Browsing by Author "Ren, X."

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Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory,
(2015) Ihrig, A.C.; Wieferink, J.; Zhang, I.Y.; Ropo, M.; Ren, X.; Rinke, P.; Scheffler, M.; Blum, V.
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree–Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2–1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.
Beyond the GW approximation: A second-order screened exchange correction
(2015) Ren, X.; Marom, N.; Caruso, F.; Scheffler, M.; Rinke, Patrick
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Motivated by the recently developed renormalized second-order perturbation theory for ground-state energy calculations, we propose a second-order screened exchange correction (SOSEX) to the GW self-energy. This correction follows the spirit of the SOSEX correction to the random-phase approximation for the electron correlation energy and can be clearly represented in terms of Feynman diagrams. We benchmark the performance of the perturbative G0W0+SOSEX scheme for a set of molecular systems, including the G2 test set from quantum chemistry as well as benzene and tetracyanoethylene. We find that G0W0+SOSEX improves over G0W0 for the energy levels of the highest occupied and lowest unoccupied molecular orbitals. In addition, it can resolve some of the difficulties encountered by the GW method for relative energy positions as exemplified by benzene where the energy spacing between certain valence orbitals is severely underestimated.
Static correlation and electron localization in molecular dimers from the self-consistent RPA and GW approximation
(2015) Hellgren, M.; Caruso, F.; Rohr, D.R.; Ren, X.; Rubio, A.; Scheffler, M.; Rinke, P.
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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.