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Efficient implementations of electronic structure methods are essential forfirst-principles modeling of molecules and solids. We here present aparticularly efficient common framework for methods beyond semilocaldensity-functional theory, including Hartree-Fock (HF), hybrid densityfunctionals, random-phase approximation (RPA), second-order M{\o}ller-Plessetperturbation theory (MP2), and the $GW$ method. This computational frameworkallows us to use compact and accurate numeric atom-centered orbitals (popularin many implementations of semilocal density-functional theory) as basisfunctions. The essence of our framework is to employ the "resolution ofidentity (RI)" technique to facilitate the treatment of both the two-electronCoulomb repulsion integrals (required in all these approaches) as well as thelinear density-response function (required for RPA and $GW$). This is possiblebecause these quantities can be expressed in terms of products ofsingle-particle basis functions, which can in turn be expanded in a set ofauxiliary basis functions (ABFs). The construction of ABFs lies at the heart ofthe RI technique, and here we propose a simple prescription for constructingthe ABFs which can be applied regardless of whether the underlying radialfunctions have a specific analytical shape (e.g., Gaussian) or are numericallytabulated. We demonstrate the accuracy of our RI implementation for Gaussianand NAO basis functions, as well as the convergence behavior of our NAO basissets for the above-mentioned methods. Benchmark results are presented for theionization energies of 50 selected atoms and molecules from the G2 ion test setas obtained with $GW$ and MP2 self-energy methods, and the G2-I atomizationenergies as well as the S22 molecular interaction energies as obtained with theRPA method.

new journal of physics

Resolution-of-identity approach to Hartree-Fock, hybrid density  functionals, RPA, MP2, and \textit{GW} with numeric atom-centered orbital  basis functions