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Static correlation and electron localization in molecular dimers from the self-consistent RPA and GW approximation

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Rubio,  Angel
Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Theory, Fritz Haber Institute, Max Planck Society;
Nano-Bio Spectroscopy Group and ETSF Scientific Development Centre, Departamento de F;

Scheffler,  Matthias
Theory, Fritz Haber Institute, Max Planck Society;

Rinke,  Patrick
Theory, Fritz Haber Institute, Max Planck Society;
COMP/Department of Applied Physics, Aalto University, P.O. Box 11100, Aalto FI-00076, Finland;

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PhysRevB.91.165110.pdf
(Publisher version), 802KB

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Citation

Hellgren, M., Caruso, F., Rohr, D. R., Ren, X., Rubio, A., Scheffler, M., et al. (2015). Static correlation and electron localization in molecular dimers from the self-consistent RPA and GW approximation. Physical Review B, 91(16): 165110. doi:10.1103/PhysRevB.91.165110.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0026-CB9A-F
Abstract
We investigate static correlation and delocalization errors in the self-consistent GW and random-phase approximation (RPA) by studying molecular dissociation of the H2 and LiH molecules. Although both approximations contain topologically identical diagrams, the nonlocality and frequency dependence of the GW self-energy crucially influence the different energy contributions to the total energy as compared to the use of a static local potential in the RPA. The latter leads to significantly larger correlation energies, which allow for a better description of static correlation at intermediate bond distances. The substantial error found in GW is further analyzed by comparing spin-restricted and spin-unrestricted calculations. At large but finite nuclear separation, their difference gives an estimate of the so-called fractional spin error normally determined only in the dissociation limit. Furthermore, a calculation of the dipole moment of the LiH molecule at dissociation reveals a large delocalization error in GW making the fractional charge error comparable to the RPA. The analyses are supplemented by explicit formulas for the GW Green's function and total energy of a simplified two-level model providing additional insights into the dissociation limit.