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  • 1
    Electronic Resource
    Electronic Resource
    Use of the discrete variable representation in the quantum dynamics by a wave packet propagation: Predissociation of NaI(1Σ+0) →NaI(0+)→Na(2S)+I(2P) (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 2593-2604 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Using the Gauss–Chebyshev discrete variable representation (DVR), the dissociative quantum dynamics for a wave packet evolving under the influence of the Hamiltonian for two interacting diabatic states of a diatomic molecule is calculated. The split time evolution operator method is used to obtain the solutions to the time-dependent Schrödinger equation. A specific example of the numerical calculation is shown for the predissociation process of NaI→Na(2S)+I(2P) from its first excited electronic state (0+). The numerical results are compared with the experimental observations from the femtosecond laser photofragmentation, recently reported by Zewail and co-workers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455957
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  • 2
    Electronic Resource
    Electronic Resource
    Efficient pointwise representations for vibrational wave functions: Eigenfunctions of H+3 (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 1774-1786 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The successive truncation–diagonalization method described in previous work [Z. Bacic, R. M. Whitnell, D. Brown and J. C. Light, Comp. Phys. Comm. (to be published)] is generalized to a three-dimensional discrete variable representation (DVR). The use of the 3D DVR leads to a sparse Hamiltonian matrix that makes the transformations used in the successive truncation-diagonalization technique very efficient. The method is applied to J=0 H+3 using a hyperspherical coordinate system. Full symmetry adaptation of the DVR is used allowing a complete resolution of the vibrational eigenfunctions into the D3h irreducible representations. Converged eigenvalues up to ∼20 000 cm−1 are reported for all representations. This method is thereby shown to be both efficient and accurate for calculating triatomic vibrational states with large amplitude motion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456071
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  • 3
    Electronic Resource
    Electronic Resource
    Accurate localized and delocalized vibrational states of HCN/HNC (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 86 (1987), S. 3065-3077 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Results of the first accurate quantum calculation of the delocalized, large amplitude motion vibrational (J=0) levels of HCN/HNC, lying above the isomerization barrier, are presented. The recently developed DVR-DGB quantum method [Z. Bacic and J. C. Light, J. Chem. Phys. 85, 4594 (1986)] is employed in this work. A model, empirical surface by Murrell et al. is used. All modes are included; the energy level calculation does not involve any approximations. Over a hundred vibrational levels are calculated accurately for this model surface. A number of them lie above the isomerization barrier; some are extensively delocalized over both HCN and HNC minima. Analysis shows that for HCN/HNC the threshold for significant delocalization is determined by the height of the vibrationally adiabatic bending barrier. In addition, the nearest neighbor level spacing distribution is obtained and compared to that of LiCN/LiNC. Various computational aspects of the DVR-DGB approach, which is applicable to any triatomic molecule, are also discussed. The method is very suitable for efficient, accurate treatment of floppy molecules and molecules which can isomerize. The DVR-DGB (i.e., ray eigenvector) basis provides a rapidly convergent expansion for the delocalized (and localized) states. Consequently, a single diagonalization of the DVR-ray eigenvector Hamiltonian matrix, whose size is modest relative to the number of accurately determined energy levels, yields the energies of both localized and delocalized states. Accurate evaluation of the two-dimensional integrals in the potential matrix elements requires only 3–4 Gauss–Hermite quadrature points per dimension.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.452017
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  • 4
    Electronic Resource
    Electronic Resource
    Erratum: A split interaction representation for quantum correlation functions of dissociative systems [J. Chem. Phys. 93, 633 (1990)] (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 832-832 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460754
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  • 5
    Electronic Resource
    Electronic Resource
    Determination of the bound and quasibound states of Ar–HCl van der Waals complex: Discrete variable representation method (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 2129-2145 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The ArHCl (HCl; ν=0) van der Waals (vdW) molecule has a large number of bound and rotationally predissociative (resonance) states for total angular momentum in the range of 0≤J≤60. Using the Jacobi coordinates and the total angular momentum representation in the body-fixed reference frame, the Hamiltonian is evaluated in the discrete variable representation (DVR) of the stretch and bend internal vibrational basis and a basis of parity adapted rotation functions. The facile and effective application of the DVR is greatly enhanced by an appropriate choice of the basis set. The sequential diagonalization and truncation of the Hamiltonian permit accurate and efficient determination of eigenstates. Using Hutson's H6 potential energy surface, the energies and wave functions of all bound and resonance states are computed for selected J's up to J=60. A novel flux projection technique facilitates semiquantitative evaluation of the lifetimes of all states and, in particular, the simple identification of the resonance states in the L 2 eigenvector basis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458004
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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    A novel wave function factorization simplifying the matrix representation of the Schrödinger equation (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 1824-1827 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In quantum scattering theory, coordinate systems with nontrivial Jacobians may arise and cause difficulty in the reduction of close coupled equations to the desired, simple, obviously Hermitian form {−@sI(d2/dx2)+@sW(x)}f=0 with @sW=@sW°. We consider x to be the translational coordinate, orthogonal to the surface coordinates, and the Schrödinger equation is represented in a basis of surface functions. We introduce a novel wave function factorization which permits reduction to the above form if the basis is (locally) independent of x for arbitrary Jacobian and general weight function for the surface functions. This factorization is compared with the more common factorization where all coordinates are treated equally. Applications to wave function matching and the calculation of surface integrals are mentioned. Several three-dimensional, orthogonal coordinate systems provide examples simplified by the novel factorization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454106
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  • 8
    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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  • 9
    Electronic Resource
    Electronic Resource
    A split interaction representation for quantum correlation functions of dissociative systems (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 633-642 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We propose and test a new general approach to the L 2 evaluation of quantum correlation functions for dissociative systems. This method introduces a split interaction representation (SIR) for the correlation function based on formally exact manipulations, and greatly enhances convergence of the correlation function with respect to the range of the L 2 basis, by suppressing the spurious "reflections'' from the "edges'' of the basis. The method is tested by applying it for the evaluation of flux autocorrelation function from which the quantal thermal rate constant is obtained by integrating it over time. Computations for the one-dimensional Eckart barrier show remarkable convergence of the flux autocorrelation function with respect to both the size and the range of the basis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459510
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  • 10
    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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