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A new D3h symmetry adapted approach to accurate calculation of high-lying rovibrational (J>0) states of floppy X3 triatomic molecules is presented, extending our recent work on J=0 bound states of D3h triatomics [Z. Bacˇic and J. Z. H. Zhang, Chem. Phys. Lett. 184, 513 (1991)]. Three sets of Jacobi coordinates are employed, allowing construction of basis sets with full S3 permutation symmetry of the three identical nuclei. Inclusion of S3 symmetry reduces substantially the size of the final matrix eigenvalue problem and the computational effort involved. It also assures unambiguous, correct symmetry assignment of the calculated rovibrational levels. Our method is especially suitable for rotating D3h molecules with strongly coupled large amplitude motions of the three atoms. An efficient quasiadiabatic diagonalization and truncation scheme is incorporated into our methodology. Application to H+3 for J=1 produced the total of 426 well converged, symmetry assigned states up to ∼24 000 cm-1 above the ground state, far more than in any previous calculation for rotating H+3. [ABSTRACT FROM AUTHOR]

We show that the triatomic adiabatic vibrational eigenstates (AVES) provide a convenient basis for accurate discrete variable representation (DVR) calculation and automatic assignment of highly excited, large amplitude motion vibrational states of floppy triatomic molecules. The DVR–AVES states are eigenvectors of the diagonal (in the stretch states) blocks of the adiabatically rearranged triatomic DVR-ray eigenvector (DVR–REV) Hamiltonian [J. C. Light and Z. Bacˇic, J. Chem. Phys. 87, 4008 (1987)]. The transformation of the full triatomic vibrational Hamiltonian from the DVR–REV basis to the new DVR–AVES basis is simple, and does not involve calculation of any new matrix elements. No dynamical approximation is made in the energy level calculation by the DVR–AVES approach; its accuracy and efficiency are identical to those of the DVR–REV method. The DVR–AVES states, as the adiabatic approximation to the vibrational states of a triatomic molecule, are labeled by three vibrational quantum numbers. Consequently, accurate large amplitude motion vibrational levels obtained by diagonalizing the full vibrational Hamiltonian transformed to the DVR–AVES basis, can be assigned automatically by the code, with the three quantum numbers of the dominant DVR–AVES state associated with the largest (by modulus) eigenvector element in the DVR–AVES basis. The DVR–AVES approach is used to calculate accurate highly excited localized and delocalized vibrational levels of HCN/HNC and LiCN/LiNC. A significant fraction of localized states of both systems, below and above the isomerization barrier, is assigned automatically, without inspection of wave function plots or separate approximate calculations. [ABSTRACT FROM AUTHOR]

All rovibrational levels of HCN/HNC up to ∼16 000 cm-1, relative to the HCN minimum, for J=0, 1, 2, have been calculated accurately. All internal degrees of freedom are included in these calculations, performed on the realistic, empirical potential surface by Murrel et al. [J. Mol. Spectrosc. 93, 307 (1982)]. Body-fixed mass-scaled Jacobi coordinates are employed, together with the discrete variable representation of the large amplitude motion (LAM) angular coordinate, and a 2-D distributed Gaussian basis for the radial degrees of freedom. The successive diagonalization–truncation procedure results in a compact matrix representation of the full rovibrational Hamiltonian, allowing accurate and efficient determination of a large number (>350 for J=2, p=0 case) of highly excited LAM rovibrational states of HCN/HNC. This approach is suitable for a broad class of floppy, isomerizing triatomic molecules and van der Waals complexes. In addition to energy levels and wave functions, expectation values of Jacobi coordinates, 〈R〉, 〈r〉, and 〈θ〉, are calculated for most states. The majority of calculated J=1,2 levels lie above the top of the isomerization barrier, and are delocalized to a varying degree over both local minima. Rotation appears to lower the energy threshold for extensive delocalization; for the states with J=1, or 2, it is ∼460–480 cm-1 below that for J=0 states. Moreover, increasing rotational excitation affects significantly the degree of localization of a given state. [ABSTRACT FROM AUTHOR]

Accurate 3D coupled channel calculations for total angular momentum J=0 for the reaction F+H2→HF+H using a realistic potential energy surface are analyzed. The reactive scattering is formulated using the hyperspherical (APH) coordinates of Pack and Parker. The adiabatic basis functions are generated quite efficiently using the discrete variable representation method. Reaction probabilities for relative collision energies of up to 17.4 kcal/mol are presented. To aid in the interpretation of the resonances and quantum structure observed in the calculated reaction probabilities, we analyze the phases of the S matrix transition elements, Argand diagrams, time delays and eigenlifetimes of the collision lifetime matrix. Collinear (1D) and reduced dimensional 3D bending corrected rotating linear model (BCRLM) calculations are presented and compared with the accurate 3D calculations. [ABSTRACT FROM AUTHOR]

We have calculated variationally highly excited vibrational (J=0) levels of the water molecule up to ∼27 000 cm-1 (relative to the minimum of the potential surface), for a global Sorbie–Murrell-type potential surface. The calculation has been performed in Radau coordinates, using the recently developed DVR-DGB variational approach [Z. Bacˇic and J. C. Light, J. Chem. Phys. 85, 4594 (1986); 86, 3065 (1987)]. 110 symmetric and 77 antisymmetric vibrational levels have been determined accurately, requiring diagonalization of relatively small Hamiltonian matrices of dimension ∼600. Many of the calculated levels correspond to large amplitude bending vibrations. Nearest neighbor level spacing statistics for the calculated levels above 18 000–20 000 cm-1 conform closely to a Wigner distribution, suggesting classically chaotic behavior in this energy range. Convergence rates of these variational calculations for H2O are comparable to those seen earlier for LiCN/LiNC and HCN/HNC. The DVR-based vibrationally adiabatic approach introduced by Light and Bacˇic [J. Chem. Phys. 87, 4008 (1987)] has also been tested here. Perturbative inclusion of the nonadiabatic corrections has allowed reliable identification of vibrational (J=0) levels of H2O up to 18 000–20 000 cm-1. With this model potential energy surface, reasonable agreement (∼1%) is obtained with experimentally known vibrational states to ∼20 000 cm-1. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. Bacˇic 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. [ABSTRACT FROM AUTHOR]

Coalescent resonances are investigated in the He/LiF(001) collisions. The giant resonance is found when the incident energy of the He atom is scanned. Similar resonance is not found when the incidence azimuthal angle is scanned. This is primarily due to the presence of other resonances which are degenerate with the coalescent ones. [ABSTRACT FROM AUTHOR]

Vibrational relaxation of CO (n1=1) in collision with ortho, para H2 is studied quantum mechanically, with the rotational degree of freedom of H2 included. This represents extension of our earlier study [Ref. 11, J. Chem. Phys. 81, 0000 (1984)], where H2 was treated as a structureless particle. The potential surface, described in detail in Ref. 11, consists of a SCF part, which includes explicitly the variation with the CO bond distance, and a damped long range dispersion contribution. The relaxation cross sections are calculated within the infinite order sudden approximation (IOSA) for CO rotation and within the coupled states approximation (CSA) for H2 rotation. Many of the trends clearly present in the cross sections can be understood in terms of the distorted wave approximation (DWA). The calculated relaxation rates in para H2 agree well (within a factor of 2) with the experimental results. However, judging from a limited number of calculated cross sections for relaxation in ortho H2, the ortho H2 relaxation rates would be comparable in magnitude to the para rates, in disagreement with experiment. Extensive comparison is made with the work of Poulsen and Billing (Ref. 12) and a number of significant, even qualitative differences regarding magnitude of some simultaneous CO vibrational and H2 rotational transitions are discussed. [ABSTRACT FROM AUTHOR]

We present a fully quantal dynamical study of vibrational relaxation of CO in collisions with H2 treating H2 as a structureless projectile. The potential energy surface consists of a SCF part, including explicitly the variation with the CO bond distance, and a damped long range dispersion part. This potential model contains only two free parameters in the damping function which have been determined previously by fitting rotationally inelastic beam data for D2–CO. The dynamical calculations are performed within the infinite order sudden approximation (IOSA) and the coupled states approximation (CSA). The IOSA relaxation cross sections are generally a factor of ∼1.5 smaller than the CSA cross sections independent on the initial rotational state of CO for j≾–6. The relaxation rate constants are very sensitive to small changes of the interaction potential. After readjusting one of the damping parameters (within a range still acceptable with the beam data) the IOSA rate constants agree very well with the experimental ones for ortho H2. It is demonstrated that on the same level of approximation the present rate constants are about three times larger than those obtained from the potential energy surface of Poulsen. [ABSTRACT FROM AUTHOR]