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The GW approximation: content, successes and limitations
Abstract
Many observables such as the density, total energy, or electric current, can be expressed explicitly in terms of the one‐body Green's function, which describes electron addition or removal to or from a system. An efficient way to determine such a Green's function is to introduce a self‐energy, which is a nonlocal and dynamic effective potential that influences the propagation of particles in an interacting system. The state‐of‐the art approximation for the self‐energy is the GW approximation, where the system to (or from) which the electron is added (or removed) is described as a polarizable, screening, medium. This is expressed by the name of the approximation: ‘GW’ stands for the one‐body Green's function G and for W, the dynamically screened Coulomb interaction. The GW approximation is very popular for the calculation of band structures in solids, and increasingly used also to describe nanostructures, clusters, and molecules. As compared to static mean‐field approximations for the effective potential, the dynamical screening of the Coulomb interaction in GW leads to a renormalization of energies, to broadening and/or to the observation of additional excitations. An analysis of the approximations that lead to the GW self‐energy, and of the underlying picture, explains the successes and the limitations of the approach. This article is categorized under: Electronic Structure Theory > Density Functional Theory Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy Structure and Mechanism > Computational Materials Science
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Citations
Cites
Self-Consistent Equations Including Exchange and Correlation Effects
Kohn, W., & Sham, L. J. (1965) · Physical Review · doi:10.1103/physrev.140.a1133 · Cited by 64,135
Self-interaction correction to density-functional approximations for many-electron systems
Perdew, J. P., & Zunger, A. (1981) · Physical Review B · doi:10.1103/physrevb.23.5048 · Cited by 20,887
Hybrid functionals based on a screened Coulomb potential
Heyd, J., Scuseria, G. E., & Ernzerhof, M. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1564060 · Cited by 19,629
A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)
Yanai, T., Tew, D. P., & Handy, N. C. (2004) · Chemical Physics Letters · doi:10.1016/j.cplett.2004.06.011 · Cited by 14,976
Influence of the exchange screening parameter on the performance of screened hybrid functionals
Krukau, A. V., Vydrov, O. A., Izmaylov, A. F., & Scuseria, G. E. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2404663 · Cited by 7,005
Hedin, L. (1965) · Physical Review · doi:10.1103/physrev.139.a796 · Cited by 5,481
Quantum theory of many-particle systems
Fetter, A. L., & Walecka, J. D. (1971) · Cited by 5,252
Zur Quantentheorie der Molekeln
Born, M., & Oppenheimer, R. (1927) · Annalen der Physik · doi:10.1002/andp.19273892002 · Cited by 4,958
Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies
Hybertsen, M. S., & Louie, S. G. (1986) · Physical Review B · doi:10.1103/physrevb.34.5390 · Cited by 3,963
Nobel Lecture: Electronic structure of matter—wave functions and density functionals
Kohn, W. (1999) · Reviews of Modern Physics · doi:10.1103/revmodphys.71.1253 · Cited by 2,637
Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules
Bartlett, R. J. (1981) · Annual Review of Physical Chemistry · doi:10.1146/annurev.pc.32.100181.002043 · Cited by 2,118
Bohm, D., & Pines, D. (1953) · Physical Review · doi:10.1103/physrev.92.609 · Cited by 1,911
Aryasetiawan, F., & Gunnarsson, O. (1998) · Reports on Progress in Physics · doi:10.1088/0034-4885/61/3/002 · Cited by 1,816
Assessment of a long-range corrected hybrid functional
Vydrov, O. A., & Scuseria, G. E. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2409292 · Cited by 1,783
Self-energy operators and exchange-correlation potentials in semiconductors
Godby, R. W., Schlüter, M., & Sham, L. J. (1988) · Physical Review B · doi:10.1103/physrevb.37.10159 · Cited by 1,406
First-Principles Theory of Quasiparticles: Calculation of Band Gaps in Semiconductors and Insulators
Hybertsen, M. S., & Louie, S. G. (1985) · Physical Review Letters · doi:10.1103/physrevlett.55.1418 · Cited by 1,389
Generalized Kohn-Sham schemes and the band-gap problem
Seidl, A., Görling, A., Vogl, P., Majewski, J. A., & Levy, M. (1996) · Physical Review B · doi:10.1103/physrevb.53.3764 · Cited by 1,269
Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids
Hedin, L., & Lundqvist, S. (1970) · Solid State Physics · doi:10.1016/s0081-1947(08)60615-3 · Cited by 1,134
Effects of the electron interaction on the energy levels of electrons in metals
Wigner, E. (1938) · Transactions of the Faraday Society · doi:10.1039/tf9383400678 · Cited by 1,108
Exchange-correlation energy of a metallic surface: Wave-vector analysis
Langreth, D. C., & Perdew, J. P. (1977) · Physical Review B · doi:10.1103/physrevb.15.2884 · Cited by 1,040
Vydrov, O. A., Heyd, J., Krukau, A. V., & Scuseria, G. E. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2244560 · Cited by 989
Quasiparticle Self-ConsistentGWTheory
van Schilfgaarde, M., Kotani, T., & Faleev, S. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.226402 · Cited by 989
New approach to the one-particle Green's function for finite Fermi systems
Schirmer, J., Cederbaum, L. S., & Walter, O. (1983) · Physical Review A · doi:10.1103/physreva.28.1237 · Cited by 726
Quasiparticle Calculations in Solids
Aulbur, W. G., Jönsson, L., & Wilkins, J. W. (2000) · Solid State Physics · doi:10.1016/s0081-1947(08)60248-9 · Cited by 662
Application of the Green’s functions method to the study of the optical properties of semiconductors
Strinati, G. (1988) · La Rivista del Nuovo Cimento · doi:10.1007/bf02725962 · Cited by 571
All-Electron Self-ConsistentGWApproximation: Application to Si, MnO, and NiO
Faleev, S. V., van Schilfgaarde, M., & Kotani, T. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.126406 · Cited by 554
Interacting Electrons: Theory and Computational Approaches
Martin, R. M., Reining, L., & Ceperley, D. M. (2016) · Cambridge University Press eBooks · doi:10.1017/cbo9781139050807 · Cited by 531
Self-citationMetal-insulator transition in Kohn-Sham theory and quasiparticle theory
Godby, R. W., & Needs, R. J. (1989) · Physical Review Letters · doi:10.1103/physrevlett.62.1169 · Cited by 496
Quasiparticle self-consistentGWmethod: A basis for the independent-particle approximation
Kotani, T., van Schilfgaarde, M., & Faleev, S. V. (2007) · Physical Review B · doi:10.1103/physrevb.76.165106 · Cited by 469
Molecular tests of the random phase approximation to the exchange-correlation energy functional
Furche, F. (2001) · Physical Review B · doi:10.1103/physrevb.64.195120 · Cited by 455
Blase, X., Attaccalite, C., & Olevano, V. (2011) · Physical Review B · doi:10.1103/physrevb.83.115103 · Cited by 448
Baerends, E. J., Gritsenko, O. V., & van Meer, R. (2013) · Physical Chemistry Chemical Physics · doi:10.1039/c3cp52547c · Cited by 446
GW 100: Benchmarking G0W0 for Molecular Systems
van Setten, M. J., Caruso, F., Sharifzadeh, S., Ren, X., Scheffler, M., Liu, F., Lischner, J., Lin, L., Deslippe, J. R., Louie, S. G., et al. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00453 · Cited by 397
Fully self-consistentGWself-energy of the electron gas
Holm, B., & von Barth, U. (1998) · Physical Review B · doi:10.1103/physrevb.57.2108 · Cited by 356
Dynamical aspects of correlation corrections in a covalent crystal
Strinati, G., Mattausch, H. J., & Hanke, W. (1982) · Physical Review B · doi:10.1103/physrevb.25.2867 · Cited by 305
The GW-Method for Quantum Chemistry Applications: Theory and Implementation
van Setten, M. J., Weigend, F., & Evers, F. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct300648t · Cited by 284
Benchmarking the Starting Points of the GW Approximation for Molecules
Bruneval, F., & Marques, M. A. L. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct300835h · Cited by 268
Rojas, H. N., Godby, R. W., & Needs, R. J. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.1827 · Cited by 265
Fuchs, M., & Gonze, X. (2002) · Physical Review B · doi:10.1103/physrevb.65.235109 · Cited by 249
Scherpelz, P., Govoni, M., Hamada, I., & Galli, G. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00114 · Cited by 239
Electronic Excitations in Metals and at Metal Surfaces
Chulkov, E. V., Borisov, A. G., Gauyacq, J. P., Sánchez-Portal, D., Silkin, V. M., Zhukov, V. P., & Echenique, P. M. (2006) · Chemical Reviews · doi:10.1021/cr050166o · Cited by 232
Lebègue, S., Arnaud, B., Alouani, M., & Bloechl, P. E. (2003) · Physical Review B · doi:10.1103/physrevb.67.155208 · Cited by 226
Electron propagator theory: an approach to prediction and interpretation in quantum chemistry
Ortiz, J. V. (2013) · WIREs Computational Molecular Science · doi:10.1002/wcms.1116 · Cited by 209
Dynamical Correlation Effects on the Quasiparticle Bloch States of a Covalent Crystal
Strinati, G., Mattausch, H. J., & Hanke, W. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.290 · Cited by 203
Benchmark ofGWmethods for azabenzenes
Marom, N., Caruso, F., Ren, X., Hofmann, O. T., Körzdörfer, T., Chelikowsky, J. R., Rubio, A., Scheffler, M., & Rinke, P. (2012) · Physical Review B · doi:10.1103/physrevb.86.245127 · Cited by 197
Self-energy of ferromagnetic nickel in the GW approximation
Aryasetiawan, F. (1992) · Physical Review B · doi:10.1103/physrevb.46.13051 · Cited by 189
First-principlesGWcalculations for DNA and RNA nucleobases
Faber, C., Attaccalite, C., Olevano, V., Runge, E., & Blase, X. (2011) · Physical Review B · doi:10.1103/physrevb.83.115123 · Cited by 179
Multiple Plasmon Satellites in Na and Al Spectral Functions from Ab Initio Cumulant Expansion
Aryasetiawan, F., Hedin, L., & Karlsson, K. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.2268 · Cited by 178
Assessment of correlation energies based on the random-phase approximation
Paier, J., Ren, X., Rinke, P., Scuseria, G. E., Grüneis, A., Kresse, G., & Scheffler, M. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/4/043002 · Cited by 166
Guzzo, M., Lani, G., Sottile, F., et al. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.166401 · Cited by 158
The self-energy beyond GW: Local and nonlocal vertex corrections
Romaniello, P., Guyot, S., & Reining, L. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3249965 · Cited by 131
Self-citationGW in the Gaussian and Plane Waves Scheme with Application to Linear Acenes
Wilhelm, J., Ben, M. D., & Hutter, J. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00380 · Cited by 121
Total energy of solids: An exchange and random-phase approximation correlation study
Miyake, T., Aryasetiawan, F., Kotani, T., van Schilfgaarde, M., Usuda, M., & Terakura, K. (2002) · Physical review. B, Condensed matter · doi:10.1103/physrevb.66.245103 · Cited by 112
Benchmark Many-Body GW and Bethe–Salpeter Calculations for Small Transition Metal Molecules
Körbel, S., Boulanger, P., Duchemin, I., Blase, X., Marques, M. A. L., & Botti, S. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct5003658 · Cited by 112
Variational energy functionals of the Green function and of the density tested on molecules
Dahlen, N. E., van Leeuwen, R., & von Barth, U. (2006) · Physical Review A · doi:10.1103/physreva.73.012511 · Cited by 107
Caruso, F., Rohr, D. R., Hellgren, M., Ren, X., Rinke, P., Rubio, Á., & Scheffler, M. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.146403 · Cited by 102
Beyond the GW approximation: Combining correlation channels
Romaniello, P., Bechstedt, F., & Reining, L. (2012) · Physical Review B · doi:10.1103/physrevb.85.155131 · Cited by 101
Self-citationEvaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes
Rangel, T., Hamed, S. M., Bruneval, F., & Neaton, J. B. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00163 · Cited by 99
First-Principles T -Matrix Theory with Application to the 6 eV Satellite in Ni
Springer, M., Aryasetiawan, F., & Karlsson, K. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.2389 · Cited by 96
García‐González, P., & Godby, R. W. (2001) · Physical review. B, Condensed matter · doi:10.1103/physrevb.63.075112 · Cited by 88
Total Energy Method from Many-Body Formulation
Aryasetiawan, F., Miyake, T., & Terakura, K. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.166401 · Cited by 73
Dynamical effects in electron spectroscopy
Zhou, J. S., Kas, J. J., Sponza, L., Reshetnyak, I., Guzzo, M., Giorgetti, C., Gatti, M., Sottile, F., Rehr, J. J., & Reining, L. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4934965 · Cited by 73
Self-citationHellgren, M., Caruso, F., Rohr, D. R., Ren, X., Rubio, Á., Scheffler, M., & Rinke, P. (2015) · Physical Review B · doi:10.1103/physrevb.91.165110 · Cited by 64
Caruso, F., Atalla, V., Ren, X., Rubio, Á., Scheffler, M., & Rinke, P. (2014) · Physical Review B · doi:10.1103/physrevb.90.085141 · Cited by 51
Variational energy functionals tested on atoms
Dahlen, N. E., & von Barth, U. (2004) · Physical Review B · doi:10.1103/physrevb.69.195102 · Cited by 51
GW and Bethe-Salpeter study of small water clusters
Blase, X., Boulanger, P., Bruneval, F., Fernández-Serra, M., & Duchemin, I. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4940139 · Cited by 46
Casida, M. E., & Chong, D. P. (1989) · Physical Review A · doi:10.1103/physreva.40.4837 · Cited by 36
van Leeuwen, R., Dahlen, N. E., & Stan, A. (2006) · Physical Review B · doi:10.1103/physrevb.74.195105 · Cited by 22
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Metadata
- Authors
- Reining, L.
- Venue
- WIREs Computational Molecular Science
- Publisher
- Wiley
- Published
- 2017-12-27
- Volume
- 8
- Issue
- 3
- ISSN
- 1759-0876 (ISSN-L)
- 1759-0884
- OpenAlex
- W2780208476
- Cited by
- 284
- References
- 68
- FWCI
- 6.88
- Type
- journal article
- Language
- en
- Open access
- closed
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