Computational Signatures of Cooper Pair and Exciton Condensation: An Open-Source PySCF Implementation for an Upper-Division Computational Laboratory

<jats:p>Identifying molecular candidates that demonstrate condensation behavior under ambient conditions could enable more-efficient energy transport and electronic devices by minimizing losses from friction. Phenomena such as superconductivity and superfluidity arise from a Bose-Einstein-like condensation of paired fermions into a single quantum state. Fermion pair condensates—the most familiar being Cooper (electron) pairs—produce electronic superfluidity, enabling perfect conductivity and diamagnetism; yet, all known superconductors require either impractically low temperatures or extreme pressures. Similarly, exciton condensates form when electron-hole pairs (excitons) condense into a shared quantum state. These condensates are predicted to support non-dissipative energy transfer at higher temperatures because of their light mass and strong binding energies, but their short lifetimes have constrained experimental realization. Progress toward discovering viable molecular condensation candidates depends on accessible computational tools; however, current methods for calculating signatures of Cooper pair and exciton condensation rely on proprietary implementations. Moreover, despite their importance in energy transport, students are rarely exposed to condensation phenomena in coursework, and even within the broader scientific community, the computational signatures of condensation are not widely known. In this work, we provide an open-source PySCF-based tool for the identification of molecular condensation candidates, an upper-division laboratory scaffolding for the exploration of a molecular-scaled analog of a graphene bilayer, and an accessible introduction to the theory underlying condensation phenomena. Together, these resources equip students and instructors with the background and tools needed to explore quantum condensation phenomena and identify molecular condensation candidates.</jats:p>