Variational derivation and extensions of distributed approximating functionals

Journal of Mathematical Chemistry

Volumn 20, Issue 1, 1996, Pages 117-140

  Hoffman, D K ^a   Marchioro II, T L ^a   Arnold, Mark ^b   Huang, Youhong ^c   Zhu, Wei ^c   Kouri, Donald J ^c  

^a IOWA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF ARKANSAS   (United States)

^c University of Houston   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030366340     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01165159     Document Type: Article

References (29)

1. The discrete grid DAF was first introduced in: D.K. Hoffman, N. Nayar, O.A. Sharafeddin and D.J. Kouri, J. Phys. Chem. 95 (1991) 8299; D.K. Hoffman and D.J. Kouri, ibid. 96 (1992) 1179.
2. The discrete grid DAF was first introduced in: D.K. Hoffman, N. Nayar, O.A. Sharafeddin and D.J. Kouri, J. Phys. Chem. 95 (1991) 8299; D.K. Hoffman and D.J. Kouri, ibid. 96 (1992) 1179.
3. The continuous DAF was first introduced in: D.J. Kouri, W. Zhu, X. Ma, B.M. Pettitt and D.K. Hoffman, J. Phys. Chem. 96 (1992) 9622; D.J. Kouri and D.K. Hoffman, ibid. 96 (1992) 9631.
4. The continuous DAF was first introduced in: D.J. Kouri, W. Zhu, X. Ma, B.M. Pettitt and D.K. Hoffman, J. Phys. Chem. 96 (1992) 9622; D.J. Kouri and D.K. Hoffman, ibid. 96 (1992) 9631.
5. D.K. Hoffman, M. Arnold and D.J. Kouri, J. Phys. Chem. 96 (1992) 6539. This paper presents an alternative approach to the continuous and discrete DAFs and analyzes their properties in more detail.
6. D.K. Hoffman, M. Arnold and D.J. Kouri, J. Phys. Chem. 97 (1993) 1110. This paper is the first to deal with DAFs in a "travelling frame of reference".
7. Dynamical effects were first incorporated into the DAF-propagator in the paper: D.K. Hoffman, M. Arnold, W. Zhu and D.J. Kouri, J. Chem. Phys. 99 (1993) 1124.
8. D.K. Hoffman and D.J. Kouri, J. Phys. Chem. 97 (1993) 4984. This article contains the generalization of the DAF for arbitrary numbers of degrees of freedom and orthogonal coordinate systems.
9. T.L. Marchioro, M. Arnold, D.K. Hoffman, W. Zhu, Y. Huang and D.J. Kouri, Phys. Rev. E50 (1994) 2320. This paper presents the generalization of the DAF propagator to include a harmonic potential.
10. Y. Huang, D.J. Kouri, M. Arnold, T.L. Marchioro and D.K. Hoffman, Comp. Phys. Commun. 80 (1994) 1. This paper describes the fast-DAF transform and periodic DAF, used for atom-corrugated surface scattering.
11. Two overviews of the DAFs are: D.J. Kouri and D.K. Hoffman, in: Time-Dependent Quantum Molecular Dynamics, eds. J. Broeckhove and L. Lathouwers, NATO ASI Series B299 (1992) 117; D.K. Hoffman and D.J. Kouri, in: Rarified Gas Dynamics: Experimental Techniques and Physical Systems, eds. B.D. Shizgal and D.P. Weaver, Prog. Astronautics and Aeronautics 158 (1994) 184.
12. Two overviews of the DAFs are: D.J. Kouri and D.K. Hoffman, in: Time-Dependent Quantum Molecular Dynamics, eds. J. Broeckhove and L. Lathouwers, NATO ASI Series B299 (1992) 117; D.K. Hoffman and D.J. Kouri, in: Rarified Gas Dynamics: Experimental Techniques and Physical Systems, eds. B.D. Shizgal and D.P. Weaver, Prog. Astronautics and Aeronautics 158 (1994) 184.
13. D.K. Hoffman and D.J. Kouri, Proc. 3rd Int. Conf. on Math. and Num. Aspects of Wave Prop. Phenom (SIAM, 1995) pp. 56-83. This work contains additional analysis and generalizations of the DAFs.
14. See, e.g., the reference W.H. Press, S.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes (Cambridge U.P., Cambridge, UK, 1986). It gives many references to a wide range of texts and other resources on numerical methods and analysis.
15. C.-E. Fröberg, Numerical Mathematics (Benjamin-Cummings, Menlo Park, CA, 1985).
16. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods in Fluid Mechanics (Springer, Berlin, 1988).
17. D. Gottlieb and S.A. Orszag, Numerical Analysis of Spectral Methods (SIAM, Philadelphia, 1977).
18. D. Funaro, Polynomial Approximations of Differential Equations (Springer, New York, 1992).
19. J.V. Lill, G.A. Parkerand J.C. Light, Chem. Phys. Lett. 89 (1982) 483.
20. G. Mansell, W. Merryfield, B. Shizgal and U. Weinert, Comp. Meth. Appl. Mech. Eng. 104 (1993) 295.
21. G.G. Balint-Kurti and P. Pulay, J. Molec. Structure (Theochem) 341 (1995) 1.
22. A.C. Peet and W. Yang, J. Chem. Phys. 90 (1989) 1746.
23. G.C. Groenenboom and H.M. Buck, J. Chem. Phys. 92 (1990) 4374.
24. N. Aronszajn, Am. Math. Soc. Trans. Ser. 2, 68 (1950) 337.
25. Y. Huang, D.J. Kouri, M. Arnold, T.L. Marchioro and D.K. Hoffman, J. Chem. Phys. 99 (1993) 1028.
26. Y. Huang, D.J. Kouri, M. Arnold and D.K. Hoffman, unpublished.
27. D.J. Kouri, M. Arnold and D.K. Hoffman, Chem. Phys. Lett. 203 (1993) 166; Y. Huang, W. Zhu, D.J. Kouri and D.K. Hoffman, ibid. 206 (1993) 96.
28. D.J. Kouri, M. Arnold and D.K. Hoffman, Chem. Phys. Lett. 203 (1993) 166; Y. Huang, W. Zhu, D.J. Kouri and D.K. Hoffman, ibid. 206 (1993) 96.
29. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Corrected and Enlarged Ed. (Academic Press, New York, 1983), EH II 159 (10), p. 1024.