Abstract
Finite size error is commonly removed from coupled cluster theory calculations by N(-1) extrapolations over correlation energy calculations of different system sizes (N), where the N(-1) scaling comes from the total energy rather than the correlation energy. However, previous studies in the quantum Monte Carlo community suggest an exchange-energy-like power law of N(-2/3) should also be present in the correlation energy when using the conventional Coulomb interaction. The rationale for this is that the total energy goes as N(-1) and the exchange energy goes as N(-2/3); thus, the correlation energy should be a combination of these two power laws. Further, in coupled cluster theory, these power laws are related to the low G scaling of the transition structure factor, S(G), which is a property of the coupled cluster wave function calculated from the amplitudes. We show here that data from coupled cluster doubles calculations on the uniform electron gas fit a function with a low G behavior of S(G) ∼ G. The prefactor for this linear term is derived from the exchange energy to be consistent with an N(-2/3) power law at large N. Incorporating the exchange structure factor into the transition structure factor results in a combined structure factor of S(G) ∼ G(2), consistent with an N(-1) scaling of the exchange-correlation energy. We then look for the presence of an N(-2/3) power law in the energy. To do so, we first develop a plane-wave cutoff scheme with less noise than the traditional basis set used for the uniform electron gas. Then, we collect data from a wide range of electron numbers and densities to systematically test five methods using N(-1) scaling, N(-2/3) scaling, or combinations of both scaling behaviors. We find that power laws that incorporate both N(-1) and N(-2/3) scaling perform better than either alone, especially when the prefactor for N(-2/3) scaling can be found from exchange energy calculations.