Free Access
Issue
ESAIM: M2AN
Volume 41, Number 2, March-April 2007
Special issue on Molecular Modelling
Page(s) 297 - 314
DOI https://doi.org/10.1051/m2an:2007023
Published online 16 June 2007
  1. D.E. Adelman, N.E. Shafer, D.A.V. Kliner and R.N. Zare, Measurement of relative state-to-state rate constants for the reaction Formula . J. Chem. Phys. 97 (1992) 7323–7341. [CrossRef] [Google Scholar]
  2. M.V. Berry and R. Lim, The Born-Oppenheimer electric gauge force is repulsive near degeneracies. J. Phys. A 23 (1990) L655–L657. [CrossRef] [Google Scholar]
  3. A. Bohm, A. Mostafazadeh, H. Koizumi, Q. Niu and J. Zwanziger, The geometric phase in quantum systems. Texts and Monographs in Physics, Springer, Heidelberg (2003). [Google Scholar]
  4. M. Born and R. Oppenheimer, Zur Quantentheorie der Molekeln. Ann. Phys. (Leipzig) 84 (1927) 457–484. [Google Scholar]
  5. R. Brummelhuis and J. Nourrigat, Scattering amplitude for Dirac operators. Comm. Partial Differential Equations 24 (1999) 377–394. [CrossRef] [MathSciNet] [Google Scholar]
  6. Y. Colin de Verdière, M. Lombardi and C. Pollet, The microlocal Landau-Zener formula. Ann. Inst. H. Poincaré Phys. Theor. 71 (1999) 95-127. [MathSciNet] [Google Scholar]
  7. J.-M. Combes, P. Duclos and R. Seiler, The Born-Oppenheimer approximation, in Rigorous Atomic and Molecular Physics, G. Velo, A. Wightman Eds., New York, Plenum (1981) 185–212. [Google Scholar]
  8. C. Emmerich and A. Weinstein, Geometry of the transport equation in multicomponent WKB approximations. Commun. Math. Phys. 176 (1996) 701–711. [CrossRef] [Google Scholar]
  9. C. Fermanian-Kammerer and P. Gérard, Mesures semi-classiques et croisement de modes. Bull. Soc. Math. France 130 (2002) 123–168. [MathSciNet] [Google Scholar]
  10. C. Fermanian-Kammerer and C. Lasser, Wigner measures and codimension 2 crossings. J. Math. Phys. 44 (2003) 507–527. [CrossRef] [MathSciNet] [Google Scholar]
  11. G.A. Hagedorn, A time dependent Born-Oppenheimer approximation. Commun. Math. Phys. 77 (1980) 1–19. [CrossRef] [Google Scholar]
  12. G.A. Hagedorn, High order corrections to the time-dependent Born-Oppenheimer approximation. I. Smooth potentials. Ann. Math. 124 (1986) 571–590. [CrossRef] [Google Scholar]
  13. G.A. Hagedorn, High order corrections to the time-independent Born-Oppenheimer approximation. I. Smooth potentials. Ann. Inst. H. Poincaré Sect. A 47 (1987) 1–19. [Google Scholar]
  14. G.A. Hagedorn, High order corrections to the time-dependent Born-Oppenheimer approximation. II. Coulomb systems. Comm. Math. Phys. 117 (1988) 387–403. [CrossRef] [MathSciNet] [Google Scholar]
  15. G.A. Hagedorn, Molecular propagation through electron energy level crossings, Memoirs of the American Mathematical Society 111 (1994). [Google Scholar]
  16. G.A. Hagedorn and A. Joye, A time-dependent Born-Oppenheimer approximation with exponentially small error estimates. Commun. Math. Phys. 223 (2001) 583–626. [CrossRef] [Google Scholar]
  17. T. Kato, On the adiabatic theorem of quantum mechanics. Phys. Soc. Jap. 5 (1950) 435–439. [CrossRef] [Google Scholar]
  18. M. Klein, A. Martinez, R. Seiler and X.P. Wang, On the Born-Oppenheimer expansion for polyatomic molecules. Commun. Math. Phys. 143 (1992) 607–639. [CrossRef] [Google Scholar]
  19. C. Lasser and S. Teufel, Propagation through conical crossings: an asymptotic transport equation and numerical experiments, Commun. Pure Appl. Math. 58 (2005) 1188–1230. [Google Scholar]
  20. R.G. Littlejohn and W.G. Flynn, Geometric phases in the asymptotic theory of coupled wave equations. Phys. Rev. A 44 (1991) 5239–5255. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  21. A. Martinez and V. Sordoni, A general reduction scheme for the time-dependent Born-Oppenheimer approximation. C. R. Acad. Sci. Paris, Sér. I 334 (2002) 185–188. [Google Scholar]
  22. C.A. Mead and D.G. Truhlar, On the determination of Born-Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei. J. Chem. Phys. 70 (1979) 2284–2296. [CrossRef] [Google Scholar]
  23. G. Nenciu and V. Sordoni, Semiclassical limit for multistate Klein-Gordon systems: almost invariant subspaces and scattering theory. J. Math. Phys. 45 (2004) 3676–3696. [CrossRef] [MathSciNet] [Google Scholar]
  24. J. von Neumann and E.P. Wigner. Z. Phys. 30 (1929) 467. [Google Scholar]
  25. G. Panati, H. Spohn and S. Teufel, Space-adiabatic perturbation theory in quantum dynamics. Phys. Rev. Lett. 88 (2002) 250405. [CrossRef] [PubMed] [Google Scholar]
  26. G. Panati, H. Spohn and S. Teufel, Space-adiabatic perturbation theory. Adv. Theor. Math. Phys. 7 (2003) 145–204. [MathSciNet] [Google Scholar]
  27. J. Sjöstrand, Projecteurs adiabatiques du point de vue pseudodifferéntiel. C. R. Acad. Sci. Paris, Sér. I 317 (1993) 217–220. [Google Scholar]
  28. V. Sordoni, Reduction scheme for semiclassical operator-valued Schrödinger type equation and application to scattering. Comm. Partial Differential Equations 28 (2003) 1221–1236. [CrossRef] [MathSciNet] [Google Scholar]
  29. H. Spohn and S. Teufel, Adiabatic decoupling and time-dependent Born-Oppenheimer theory. Commun. Math. Phys. 224 (2001) 113–132. [CrossRef] [Google Scholar]
  30. S. Teufel, Adiabatic perturbation theory in quantum dynamics, Lecture Notes in Mathematics 1821. Springer (2003). [Google Scholar]
  31. S. Weigert and R.G. Littlejohn, Diagonalization of multicomponent wave equations with a Born-Oppenheimer example. Phys. Rev. A 47 (1993) 3506–3512. [CrossRef] [PubMed] [Google Scholar]
  32. Y.-S.M. Wu and A. Kupperman, Prediction of the effect of the geometric phase on product rotational state distributions and integral cross sections. Chem. Phys. Lett. 201 (1993) 178–186. [CrossRef] [Google Scholar]
  33. L. Yin and C.A. Mead, Magnetic screening of nuclei by electrons as an effect of geometric vector potential. J. Chem. Phys. 100 (1994) 8125–8131. [CrossRef] [Google Scholar]

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