Electron correlation from path resummations: the double-excitation star

Resummation over a selected subset of paths allows the approximate evaluation of an N-electron path-integral. In particular, we show that the double excitation star graph, consisting of all doubly excited determinants attached to the reference Hartree-Fock determinant, has an energy which is easily calculated in O[N-4] time after integral precomputation, and produces binding curves of a similar quality to CCSD theory for a range of systems including the N-2 molecule, the hydrogen-bonded water dimer, and dispersion dominated Ne-2 and Ar-2 dimers.