Project description
A new mathematical approach for accessing excited electronic states
Catalysis and solar cell technologies are underpinned by a fundamental process: that of exciting systems to a higher energy level than the ground state. Defining an effective method to achieve this that also provides accurate energies of the excited states is often a challenge. The EU-funded PTEROSOR project will tackle this fundamental problem using mathematical techniques. The researchers' novel approach for measuring the energies of excited states and defining wave functions in molecular systems will hinge on the use of a general class of Hamiltonians with parity-time (PT) symmetry. The gateway between ground and excited states will be provided by exceptional points which lie at the boundary between broken and unbroken PT-symmetric regions.
Objective
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 at developing a totally novel approach to obtain excited-state energies and wave functions in molecular sys- tems 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. PTEROSOR’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 which lie at the boundary between broken and unbroken PT-symmetric regions.
Fields of science
Programme(s)
Funding Scheme
ERC-COG - Consolidator GrantHost institution
75794 Paris
France