Convergence of many-body wavefunction expansions using a plane wave basis in the thermodynamic limit

Abstract

Basis set incompleteness error and finite size error can manifest concurrently in systems for which the two effects are phenomenologically well-separated in length scale. When this is true, we need not necessarily remove the two sources of error simultaneously. Instead, the errors can be found and remedied in different parts of the basis set. This would be of great benefit to a method such as coupled cluster theory since the combined cost of $n_{occ}^6{n}_{virt}^4$ could be separated into $n_{occ}^6$ and $n_{virt}^4$ costs with smaller prefactors. In this Communication, we present analysis on a data set due to Baardsen and coworkers, containing coupled cluster doubles energies for the 2DEG for $r_s=$ 0.5, 1.0 and 2.0 a.u.~at a wide range of basis set sizes and particle numbers. In obtaining complete basis set limit thermodynamic limit results, we find that within a small and removable error the above assertion is correct for this simple system. This approach allows for the combination of methods which separately address finite size effects and basis set incompleteness error.

Submitted to JCP as a Communication. Questions and comments welcome. Data set will be published elsewhere

References in corpus (8)

• Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation
• The Finite Size Error in Many-body Simulations with long-Ranged Interactions
• Predictive GW calculations using plane waves and pseudopotentials
• Finite-size correction in many-body electronic structure calculations
• Fermionic path integral Monte Carlo results for the uniform electron gas at finite temperature
• Towards ab initio thermodynamics of the electron gas at strong degeneracy
• The self-energy of the uniform electron gas in the second order of exchange
• Towards a fully size-consistent method of increments

Cited by in corpus (11)

• The HANDE-QMC project: open-source stochastic quantum chemistry from the ground state up
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• Dynamical correlation energy of metals in large basis sets from downfolding and composite approaches
• Ab Initio Lifetime and Concomitant Double-Excitation Character of Plasmons at Metallic Densities
• Large Scale Parallelization in Stochastic Coupled Cluster
• Computational Nuclear Physics and Post Hartree-Fock Methods
• Machine learning for a finite size correction in periodic coupled cluster theory calculations
• Accelerating Stochastic Quantum Chemistry
• Accelerating convergence to the thermodynamic limit with twist angle selection applied to methods beyond many-body perturbation theory