A study of the dense uniform electron gas with high orders of coupled cluster

Abstract

We investigate the accuracies of different coupled cluster levels in a finite model solid, the 14 electron spin-non-polarised uniform electron gas. For densities between r = 0.5 a and r = 5 a, we calculate ground state correlation energies with stochastic coupled cluster ranging from coupled cluster singles and doubles (CCSD) to coupled cluster including all excitations up to quintuples (CCSDTQ5). We find the need to add triple excitations for an accuracy of 0.01 eV/electron beyond r = 0.5 a. Quadruple excitations start being significant past r = 3 a. At r = 5 a, CCSD gives a correlation energy with a 16% error and coupled cluster singles doubles and triples is in error by 2% compared to the CCSDTQ5 result. CCSDTQ5 gives an energy in agreement with full configuration interaction quantum Monte Carlo results.

An auxiliary-Field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree-Fock trial wavefunctions

“…2 and Table II where on the order of 2000 PWs are necessary to converge the total energy to within 1 mHa in absolute energy (not per electron). Similar to previous studies we observe a more or less linear relationship between E c and 1/M for M greater than 925 61,66 . The linear extrapolation to the CBS limit when using PWs was thoroughly studied and understood by Shepherd and co-workers in Ref.…”

“…Recently, the formally exact full configuration interaction quantum Monte Carlo method 12,60 (FCIQMC) provided benchmark results for a range of densities for a 14-and 54-electron system 61,62 . These FCIQMC studies also motivated recent coupled-cluster Monte Carlo 63-65 studies on the 14-electron UEG model by Neufeld and Thom where they provided CCSD, CCSD and triples (CCSDT), CCSDT and quadruples (CCSDTQ) with RHF references results for a wide range of r s and basis sets 66 . As the scope of truncated spin-restricted CC (RCC) approaches is relatively well understood, comparing HF+ph-AFQMC against these results will lead us to a better understanding of the scope of HF+ph-AFQMC.…”

“…We see that ph-AFQMC agrees well with i-FCIQMC within the error bar up to M = 179 and it starts to deviate from i-FCIQMC beyond that. However, i-FCIQMC numbers for the larger M values should be taken cautiously as it has been noted elsewhere that the bias from the initiator approximation was not completely removed 66 and that the i-FCIQMC results for r s = 0.5 may be too low by approximately 1 mE h .…”

Variational and diffusion quantum Monte Carlo calculations with the CASINO code

“…The coefficients of symmetry-equivalent determinants in the expansion have been constrained to be equal, so, e.g., the expansion with 30 optimizable coefficients contains 1273 determinants, by which point the backflow DMC energy has converged to within ∼ 35 µHa per electron of the exact energy, obtained using FCIQMC. 233 Also shown in Fig. 26 is the basis-set limit of the backflow DMC energy obtained with an MAGP wave function, 104 described in Sec.…”

An optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas

“…Overall, the results here should improve our ability to understand infinite-sized model systems that are necessarily represented as finite systems, such as the electron gas with varying dimensions, the Hubbard model, and the models of nuclear matter we previ-ously studied. 129,133,134 This communication is timely due to a resurgence of interest in the uniform electron gas 68,96,127,[135][136][137][138][139][140] and of twist-averaged coupled cluster calculations. 2,141 We expect this work can immediately be applied to improve calculations.…”