Implementation and Validation of Fully RelativisticGWCalculations: Spin–Orbit Coupling in Molecules, Nanocrystals, and Solids

Abstract

We present an implementation of G0W0 calculations including spin-orbit coupling (SOC) enabling investigations of large systems, with thousands of electrons, and we discuss results for molecules, solids, and nanocrystals. Using a newly developed set of molecules with heavy elements (called GW-SOC81), we find that, when based upon hybrid density functional calculations, fully relativistic (FR) and scalar-relativistic (SR) G0W0 calculations of vertical ionization potentials both yield excellent performance compared to experiment, with errors below 1.9%. We demonstrate that while SR calculations have higher random errors, FR calculations systematically underestimate the VIP by 0.1 to 0.2 eV. We further verify that SOC effects may be well approximated at the FR density functional level and then added to SR G0W0 results for a broad class of systems. We also address the use of different root-finding algorithms for the G0W0 quasiparticle equation and the significant influence of including d electrons in the valence partition of the pseudopotential for G0W0 calculations. Finally, we present statistical analyses of our data, highlighting the importance of separating definitive improvements from those that may occur by chance due to a limited number of samples. We suggest the statistical analyses used here will be useful in the assessment of the accuracy of a large variety of electronic structure methods.

A Density Functional Prediction of the Geometries, Stabilities, and Electronic Properties of Nanosize Cage‐Like (InN)2n (n = 6–27, 45, 54) Semiconductor Materials

“…The calculated triplet InN bond length is 2.04Å, which is in good agreement with experimental measurement of 2.10Å. [23] However, full relativistic calculation is very expensive. [22] This energy difference maybe causes by relativistic effect due to the neglect of the spin-orbit coupling effect in scalar relativistic calculation.…”

“…[22] This energy difference maybe causes by relativistic effect due to the neglect of the spin-orbit coupling effect in scalar relativistic calculation. [23] However, full relativistic calculation is very expensive. Our calculated In-In bond length in singlet In 2 dimer is 2.85Å.…”

The GW approximation: content, successes and limitations

“…One can easily understand that in periodic systems basis sets such as plane waves are often a good choice, whereas in small systems a localized basis may be more suitable. Various implementations have been proposed and described in detail (see, e.g., Refs and ), which are often adapted to standard quantum chemistry packages. These implementations have been used for extensive benchmarking.…”

“…The work of Ref focused on a test set of 29 molecules ranging from H 2 to tetrathiafulvalene. The systems examined in Ref include the benzene and other molecules, water clusters containing up to 480 atoms, small CdSe nanoparticles, and linear acenes, whereas the work of Ref concentrates on relativistic effects, which are studied in molecules, solids, and nanocrystals. A large set of benchmark molecules proposed to benchmark GWA calculations is the GW100 set of Ref .…”

“…Overall, and in view of the fact that with today's implementations of the GWA systems of hundreds or a few thousands of electrons can be studied (see, e.g., Ref ), it seems worthwhile to further investigate the potential of GWA calculations in a context of quantum chemistry.…”