Descripción del proyecto
Un método matemático nuevo para acceder a los estados electrónicos excitados
Las tecnologías de catálisis y celda fotovoltaica se basan en procesos fundamentales como la excitación de sistemas a un nivel de energía superior al base, pero definir un método eficaz para lograr dicho proceso de catálisis y que también ofrezca las energías precisas de los estados excitados suele ser complejo. El proyecto financiado con fondos europeos PTEROSOR resolverá este problema fundamental mediante técnicas matemáticas. El método innovador de los investigadores para medir las energías de los estados excitados y definir las funciones de onda en sistemas moleculares dependerá del uso de una clase general de hamiltonianos con simetría en paridad-tiempo (PT). La pasarela entre los estados base y excitado se generará mediante puntos excepcionales situados en los límites entre regiones simétricas en paridad-tiempo quebradas y no quebradas.
Objetivo
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.
Ámbito científico
Programa(s)
Régimen de financiación
ERC-COG - Consolidator GrantInstitución de acogida
75794 Paris
Francia