One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms

Hirata, So; Doran, Alexander E.; Knowles, Peter J.; Ortiz, J. V.

doi:10.1063/1.4994837

One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms

Journal Article · Thu Jul 27 00:00:00 EDT 2017 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4994837· OSTI ID:1473852

^[1]; Doran, Alexander E. ^[2]; ^[3]; Ortiz, J. V. ^[4]

Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Chemistry; Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Chemistry
Cardiff Univ., Park Place, Cardiff (United Kingdom). School of Chemistry
Auburn Univ., AL (United States). Dept. of Chemistry and Biochemistry

A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green’s function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green’s function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green’s function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green’s function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green’s function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Illinois, Urbana-Champaign, IL (United States)

Sponsoring Organization:: CREST, Japan Science and Technology Agency; National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0006028

OSTI ID:: 1473852

Alternate ID(s):: OSTI ID: 1372946

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 4 Vol. 147; ISSN JCPSA6; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (119)

Size consistency of an algebraic propagator approach Schirmer, J.; Mertins, F. International Journal of Quantum Chemistry, Vol. 58, Issue 4 https://doi.org/10.1002/(sici)1097-461x(1996)58:4<329::aid-qua2>3.0.co;2-#	journal	January 1996
Partial third-order quasiparticle theory: An application to the photoelectron spectrum of S-tetrazine Ortiz, J. V. International Journal of Quantum Chemistry, Vol. 63, Issue 2 https://doi.org/10.1002/(sici)1097-461x(1997)63:2<291::aid-qua2>3.0.co;2-r	journal	January 1997
Exact exchange kernel for time-dependent density-functional theory G�rling, Andreas International Journal of Quantum Chemistry, Vol. 69, Issue 3 https://doi.org/10.1002/(sici)1097-461x(1998)69:3<265::aid-qua6>3.0.co;2-t	journal	January 1998
Theoretical Aspects of Ionization Potentials and Photoelectron Spectroscopy: A Green's Function Approach Cederbaum, L. S.; Domcke, W. Advances in Chemical Physics, Vol. 36 https://doi.org/10.1002/9780470142554.ch4	book	January 2007
Propagator Methods Oddershede, Jens Advances in Chemical Physics: Ab Initio Methods in Quantum Chemistry Part 2 https://doi.org/10.1002/9780470142943.ch3	book	January 2007
The linked-diagram expansion of the ground state of a many-electron system: A time-independent derivation Manne, Rolf International Journal of Quantum Chemistry, Vol. 12, Issue S11 https://doi.org/10.1002/qua.560120822	journal	January 1977
Coupled cluster approach to the single-particle Green's function Nooijen, Marcel; Snijders, Jaap G. International Journal of Quantum Chemistry, Vol. 44, Issue S26 https://doi.org/10.1002/qua.560440808	journal	March 1992
Coupled cluster Green's function method: Working equations and applications Nooijen, Marcel; Snijders, Jaap G. International Journal of Quantum Chemistry, Vol. 48, Issue 1 https://doi.org/10.1002/qua.560480103	journal	October 1993
Semidirect algorithms for third-order electron propagator calculations Zakrzewski, V. G.; Ortiz, J. V. International Journal of Quantum Chemistry, Vol. 53, Issue 6 https://doi.org/10.1002/qua.560530602	journal	March 1995
Electron propagator theory: an approach to prediction and interpretation in quantum chemistry: Electron propagator theory Ortiz, Joseph Vincent Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 3, Issue 2 https://doi.org/10.1002/wcms.1116	journal	September 2012
Propagator Methods Burke, Philip G. R-Matrix Theory of Atomic Collisions https://doi.org/10.1007/978-3-642-15931-2_17	book	November 2010
Degenerate Perturbation Theory Brandow, Baird New Horizons of Quantum Chemistry https://doi.org/10.1007/978-94-009-7950-5_4	book	January 1983
An alternative method of quantization: the existence of classical fields Crawford, J. A. Il Nuovo Cimento, Vol. 10, Issue 4 https://doi.org/10.1007/bf02859806	journal	November 1958
Thermodynamic limit and size-consistent design Hirata, So Theoretical Chemistry Accounts, Vol. 129, Issue 6 https://doi.org/10.1007/s00214-011-0954-4	journal	June 2011
Improved decoupling procedure for green functions Linderberg, Jan; Öhrn, Yngve Chemical Physics Letters, Vol. 1, Issue 7 https://doi.org/10.1016/0009-2614(67)80025-3	journal	September 1967
Moment-conserving decoupling of green functions via pade approximants Goscinski, O.; Lukman, B. Chemical Physics Letters, Vol. 7, Issue 6 https://doi.org/10.1016/0009-2614(70)87007-5	journal	December 1970
On the breakdown of the Koopmans' theorem for nitrogen Cedérbaum, L. S.; Hohlneicher, G.; von Niessen, W. Chemical Physics Letters, Vol. 18, Issue 4 https://doi.org/10.1016/0009-2614(73)80451-8	journal	February 1973
A comment on a theory of electron affinities Purvis, George D.; Öhrn, Ynge Chemical Physics Letters, Vol. 33, Issue 2 https://doi.org/10.1016/0009-2614(75)80187-4	journal	June 1975
A method for molecular ionization potentials Baker, J.; Pickup, B. T. Chemical Physics Letters, Vol. 76, Issue 3 https://doi.org/10.1016/0009-2614(80)80663-4	journal	December 1980
A new determinant-based full configuration interaction method Knowles, P. J.; Handy, N. C. Chemical Physics Letters, Vol. 111, Issue 4-5 https://doi.org/10.1016/0009-2614(84)85513-x	journal	November 1984
Is fifth-order MBPT enough? Laidig, William D.; Fitzgerald, George; Bartlett, Rodney J. Chemical Physics Letters, Vol. 113, Issue 2 https://doi.org/10.1016/0009-2614(85)80934-9	journal	January 1985
The calculation of higher-order energies in the many-body perturbation theory series Knowles, P. J.; Somasundram, K.; Handy, N. C. Chemical Physics Letters, Vol. 113, Issue 1 https://doi.org/10.1016/0009-2614(85)85002-8	journal	January 1985
Slow convergence of the møller-plesset perturbation series: the dissociation energy of hydrogen cyanide and the electron affinity of the cyano radical Nobes, Ross H.; Pople, John A.; Radom, Leo Chemical Physics Letters, Vol. 138, Issue 5 https://doi.org/10.1016/0009-2614(87)80545-6	journal	July 1987
Many-body basis for the optical model Frantz, Lee M.; Mills, Robert L. Nuclear Physics, Vol. 15 https://doi.org/10.1016/0029-5582(60)90278-9	journal	February 1960
Computational methods for the one-particle green's function von Niessen, W.; Schirmer, J.; Cederbaum, L. S. Computer Physics Reports, Vol. 1, Issue 2 https://doi.org/10.1016/0167-7977(84)90002-9	journal	April 1984
Relationship between one-electron green's function and quantum chemical theories Tsui, Francis S. M.; Freed, Karl F. Chemical Physics, Vol. 5, Issue 3 https://doi.org/10.1016/0301-0104(74)85037-8	journal	September 1974
Analysis of third order contributions to equations of motion—green's function ionization potentials: Application to N2 Herman, Michael F.; Yeager, Danny L.; Freed, Karl F. Chemical Physics, Vol. 29, Issue 1-2 https://doi.org/10.1016/0301-0104(78)85063-0	journal	March 1978
Theoretical Studies of Negative Molecular Ions Simons, Jack Theoretical Chemistry Volume 3 https://doi.org/10.1016/b978-0-12-681903-8.50007-2	book	January 1978
Towards an exact correlated orbital theory for electrons Bartlett, Rodney J. Chemical Physics Letters, Vol. 484, Issue 1-3 https://doi.org/10.1016/j.cplett.2009.10.053	journal	December 2009
High-order coupled-cluster calculations through connected octuple excitations Hirata, So; Bartlett, Rodney J. Chemical Physics Letters, Vol. 321, Issue 3-4 https://doi.org/10.1016/s0009-2614(00)00387-0	journal	April 2000
High-order determinantal equation-of-motion coupled-cluster calculations for electronic excited states Hirata, So; Nooijen, Marcel; Bartlett, Rodney J. Chemical Physics Letters, Vol. 326, Issue 3-4 https://doi.org/10.1016/s0009-2614(00)00772-7	journal	August 2000
High-order determinantal equation-of-motion coupled-cluster calculations for ionized and electron-attached states Hirata, So; Nooijen, Marcel; Bartlett, Rodney J. Chemical Physics Letters, Vol. 328, Issue 4-6 https://doi.org/10.1016/s0009-2614(00)00965-9	journal	October 2000
Perturbation theory of large quantum systems Hugenholtz, N. M. Physica, Vol. 23, Issue 1-5 https://doi.org/10.1016/s0031-8914(57)92950-6	journal	January 1957
Time-Independent Diagrammatic Approach to Perturbation Theory of Fermion Systems Paldus, J.; čížek, J. Advances in Quantum Chemistry Volume 9 https://doi.org/10.1016/s0065-3276(08)60040-4	book	January 1975
Molecular Electron Propagator Theory and Calculations Öhrn, Y.; Born, G. Advances in Quantum Chemistry https://doi.org/10.1016/s0065-3276(08)60291-9	book	January 1981
Toward an Exact One–Electron Picture of Chemical Bonding Ortiz, J. V. Advances in Quantum Chemistry https://doi.org/10.1016/s0065-3276(08)60454-2	book	January 1999
The Configuration Interaction Method: Advances in Highly Correlated Approaches David Sherrill, C.; Schaefer, III, Henry F. Advances in Quantum Chemistry https://doi.org/10.1016/s0065-3276(08)60532-8	book	January 1999
Many – Body Methods in Chemistry and Physics Shavitt, Isaiah; Bartlett, Rodney J. https://doi.org/10.1017/CBO9780511596834	book	January 2009
General-Order Many-Body Green’s Function Method Hirata, So; Hermes, Matthew R.; Simons, Jack Journal of Chemical Theory and Computation, Vol. 11, Issue 4 https://doi.org/10.1021/acs.jctc.5b00005	journal	March 2015
The GW -Method for Quantum Chemistry Applications: Theory and Implementation van Setten, M. J.; Weigend, F.; Evers, F. Journal of Chemical Theory and Computation, Vol. 9, Issue 1 https://doi.org/10.1021/ct300648t	journal	December 2012
Symbolic Algebra Development for Higher-Order Electron Propagator Formulation and Implementation Tamayo-Mendoza, Teresa; Flores-Moreno, Roberto Journal of Chemical Theory and Computation, Vol. 10, Issue 6 https://doi.org/10.1021/ct500204v	journal	May 2014
Tensor Contraction Engine: Abstraction and Automated Parallel Implementation of Configuration-Interaction, Coupled-Cluster, and Many-Body Perturbation Theories Hirata, So The Journal of Physical Chemistry A, Vol. 107, Issue 46 https://doi.org/10.1021/jp034596z	journal	November 2003
The initial implementation and applications of a general active space coupled cluster method Olsen, Jeppe The Journal of Chemical Physics, Vol. 113, Issue 17 https://doi.org/10.1063/1.1290005	journal	November 2000
Can optimized effective potentials be determined uniquely? Hirata, So; Ivanov, Stanislav; Grabowski, Ireneusz The Journal of Chemical Physics, Vol. 115, Issue 4 https://doi.org/10.1063/1.1381013	journal	July 2001
Ab initio density functional theory: OEP-MBPT(2). A new orbital-dependent correlation functional Grabowski, Ireneusz; Hirata, So; Ivanov, Stanislav The Journal of Chemical Physics, Vol. 116, Issue 11 https://doi.org/10.1063/1.1445117	journal	March 2002
Formulation and implementation of the full coupled-cluster method through pentuple excitations Musiał, M.; Kucharski, S. A.; Bartlett, R. J. The Journal of Chemical Physics, Vol. 116, Issue 11 https://doi.org/10.1063/1.1445744	journal	March 2002
Many‐Body Green's Functions for Finite, Nonuniform Systems: Applications to Closed Shell Atoms Doll, Jimmie D.; Reinhardt, William P. The Journal of Chemical Physics, Vol. 57, Issue 3 https://doi.org/10.1063/1.1678374	journal	August 1972
Theory of electron affinities of small molecules Simons, Jack; Smith, Wesley D. The Journal of Chemical Physics, Vol. 58, Issue 11 https://doi.org/10.1063/1.1679074	journal	June 1973
Degenerate RS perturbation theory Hirschfelder, Joseph O.; Certain, Phillip R. The Journal of Chemical Physics, Vol. 60, Issue 3 https://doi.org/10.1063/1.1681123	journal	February 1974
Perturbation corrections to Koopmans' theorem. I. Double‐zeta Slater‐type‐orbital basis Chong, Delano P.; Herring, F. Geoffrey; McWilliams, Denis The Journal of Chemical Physics, Vol. 61, Issue 1 https://doi.org/10.1063/1.1681673	journal	July 1974
Degenerate perturbation theory Klein, D. J. The Journal of Chemical Physics, Vol. 61, Issue 3 https://doi.org/10.1063/1.1682018	journal	August 1974
Perturbation corrections to Koopmans' theorem. II. A study of basis set variation Chong, Delano P.; Herring, F. Geoffrey; McWilliams, Denis The Journal of Chemical Physics, Vol. 61, Issue 3 https://doi.org/10.1063/1.1682042	journal	August 1974
Perturbation corrections to Koopmans' theorem. III. Extension to molecules containing Si, P, S, and Cl and comparison with other methods Chong, Delano P.; Herring, F. Geoffrey; McWilliams, Denis The Journal of Chemical Physics, Vol. 61, Issue 9 https://doi.org/10.1063/1.1682536	journal	November 1974
Independent particle theory with electron correlation Beste, Ariana; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 120, Issue 18 https://doi.org/10.1063/1.1691402	journal	May 2004
Ab initio density functional theory: The best of both worlds? Bartlett, Rodney J.; Lotrich, Victor F.; Schweigert, Igor V. The Journal of Chemical Physics, Vol. 123, Issue 6 https://doi.org/10.1063/1.1904585	journal	August 2005
Correlated one-particle method: Numerical results Beste, Ariana; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 123, Issue 15 https://doi.org/10.1063/1.2039082	journal	October 2005
Higher-order equation-of-motion coupled-cluster methods for ionization processes Kamiya, Muneaki; Hirata, So The Journal of Chemical Physics, Vol. 125, Issue 7 https://doi.org/10.1063/1.2244570	journal	August 2006
Higher-order equation-of-motion coupled-cluster methods for electron attachment Kamiya, Muneaki; Hirata, So The Journal of Chemical Physics, Vol. 126, Issue 13 https://doi.org/10.1063/1.2715575	journal	April 2007
Higher‐order decoupling of the electron propagator Redmon, Lynn Tyner; Purvis, George; Öhrn, Yngve The Journal of Chemical Physics, Vol. 63, Issue 11 https://doi.org/10.1063/1.431200	journal	December 1975
A complete treatment of the electron propagator through third order Jo/rgensen, Poul; Simons, Jack The Journal of Chemical Physics, Vol. 63, Issue 12 https://doi.org/10.1063/1.431332	journal	December 1975
Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces Olsen, Jeppe; Roos, Björn O.; Jo/rgensen, Poul The Journal of Chemical Physics, Vol. 89, Issue 4 https://doi.org/10.1063/1.455063	journal	August 1988
Electron binding energies of anionic alkali metal atoms from partial fourth order electron propagator theory calculations Ortiz, J. V. The Journal of Chemical Physics, Vol. 89, Issue 10 https://doi.org/10.1063/1.455401	journal	November 1988
Electron binding energies of anionic alkali metal triatomics from partial fourth order electron propagator theory calculations Ortiz, J. V. The Journal of Chemical Physics, Vol. 89, Issue 10 https://doi.org/10.1063/1.455402	journal	November 1988
Time‐independent theory of one‐particle Green’s functions Kutzelnigg, Werner; Mukherjee, Debashis The Journal of Chemical Physics, Vol. 90, Issue 10 https://doi.org/10.1063/1.456411	journal	May 1989
On Green’s function calculations of the static self‐energy part, the ground state energy and expectation values Schirmer, J.; Angonoa, G. The Journal of Chemical Physics, Vol. 91, Issue 3 https://doi.org/10.1063/1.457081	journal	August 1989
Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method Stanton, John F.; Gauss, Jürgen The Journal of Chemical Physics, Vol. 101, Issue 10 https://doi.org/10.1063/1.468022	journal	November 1994
Equation of motion coupled cluster method for electron attachment Nooijen, Marcel; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 102, Issue 9 https://doi.org/10.1063/1.468592	journal	March 1995
Description of core‐excitation spectra by the open‐shell electron‐attachment equation‐of‐motion coupled cluster method Nooijen, Marcel; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 102, Issue 17 https://doi.org/10.1063/1.469147	journal	May 1995
Perspective on density functional theory Burke, Kieron The Journal of Chemical Physics, Vol. 136, Issue 15 https://doi.org/10.1063/1.4704546	journal	April 2012
Partial third‐order quasiparticle theory: Comparisons for closed‐shell ionization energies and an application to the Borazine photoelectron spectrum Ortiz, J. V. The Journal of Chemical Physics, Vol. 104, Issue 19 https://doi.org/10.1063/1.471468	journal	May 1996
A test of partial third order electron propagator theory: Vertical ionization energies of azabenzenes Ortiz, J. V.; Zakrzewski, V. G. The Journal of Chemical Physics, Vol. 105, Issue 7 https://doi.org/10.1063/1.472138	journal	August 1996
Surprising cases of divergent behavior in Mo/ller–Plesset perturbation theory Olsen, Jeppe; Christiansen, Ove; Koch, Henrik The Journal of Chemical Physics, Vol. 105, Issue 12 https://doi.org/10.1063/1.472352	journal	September 1996
A generalized many-body expansion and a unified view of fragment-based methods in electronic structure theory Richard, Ryan M.; Herbert, John M. The Journal of Chemical Physics, Vol. 137, Issue 6 https://doi.org/10.1063/1.4742816	journal	August 2012
A nondiagonal, renormalized extension of partial third-order quasiparticle theory: Comparisons for closed-shell ionization energies Ortiz, J. V. The Journal of Chemical Physics, Vol. 108, Issue 3 https://doi.org/10.1063/1.475463	journal	January 1998
Direct ΔMBPT(2) method for ionization potentials, electron affinities, and excitation energies using fractional occupation numbers Beste, Ariana; Vázquez-Mayagoitia, Álvaro; Ortiz, J. V. The Journal of Chemical Physics, Vol. 138, Issue 7 https://doi.org/10.1063/1.4790626	journal	February 2013
A simple scheme for the direct calculation of ionization potentials with coupled-cluster theory that exploits established excitation energy methods Stanton, John F.; Gauss, Jürgen The Journal of Chemical Physics, Vol. 111, Issue 19 https://doi.org/10.1063/1.479673	journal	November 1999
Extension of many-body theory and approximate density functionals to fractional charges and fractional spins Yang, Weitao; Mori-Sánchez, Paula; Cohen, Aron J. The Journal of Chemical Physics, Vol. 139, Issue 10 https://doi.org/10.1063/1.4817183	journal	September 2013
Computing coupled-cluster wave functions with arbitrary excitations Kállay, Mihály; Surján, Péter R. The Journal of Chemical Physics, Vol. 113, Issue 4 https://doi.org/10.1063/1.481925	journal	July 2000
Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory Phillips, Jordan J.; Zgid, Dominika The Journal of Chemical Physics, Vol. 140, Issue 24 https://doi.org/10.1063/1.4884951	journal	June 2014
Coupled-cluster representation of Green function employing modified spectral resolutions of similarity transformed Hamiltonians Kowalski, K.; Bhaskaran-Nair, K.; Shelton, W. A. The Journal of Chemical Physics, Vol. 141, Issue 9 https://doi.org/10.1063/1.4893527	journal	September 2014
Self-consistent second-order Green’s function perturbation theory for periodic systems Rusakov, Alexander A.; Zgid, Dominika The Journal of Chemical Physics, Vol. 144, Issue 5 https://doi.org/10.1063/1.4940900	journal	February 2016
Coupled cluster Green function: Model involving single and double excitations Bhaskaran-Nair, Kiran; Kowalski, Karol; Shelton, William A. The Journal of Chemical Physics, Vol. 144, Issue 14 https://doi.org/10.1063/1.4944960	journal	April 2016
On the Green's functions of quantized fields. I Schwinger, J. Proceedings of the National Academy of Sciences, Vol. 37, Issue 7 https://doi.org/10.1073/pnas.37.7.452	journal	July 1951
Propagators and their implications Öhrn, Yngve; Linderberg, Jan Molecular Physics, Vol. 108, Issue 21-23 https://doi.org/10.1080/00268976.2010.513342	journal	November 2010
Direct calculation of ionization energies: I. Closed shells† Supported by the Swedish Natural Sciences Research Council. Pickup, B. T.; Goscinski, O. Molecular Physics, Vol. 26, Issue 4 https://doi.org/10.1080/00268977300102261	journal	October 1973
One-body Green's function for atoms and molecules: theory and application Cederbaum, L. S. Journal of Physics B: Atomic and Molecular Physics, Vol. 8, Issue 2 https://doi.org/10.1088/0022-3700/8/2/018	journal	February 1975
The GW method Aryasetiawan, F.; Gunnarsson, O. Reports on Progress in Physics, Vol. 61, Issue 3 https://doi.org/10.1088/0034-4885/61/3/002	journal	March 1998
George Green and physics Dyson, Freeman Physics World, Vol. 6, Issue 8 https://doi.org/10.1088/2058-7058/6/8/28	journal	August 1993
Generation of finite difference formulas on arbitrarily spaced grids Fornberg, Bengt Mathematics of Computation, Vol. 51, Issue 184 https://doi.org/10.1090/s0025-5718-1988-0935077-0	journal	January 1988
Derivation of the Brueckner many-body theory Goldstone, Jeffrey Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 239, Issue 1217, p. 267-279 https://doi.org/10.1098/rspa.1957.0037	journal	February 1957
Improved single-particle propagators in the theory of conjugated systems Linderberg, J.; Öhrn, Y. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 285, Issue 1402, p. 445-456 https://doi.org/10.1098/rspa.1965.0116	journal	May 1965
Many-Body Problem for Strongly Interacting Particles. II. Linked Cluster Expansion Brueckner, K. A. Physical Review, Vol. 100, Issue 1 https://doi.org/10.1103/physrev.100.36	journal	October 1955
Propagators for Alternant Hydrocarbon Molecules Öhrn, Yngve; Linderberg, Jan Physical Review, Vol. 139, Issue 4A https://doi.org/10.1103/physrev.139.a1063	journal	August 1965
Studies in Perturbation Theory. X. Lower Bounds to Energy Eigenvalues in Perturbation-Theory Ground State Löwdin, Per-Olov Physical Review, Vol. 139, Issue 2A https://doi.org/10.1103/physrev.139.a357	journal	July 1965
New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem Hedin, Lars Physical Review, Vol. 139, Issue 3A https://doi.org/10.1103/physrev.139.a796	journal	August 1965
Note on an Approximation Treatment for Many-Electron Systems Møller, Chr.; Plesset, M. S. Physical Review, Vol. 46, Issue 7 https://doi.org/10.1103/physrev.46.618	journal	October 1934
The Radiation Theories of Tomonaga, Schwinger, and Feynman Dyson, F. J. Physical Review, Vol. 75, Issue 3 https://doi.org/10.1103/physrev.75.486	journal	February 1949
Bound States in Quantum Field Theory Gell-Mann, Murray; Low, Francis Physical Review, Vol. 84, Issue 2 https://doi.org/10.1103/physrev.84.350	journal	October 1951
Optimized effective atomic central potential Talman, James D.; Shadwick, William F. Physical Review A, Vol. 14, Issue 1 https://doi.org/10.1103/physreva.14.36	journal	July 1976
Beyond the random-phase approximation: A new approximation scheme for the polarization propagator Schirmer, Jochen Physical Review A, Vol. 26, Issue 5 https://doi.org/10.1103/physreva.26.2395	journal	November 1982
New approach to the one-particle Green's function for finite Fermi systems Schirmer, J.; Cederbaum, L. S.; Walter, O. Physical Review A, Vol. 28, Issue 3 https://doi.org/10.1103/physreva.28.1237	journal	September 1983
Some aspects of self-consistent propagator theories Prasad, M. Durga; Pal, Sourav; Mukherjee, Debashis Physical Review A, Vol. 31, Issue 3 https://doi.org/10.1103/physreva.31.1287	journal	March 1985
Exact Kohn-Sham scheme based on perturbation theory Görling, Andreas; Levy, Mel Physical Review A, Vol. 50, Issue 1 https://doi.org/10.1103/physreva.50.196	journal	July 1994
Exact exchange-correlation kernel for dynamic response properties and excitation energies in density-functional theory Görling, Andreas Physical Review A, Vol. 57, Issue 5 https://doi.org/10.1103/physreva.57.3433	journal	May 1998
Application of Many-Body Green's Functions to the Scattering and Bound-State Properties of Helium Yarlagadda, Bhagat S.; Csanak, György; Taylor, Howard S. Physical Review A, Vol. 7, Issue 1 https://doi.org/10.1103/physreva.7.146	journal	January 1973
Exact-exchange time-dependent density-functional theory with the frequency-dependent kernel Shigeta, Yasuteru; Hirao, Kimihiko; Hirata, So Physical Review A, Vol. 73, Issue 1 https://doi.org/10.1103/physreva.73.010502	journal	January 2006
Coupled-cluster Green's function: Analysis of properties originating in the exponential parametrization of the ground-state wave function Peng, Bo; Kowalski, Karol Physical Review A, Vol. 94, Issue 6 https://doi.org/10.1103/physreva.94.062512	journal	December 2016
Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies Hybertsen, Mark S.; Louie, Steven G. Physical Review B, Vol. 34, Issue 8, p. 5390-5413 https://doi.org/10.1103/physrevb.34.5390	journal	October 1986
Density-Functional Theory of the Energy Gap Sham, L. J.; Schlüter, M. Physical Review Letters, Vol. 51, Issue 20 https://doi.org/10.1103/physrevlett.51.1888	journal	November 1983
Exact Exchange Treatment for Molecules in Finite-Basis-Set Kohn-Sham Theory Ivanov, Stanislav; Hirata, So; Bartlett, Rodney J. Physical Review Letters, Vol. 83, Issue 26 https://doi.org/10.1103/physrevlett.83.5455	journal	December 1999
New KS Method for Molecules Based on an Exchange Charge Density Generating the Exact Local KS Exchange Potential Görling, Andreas Physical Review Letters, Vol. 83, Issue 26 https://doi.org/10.1103/physrevlett.83.5459	journal	December 1999
Space-Time Approach to Non-Relativistic Quantum Mechanics Feynman, R. P. Reviews of Modern Physics, Vol. 20, Issue 2 https://doi.org/10.1103/revmodphys.20.367	journal	April 1948
Electronic excitations: density-functional versus many-body Green’s-function approaches Onida, Giovanni; Reining, Lucia; Rubio, Angel Reviews of Modern Physics, Vol. 74, Issue 2 https://doi.org/10.1103/revmodphys.74.601	journal	June 2002
Coupled-cluster theory in quantum chemistry Bartlett, Rodney J.; Musiał, Monika Reviews of Modern Physics, Vol. 79, Issue 1 https://doi.org/10.1103/revmodphys.79.291	journal	February 2007
Extensivity of Energy and Electronic and Vibrational Structure Methods for Crystals Hirata, So; Keçeli, Murat; Ohnishi, Yu-ya Annual Review of Physical Chemistry, Vol. 63, Issue 1 https://doi.org/10.1146/annurev-physchem-032511-143718	journal	May 2012
Theoretical Studies of Negative Molecular Ions Simons, J. Annual Review of Physical Chemistry, Vol. 28, Issue 1 https://doi.org/10.1146/annurev.pc.28.100177.000311	journal	October 1977
Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules Bartlett, R. J. Annual Review of Physical Chemistry, Vol. 32, Issue 1 https://doi.org/10.1146/annurev.pc.32.100181.002043	journal	October 1981
Propagator Methods Gingrich, Douglas M. Practical Quantum Electrodynamics https://doi.org/10.1201/b15918-12	book	May 2006
Perspective on density functional theory Burke, Kieron arXiv https://doi.org/10.48550/arxiv.1201.3679	text	January 2012

Cited By (8)

What is semiempirical molecular orbital theory approximating? Margraf, Johannes T.; Dral, Pavlo O. Journal of Molecular Modeling, Vol. 25, Issue 5 https://doi.org/10.1007/s00894-019-4005-8	journal	April 2019
Similarity-transformed equation-of-motion vibrational coupled-cluster theory Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So The Journal of Chemical Physics, Vol. 148, Issue 5 https://doi.org/10.1063/1.5004151	journal	February 2018
Green’s function coupled cluster formulations utilizing extended inner excitations Peng, Bo; Kowalski, Karol The Journal of Chemical Physics, Vol. 149, Issue 21 https://doi.org/10.1063/1.5046529	journal	December 2018
Monte Carlo explicitly correlated many-body Green’s function theory Johnson, Cole M.; Doran, Alexander E.; Ten-no, Seiichiro L. The Journal of Chemical Physics, Vol. 149, Issue 17 https://doi.org/10.1063/1.5054610	journal	November 2018
Explicitly correlated renormalized second-order Green’s function for accurate ionization potentials of closed-shell molecules Teke, Nakul K.; Pavošević, Fabijan; Peng, Chong The Journal of Chemical Physics, Vol. 150, Issue 21 https://doi.org/10.1063/1.5090983	journal	June 2019
Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green’s function implementation Banerjee, Samragni; Sokolov, Alexander Yu. The Journal of Chemical Physics, Vol. 151, Issue 22 https://doi.org/10.1063/1.5131771	journal	December 2019
Finite-temperature many-body perturbation theory in the canonical ensemble Jha, Punit K.; Hirata, So Physical Review E, Vol. 101, Issue 2 https://doi.org/10.1103/physreve.101.022106	journal	February 2020
Finite-Temperature Many-Body Perturbation Theory in the Canonical Ensemble Jha, Punit K.; Hirata, So arXiv https://doi.org/10.48550/arxiv.1910.07628	text	January 2019

Similar Records

Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles

Journal Article · Mon Sep 06 20:00:00 EDT 2021 · Journal of Chemical Physics · OSTI ID:1818887

Nonconvergence of the Feynman-Dyson diagrammatic perturbation expansion of propagators

Journal Article · Wed May 15 20:00:00 EDT 2024 · Physical Review A · OSTI ID:2345279

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

Journal Article · Sun Aug 27 20:00:00 EDT 2023 · Journal of Chemical Physics · OSTI ID:1993171

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms

Citation Formats

References (119)

Cited By (8)

Similar Records

Related Subjects