The PTEROSOR project aims to advance the theoretical description of excited states in molecular systems. Excited states arise when molecules absorb light and reorganize their electronic structure. They govern light–matter interactions and underpin processes such as photosynthesis, vision, atmospheric photochemistry, light emission, and solar-energy conversion. A reliable understanding of excited states is therefore essential for the rational design of photovoltaic materials, photocatalysts, light-emitting devices, and other functional systems of societal relevance in energy and environmental science.
Despite their importance, excited states remain significantly harder to describe than ground states. While ground-state electronic-structure theory has achieved high predictive accuracy, excited-state methods are often less robust and less systematically improvable. The field has also been fragmented, with many different many-body approaches developing in parallel and limited conceptual unification. In addition, the scarcity of high-quality benchmark datasets has hindered objective accuracy assessment. Achieving reliable and predictive excited-state calculations, therefore, remains a central open challenge in quantum chemistry.
PTEROSOR addressed this challenge through a comprehensive strategy combining conceptual innovation, methodological development, and computational implementation. A central pillar of the project was the exploration of non-Hermitian quantum mechanics as a new framework for excited-state theory. Instead of restricting Hamiltonians to conventional Hermitian operators, the project investigated complex extensions, including PT-symmetric and more general non-Hermitian Hamiltonians, as a route to access excited-state energies and wave functions.
The key idea was to use analytical continuation into the complex plane to connect ground and excited states within a unified formalism. By extending mean-field and correlated methods into the complex domain, the project uncovered hidden mathematical structures governing excited states. In particular, we analyzed how singularities, known as exceptional points, control the convergence of perturbative expansions and limit the radius of convergence of many-body series. This work clarified why certain approximations fail and how more robust approaches can be designed.
Complementary objectives included establishing reliable and openly accessible benchmark datasets for excitation energies; unifying wave-function and Green’s-function many-body approaches; introducing advanced diagrammatic techniques such as the parquet formalism into molecular quantum chemistry; developing state-specific and systematically improvable excited-state methods; and gaining insight into exact excited-state density functionals.
All major developments were implemented within Quantum Package, an open-source quantum chemistry platform developed by the group and collaborators, ensuring that theoretical advances were translated into practical and reproducible computational tools.
By the end of the project, these objectives were achieved and, in several cases, exceeded. The non-Hermitian framework clarified the analytic structure of excited states and the role of exceptional points. The QUEST database established a new benchmark standard for excitation energies. The unification of many-body perturbation theory and coupled-cluster theory strengthened the theoretical foundations of correlated methods. The introduction of parquet theory to molecular systems opened a new research direction, and state-specific coupled-cluster methods provided alternative systematically improvable routes to excited-state calculations.
