CE29 - Chimie : analyse, théorie, modélisation

A Complex Adiabatic Connection for electronic states – CACO

Submission summary

Processes related to electronically excited states are central in chemistry, physics, and biology, playing a key role in ubiquitous processes such as photochemistry, catalysis, and solar cell technology.
However, defining an effective method that reliably provides accurate excited-state energies remains a major challenge in theoretical chemistry.
In CACO, we aim at developing a totally novel approach to obtain excited-state energies and wave functions in molecular systems thanks to the properties of non-Hermitian Hamiltonians.
Our key idea is to perform an analytic continuation of conventional computational chemistry methods.
Indeed, through the complex plane, ground and excited states can be naturally connected.
In a non-Hermitian complex picture, the energy levels are sheets of a more complicated topological manifold called Riemann surface and they are smooth and continuous analytic continuation of one another.
CACO's main goal is to develop a new theoretical approach allowing to connect, through the complex plane, electronic states.
Instead of Hermitian Hamiltonians, we propose to use a more general class of Hamiltonians which have the property of being PT-symmetric, i.e., invariant with respect to combined parity reflection P and time reversal T.
This weaker condition ensures a real energy spectrum in unbroken PT-symmetric regions.
PT-symmetric Hamiltonians can be seen as analytic continuation of conventional Hermitian Hamiltonians.
Using PT-symmetric quantum theory, an Hermitian Hamiltonian can be analytically continued into the complex plane, becoming non-Hermitian in the process and exposing the fundamental topology of eigenstates.
Our gateway between ground and excited states are provided by exceptional points, the non-Hermitian analogs of conical intersections, which lie at the boundary between broken and unbroken PT-symmetric regions.

Project coordination


The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.



Help of the ANR 204,098 euros
Beginning and duration of the scientific project: December 2019 - 48 Months

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