The above (and perhaps other) approaches all reduce the basis compared to an unre-stricted basis. And this does result in a major reduction in the size of the H-matrix. We might refer to this as a basis-restricted H-matrix. It is possible to go further and directly eliminate elements of the matrix. This has been done, albeit rarely, in the vibrational dynamics literature. One example uses a method suggested by Handy and Carter and used for vibrational energies of C 2 H 4 and CH 3 NO 2 . The method is based on second-order perturbation theory to eliminate elements and borrows from similar ideas in electronic structure theory. A direct approach has been given in ref. 17 as a means to reduce the storage of the H-matrix, illustrated for C 2 H 4 . This is simply to neglect Hamiltonian matrix elements below an absolute value of about 0.00002 cm -1 . Doing so resulted in a major reduction is the number of elements stored in memory.