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  • 1
    Electronic Resource
    Electronic Resource
    A single Lanczos propagation method for calculating transition amplitudes. II. Modified QL and symmetry adaptation (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 114 (2001), S. 1467-1472 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The recently proposed single Lanczos propagation method [J. Chem. Phys. 111, 9944 (1999)] for calculating multiple transition amplitudes is made more efficient in several aspects. It is shown that the amplitudes can be calculated without the explicit calculation and storage of the Lanczos eigenvectors, thus significantly reducing the computational costs, particularly for long propagation. It is also shown that symmetry adaptation can be implemented in the Lanczos propagation in a straightforward manner. In particular, eigenspectra in multiple irreducible representations can be determined from a single recursion by projecting the symmetrized Lanczos states at each step. The accuracy and efficiency of the improved methods are ascertained by numerical tests of realistic triatomic and tetratomic systems. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1331356
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  • 2
    Electronic Resource
    Electronic Resource
    Six-dimensional quantum calculations of highly excited vibrational energy levels of hydrogen peroxide and its deuterated isotopomers (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 114 (2001), S. 4763-4774 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report accurate calculations of vibrational energy levels of HOOH, DOOD, and HOOD up to 10 000 cm−1 above the zero-point energy levels on a high-quality ab initio potential energy surface. These energies were determined by the Lanczos algorithm based on repetitive matrix-vector multiplication. The six-dimensional vibrational Hamiltonian in the diatom–diatom Jacobi coordinate system was discretized in a mixed basis/grid representation. A direct product potential optimized discrete variable representation was used for the radial coordinates, while nondirect product spherical harmonics were employed for the angular degrees of freedom. The calculation and storage of the potential matrix in the angular finite basis representation were avoided by using a series of one-dimensional pseudo-spectral transformations to a direct product angular coordinate grid. The diatom–diatom exchange symmetry, when applicable, was incorporated into the basis, which significantly enhanced the efficiency for symmetric isotopomers. A few hundred low-lying vibrational levels of each isotopomer were assigned and compared with experimental data. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1348274
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  • 3
    Electronic Resource
    Electronic Resource
    Comparison of Chebyshev, Faber, and Lanczos propagation-based methods for calculating resonances (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 5263-5269 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We compare the numerical performance of three recursive methods for calculating collisional resonances, which are characterized by complex eigenenergies of an optical potential augmented Hamiltonian. The first approach involves a modified Chebyshev propagation of a real wave packet, followed by low-storage filter-diagonalization. A similar filter-diagonalization scheme replaces the Chebyshev propagation with a more general Faber recursion associated with a specific conformal mapping in the complex plane. The complex resonance eigenenergies are also obtained using a complex-symmetric version of the Lanczos algorithm. Numerical tests for a realistic triatomic system (HCO) indicate that the Lanczos method and the low-storage filter-diagonalization based on the Chebyshev propagation are much more efficient than the Faber approach. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481096
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  • 4
    Electronic Resource
    Electronic Resource
    A single Lanczos propagation method for calculating transition amplitudes (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 9944-9951 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A method using only a single Lanczos propagation to determine multiple transition amplitudes without the explicit calculation of the eigenstates is proposed. Comparing with methods requiring multiple propagations, this method is very attractive for large dimensional problems since the propagation is usually the most computationally intensive step. When overlaps between eigenstates and pre-specified quantum states are of interest, it is shown that the "spurious" Lanczos eigenvalues cannot be simply deleted as done in the Cullum–Willoughby procedure. Practical procedures for calculating the overlaps are provided, which take into consideration numerical behaviors of the Lanczos algorithm in finite precision arithmetic, such as the loss of global orthogonality and emergence of "spurious" eigenvalues. Numerical tests in a realistic triatomic system confirm the accuracy of the present method. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.480347
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  • 5
    Electronic Resource
    Electronic Resource
    Efficient calculation of matrix elements in low storage filter diagonalization (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 464-471 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Efficient extraction of frequency information from a discrete sequence of time signals can be achieved using the so-called low storage filter diagonalization approach. This is possible because the signal sequence can be considered as a correlation function associated with a quantum Hamiltonian. The eigenvalues of the Hamiltonian (i.e., the frequencies in the signal) in a pre-specified energy range are obtainable from a low-rank generalized eigenequation in a subspace spanned by the filtered states. This work presents an efficient and accurate method to construct the Hamiltonian and overlap matrices directly from correlation functions for several types of propagators. Emphasis is placed on a recurrence relationship between the Hamiltonian and overlap matrices. This method is similar to, but more efficient than, several existing methods. Numerical testing in a triatomic system (HOCl) confirms its accuracy and efficiency. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479327
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  • 6
    Electronic Resource
    Electronic Resource
    Theoretical studies of rotation induced Fermi resonances in HOCl (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 7290-7297 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Theoretical investigations of rotation induced Fermi resonances in HOCl are carried out using several different quantum mechanical methods. Due to shape differences of the eigenfunctions, nearby vibrational levels may be energetically tuned to form Fermi (or anharmonic) resonances by varying rotational quantum numbers. Such rotation induced Fermi resonances have been observed experimentally in HOCl, for example, for bright states (3,2,0) and (4,0,0) by Abel et al. [J. Chem. Phys. 104, 3189 (1996) and ibid. 106, 3103 (1997)]. Using an ab initio potential, this work shows that the (3,2,0) state is significantly mixed with the (2,3,3) state near J=28 and K=4, and J=14 and K=3, while the (4,0,0) state forms a Fermi pair with (3,2,1) near J=43 and K=8. The wave functions of the Fermi pairs display significant deformation due to the mixing. Both the rotation induced degeneracy and coupling strength are found to be important. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.480053
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  • 7
    Electronic Resource
    Electronic Resource
    Extended symmetry-adapted discrete variable representation and accelerated evaluation of H(circumflex)ψ (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 2771-2777 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: It has long been realized that symmetry-adapted discrete variable representation for molecular systems with nontrivial symmetry leads to significant reduction of the grid size, and thus computational costs. In this work, we show that even for molecules with no symmetry it is still possible to achieve significant computational savings by symmetry adaptation. The extended symmetry-adapted discrete variable representation takes advantage of the higher symmetry in a part of the total Hamiltonian denoted as the reference Hamiltonian, e.g., a kinetic energy operator. When the evaluation of its action constitutes the more expensive part of the calculation such as in discrete variable representation (DVR) based methods, significant savings may ensue. Applications to several commonly used kinetic energy operators are discussed. Numerical tests in simple as well as realistic systems are carried out to demonstrate the efficiency of the method. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477920
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  • 8
    Electronic Resource
    Electronic Resource
    Short-time Chebyshev propagator for the Liouville–von Neumann equation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 6626-6634 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A Chebyshev interpolation scheme is proposed for the short-time Liouville–von Neumann propagator. For each propagation step, a small number of Chebyshev polynomials is used to construct the propagator. The method involves only matrix-vector multiplication and is memory efficient since the three-term Chebyshev recursion needs only two vectors stored. It is also numerically stable since neither matrix diagonalization nor inversion is involved. The short Chebyshev recursion ensures that the divergence due to the complex eigenvalues of the Liouville superoperator is kept under control. Numerical tests carried out for the Redfield equation of a one-dimensional dissipative harmonic system demonstrate that the short-time Chebyshev propagator is accurate and significantly more efficient than the commonly used fourth-order Runge–Kutta scheme. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478570
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  • 9
    Electronic Resource
    Electronic Resource
    Discrete energy representation and generalized propagation of physical systems (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 6068-6077 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This work discusses the discrete energy representation based on generalized propagation of a physical system. Here, the propagation is defined as a recursion scheme which generates a series of system states from a given initial state. Examples of such schemes include the time propagation and polynomial recursion. It is argued that each propagation determines a set of energy points, which form the discrete energy representation. A unitary transformation can be established between the discrete energy representation and the generalized time representation, much like the well-known transformation between the discrete variable representation and the finite basis representation. Such a collocation approach can be useful in calculating many properties that are local in the energy domain. Numerical examples are presented to demonstrate the utility in filter diagonalization. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.476017
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  • 10
    Electronic Resource
    Electronic Resource
    Evolution of quantum system in order domain of Chebyshev operator (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 3569-3578 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A cosine transform between the order and angle of the Chebyshev operator is identified. Because the order and angle form a conjugate pair similar to energy and time, the Chebyshev state can be considered as a cosine-type evolution state in the order domain, analogous to a time-dependent wave packet. The order/angle formulation is analytically equivalent to the time/energy formulation, but the former may have some numerical advantages in certain applications. This is illustrated by examining the spectral method and the filter-diagonalization method in both formulations. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.472228
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