Analysis of geometric phase effects in the quantum-classical Liouville formalism
Analysis of geometric phase effects in the quantum-classical Liouville formalism
Publication Type:
Journal ArticleSource:
Journal of Chemical Physics, American Institute of Physics Inc., Volume 140, Number 8 (2014)URL:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84896751426&doi=10.1063%2f1.4866366&partnerID=40&md5=f6512eb67033d8bebc04a86c6edb6c58Keywords:
Adiabatic potentials, Calculations, Conical intersection, Double-valued functions, Electronic states, Electronic structure, Electronic structure calculations, Equation of motion, Equations of motion, Liouville formalism, Wigner transformation, Wigner transformsAbstract:
We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors. © 2014 AIP Publishing LLC.
