Logo image
Back
How the Exchange Energy Can Affect the Power Laws Used to Extrapolate the Coupled Cluster Correlation Energy to the Thermodynamic Limit
Journal article   Open access   Peer reviewed

How the Exchange Energy Can Affect the Power Laws Used to Extrapolate the Coupled Cluster Correlation Energy to the Thermodynamic Limit

Tina N Mihm, Laura Weiler and James J Shepherd
Journal of chemical theory and computation, Vol.19(6), pp.1686-1697
03/2023
DOI: 10.1021/acs.jctc.2c00737
PMCID: PMC10061680
PMID: 36918372
Appears in  UI Libraries Support Open Access
url
https://doi.org/10.1021/acs.jctc.2c00737View
Published (Version of record) Open Access

Related content

Is publication of

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) ∼ G2, 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.
 UIOWA OA Agreement

Details

Metrics

9 Record Views
9 Times Cited - Web of Science
Logo image