2024
DOI: 10.1021/acs.chemmater.3c02667
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Toward a Topological Classification of Nonadiabaticity in Chemical Reactions

Christopher Daggett,
Kaijie Yang,
Chao-Xing Liu
et al.

Abstract: The application of topology, a branch of mathematics, to the study of electronic states in crystalline materials has had a revolutionary effect on the field of condensed matter physics. For example, the development of topological band theory has delivered new approaches and tools for characterizing the electronic structure of materials, resulting in the discovery of new phases of matter with exotic properties. In the framework of topological band theory, the crossings between energy levels of electrons are cha… Show more

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“…Here, the tilde in β̃ refers to the projection of the potentially complex-valued eigenvector |β⟩ onto a real-valued vector, in order to ensure that the physical momentum coordinate remains real-valued, and same for α̃. Complex values for eigenvectors may arise due to an arbitrary global phase, complex basis transformations followed by basis truncations, and geometric phase effects. In a recent work, we have proposed a means to perform this projection onto real-valued vectors while ensuring gauge-invariance …”
Section: Theorymentioning
confidence: 99%
“…Here, the tilde in β̃ refers to the projection of the potentially complex-valued eigenvector |β⟩ onto a real-valued vector, in order to ensure that the physical momentum coordinate remains real-valued, and same for α̃. Complex values for eigenvectors may arise due to an arbitrary global phase, complex basis transformations followed by basis truncations, and geometric phase effects. In a recent work, we have proposed a means to perform this projection onto real-valued vectors while ensuring gauge-invariance …”
Section: Theorymentioning
confidence: 99%