Preprint
How the exchange energy can affect the power laws used to extrapolate the coupled cluster correlation energy to the thermodynamic limit
ArXiv.org
02/10/2023
DOI: 10.48550/arxiv.2302.05051
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. However, previous studies in the quantum Monte Carlo community suggest
an exchange-energy-like power law of $N^{-2/3}$ is 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 as $N^{-2/3}$; so, the correlation energy should be a combination of the
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 wavefunction calculated from the
amplitudes. We show that data from coupled cluster doubles calculations on the
uniform electron gas(UEG) fit a function with a low $G$ behavior of $S(G)$~$G$.
The pre-factor 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. First, we develop a plane-wave cutoff
scheme with less noise than the traditional basis set used for the UEG. Then,
we collect data from a wide range of electron numbers and densities to
systematically test 5 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 pre-factor for $N^{-2/3}$ scaling can be found from
exchange energy calculations.
Details
- Title: Subtitle
- How the exchange energy can affect the power laws used to extrapolate the coupled cluster correlation energy to the thermodynamic limit
- Creators
- Tina N MihmLaura WeilerJames J Shepherd
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2302.05051
- ISSN
- 2331-8422
- Language
- English
- Date posted
- 02/10/2023
- Academic Unit
- Chemistry
- Record Identifier
- 9984365912102771
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