Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

Abstract

A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basisfunction products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron manybody perturbation theory with significantly reduced computational and memory cost.

Towards Efficient Orbital-Dependent Density Functionals for Weak and Strong Correlation

“…All calculations in this work, with the exception of coupled-cluster singles, doubles and perturbative triples (CCSD(T)), have been carried out with the FHI-aims code [37][38][39]. The full-configuration interaction (FCI) results were obtained with FHI-aims and the quantum Monte Carlo framework of Booth et al [40].…”

Main-group test set for materials science and engineering with user-friendly graphical tools for error analysis: systematic benchmark of the numerical and intrinsic errors in state-of-the-art electronic-structure approximations

“…Two methods at such level, MP2 [53] and RPA [18,34,35,[54][55][56]113], are stateof-the-art in computational materials science [34,76,77,85,87,[114][115][116][117]. The numerical errors in these methods can either be inherited from the aforementioned algorithms to solve the one-electron Kohn-Sham (or Hartree-Fock) equations, or arise from extra algorithms, such as the choice of the self-consistent Kohn-Sham orbitals for the post-processing evaluations [118], the resolution-of-identity technique to handle the twoelectron four-center integrals [18,[119][120][121], and the localization approximations [114,122,123] to reduce the computational scaling in these advanced correlation methods.…”

“…Due to the use of NAO basis sets, the electronic-structure problem is addressed using numerical integration in FHI-aims. The specific technical aspects, including the implementation of localized resolution-of-identity (called 'RI-LVL') method, are described in [24,52,121]. We have systematically examined the numerical convergence in terms of relevant numerical parameters, and also k-mesh and basis set sizes.…”

Wave-function inspired density functional applied to the H2/${{\rm{H}}}_{2}^{+}$ challenge

“…All results are obtained with input KS orbitals from a PBE0 calculation [80][81][82]. All calculations, including the CISD reference, are carried out with FHI-aims using the NAO-VCC-5Z basis set [79,83]. In figure 6 we show the same curves for RPA, rPT2 and BGE2 for different starting points (PBE, PBE0 and HF).…”