Quantum Reactive Scattering Calculations

Green Function Evaluation in Quantum Reactive Scattering Calculations. 

T. Takayanagi, A. Wada, Quantum reactive scattering calculations of photodetachment spectra of the FHD- anion, Chem. Phys. Lett. 348 (2001) 514. 

The first exact quantum calculations of integral and differential cross sections on the adiabatic state were reported in 2001 by Honvault and Laimay [15,81]. They have carried out quantum reactive scattering calculations of the title reaction on the DK PES within the Time Independent Quantum Mechanical (HQM) framework using the hyperspherical close-coupling method. 

Garton, D. J.. Minton, T. K., Maiti, B., Troya, D., Schatz, G.C. (2003) A crossed molecular beams study of the O( P) -I- H2 reaction comparison of excitation function with accurate quantum reactive scattering calculations, J. Chem. Phys. 118, pp. 1585-1588. 

Quantum reactive scattering calculations arc based on the integration of the time-dependent Schrodinger equation... 

X. Wu, R. E. Wyatt, and M. D Mello, Inclusion of the geometric phase in quantum reactive scattering calculations A variational formulation,/. Chem. Phys. 101 2953 (1994). 

The theoretical simulations entailed time-independent, fully quantum, reactive scattering calculations on the LWA-78 PES by Alexander and coworkers. These calculations include explicitly all three PESs shown schematically in Fig. 4.2. LWA-78 PES overcomes the drawback on the ASW PES developed by Werner and coworkers [10, 23, 24], namely the underestimation by 0.7 kcal/mol of the F -I- H2 reaction exoergicity. Although this error is much smaller than the typical accuracy of ab initio calculations of PESs, it is a large fraction of the F -I- H2 (D2)... 

The good agreement between experiments and quantum scattering calculations demonstrates that modem quantum reactive scattering calculations, which in the past were verihed only for three-atom systems in three dimensions, are now able to predict vibrational energy disposal in four-atom reactions, which involve six dimensions (see Pogrebnya et al. (2000)). 

The quantum reactive scattering calculations for the D + H2(v, j) HD(v, /)-FH reaction were done for each value of total angular momentum... 

We reviewed the fundamental theory for including the geometric phase in quantum reactive scattering calculations based on a single adiabatic electronic potential energy surface. Two methods were discussed. In one... 

Quantum reactive scattering calculations on the state-to-state dynamics of gas phase chemical reactions involving four or more atoms can now be carried out. This article describes how the Rotating Bond Approximation (RBA) can be applied to the four-atom reactions OH +... 

The first quantum reactive scattering calculations on a realistic four-atom reaction were done on the H2 + CN H + HCN reaction with linear geometry [10,11]. The first quantum reactive scattering calculation on a state-selected four-atom reaction with non-linear geometry was reported in 1991 [12] in which the reaction OH + H2 H2O + H and the reverse reaction H + H2O —> OH + H2 was... 

Takayanagi, T., Wada, A. Reduced dimensionality quantum reactive scattering calculations on the ab initio potential energy surface for the 0( D) + N2O NO + NO reaction. Chem. Phys. 269, 37 7 (2001)... 

Many of the recent accurate quantum reactive scattering calculations have utilised the above approach [35, 33, 79, 80, 81, 82, 83]. Methods using hyper-spherical coordinates have been the primary alternative [84, 85, 86]. Complete state-to-state differential cross section calculations have been carried out for the H+H2 reaction, its isotopic variants [81, 83] and also for the F+H2->HFH-H reaction [84]. Calculations for many other reactions have been carried out mostly for J=0 only. 

In the earliest exact 3D quantum reactive scattering calculations for H-hH2 of Kuppermann and Schatz [11, 106, 107], Elkowitz and Wyatt [50, 108] and Walker, Stechel and Light [109] extensions of the natural collision coordinates, introduced by Marcus [110], have been used. For the simple case of a collinear atom-diatom reaction the natural collision coordinates swung smoothly from... 

We define the precise linear system to be solved for the D-f H2 quantum reactive scattering calculations. This entails the choice of system coordinates, basis set, asymptotic state, and absorbing potential. We note that, with respect to the coordinates and basis set, much of our work parallels that of Choi and Light [33] in their calculations on the Ar-HCl van der Waals complex. 

We now present the results of our quantum reactive scattering calculations on the D-(-H2(u = 1, j) system. As stated in the Introduction, the present Chapter has two main goals. The first is to demonstivite the efficiency of the present method in a non-trivial application. For this purpose, we report the D-f H2 reaction probabilities P ji Et) and cross sections av,j Et) in addition to the typical amounts of core memory and CPU time required for these calculations. The second objective is to determine the j and T dependence of kv=i,j[T), for the purpose of comparison with both experiment and approximate theory. 

Table 5.1 Optimized convergence parameters for the present quantum reactive scattering calculations. These values aie sufficient to give better than 3% accuracy for 0.15 eV < Ei < 0.37 eV, and better than 6% accuracy otherwise. E = total scattering energy, Re is reactant, and Pr is product.

We have analyzed the sensitivity of quantum reactive scattering calculations for H+H2 to small changes in the molecidar potential, and find no qualitative changes and very small quantitative changes in the resulting cross sections. The fact that these calculations (at least for H+H2) do not show anomalous sensitivity helps to put ah initio reaction dynamics on firm ground. It is true that the difference between the potentials considered in Chapter 2 is, in some sense, trivial. Nevertheless, the fact that the difference in the resulting dynamics is also trivial is an important result. 

In this article, we have considered four very different methods for solving the state to state reactive scattering problem in the simple (but nonetheless typical) context of a collinear A -t- BC AB -t- C reaction. Of these four methods, the natural collision coordinates described in Section 3 are now simply of historical interest, but the remaining three methods are all still widely used in quantum reactive scattering calculations. The very fact that this is the case shows that all three methods have their advantages and disadvantages, and that no one method has yet been discovered that is ideal for every reaction. In order to emphasize this fact, we shall now close with a few comparative remarks on the merits of each method in turn. 

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