Scattering, reactive

This gives a stable algorithm, and is moderately efficient [108] (although not as efficient as the original split-operator based algorithm). However, this is an unacceptable compromise because the convergence is again second order in t. 

In the following Chapter, we discuss native to the Lanczos baised 

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Studies of inelastic scattering are of considerable interest in heterogeneous catalysis. The degree to which molecules are scattered specularly gives information about their residence time on the surface. Often new chemical species appear, whose trajectory from the surface correlates to some degree with that of the incident beam of molecules. The study of such reactive scattering gives mechanistic information about surface reactions. 

A comprehensive discussion of wavepackets, classical-quantum correspondence, optical spectroscopy, coherent control and reactive scattering from a unified, time dependent perspective. 

The cross section a -is related to the partial wave reactive scattering matrix , tln-ough the partial wave sum... 

Kuppermann A 1997 Reactive scattering with row-orthonormal hyperspherical coordinates. 2. 

Balint-Kurti G G, Dixon R N and Marston C C 1992 Grid methods for solving the Schrodinger equation and time-dependent quantum dynamics of molecular photofragmentation and reactive scattering processes/of. Rev. Phys. Chem. 11 317—44... 

Reactive scattering or a chemical reaction is characterized by a rearrangement of the component particles within the collision system, thereby resulting in a change of the physical and chemical identity of the original collision reactants A + B into different collision products C + D. Total mass is conserved. The reaction is exothemiic when rel(CD) > (AB) and is endothermic when rel(CD) < (AB). A threshold energy is required for the endothemiic reaction. 

The first half of this section discusses the use of the crossed beams method for the study of reactive scattering, while the second half describes the application of laser-based spectroscopic metliods, including laser-mduced fluorescence and several other laser-based optical detection teclmiques. Furtlier discussion of both non-optical and optical methods for the study of chemical reaction dynamics can be found in articles by Lee [8] and Dagdigian [9]. 

If the molecules could be detected with 100% efficiency, the fluxes quoted above would lead to impressive detected signal levels. The first generation of reactive scattering experiments concentrated on reactions of alkali atoms, since surface ionization on a hot-wire detector is extremely efficient. Such detectors have been superseded by the universal mass spectrometer detector. For electron-bombardment ionization, the rate of fonnation of the molecular ions can be written as... 

The molecular beam and laser teclmiques described in this section, especially in combination with theoretical treatments using accurate PESs and a quantum mechanical description of the collisional event, have revealed considerable detail about the dynamics of chemical reactions. Several aspects of reactive scattering are currently drawing special attention. The measurement of vector correlations, for example as described in section B2.3.3.5. continue to be of particular interest, especially the interplay between the product angular distribution and rotational polarization. 

Lee Y T, McDonald J D, LeBreton P R and Herschbach D R 1969 Molecular beam reactive scattering apparatus with electron bombardment detector Rev. Sol. Instrum 40 1402-8... 

Chapman W B, Blackman B W, Nizkorodov S and Nesbitt D J 1998 Quantum-state resolved reactive scattering of F + H2 in supersonic jets Nascent HF(v,J) rovibrational distributions via IR laser direct absorption methods J. Chem. Rhys. 109 9306-17... 

Lee Y T 1988 Reactive scattering I nonoptical methods Atomic and Molecular Beam Methods vol 1, ed G Scoles et a/(New York Oxford University Press) pp 553-68... 

Dharmasena G, Copeland K, Young J H, Lasell R A, Phillips T R, Parker G A and Keil M 1997 Angular dependence for v /-resolved states in F + H2 -> HF(v /) + H reactive scattering using a new atomic beam source J. Rhys. Chem. A101 6429—40... 

Baer M 1985 The general theory of reactive scattering the differential equations approach Theory of... 

Neuhauser D, Baer M and Kouri D J 1990 The application of optical potentials for reactive scattering a case study J. Chem. Phys. 93 2499... 

Zhang J Z H and Miller W H 1989 Quantum reactive scattering via the S-matrix version of the Kohn variational principle—differential and integral cross sections for D + Hj —> HD + H J. Chem. Phys. 91 1528... 

Schatz G C and Kuppermann A 1975 Quantum mechanical reactive scattering an accurate three-dimensional calculation J. Chem. Phys. 62 2502... 

Bacic Z, Kress J D, Parker G A and Pack R T 1990 Quantum reactive scattering in 3 dimensions using hyperspherical (APH) coordinates. 4. discrete variable representation (DVR) basis functions and the analysis of accurate results for F + Hg d. Chem. Phys. 92 2344... 

Kuppermann A 1996 Reactive scattering with row-orthonormal hyperspherical coordinates. I. Transformation properties and Hamiltonian for triatomic systems J. Phys. Chem. 100 2621... 

Peskin U, Miller W H and Ediund A 1995 Quantum time evolution in time-dependent fields and time-independent reactive-scattering calculations via an efficient Fourier grid preconditioner J. Chem. Phys. 103 10 030... 

Gray S K and Balint-Kurti G G 1998 Quantum dynamics with real wave packets, including application to three-dimensional (J = 0)D + H2 HD + H reactive scattering J. Chem. Phys. 108 950... 

Mandelshtam V A and Taylor H S 1995 A simple recursion polynomial expansion of the Green s function with absorbing boundary conditions. Application to the reactive scattering J. Chem. Phys. 102... 

Neuhauser D, Judson R S, Baer M and Kouri D J 1997 State-to-state time-dependent wavepacket approach to reactive scattering State-resolved cross-sections for D + H2(u = 1,y = 1, m) H + DH(v, J), J. Chem. See. Faraday Trans. 93 727... 

Neuhauser D 1992 Reactive scattering with absorbing potentials in general coordinate systems Chem. 

Poliak E 1985 Periodic orbits and the theory of reactive scattering Theory of Chemical Reaction Dynamics vol III, ed M Baer (Boca Raton, FL CRC Press)... 

Yu M L and DeLouise L A 1994 Surface chemistry on semiconductors studied by molecular beam reactive scattering Surf. Sc/. Rep. 19 285-380... 

Carter L E, Khodabandeh S, Weakliem P C and Carter E A 1994 First-principles-derived dynamics of Fj reactive scattering on Si(100)-2 x 1 j. Chem Phys. 100 2277-88... 

The ADT matrix for the lowest two electronic states of H3 has recently been obtained [55]. These states display a conical intersection at equilateral triangle geometi ies, but the GP effect can be easily built into the treatment of the reactive scattering equations. Since, for two electronic states, there is only one nonzero first-derivative coupling vector, w5 2 (Rl), we will refer to it in the rest of this... 

In a two-lowest-electronic-state Bom-Huang description for a chemical reaction, the nuclei can move on both of two corresponding PESs during the reaction, due to the electronically non-adiabatic couplings between those states. A reactive scattering formalism for such a reaction involving a triatomic system... 

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