Theoretical studies of H+H2 reactive scattering

1976

363

104

Accurate three-dimensional reactive and nonreactive quantum mechanical cross sections for the H+H 2 exchange reaction on the Porter-Karplus potential energy surface are presented. Tests of convergence in the calculations indicate an accuracy of better than 5% for most of the results in the energy range considered (0.3 to 0.7 eV total energy). The reactive differential cross sections are exclusively backward peaked, with peak widths increasing monotonically from about 32° at 0.4 eV to 51° at 0.7 eV. Nonreactive inelastic differential cross sections show backwards to sidewards peaking, while elastic ones are strongly forward peaked with a nearly monotonic decrease with increasing scattering angle. Some oscillations due to interferences between the direct and exchange amplitudes are obtained in the para-topara and ortho-to-ortho antisymmetrized cross sections above the effective threshold for reaction. Nonreactive collisions do not show a tendency to satisfy a "j,-conserving" selection rule. The reactive cross sections show significant rotational angular momentum polarization with the mi = m 'i = 0 transition dominating for low reagent rotational quantum number j. In constrast, the degeneracy averaged rotational distributions can be fitted to statistical temperaturelike expressions to a high degree of accuracy. The integral cross sections have an effective threshold total energy of about 0.55 eV, and differences between this quantity and the corresponding ID and 2D results can largely be interpreted as resulting from bending motions in the transition state. In comparing these results with those of previous approximate dynamical calculations, we find best overall agreement between our reactive integral and differential cross sections and the quasiclassical ones of Karplus, Porter, and Sharma (J. Chern. Phys. 43, 3259 (1965)], at energies above the quasiclassical effective thresholds. This results in the near equality of the quantum and quasiclassical thermal rate constants at 600 K. At lower temperatures, however, the effects of tunneling become very important with the quantum rate constant achieving a value larger than the quasiclassical one by a factor of 3.2 at 300 K and 18 at 200 K.

Section: (Wk) ·mentioning

confidence: 87%

Section: (Wk) ·mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. II. Accurate cross sections for H+H2

1976

363

104

“…Quite recently, Elkowitz and Wyatt 1 6a have applied this procedure to the three-dimensional H + H 2 reaction. Wolken and Karplus 17 have applied an integrodifferential equation method proposed by Miller 18 to 3D H + H 2 using a one-vibrational-basis-function approximation.…”

Section: Introductionmentioning

confidence: 99%

Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. I. Theory

1976

335

165

A method is presented for accurately solving the Schri:idinger equation for the reactive collision of an atom with a diatomic molecule in three dimensions on a single Born-Oppenheimer potential energy surface. The Schri:idinger equation is first expressed in body-fixed coordinates. The wavefunction is then expanded in a set of vibration-rotation functions, and the resulting coupled equations are integrated in each of the three arrangement channel regions to generate primitive solutions. Next, these are smoothly matched to each other on three matching surfaces which appropriately separate the arrangement channel regions. The resulting matched solutions are linearly combined to generate wavefunctions which satisfy the reactance and scattering matrix boundary conditions, from which the corresponding R and S matrices are obtained. The scattering amplitudes in the helicity representation are easily calculated from the body fixed S matrices, and from these scattering amplitudes several types of differential and integral cross sections are obtained. Simplifications arising from the use of parity symmetry to decouple the coupled-channel equations, the matching procedures and the asymptotic analysis are discussed in detail. Relations between certain important angular momentum operators in body-fixed coordinate systems are derived and the asymptotic solutions to the body-fixed Schri:idinger equation are analyzed extensively. Application of this formalism to the three-dimensional H + H 2 reaction is considered including the use of arrangement channel permutation symmetry, even-

“…We repeated these calculations with a converged rotational basis set but with only one vibrational basis function, in analogy to what Saxon and Light 1 and Wolken and Karplus, 2 respectively, did for the similar coplanar and three dimensional reaction. The vibrationally converged and one-vibration results differ substantially for the coplanar as well as the collinear reaction, indicating the crucial role played by virtual vibrational channels.…”

mentioning

confidence: 99%

Coplanar and collinear quantum mechanical reactive scattering: The importance of virtual vibrational channels in the H + H2 exchange reaction

Baer

1974

We have performed accurate quantum mechanical calculations for the coplanar H + H 2 exchange reaction, using sufficient rotational and vibrational basis functions in the close-coupling expansion to ensure convergence. We repeated these calculations with a converged rotational basis set but with only one vibrational basis function, in analogy to what Saxon and Light 1 and Wolken and Karplus, 2 respectively, did for the similar coplanar and three dimensional reaction. The vibrationally converged and one-vibration results differ substantially for the coplanar as well as the collinear reaction, indicating the crucial role played by virtual vibrational channels.To solve the Schrodinger equation for the coplanar reaction, we first integrated the appropriate coupled equations into the interaction region from each of the three arrangement channel regions, using an extension of the method developed by Kuppermann.3 The resulting solutions were then smoothly matched on three conveniently chosen surfaces in configuration S{>ace. The R matrix and other asymptotic quantities were then obtained.Calculations for the Porter-Karplus surface 4 using 4 or 5 vibrations and 10 or 12 rotations per vibration for a total of 40 to 60 channels yielded reaction probabilities that change by less than 2%-5% as additional vibrational or rotational basis functions are added, over the total energy range 0. 30-0.60 eV. Without forcing orthogonalization at any time, the results satisfy conservation of flux to 0. 5% or better and time reversal invariance to 6% or better. The calculations were repeated using the same number of rotations but only one vibration, and introducing an appropriate vibrational orthogonalization.The resulting total reaction cross sections a~ are plotted in Figs. 1(a) and 1(b) and show differences between the vibrationally converged and one-vibration results greater than 3 orders of magnitude at low energies. The ratio of the one-vibration to vibrationally converged ortho-para rate constants is 3. 15 at 300 oK and 532 at 100°K.Using the method developed previously, 3 we calculated the collinear converged 5 and one-vibration reaction probabilities for the same potential energy surface. The ratios of the coplanar to collinear cross sections are plotted in Fig. l(c). Although these cross sections vary individually by about 12 orders of magnitude over the energy range considered, their ratios vary by less than 2 orders of magnitude, indicating a remarkably similar energy dependence. Virtual vibrational channels are furthermore about equally important in the collinear 6 and coplanar H + H 2 reaction. This will probably still be the case for this system in three dimensions as well as for other reactions.We have also calculated the reactive, inelastic, and antisymmetrized differential cross sections for coplanar where Pf is the collinear total reaction probability (the collinear total reaction cross section) for reagents H 2 in"= 0 initially. In all cases, a solid line indicates vibrationally converged results, while a dashed line ...