Abstract
In this Chapter we review the exact factorization of the electron-nuclear wave function. The molecular wave function, solution of a time-dependent Schröodinger equation, is factored into a nuclear wave function and an electronic wave function with parametric dependence on nuclear configuration. This factorization resembles the (approximate) adiabatic product of a single Born-Oppenheimer state and a time-dependent nuclear wave packet, but it introduces a fundamental difference: both terms of the product are explicitly time-dependent. Such feature introduces new concepts of time-dependent vector potential and time-dependent potential energy surface that allow for the treatment of nonadiabatic dynamics, thus of dynamics beyond the Born-Oppenheimer approximation. The theoretical framework of the exact factorization is presented, also in connection to the more standard Born-Huang (still exact) representation of the molecular wave function. A trajectory-based approach to nonadiabatic dynamics is derived fromthe exact factorization. A discussion on the connection between the molecular Berry phase and the corresponding quantity arising from the exact factorization is briefly discussed.
Original language | English |
---|---|
Title of host publication | Quantum Chemistry and Dynamics of Excited States |
Subtitle of host publication | Methods and Applications |
Publisher | wiley |
Pages | 531-562 |
Number of pages | 32 |
ISBN (Electronic) | 9781119417774 |
ISBN (Print) | 9781119417750 |
DOIs | |
State | Published - 1 Jan 2020 |
Bibliographical note
Publisher Copyright:© 2021 John Wiley & Sons Ltd. All rights reserved.
Keywords
- Born-Oppenheimer framework
- Electron-nuclear wave function
- Exact factorization
- Molecular berry phase
- Time-dependent molecular