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

By Xinguo Ren, Patrick Rinke, Volker Blum, Jürgen Wieferink, Alexandre Tkatchenko, A. Sanfilippo, Karsten Reuter, Matthias Scheffler. 2012

664 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

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In Atomic and Molecular Physics, and Optics

1. Marcella Iannuzzi
2. F. Schiffmann
3. Juerg Hutter
4. Joost VandeVondele
5. Xia Leng
6. Fan Jin
7. Min Wei
8. Yuchen Ma

In Materials Chemistry

1. Marcella Iannuzzi
2. F. Schiffmann
3. Joost VandeVondele
4. Juerg Hutter

Citations in the corpus

• GW method and Bethe–Salpeter equation for calculating electronic excitations (2016, background): “Some literatures have discussed this issues for basis sets composed by Gaussian orbitals, numerically atomic orbitals, and so forth.(38,40,46,47,54,92,97)”
• cp2k: atomistic simulations of condensed matter systems (2014, methodology): “Recently, post-Hartree–Fock type calculations such as double hybrids and MP2 have been implemented [52], and with resolution-of-identity methods, MP2 and RPA energy expressions [53, 54] can be efficiently calculated for periodic systems.”