Abstract
The efficient implementation of electronic structure methods is essential for first principles modeling of molecules and solids. We present here a particularly efficient common framework for methods beyond semilocal density-functional theory (DFT), including Hartree–Fock (HF), hybrid density functionals, random-phase approximation (RPA), second-order Møller–Plesset perturbation theory (MP2) and the GW method. This computational framework allows us to use compact and accurate numeric atom-centered orbitals (NAOs), popular in many implementations of semilocal DFT, as basis functions. The essence of our framework is to employ the ‘resolution of identity (RI)’ technique to facilitate the treatment of both the two-electron Coulomb repulsion integrals (required in all these approaches) and the linear density-response function (required for RPA and GW). This is possible because these quantities can be expressed in terms of the products of single-particle basis functions, which can in turn be expanded in a set of auxiliary basis functions (ABFs). The construction of ABFs lies at the heart of the RI technique, and we propose here a simple prescription for constructing ABFs which can be applied regardless of whether the underlying radial functions have a specific analytical shape (e.g. Gaussian) or are numerically tabulated. We demonstrate the accuracy of our RI implementation for Gaussian and NAO basis functions, as well as the convergence behavior of our NAO basis sets for the above-mentioned methods. Benchmark results are presented for the ionization energies of 50 selected atoms and molecules from the G2 ion test set obtained with the GW and MP2 self-energy methods, and the G2-I atomization energies as well as the S22 molecular interaction energies obtained with the RPA method.
Highlights
Accurate quantum-mechanical predictions of the properties of molecules and materials from first principles play an important role in chemistry and condensed-matter research today
There is much ongoing work to extend the reach of Density-functional theory (DFT), e.g. meta-generalized gradient approximation (GGA) [20,21,22], formalisms to include van der Waals interactions [23,24,25,26,27,28], hybrid functionals [29,30,31,32,33,34] or approaches based on the random-phase approximation (RPA) [35,36,37,38,39,40,41,42] that deal with the non-local correlations in a more systematic and non-empirical way
In order to avoid any secondary effects from different scalar-relativistic approximations to the kinetic energy operator, in figure 10 we first compare the convergence of non-relativistic (NREL) HF total energies with numeric atom-centered orbitals (NAOs) basis size for the coinage metal dimers Cu2, Ag2 and Au2 at a fixed binding distance, d = 2.5 Å. (The experimental binding distances are 2.22 Å [163], 2.53 Å [164, 165] and 2.47 Å [163], respectively.) Again, we find that KLI-derived minimal basis sets are noticeably better converged than local-density approximation (LDA)-derived minimal basis sets
Summary
Accurate quantum-mechanical predictions of the properties of molecules and materials (solids, surfaces, nano-structures, etc) from first principles play an important role in chemistry and condensed-matter research today. There is much ongoing work to extend the reach of DFT, e.g. meta-GGAs [20,21,22], formalisms to include van der Waals interactions [23,24,25,26,27,28], hybrid functionals [29,30,31,32,33,34] or approaches based on the random-phase approximation (RPA) [35,36,37,38,39,40,41,42] that deal with the non-local correlations in a more systematic and non-empirical way Another avenue is provided by the approaches of quantum chemistry that start with Hartree–Fock (HF) theory [43, 44].
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