**Memoirs of the American Mathematical Society**

1994;
130 pp;
Softcover

MSC: Primary 81;
Secondary 92; 35

Print ISBN: 978-0-8218-2605-8

Product Code: MEMO/111/536

List Price: $42.00

Individual Member Price: $25.20

**Electronic ISBN: 978-1-4704-0115-3
Product Code: MEMO/111/536.E**

List Price: $42.00

Individual Member Price: $25.20

# Molecular Propagation through Electron Energy Level Crossings

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*George A. Hagedorn*

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.

#### Readership

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

#### Table of Contents

# Table of Contents

## Molecular Propagation through Electron Energy Level Crossings

- Table of Contents v6 free
- 1. Introduction 18 free
- 2. Generic Minimal Multiplicity Quantum Eigenvalue Crossings 916 free
- 3. Technical Preliminaries 2835
- 4. Born-Oppenheimer Propagation Away from Crossings 3946
- 5. Codimension 1 Crossings 4956
- 6. Codimension 2 Crossings 8087
- 7. Codimension 3 Crossings 113120
- 8. Codimension 5 Crossings 121128
- References 127134