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Molecular Propagation through Electron Energy Level Crossings
George A. Hagedorn

Memoirs of the American Mathematical Society
1994; 130 pp; softcover
Volume: 111
ISBN-10: 0-8218-2605-0
ISBN-13: 978-0-8218-2605-8
List Price: US$42
Individual Members: US$25.20
Institutional Members: US$33.60
Order Code: MEMO/111/536
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This largely self-contained book provides a thorough discussion of the mathematics of molecular dynamics and fills a gap in the theoretical knowledge of the subject. Most knowledge of molecular propagation is derived from the time-dependent Born-Oppenheimer approximation. This approximation breaks down at electron energy level crossings, which are prevalent in molecular systems. Hagedorn classifies generic, minimal multiplicity level crossings and derives a normal form for the electron Hamiltonian near each type of crossing. He then extends the time-dependent Born-Oppenheimer approximation to accommodate the propagation of nuclei through each type of electron energy level crossing.


Mathematical physicists interested in quantum mechanics; molecular physicists; theoretical chemists.

Table of Contents

  • Introduction
  • Generic minimal multiplicity quantum eigenvalue crossings
  • Technical preliminaries
  • Born-Oppenheimer propagation away from crossings
  • Codimension 1 crossings
  • Codimension 2 crossings
  • Codimension 3 crossings
  • Codimension 5 crossings
  • References
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