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  • 1
    Electronic Resource
    Electronic Resource
    Nonrelativistic Compton scattering in Furry's picture. II. Bethe surface by means of the complex-coordinate method (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 2305-2312 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Bethe surface as a means of characterizing the inelastic scattering of photons and electrons on atomic targets is discussed, and framed within the two-potential Furry's picture of scattering theory. In particular, the cross section for inelastic photon scattering is considered, and its first distorted Born approximation is identified to be given in terms of Bethe surface along the path conserving energy and momentum transfer. The difficulties in obtaining accurate cross sections in situations where the energy transfer is close to the ionization threshold are indicated, and related to the so-called Compton defect. The method for calculating the inelastic photon scattering cross section, introduced in Part I of this work [J. Chem. Phys. 80, 5669 (1984)] is summarized. The scattering cross section, and the entire Bethe surface, is obtained by means of the L2 discretization of the continuum and implemented in terms of the complex-coordinate method, without explicit calculation of the final scattering waves. The method is tested for the case of photon scattering off the hydrogen atom. The results are encouraging, and may be relevant for applications of the complex-coordinate method to calculations of more general transition amplitudes. The method is predicted to be most useful in cases close to ionization threshold (e.g., appearance edges in Compton scattering, Compton defect). Although applied to the one-electron problem the procedure is readily applicable to many electron atoms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.448326
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  • 2
    Electronic Resource
    Electronic Resource
    Nonrelativistic Compton scattering in Furry's picture. III. Kramers–Heisenberg transition amplitude by means of the complex-coordinate method (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 1456-1461 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The procedure for calculating the general Kramers–Heisenberg transition amplitude for scattering of light is presented. The procedure is based on L2 atomic structure calculations implemented within the framework of the complex-coordinate method, gives the transition amplitudes without explicit calculation of the final states, and includes the contribution from A¯ 2 terms, p¯A¯ terms to second order, and interference terms between these scattering contributions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451236
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  • 3
    Electronic Resource
    Electronic Resource
    Study of mode specificity by the natural expansion analysis (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 3924-3931 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The self-consistent field (SCF) method beyond its computational advantage lends meaning to the concept of local modes and its applicability implies mode specificity in the unimolecular reaction being studied. The natural expansion (NE) analysis of stable or metastable vibrational states is presented here first. The NE analysis enables us to determine the applicability of the SCF approximation, the optimal molecular modes for any given vibrational energy and therefore provides a positive test for mode specificity. Moreover, it is shown here that even when the internal coordinates of the Hamiltonian are not optimized and there are several dominant configurations in the NE, mode specificity can be indicated by analyzing these configurations. As examples, the mode specificity in the unimolecular decomposition of CO2 to CO+O and in the dissociation of formaldehyde to H2+CO are studied by the NE analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449104
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  • 4
    Electronic Resource
    Electronic Resource
    Resonances from the complex dilated Hamiltonians in a dilation-adapted basis set with a new stabilization parameter (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 3931-3936 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Explicit consideration of the analytic properties of the solutions to the dilated Hamiltonian is taken into account in the construction of the matrix representation of the latter in an L2 basis. The total dilated matrix is blocked according to division of the basis into "bound'' and "scattering'' subspaces, which are interacting via the off-diagonal blocks, leading to a coupling maintaining the adequacy of the bound part of the basis throughout the wide range of the dilation angle. The size of the bound subspace, M, becomes a new stabilization parameter; its variation covers the entire range of situations between a real stabilization calculation and the conventional complex-scaling calculation. This construction allows for a systematic analysis of the dilated Hamiltonian, bringing forward the physical interpretation of the configuration interaction while suppressing the disadvantageous effects of the dilation transformation, manifested by poor convergence. The connections to Junker's complex stabilization method are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.450103
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  • 5
    Electronic Resource
    Electronic Resource
    Some properties of the bivariational Hartree-Fock scheme for complex symmetric many-particle operatorsSome of the results of this paper were first presented as a poster contribution at the 1987 Sanibel Symposium on Atomic, Molecular, and Solid-State Theory, March 1987. (1989)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 36 (1989), S. 93-103 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The bivariational Hartree-Fock scheme for a general many-body operator T is discussed with particular reference to the complex symmetric case: T† = T*. It shown that, even in the case when the complex symmetric operator T is real and hence also self-adjoint, the complex symmetric Hartree-Fock scheme does not reduce to the conventional real form, unless one introduces the constraint that the N-dimensional space spanned by the Hartree-Fock functions φ should be stable under complex conjugation, so that φ* = φα. If one omits this constraint, one gets a complex symmetric formulation of the Hartree-Fock scheme for a real N-electron Hamiltonian having the properties H = H* = H†, in which the effective Hamiltonian Heff (1) may have complex eigenvalues εk. By using the method of complex scaling, it is indicated that these complex eigenvalues - at least for certain systems - may be related to the existence of so-called physical resonance states, and a simple example is given. Full details will be given elsewhere.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560360202
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  • 6
    Electronic Resource
    Electronic Resource
    Implementation of the complex coordinate method for resonances and photoionization cross sections by means of matrix element extrapolation (1987)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 31 (1987), S. 823-831 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new implementation of the complex coordinate method for calculation of molecular resonances and photoionization cross sections is presented. The method originates from the idea of analytic continuation of stabilization graphs, but instead all matrix elements are numerically continued. Exterior scaling is invoked in conjunction with the use of dilationally adapted basis sets. It is operationally equivalent to the bivariational method in the Feshbach-partitioned manifold of complex basis functions, but no complex integrals are calculated. Instead, the complex eigenvalue problem arises from the analytical continuation of the realvalued matrix elements pertinent to any atomic or molecular structure code in its standard (real) form. That includes the possibility of using numerical basis sets. Since the method does not require modification of existing numerical codes, it can serve as a complement to any large scale CI or MCSCF molecular structure calculation.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560310510
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