An Optimisation on the Grassmannian with Applications toQuantum Chemistry

In this work we propose an algorithm to find critical points of the inner product between an element of the Grassmannian and a fixed point of the projective space of the exterior algebra where the Grassmannian is embedded. This has interesting applications to electronic structure theory, where the wave functions are represented by elements of the exterior algebra. This method is exemplified for a Grassmannian that is a model for the hydrogen molecule, H 2 .