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Bibliography

1
W. C. Gardiner, Combustion Chemistry (Springer, Berlin FRG, 1984).

2
N. Fujii and K. S. Shin, Chem. Phys. Lett. 151, 461 (1988).

3
K. S. Shin and J. V. Michael, J. Chem. Phys. 95, 263 (1991).

4
T. Yuan, C. Wang, C.-L. Yu, M. Frenklach, and M. J. Rabinowitz, J. Phys. Chem. 95, 1258 (1991).

5
H. Yang, W. C. Gardiner, K. S. Shin, and N. Fujii, Chem. Phys. Lett. 231, 449 (1994).

6
H. Du and J. P. Hessler, J. Chem. Phys. 96, 1077 (1992).

7
C.-L. Yu, M. Frenklach, D. A. Masten, R. K. Hanson, and C. T. Bowman, J. Phys. Chem. 98, 4770 (1994).

8
Y. Matsumi, N. Shafer, K. Tonokura, M. Kawasaki, and H. L. Kim, J. Chem. Phys. 95, 4972 (1991).

9
A. Jacobs, H. R. Volpp, and J. Wolfrum, Chem. Phys. Lett. 177, 200 (1991).

10
K. Keßler and K. Kleinermanns, J. Chem. Phys. 97, 374 (1992).

11
A. Jacobs, F. M. Schuler, H. R. Volpp, M. Wahl, and J. Wolfrum, Ber. Bunsenges. Phys. Chem. 94, 1390 (1990).

12
S.-O. Ryu, S. M. Hwang, and M. J. Rabinowitz, J. Phys. Chem. 99, 13984 (1995).

13
K. Honma, J. Chem. Phys. 102, 7856 (1995).

14
K. Kleinermanns, Radiochimica Acta 43, 118 (1988).

15
H. L. Kim, M. A. Wickramaaratchi, X. Zheng, and G. E. Hall, J. Chem. Phys. 101, 2033 (1994).

16
M. J. Bronikowski, R. Zhang, D. J. Rakestraw, and R. N. Zare, Chem. Phys. Lett. 156, 7 (1989).

17
A. Banerjee and N. P. Adams, Int. J. Quant. Chem. S25, 311 (1991).

18
J. A. Miller and B. C. Garrett, Int. J. Chem. Kin. 29, 275 (1997).

19
A. J. C. Varandas, Mol. Phys. 85, 1159 (1995).

20
A. J. C. Varandas, Chem. Phys. Lett. 235, 111 (1995).

21
V. Klimo, M. Bittererová, S. Biskupic, and J. Urban, Chem. Phys. 173, 367 (1993).

22
C. J. Cobos, Chem. Phys. Lett. 152, 371 (1988).

23
A. J. C. Varandas, Chem. Phys. Lett. 225, 18 (1994).

24
A. J. C. Varandas, J. Brandão, and M. R. Pastrana, J. Chem. Phys. 96, 5137 (1992).

25
A. J. C. Varandas, J. Chem. Phys. 99, 1076 (1993).

26
K. Kleinermanns and R. Schinke, J. Chem. Phys. 80, 1440 (1984).

27
K. Kleinermanns, E. Linnebach, and M. Pohl, J. Chem. Phys. 91, 2181 (1989).

28
R. A. Fei, X. S. Zheng, and G. E. Hall, J. Phys. Chem. A 101, 2541 (1997).

29
B. Kendrick and R. T Pack, J. Chem. Phys. 104, 7475 (1996).

30
B. Kendrick and R. T Pack, J. Chem. Phys. 104, 7502 (1996).

31
B. Kendrick and R. T Pack, Chem. Phys. Lett. 235, 291 (1995).

32
J. Q. Dai and J. Z. H. Zhang, J. Phys. Chem. 100, 6898 (1996).

33
D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys. 101, 3671 (1994).

34
R. T Pack, E. A. Butcher, and G. A. Parker, J. Chem. Phys. 102, 5998 (1995).

35
R. T Pack, E. A. Butcher, and G. A. Parker, J. Chem. Phys. 99, 9310 (1993).

36
C. Leforestier and W. H. Miller, J. Chem. Phys. 100, 733 (1994).

37
I. Glassman, Combustion (Academic Press, New York NY, 1996).

38
J. A. Miller, R. J. Kee, and C. K. Westbrook, Annu. Rev. Phys. Chem. 41, 345 (1990), and references therein.

39
C. Y. Yang and S. J. Klippenstein, J. Chem. Phys. 103, 7287 (1995), and references therein.

40
C. F. Melius and R. J. Blint, Chem. Phys. Lett. 64, 183 (1979).

41
M. R. Pastrana, L. A. M. Quintales, J. Brandão, and A. J. C. Varandas, J. Phys. Chem. 94, 8073 (1990).

42
V. A. Mandelshtam, H. S. Taylor, and W. H. Miller, J. Chem. Phys. 105, 496 (1996).

43
V. A. Mandelshtam, T. P. Grozdanov, and H. S. Taylor, J. Chem. Phys. 103, 10074 (1995).

44
A. J. Dobbyn, M. Stumpf, H.-M. Keller, and R. Schinke, J. Chem. Phys. 104, 8357 (1996).

45
A. J. Dobbyn, M. Stumpf, H.-M. Keller, and R. Schinke, J. Chem. Phys. 103, 9947 (1995).

46
K. Song, G. H. Peslherbe, W. L. Hase, A. J. Dobbyn, M. Stumpf, and R. Schinke, J. Chem. Phys. 103, 8891 (1995).

47
R. Chen and H. Guo, Chem. Phys. Lett. 277, 191 (1997).

48
X. Wu and E. F. Hayes, J. Chem. Phys. 107, 2705 (1997).

49
E. M. Goldfield and S. K. Gray, Comput. Phys. Commun. 98, 1 (1996).

50
E. M. Goldfield and S. K. Gray, J. Chem. Soc. Faraday Trans. 93, 909 (1997).

51
E. M. Goldfield and S. K. Gray, Chem. Phys. Lett. 276, 1961 (1997).

52
R. Kosloff, J. Phys. Chem. 92, 2087 (1988).

53
See thematic issue on Time Dependent Methods for Quantum Dynamics, edited by K. C. Kulander, Comput. Phys. Commun. 63, (1991).

54
See several articles in Special issue on Quantum Theory of Chemical Reactions, J. Chem. Soc. Faraday Trans. 93, (1997).

55
C. Schwartz, J. Math. Phys. 26, 411 (1985).

56
D. T. Colbert and W. H. Miller, J. Chem. Phys. 96, 1982 (1992).

57
G. C. Groenenboom and D. T. Colbert, J. Chem. Phys. 99, 9681 (1993).

58
J. C. Light, I. P. Hamilton, and J. V. Lill, J. Chem. Phys. 82, 1400 (1985).

59
S. E. Choi and J. C. Light, J. Chem. Phys. 90, 2593 (1989).

60
A. S. Dickinson and P. R. Certain, J. Chem. Phys. 49, 4209 (1968).

61
S. K. Gray and C. E. Wozny, J. Chem. Phys. 91, 7671 (1989).

62
R. T Pack, J. Chem. Phys. 60, 633 (1974), and references therein.

63
Y. Sun, R. S. Judson, and D. J. Kouri, J. Chem. Phys. 90, 241 (1989).

64
G. Herzberg, Molecular Spectra and Molecular Structure (Krieger, Malabar, 1991).

65
J. M. Brown, J. T. Hougen, K.-P. Huber, J. W. C. Johns, I. Kopp, H. Lefebvre-Brion, A. J. Merer, D. A. Ramsay, J. Rostas, and R. N. Zare, J. Mol. Spectrosc. 55, 500 (1975).

66
A. van der Avoird, P. E. S. Wormer, and R. Moszynski, Chem. Rev. 94, 1931 (1994).

67
J. Tennyson and B. T. Sutcliffe, J. Chem. Phys. 77, 4061 (1982).

68
J. Tennyson and B. T. Sutcliffe, J. Mol. Spectrosc. 101, 71 (1983).

69
E. M. Goldfield, S. K. Gray, and L. B. Harding, J. Chem. Phys. 99, 5812 (1993).

70
E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University, Cambridge UK, 1935).

71
R. T Pack and G. A. Parker, J. Chem. Phys. 87, 3888 (1987).

72
M. E. Rose, Elementary Theory of Angular Momentum (J. Wiley and Sons, New York NY, 1957).

73
Note the error with the signs in Ref. [57][91].

74
S. K. Gray and D. E. Manolopoulos, J. Chem. Phys. 104, 7099 (1996).

75
D. Kosloff and R. Kosloff, J. Comput. Phys. 63, 363 (1986).

76
R. H. Bisseling, R. Kosloff, and J. Manz, J. Chem. Phys. 83, 993 (1985).

77
W. Gropp, E. Lusk, and A. Skjellum, Using MPI: Portable Parallel Programming with the Message-Passing Interface (MIT Press, Cambridge MA, 1994).

78
M. Snir, S. W. Otto, S. Huss-Ledermann, D. W. Walker, and J. Dongarra, MPI: The Complete Reference (MIT Press, Cambridge MA, 1994).

79
See also: WWW: http://www.mcs.anl.gov/mpi and http://www.mcs.anl.gov/mpi/mpich.

80
E. M. Goldfield, S. K. Gray, and G. C. Schatz, J. Chem. Phys. 102, 8807 (1995).

81
See WWW:http://dynamo.chem.wayne.edu/anthony/publications/pub.html for the full proof in gzipped Postscript format or request it via an e-mail to Anthony Meijer at
anthony@dynamo.chem.wayne.edu.

82
A. Messiah, Quantum Mechanics (North Holland, Amsterdam NL, 1961).

83
J. P. Maillard, J. Chauville, and A. W. Mantz, J. Mol. Spec. 63, 120 (1976).

84
A J H M Meijer and E M Goldfield, work in progress.

85
R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and Chemical Reactivity (Oxford University, Oxford GB, 1987).

86
J. M. Bowman, J. Phys. Chem. 95, 4960 (1991), and references therein.

87
J. M. Bowman, Chem. Phys. Lett. 217, 36 (1994).

88
J. Qi and J. M. Bowman, J. Chem. Phys. 105, 9884 (1996).

89
R. T Pack, in Advances in Molecular Vibrations and Collision Dynamics, edited by J. M. Bowman (JAI Press, Greenwich CT, 1993), Vol. II-A, pp. 111-145.

90
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran: the art of scientific computing, 2nd ed. (Cambridge University Press, New York NY, 1992).

91
G. C. Groenenboom, private communication.

  
Figure: Total reaction probability as a function of total energy for J=0 at total propagation time T=15 000 a.u, T=30 000 a.u, and T=150 000 a.u.
\begin{figure}\epsfig{file=fig1.ps,width=15cm}\end{figure}


  
Figure: Total reaction probability as a function of total energy for J=1 at total propagation time T=15 000 a.u, T=30 000 a.u, and T=50 000 a.u.
\begin{figure}\epsfig{file=fig2.ps,width=15cm}\end{figure}


  
Figure 3: Total reaction probability as a function of total angular momentum J for J=0, 1, 2, and 5.
\begin{figure}\epsfig{file=fig3.ps,width=15cm}\end{figure}


  
Figure: Reaction probability for different J as a function of initial $\Omega $ substate. Panel (a): J=1. Panel (b): J=2. Panel (c): J=5. The PJ=0(E) curve in each panel is given for reference purposes.
\begin{figure}\epsfig{file=fig4a.ps,width=15cm}\end{figure}


\begin{figure}\epsfig{file=fig4b.ps,width=15cm}\end{figure}


\begin{figure}\epsfig{file=fig4c.ps,width=15cm}\end{figure}


  
Figure: Reaction probability for J=0, 1, 2, and 5 for the $\Omega _i=0^+$ initial state.
\begin{figure}\epsfig{file=fig5.ps,width=15cm}\end{figure}


  
Figure 6: points on PES
\begin{figure}\epsfig{file=fig6.ps,width=15cm}\end{figure}


  
Figure 7: selected points
\begin{figure}\epsfig{file=fig7.ps,width=15cm}\end{figure}


 
Table I: Parameters for the calculation
 
Quantity Value
$\beta$ 0.18 a.u.
k0 11.9366 a.u.
R0 8.5 a.u.
$R_{\rm min}$ 0.6 a.u.
$R_{\rm max}$ 11.6 a.u.
NR 125
$r_{\rm min}$ 1.3 a.u.
$r_{\rm max}$ 14.0 a.u.
Nr 175
$V^{(o)}_{\rm cut}$ 4.0 eV[1]
$V^{(i)}_{\rm cut}$ 8.0 eV[1]
ji 1
$j_{\rm max}$ 89
$\nu_i$ 0
$\Delta t$ 7.5 a.u.[2]
Nt 10 time steps
BR 0.05 a.u.
$R_{\rm abs}$ 10.0 a.u.
Br 0.01 a.u.
$r_{\rm abs}$ 11.0 a.u.
Rs 9.4 a.u.
rs 10.4 a.u.
[1]See the Appendix. [2]For the J=5 calculations we used $\Delta t$ = 5 a.u.


 
Table: Reaction probability per substate $\Omega $ for a given initial substate $\Omega _i$ for a few selected energies for J=5
 
Energy (eV) 0.800 1.00 1.20 1.40 1.60 1.80
$\Omega_i=0^{+},\Omega_f=0^{+}$ 6.82 10-5 2.93 10-3 1.26 10-2 2.47 10-2 3.78 10-2 7.40 10-2
$\hphantom{\Omega_i=0^{+},}\Omega_f=1^{+}$ 1.08 10-4 6.30 10-3 1.61 10-2 2.08 10-2 5.35 10-2 8.97 10-2
$\hphantom{\Omega_i=0^{+},}\Omega_f=2^{+}$ 1.25 10-4 3.83 10-3 3.02 10-2 3.17 10-2 6.98 10-2 8.32 10-2
$\hphantom{\Omega_i=0^{+},}\Omega_f=3^{+}$ 4.10 10-5 7.26 10-3 2.38 10-2 4.26 10-2 8.65 10-2 9.21 10-2
$\hphantom{\Omega_i=0^{+},}\Omega_f=4^{+}$ 5.05 10-5 3.21 10-3 1.32 10-2 2.39 10-2 5.22 10-2 8.99 10-2
$\hphantom{\Omega_i=0^{+},}\Omega_f=5^{+}$ 1.94 10-5 4.92 10-3 7.89 10-3 9.83 10-3 1.73 10-2 2.04 10-2
Total 4.13 10-4 2.85 10-2 1.04 10-1 1.54 10-1 3.17 10-1 4.49 10-1
             
$\Omega_i=1^{+},\Omega_f=0^{+}$ 1.27 10-4 6.42 10-3 1.96 10-2 1.94 10-2 3.37 10-2 4.12 10-2
$\hphantom{\Omega_i=1^{+},}\Omega_f=1^{+}$ 2.29 10-4 5.46 10-3 1.09 10-2 3.34 10-2 2.65 10-2 3.60 10-2
$\hphantom{\Omega_i=1^{+},}\Omega_f=2^{+}$ 6.16 10-5 9.22 10-3 1.41 10-2 3.40 10-2 3.87 10-2 4.89 10-2
$\hphantom{\Omega_i=1^{+},}\Omega_f=3^{+}$ 1.35 10-5 1.12 10-2 8.14 10-3 1.48 10-2 2.42 10-2 2.91 10-2
$\hphantom{\Omega_i=1^{+},}\Omega_f=4^{+}$ 8.28 10-6 3.01 10-3 4.17 10-3 5.38 10-3 7.80 10-3 1.50 10-2
$\hphantom{\Omega_i=1^{+},}\Omega_f=5^{+}$ 1.18 10-5 4.55 10-3 2.81 10-3 3.33 10-3 5.33 10-3 7.57 10-3
Total 4.51 10-4 3.98 10-2 5.97 10-2 1.10 10-1 1.36 10-1 1.78 10-1
             
$\Omega_i=1^{-}, \Omega_f=1^{-}$ 2.82 10-5 1.34 10-3 4.13 10-3 6.30 10-3 1.03 10-2 8.55 10-3
$\hphantom{\Omega_i=1^{-}, }\Omega_f=2^{-}$ 1.57 10-5 3.12 10-3 7.96 10-3 1.06 10-2 8.30 10-3 1.71 10-2
$\hphantom{\Omega_i=1^{-}, }\Omega_f=3^{-}$ 2.08 10-5 5.03 10-3 1.59 10-2 1.87 10-2 2.85 10-2 3.62 10-2
$\hphantom{\Omega_i=1^{-}, }\Omega_f=4^{-}$ 4.17 10-5 1.87 10-2 1.08 10-2 2.79 10-2 4.24 10-2 6.55 10-2
$\hphantom{\Omega_i=1^{-}, }\Omega_f=5^{-}$ 2.97 10-5 1.01 10-2 1.21 10-2 1.55 10-2 1.60 10-2 4.19 10-2
Total 1.36 10-4 3.83 10-2 5.09 10-2 7.90 10-2 1.06 10-1 1.69 10-1


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Next: About this document ... Up: Time-dependent quantum mechanical calculations O Previous: Appendix
Anthony J. H. M. Meijer
1998-02-20