Extended (PTEROSOR + T-REX) group picture

From left to right: Enzo Monino, Anthony Scemama, Yann Damour, Abdallah Ammar, Vijay Gopal Chilkuri, Fabris Kossoski, Pierre-Francois Loos, Raul Quintero-Monsebaiz, and Evgeny Posenitskiy.

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The PTEROSOR project

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 PTEROSOR, we aim to develop 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 a smooth and continuous analytic continuation of one another. PTEROSOR’s main goal is to develop a new theoretical approach allowing connection, 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 an analytic continuation of conventional Hermitian Hamiltonians. Using PT-symmetric quantum theory, a 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 is provided by exceptional points that lie at the boundary between broken and unbroken PT-symmetric regions.

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 863481).