Asymptotic analysis of the Berry curvature in the $E\otimes e$ Jahn-Teller model

Abstract

The effective Hamiltonian for the linear $E\otimes e$ Jahn-Teller model describes the coupling between two electronic states and two vibrational modes in molecules or bulk crystal impurities. While in the Born-Oppenheimer approximation the Berry curvature has a delta function singularity at the conical intersection of the potential energy surfaces, the exact Berry curvature is a smooth peaked function. Numerical calculations revealed that the characteristic width of the peak is $\hslash K^{1/2}/g{M}^{1/2}$, where $M$ is the mass associated with the relevant nuclear coordinates, $K$ is the effective internuclear spring constant and $g$ is the electronic-vibrational coupling. This result is confirmed here by an asymptotic analysis of the $M\to \infty$ limit, an interesting outcome of which is the emergence of a separation of length scales. Being based on the exact electron-nuclear factorization, our analysis does not make any reference to adiabatic potential energy surfaces or nonadiabatic couplings. It is also shown that the Ham reduction factors for the model can be derived from the exact geometric phase.

arXiv comment12 pages, 8 figures

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• On the Numerical Solution of the Exact Factorization Equations
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• Quantum-classical nonadiabatic dynamics of Floquet driven systems
• Evolution of hybrid quantum-classical wavefunctions
• Regularized Born-Oppenheimer molecular dynamics
• Dynamic Jahn-Teller Phenomena in Heavy Transition Metal Compounds
• Berry phase of adiabatic electronic configurations in fullerene anions
• Quantum covariant derivative
• Electronic decoherence along a single nuclear trajectory
• Holonomy and vortex structures in quantum hydrodynamics
• Geometry of quantum hydrodynamics in theoretical chemistry
• On the Geometric Potential and the Relationship between the Exact Electron Factorization and Density Functional Theory