The complexity of the standard hierarchy of quantum chemistry methods is not
invariant to the choice of representation. This work explores how the scaling
of common quantum chemistry methods can be reduced using real-space,
momentum-space, and time-dependent intermediate representations without
introducing approximations. We find the scalings of exact Gaussian basis
Hartree--Fock theory, second-order M{\o}ller-Plesset perturbation theory, and
coupled cluster theory (specifically, linearized coupled cluster doubles and
the distinguishable cluster approximation with doubles) to be
O(N3), O(N3), and O(N5) respectively,
where N denotes system size. These scalings are not asymptotic and hold over
all ranges of N