Molecular Propagation Through Electron Energy Level Crossings (memoirs Of The American Mathematical Society)

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. The principal results of this paper involve the extension of the time-dependent Born-Oppenheimer approximation to accommodate the propagation of nuclei through generic, minimal multiplicity electron energy level crossings. The Born-Oppenheimer approximation breaks down at electron energy level crossings, which are prevalent in molecular systems. We classify generic, minimal multiplicity level crossings and derives a normal form for the electron Hamiltonian near each type of crossing. We then extend the time-dependent Born-Oppenheimer approximation to accommodate the propagation of nuclei through each type of electron energy level crossing