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  • 1
    Electronic Resource
    Electronic Resource
    Eigensolution of a singular operator δ(x)d/dx+d/dxδ(x) (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 671-671 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The title operator can often be found in the flux operator which has been first introduced by Miller. From the numerical implementations, the flux operator is known to have such peculiar properties as follows: 1) it has two nonzero eigenvalues of same magnitude with opposite signs and all other eigenvalues being zero; 2) eigenvectors with nonzero eigenvalues are localized. In this work we have analytically solved the eigenvalue equation for the operator in the title whose eigensolutions reveal the properties mentioned above. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.474429
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  • 2
    Electronic Resource
    Electronic Resource
    Oscillating Franck–Condon factor in the time-relaxed harmonic oscillator (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 9259-9260 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471715
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  • 3
    Electronic Resource
    Electronic Resource
    Unitary quantum time evolution by iterative Lanczos reduction (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 5870-5876 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A general unitary time evolution method for wave packets defined on a fixed L2 basis is developed. It is based on the Lanczos reduction of the full N×N Hamiltonian to a p-dimensional subspace defined by the application of H p−1 times to the initial vector. Unitary time evolution in the subspace is determined by exp{−iHpt}, retaining accuracy for a time interval τ, which can be estimated from the Lanczos reduced Hamiltonian Hp. The process is then iterated for additional time intervals. Although accurate results over long times can be obtained, the process is most efficient for large systems over short times. Time evolution employing this method in one- (unbounded) and two-dimensional (bounded) potentials are done as examples using a distributed Gaussian basis. The one-dimensional application is to direct evaluation of a thermal rate constant for the one-dimensional Eckart barrier.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451548
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  • 4
    Electronic Resource
    Electronic Resource
    Quantum thermal rate constants for the exchange reactions of hydrogen isotopes: D+H2 (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 2946-2955 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Accurate thermal rate constants for the D+H2 reactions are determined for the Liu–Siegbahn–Truhlar–Horowitz potential energy surface over the temperature range 300–1500 K. We evaluate the rate constants via the quantum flux–flux autocorrelation function formulation of Miller [J. Chem. Phys. 61, 1823 (1974)] using the adiabatically adjusted principal axis hyperspherical coordinates of Pack [Chem. Phys. Lett. 108, 333 (1984)] and a symmetry adapted discrete variable representation used earlier for the H+H2 reaction [T. J. Park and J. C. Light, J. Chem. Phys. 91, 974 (1989)]. The initial L2 basis of ∼15 000 functions is sequentially diagonalized and truncated, with a final reduction to ∼420 accurate eigenvectors of the symmetry adapted (C2v) Hamiltonians for J=0. Direct products of these functions with symmetry adapted rotation functions are then used as the basis for the J〉0 Hamiltonians. Nuclear spin symmetries are also included. For J〉0, the individual J, KJ blocks of the Hamiltonian are diagonalized, the Coriolis coupling is neglected, and the KJ±2 coupling is included by perturbation theory. The thermal rate constants are evaluated for each total angular momentum from the flux–flux autocorrelation function. Angular momenta up to J=25 are required to converge the rate constants at 1500 K to ∼5%. Thermal rate constants as functions of T (and J) are presented for the D+H2 reaction and compared with experiment and other calculations. Agreement with experiment for D+H2 is excellent up to about 1000 K and remains within a factor of 2 of the experimental rate constant up to 1500 K. Thus agreement of the rates over more than four orders of magnitude is quite reasonable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459817
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  • 5
    Electronic Resource
    Electronic Resource
    Accurate quantum thermal rate constants for the three-dimensional H+H2 reaction (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 974-988 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The rate constants for the three-dimensional H+H2 reaction on the Liu–Siegbahn–Truhlar–Horowitz (LSTH) surface are calculated using Pack–Parker hyperspherical (APH) coordinates and a C2v symmetry adapted direct product discrete variable representation (DVR). The C2v symmetry decomposition and the parity decoupling on the basis are performed for the internal coordinate χ. The symmetry decomposition results in a block diagonal representation of the flux and Hamiltonian operators. The multisurface flux is introduced to represent the multichannel reactive flux. The eigenvalues and eigenvectors of the J=0 internal Hamiltonian are obtained by sequential diagonalization and truncation. The individual symmetry blocks of the flux operator are propagated by the corresponding blocks of the Hamiltonian, and the J=0 rate constant k0(T) is obtained as a sum of the rate constants calculated for each block. k0(T) is compared with the exact k0(T) obtained from thermal averaging of the J=0 reaction probabilities; the errors are within 5%–20% up to T=1500 K. The sequential diagonalization–truncation method reduces the size of the Hamiltonian greatly, but the resulting Hamiltonian matrix still describes the time evolution very accurately. For the J≠0 rate constant calculations, the truncated internal Hamiltonian eigenvector basis is used to construct reduced (JKJ) blocks of the Hamiltonian. The individual (JKJ) blocks are diagonalized neglecting Coriolis coupling and treating the off-diagonal KJ±2 couplings by second order perturbation theory. The full wave function is parity decoupled. The rate constant is obtained as a sum over J of (2J+1)kJ(T). The time evolution of the flux for J≠0 is again very accurately described to give a well converged rate constant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457149
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  • 6
    Electronic Resource
    Electronic Resource
    Quantum calculation of thermal rate constants for the H+D2 reaction (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 8853-8862 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Thermal rate constants for the H+D2 reaction on the LSTH potential-energy surface are determined quantum mechanically over T=300–1500 K using the quantum flux–flux autocorrelation function of Miller [J. Chem. Phys. 61, 1823 (1974)]. Following earlier works [T. J. Park and J. C. Light, J. Chem. Phys. 91, 974 (1989); T. J. Park and J. C. Light, ibid. 94, 2946 (1991)], we use the adiabatically adjusted principal axis hyperspherical coordinates of Pack [Chem. Phys. Lett. 108, 333 (1984)] and a direct product C2v symmetry-adapted discrete variable representation to evaluate the Hamiltonian and flux. The initial representation of the J=0 Hamiltonian in the L2 basis of ∼14 000 functions is sequentially diagonalized and truncated to yield ∼600 accurate eigenvalues and eigenvectors for each symmetry species block. The J〉0 Hamiltonian is evaluated in the direct product basis of truncated J=0 eigenvectors and parity decoupled Wigner rotation functions. Diagonalization of the J〉0 Hamiltonian is performed separately for each KJ block by neglecting Coriolis coupling and approximating K coupling by perturbation. Both eigenvalues and eigenvectors are corrected by the perturbation. Thermal rate constants for each J, kJ(T), are then determined by the flux–flux autocorrelation function considering nuclear spins. Due to the eigenvector corrections, both parity calculations are required to determine kJ(T). Overall thermal rate constants k(T) are obtained by summing kJ(T) over J with the weight of 2J+1 up to J=30. The results show good agreement with experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462242
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  • 7
    Electronic Resource
    Electronic Resource
    Quantum flux operators and thermal rate constant: Collinear H+H2 (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 4897-4912 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The exact quantum formulation of the thermal rate constant, k(T), given by Miller et al. [W. H. Miller, J. Chem. Phys. 61, 1823 (1974); W. H. Miller, S. D. Schwartz, and J. W. Tromp, ibid. 79, 4889 (1983)] is evaluated in a localized @sL2 basis (distributed Gaussian basis) for two model problems. In considering the accuracy, feasibility, and computational efficiency of this approach, we demonstrate novel properties of the flux operator, namely the paucity of nonzero eigenvalues. This contributes greatly to the efficiency of the @sL2 approach. Finally, we show that Lanczos reduction can be used effectively for determining the thermal flux projectors and their time evolution as is required for evaluation of k(T).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454702
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  • 8
    Electronic Resource
    Electronic Resource
    The Wealth Effects of Capital Investment Decisions: An Empirical Comparison of Korean Chaebol and Non-Chaebol Firms (2005)
    Oxford, UK; Malden, USA : Blackwell Publishing Ltd/Inc.
    Journal of business finance & accounting 32 (2005), S. 0 
    Details
    ISSN: 1468-5957
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Economics
    Notes: Abstract:  This paper investigates the capital investment decisions of Korean firms and their impact on shareholder wealth. Overall, we find positive abnormal returns surrounding the announcements of 697 cases of investment projects during the period 1992–1999. This paper also finds that the investment decisions of business group (chaebol-affiliated) firms do not increase shareholder wealth, while the capital investment decisions of non-chaebol firms generate significantly positive abnormal returns. The multivariate tests provide consistent evidence that the announcement effects for chaebol firms are lower than for non-chaebol firms, after growth opportunities, investment size and firm size are controlled for. The findings support the view that the organizational structure of Korean chaebols creates an incentive for managers to make non-value maximizing capital investment decisions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0306-686X.2005.00618.x
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  • 9
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    Structure–property relationship amphoteric oxide systems via phase stability and ionic structural analysis (2020)
    Wiley
    Details
    Publication Date: 2020-09-11
    Print ISSN: 0002-7820
    Electronic ISSN: 1551-2916
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Wiley on behalf of American Ceramic Society.
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  • 10
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    Analytical Derivation of Interference Dips in Molecular Absorption Spectra: Molecular Properties and Relationships to Fano's Antiresonance (2000)
    American Physical Society
    Details
    Publication Date: 2000-12-18
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society
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