Comparison of low-rank tensor expansions for the acceleration of quantum chemistry computations

Low-rank spectral expansion and tensor hypercontraction are two promising techniques for reducing the size of the two-electron excitation tensor by factorizing it into products of smaller tensors. Both methods can potentially realize an O(r(4)) quantum chemistry method where r is the number of one-electron orbitals. We compare the two factorizations in this paper by applying them to the parametric 2-electron reduced density matrix method with the M functional [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. We study several inorganic molecules, alkane chains, and potential curves as well as reaction and dissociation energies. The low-rank spectral expansion, we find, is typically more efficient than tensor hypercontraction due to a faster convergence of the energy and a smaller constant prefactor in the energy optimization. Both factorizations are applicable to the acceleration of a wide range of wavefunction and reduced-density-matrix methods.