Cumulant-based calculations of the correlation energy in a molecule

The problem of constructing a guaranteed convergent sequence of corrections to the Hartree--Fock ground state energy of a molecule without storing the many-electron wave function is considered. Several methods based on cumulants are considered and it is shown that such a sequence is obtained by Lanczos tridiagonalization, in which the elements of the tridiagonal matrix are calculated through cumulants.