Free Access
Volume 41, Number 2, March-April 2007
Special issue on Molecular Modelling
Page(s) 297 - 314
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. [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you