Communication: Convergence of many-body wave-function 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 6 occ n 4 virt could be separated into n 6 occ and n 4 virt 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.

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

“…26,46,47 . CCSD and CCSDT have been applied to the finite three-dimensional (3D) UEG 14,29,34,[48][49][50] . Shepherd 50 has extrapolated finite CCSD/CCD results in the 3D UEG to the thermodynamic limit and has compared them to Ceperley and Alder's DMC energies 37 (see figure 2c in Ref.…”

Dynamical correlation energy of metals in large basis sets from downfolding and composite approaches

“…[27][28][29][30][31] Although coupled-cluster theory has been successfully applied to an increasing number of atomistic semiconductors and insulators, 14,15,[32][33][34][35][36][37] its applicability for metals has been primarily focused around the UEG, also known as jellium. 29,[38][39][40][41][42][43][44][45] Despite their reasonable accuracy, these calculations have demonstrated the typical slow convergence of the correlation energy as a function of the number of virtual (unoccupied) orbitals included. 11,40,46,47 This slow convergence is especially problematic because of the high cost of coupled-cluster calculations with large basis sets.…”

“…29,[38][39][40][41][42][43][44][45] Despite their reasonable accuracy, these calculations have demonstrated the typical slow convergence of the correlation energy as a function of the number of virtual (unoccupied) orbitals included. 11,40,46,47 This slow convergence is especially problematic because of the high cost of coupled-cluster calculations with large basis sets. For example, coupled-cluster theory with single and double excitations (CCSD) has a computational cost that scales as O(N 2 M 4 ), where N and M are the number of electrons and basis functions respectively.…”

Effective Hamiltonians for the study of real metals using quantum chemical theories

“…In particular, these include the coupled cluster method and its different approximations, such as the widelyused coupled cluster singles and doubles plus perturbative triples theory (CCSD(T)) [7]. Yet despite the great advances of modern coupled cluster theory approximations and their applications to molecules, surfaces, and solids it remains difficult to treat metallic systems at the same level of theory, with the exception of applications to simple model Hamiltonians such as the uniform electron gas [8][9][10][11][12][13][14][15][16][17][18]. This constitutes a significant obstacle in modern computational materials science, where accurate benchmark results obtained with high-level theories for all types of materials are desperately needed to complement computationally more-efficient but less-accurate density functional theory calculations.…”

“…However, for the uniform electron gas, which is the simplest and most popular metallic model Hamiltonian, each of these barriers can be overcome. [9,[13][14][15][16][17][18] Through scrupulous accounting for error and its cancellation, we have found that it is possible to converge each component of the total energy to reach benchmark accuracy. On the journey to a universal application of single-reference coupled cluster theory to all solids, the final hurdle is to transfer these successes to real metals.…”