A Complex Adiabatic Connection for electronic states – CACO

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.