Developments in stochastic coupled cluster theory: The initiator approximation and application to the uniform electron gas

Abstract

We describe further details of the stochastic coupled cluster method and a diagnostic of such calculations, the shoulder height, akin to the plateau found in full configuration interaction quantum Monte Carlo. We describe an initiator modification to stochastic coupled cluster theory and show that initiator calculations can at times be extrapolated to the unbiased limit. We apply this method to the 3D 14-electron uniform electron gas and present complete basis set limit values of the coupled cluster singles and doubles (CCSD) and previously unattainable coupled cluster singles and doubles with perturbative triples (CCSDT) correlation energies for up to r(s) = 2, showing a requirement to include triple excitations to accurately calculate energies at high densities.

Communication: Convergence of many-body wave-function expansions using a plane-wave basis in the thermodynamic limit

“…The extrapolated energy is 91.6% ± 0.5% of the GFMC energy, which is in agreement with similar previous findings for 3D electron gases. 43,46 Repeating this procedure gives E = −0.257 ± 0.004 Ry and E = −0.140 ± 0.001 Ry for r s = 0.5 and 2.0, respectively.…”

“…The power-laws derived were used in the years leading up to that study and then subsequently to achieve complete basis set results for a variety of systems [37][38][39] and in particular the uniform electron gas. [40][41][42][43][44][45][46][47][48][49][50][51] In recent times, several further major developments addressing plane wave basis set incompleteness error have been made. In particular, explicit correlation has been applied to a planewave basis, including F12 methods [52][53][54] and transcorrelation; 55 corrections have been derived for a semi-analytical correction which has been found for the direct term MP2 and for dRPA; 56 and hybrid basis sets of plane-wave derived occupied orbitals and Gaussian virtual orbitals have been implemented.…”

Spectral functions of the uniform electron gas via coupled-cluster theory and comparison to theGWand related approximations

“…2(c) shows the quasiparticle energies as function of the electron wave vector, i.e. the energy dispersion relation, for the 114 electron system with results extrapolated to the complete basis set limit 51 . The inferred bandwidths are 2.96 eV for CCSD, 3.79 eV for HF+GW, 2.77 eV for LDA+GW, and 2.56 eV for LDA+GW xc ; selfconsistency treated within the quasiparticle self-consistent GW scheme gives only a minor bandwidth narrowing compared to LDA+G 0 W 0 .…”

“…Since the submission of this article, two relevant articles have been published: Spencer and Thom have applied a stochastic implementation of CCSDT to the 14-electron UEG for r s ≤ 2 59 and Bhaskaran-Nair et al have calculated the CCSD Green's function for small molecules at a few frequency values. 60 …”

“…CCSDT calculations were performed using a modified version of the CFOUR code. 62 Dynamical DMRG calculations were done with the BLOCK code. …”