Toric degenerations arising from quantum chemistry

The high dimensional eigenvalue problem that encodes the electronic Schrödinger equation can be approximated by a hierarchy of polynomial systems at various levels of truncation, called the coupled cluster (CC) equations. The exponential parametrization of the eigenstates gives rise to truncation varieties. These generalize Grassmannians in their Plücker embedding. We determine the number of complex solutions to the CC equations over the Grassmannian. This rests on the geometry of the graph of a birational parametrization of the Grassmannian. We present a squarefree Gröbner basis for this graph, and we develop connections to toric degenerations from representation theory.