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  • 1
    Electronic Resource
    Electronic Resource
    Phase space optimization of quantum representations: Direct-product basis sets (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 4869-4885 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The quantitative phase space similarities between the uniformly mixed ensembles of eigenstates, and the quasiclassical Thomas–Fermi distribution, are exploited in order to generate a nearly optimal basis representation for an arbitrary quantum system. An exact quantum optimization functional is provided, and the minimum of the corresponding quasiclassical functional is proposed as an excellent approximation in the limit of large basis size. In particular, we derive a stationarity condition for the quasiclassical solution under the constraint of strong separability. The corresponding quantum result is the phase space optimized direct-product basis—customized with respect to the Hamiltonian itself, as well as the maximum energy of interest. For numerical implementations, an iterative, self-consistent-field-like algorithm based on optimal separable basis theory is suggested, typically requiring only a few reduced-dimensional integrals of the potential. Results are obtained for a coupled oscillator system, and also for the 2D Henon–Heiles system. In the latter case, a phase space optimized discrete variable representation (DVR) is used to calculate energy eigenvalues. Errors are reduced by several orders of magnitude, in comparison with an optimized sinc-function DVR of comparable size. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479747
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  • 2
    Electronic Resource
    Electronic Resource
    Efficient distributed Gaussian basis for rovibrational spectroscopy calculations (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 211-217 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We examine the problem of choosing efficient basis sets for the calculation of vibrational states of molecules. An exact quantum functional is derived for optimizing the parameters of distributed Gaussian basis sets (DGBs). For a given Hamiltonian and energy range, the basis is optimized with respect to the accuracy of the computed eigenvalues. This procedure demonstrates that optimized DGBs are remarkably efficient, being essentially exact for the one-dimensional harmonic oscillator, and orders of magnitude more accurate for the 23-state Morse oscillator than previous DGB calculations of comparable size. Contrary to expectations however, the quantum optimized DGBs have large overlaps, resulting in nearly singular overlap matrices that may cause numerical instabilities in larger calculations. On the other hand, the optimized eigenvalue calculation is shown to be fairly robust with respect to DGB parameter variations, implying that accurate results are possible using more numerically stable DGBs. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481787
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  • 3
    Electronic Resource
    Electronic Resource
    Six-dimensional quantum calculation of the intermolecular bound states for water dimer (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 168-176 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present results of six-dimensional bound-state calculations of the vibrations of rigid water dimer based on two older and two very recent potential energy surfaces. The calculations are done by a new sequential diagonalization–truncation approach using the symmetrized angular basis presented most recently by Althorpe and Clary [J. Chem. Phys. 101, 3603 (1994)] and a potential optimized discrete variable representation (DVR) in the monomer–monomer distance coordinate. The lowest ten or so states of each symmetry are apparently converged to 0.5 cm−1 using a coupled angular basis of Wigner rotation functions with Jmax=11 and mmax=5 on each monomer. The results differ significantly from the results presented by Leforestier et al. [J. Chem. Phys. 106, 8527 (1997)] and demonstrate that the ASP-S potential yields more accurate tunneling splittings than the more recent ASP-Wx potentials [C. Millot et al., J. Phys. Chem. A 102, 754 (1998)]. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478092
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  • 4
    Electronic Resource
    Electronic Resource
    Vibrations of the carbon dioxide dimer (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 5070-5080 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Fully coupled four-dimensional quantum-mechanical calculations are presented for intermolecular vibrational states of rigid carbon dioxide dimer for J=0. The Hamiltonian operator is given in collision coordinates. The Hamiltonian matrix elements are evaluated using symmetrized products of spherical harmonics for angles and a potential optimized discrete variable representation (PO-DVR) for the intermolecular distance. The lowest ten or so states of each symmetry are reported for the potential energy surface (PES) given by Bukowski et al. [J. Chem. Phys. 110, 3785 (1999)]. Due to symmetries, there is no interconversion tunneling splitting for the ground state. Our calculations show that there is no tunneling shift of the ground state within our computation precision (0.01 cm−1). Analysis of the wave functions shows that only the ground states of each symmetry are nearly harmonic. The van der Waals frequencies and symmetry adapted force constants are found and compared to available experimental values. Strong coupling between the stretching coordinates and the bending coordinates are found for vibrationally excited states. The interconversion tunneling shifts are discussed for the vibrationally excited states. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481061
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  • 5
    Electronic Resource
    Electronic Resource
    Surface self-diffusion of hydrogen on Cu(100): A quantum kinetic equation approach (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 1204-1216 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The self-diffusion of hydrogen on the (100) copper surface is investigated using a quantum kinetic equation approach. The dynamics of the adatom is described with a multiple-band model and the surface phonons represent the thermal bath responsible for the diffusion mechanism. Using the Wigner distribution formalism, the diffusive motion of the adatom is characterized in terms of the correlation functions of the adatom–phonon interaction. The diffusion coefficient exhibits two terms related to phonon mediated tunneling (incoherent part) and to dephasing limited coherent motion (coherent part). The competition between these two contributions induced a transition from a thermally activated regime to an almost temperature independent regime at a crossover temperature T*. A numerical analysis is performed using a well-established semiempirical potential to describe the adatom–surface interaction and a slab calculation to characterize the surface phonons. These calculations show that two-phonon processes represent the relevant contribution involved in the adatom–phonon coupling. The temperature dependence of the diffusion constant is thus presented and the relative contribution of the incoherent versus the coherent part is analyzed. Both contributions exhibit a change of behavior around 100 K from an exponential to a power law temperature dependence as the temperature decreases. This change is due to the confinement of the motion of the adatom in the ground energy band at low temperature. The incoherent part is shown to be the dominant contribution at high temperature and is characterized by an activation energy and a prefactor equal to ΔE=0.49±0.01 eV and D0(approximate)2.44×10−3 cm2/s, respectively. At low temperature, the power law dependence of the two contributions is different since the coherent part increases slowly as the temperature decreases whereas the incoherent part decreases. The crossover temperature is estimated to be equal to T*=125 K. Below T*, the coherent part becomes the main contribution and the diffusion constant exhibits an almost temperature independent behavior. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481899
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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Adiabatic approximation and nonadiabatic corrections in the discrete variable representation: Highly excited vibrational states of triatomic molecules (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 4008-4019 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An adiabatic approximation for the calculation of excited vibrational (J=0) levels of triatomic molecules is developed using the discrete variable representation (DVR). The DVR is in the large amplitude bending motion coordinate which is taken to be the adiabatic degree of freedom. We show that the adiabatic treatment in the DVR has some major advantages over the usual formulation in the finite basis representation (FBR), namely improved accuracy and broader range of applicability. An adiabatic rearrangement of the full Hamiltonian matrix in the DVR-ray eigenvector (REV) basis is defined, such that the diagonal blocks provide the rigorous matrix representation of the adiabatic bend Hamiltonian; their diagonalization yields bending level progressions corresponding to various stretching states. The off-diagonal blocks contain all nonadiabatic coupling matrix elements. The nonadiabatic corrections to the adiabatic vibrational levels are readily taken into account via second-order perturbation theory. One unique feature of our approach is that, in contrast to the FBR formulation, evaluation of the adiabatic and nonadiabatic matrix elements does not require evaluation of derivatives of the stretching wave functions with respect to the adiabatic variable. This approach is tested on the two-mode LiCN/LiNC (fixed CN distance) and the three-mode HCN/HNC. The adiabatic vibrational levels are in good agreement with accurate variational results. When corrected by second-order perturbative treatment, many levels are given very accurately (to within 0.1%) even for energies above the isomerization barriers. More localized states are better represented in the adiabatic approximation then delocalized vibrational states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.452904
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  • 8
    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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  • 9
    Electronic Resource
    Electronic Resource
    Reactive scattering of H+H2 and its isotopic analogs (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 4744-4745 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451751
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  • 10
    Electronic Resource
    Electronic Resource
    Quantum transport theory of vibrons in a molecular monolayer (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 114 (2001), S. 4955-4967 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We establish a quantum kinetic equation describing the transport properties of the vibrons in a molecular monolayer adsorbed on a dielectric substrate. A renormalization procedure is applied to the Hamiltonian of the system which is then separated in a vibron Hamiltonian, a bath Hamiltonian connected the external motions and a coupling Hamiltonian between the vibrons and the external modes. A perturbative analysis based on the projector method allows us to eliminate the irrelevant information related to the bath dynamics. The use of conventional approximations (Markov limit and Wick theorem) leads us to write the kinetic equation in a form exhibiting linear and nonlinear contributions. The linear term characterizes irreversible processes connected to the bath fluctuations whereas the nonlinear term represents a self-modulation of the dynamical matrix with respect to the vibron distribution. An application of the transport of CO vibrons on NaCl(100) illustrates the method. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1349896
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