between more distant channels dominates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.452339
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  • 7
    Electronic Resource
    Electronic Resource
    Tunneling rates in a two-dimensional symmetric double-well potential surface by the exterior scaling procedure (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 3562-3569 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Time-independent methods which were recently developed [J. Chem. Phys. 91, 6246 (1989); 93, 3413 (1990)] to calculate tunneling rates in bound systems are applied to a two-dimensional symmetrical double-well surface proposed by Makri and Miller [J. Chem. Phys. 86, 1451 (1987)] to describe intramolecular H-atom transfer. The methods are based on exterior complex scaling either with basis-set expansions or with an iterative multichannel propagation and matching procedure. Exterior complex scaling is used to identify the initial well (characterized by an unscaled reaction coordinate) and the final well (with a complex-scaled reaction coordinate). The quantized energies of the system become complex, with imaginary parts providing the rates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460858
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  • 8
    Electronic Resource
    Electronic Resource
    Positions, lifetimes, and partial widths of metastable quasienergy states by solving the time-dependent complex-scaled Schrödinger equation (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 7311-7318 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The method presented here is based on the solution of the time-dependent complex-scaled Schrödinger equation to provide the complex-scaled evolution operator after one optical cycle. This method is mainly suitable in the study of multiphoton ionization or dissociation under the influence of high intense fields. An illustrative numerical example is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460215
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  • 9
    Electronic Resource
    Electronic Resource
    Tunneling rates in bound systems using smooth exterior complex scaling within the framework of the finite basis set approximation (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 3413-3419 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A basis-set time-independent method to calculate tunneling rates in bound systems through a potential barrier is presented. The tunneling decay rates are associated with the imaginary parts of the complex eigenvalues of the Schrödinger equation where the reaction coordinate r' is complex scaled such that, dr = dr'[1/cos θ(r')]exp (iθ(r')), where tan θ(r') = tan θ∞g(r'). The function g(r') fulfills 0 ≤ g(r') ≤ 1 and shows a smooth transition from 0 to 1 near r' = r0 which is the location of the top of the barrier. The value of θ∞ should be larger than a critical value for which a sharp transition from a real eigenvalue spectrum to a complex one is obtained. Illustrative numerical applications to two isomerization reaction models are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458821
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  • 10
    Electronic Resource
    Electronic Resource
    Highly excited vibrational states by adiabatic vs self-consistent-field methods (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 86 (1987), S. 2146-2151 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Highly excited states for model Hamiltonians of two strongly coupled modes are calculated by adiabatic and by the self-consistent-field methods. The energy spectra obtained by the two separation methods are similar and deviate from the accurate spectrum in the stochastic energy regime where the system is far from separability. However, the natural expansion analysis of the adiabatic wave functions in the stochastic energy region shows that the adiabatic approach did not totally suppress the stochastic information about the eigenstates, and the adiabatic natural expansion coefficients are in very good agreement with the accurate ones.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.452112
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