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Quintero-Monsebaiz R, Monino E, Marie A, Loos PF. Connections between many-body perturbation and coupled-cluster theories. J Chem Phys 2022; 157:231102. [PMID: 36550046 DOI: 10.1063/5.0130837] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
Here, we build on the works of Scuseria et al. [J. Chem. Phys. 129, 231101 (2008)] and Berkelbach [J. Chem. Phys. 149, 041103 (2018)] to show connections between the Bethe-Salpeter equation (BSE) formalism combined with the GW approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the GW and Bethe-Salpeter equations as non-linear CC-like equations. Similitudes between BSE@GW and the similarity-transformed equation-of-motion CC method are also put forward. The present work allows us to easily transfer key developments and the general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the GW and BSE frameworks.
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Affiliation(s)
- Raúl Quintero-Monsebaiz
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Enzo Monino
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Antoine Marie
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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Di Sabatino S, Loos PF, Romaniello P. Scrutinizing GW-Based Methods Using the Hubbard Dimer. Front Chem 2021; 9:751054. [PMID: 34778206 PMCID: PMC8586429 DOI: 10.3389/fchem.2021.751054] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Accepted: 09/28/2021] [Indexed: 12/03/2022] Open
Abstract
Using the simple (symmetric) Hubbard dimer, we analyze some important features of the GW approximation. We show that the problem of the existence of multiple quasiparticle solutions in the (perturbative) one-shot GW method and its partially self-consistent version is solved by full self-consistency. We also analyze the neutral excitation spectrum using the Bethe-Salpeter equation (BSE) formalism within the standard GW approximation and find, in particular, that 1) some neutral excitation energies become complex when the electron-electron interaction U increases, which can be traced back to the approximate nature of the GW quasiparticle energies; 2) the BSE formalism yields accurate correlation energies over a wide range of U when the trace (or plasmon) formula is employed; 3) the trace formula is sensitive to the occurrence of complex excitation energies (especially singlet), while the expression obtained from the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is more stable (yet less accurate); 4) the trace formula has the correct behavior for weak (i.e., small U) interaction, unlike the ACFDT expression.
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Affiliation(s)
- S. Di Sabatino
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS and ETSF, Toulouse, France
| | - P.-F. Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - P. Romaniello
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS and ETSF, Toulouse, France
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Maradzike E, DePrince AE. Modeling core-level excitations with variationally optimized reduced-density matrices and the extended random phase approximation. J Chem Phys 2018; 149:234101. [PMID: 30579305 DOI: 10.1063/1.5048924] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The information contained within ground-state one- and two-electron reduced-density matrices (RDMs) can be used to compute wave functions and energies for electronically excited states through the extended random phase approximation (ERPA). The ERPA is an appealing framework for describing excitations out of states obtained via the variational optimization of the two-electron RDM (2-RDM), as the variational 2-RDM (v2RDM) approach itself can only be used to describe the lowest-energy state of a given spin symmetry. The utility of the ERPA for predicting near-edge features relevant to x-ray absorption spectroscopy is assessed for the case that the 2-RDM is obtained from a ground-state v2RDM-driven complete active space self-consistent field (CASSCF) computation. A class of killer conditions for the CASSCF-specific ERPA excitation operator is derived, and it is demonstrated that a reliable description of core-level excitations requires an excitation operator that fulfills these conditions; the core-valence separation (CVS) scheme yields such an operator. Absolute excitation energies evaluated within the CASSCF/CVS-ERPA framework are slightly more accurate than those obtained from the usual random phase approximation (RPA), but the CVS-ERPA is not more accurate than RPA for predicting the relative positions of near-edge features. Nonetheless, CVS-ERPA is established as a reasonable starting point for the treatment of core-level excitations using variationally optimized 2-RDMs.
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Affiliation(s)
- Elvis Maradzike
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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Peng D, Yang Y, Zhang P, Yang W. Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations. J Chem Phys 2015; 141:214102. [PMID: 25481124 DOI: 10.1063/1.4901716] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N(4)). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as ⟨Ŝ(2)⟩ are also developed and tested.
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Affiliation(s)
- Degao Peng
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Yang Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Peng Zhang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Weitao Yang
- Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708, USA
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Peng D, van Aggelen H, Yang Y, Yang W. Linear-response time-dependent density-functional theory with pairing fields. J Chem Phys 2014; 140:18A522. [DOI: 10.1063/1.4867540] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Peng D, Steinmann SN, van Aggelen H, Yang W. Equivalence of particle-particle random phase approximation correlation energy and ladder-coupled-cluster doubles. J Chem Phys 2014; 139:104112. [PMID: 24050333 DOI: 10.1063/1.4820556] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
The recent proposal to determine the (exact) correlation energy based on pairing matrix fluctuations by van Aggelen et al. ["Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation," preprint arXiv:1306.4957 (2013)] revived the interest in the simplest approximation along this path: the particle-particle random phase approximation (pp-RPA). In this paper, we present an analytical connection and numerical demonstrations of the equivalence of the correlation energy from pp-RPA and ladder-coupled-cluster doubles. These two theories reduce to identical algebraic matrix equations and correlation energy expressions. The numerical examples illustrate that the correlation energy missed by pp-RPA in comparison with coupled-cluster singles and doubles is largely canceled out when considering reaction energies. This theoretical connection will be beneficial to design density functionals with strong ties to coupled-cluster theories and to study molecular properties at the pp-RPA level relying on well established coupled cluster techniques.
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Affiliation(s)
- Degao Peng
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
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Extended random phase approximation method for atomic excitation energies from correlated and variationally optimized second-order density matrices. COMPUT THEOR CHEM 2013. [DOI: 10.1016/j.comptc.2012.09.036] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Cederbaum LS, Domcke W. Theoretical Aspects of Ionization Potentials and Photoelectron Spectroscopy: A Green's Function Approach. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470142554.ch4] [Citation(s) in RCA: 709] [Impact Index Per Article: 41.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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Longo RL. Spin Density Properties from the Electron Propagator: Hyperfine Nuclear Spin-Spin Couplings. ADVANCES IN QUANTUM CHEMISTRY 1999. [DOI: 10.1016/s0065-3276(08)60455-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Catara F, Piccitto G, Sambataro M. Towards a self-consistent random-phase approximation for Fermi systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:17536-17546. [PMID: 9985877 DOI: 10.1103/physrevb.54.17536] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hirsch JG, Hess PO, Civitarese O. Renormalized quasiparticle random phase approximation and double beta decay: A critical analysis of double Fermi transitions. PHYSICAL REVIEW. C, NUCLEAR PHYSICS 1996; 54:1976-1981. [PMID: 9971546 DOI: 10.1103/physrevc.54.1976] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Ito H, Kameshima H, Shibuya T. Equations‐of‐motion method for the spin–orbit coupling of aromatic molecules: Application to the phosphorescence lifetime of benzene. J Chem Phys 1996. [DOI: 10.1063/1.470788] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sambataro M, Catara F. Extended random-phase approximation in a boson formalism with Pauli principle. PHYSICAL REVIEW. C, NUCLEAR PHYSICS 1995; 51:3066-3077. [PMID: 9970407 DOI: 10.1103/physrevc.51.3066] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Zettili N. Small-amplitude limit of the nuclear Born-Oppenheimer method. PHYSICAL REVIEW. C, NUCLEAR PHYSICS 1995; 51:1777-1783. [PMID: 9970247 DOI: 10.1103/physrevc.51.1777] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Lorenzana J, Grynberg MD, Yu L, Yonemitsu K, Bishop AR. Dynamic and static correlation functions in the inhomogeneous-Hartree-Fock-state approach with random-phase-approximation fluctuations. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:13156-13163. [PMID: 10005619 DOI: 10.1103/physrevb.47.13156] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Walet NR, Klein A. Quantum corrections to the potential energy for large amplitude collective motion. PHYSICAL REVIEW. C, NUCLEAR PHYSICS 1992; 45:249-260. [PMID: 9967751 DOI: 10.1103/physrevc.45.249] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Reinhard P, Brack M, Genzken O. Random-phase approximation in a local representation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:5568-5582. [PMID: 9902944 DOI: 10.1103/physreva.41.5568] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Klein A, Une T. Pseudo-Hamiltonian approach to a theory of effective interactions in the particle-hole channel: Phenomenology. PHYSICAL REVIEW. C, NUCLEAR PHYSICS 1988; 38:1886-1896. [PMID: 9955000 DOI: 10.1103/physrevc.38.1886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Tomasello P. Fourth order many‐body Green’s function: Application of a simplified model to the ionization energies of N2. J Chem Phys 1987. [DOI: 10.1063/1.453358] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Faessler A, Krewald S, Plastino A, Speth J. Ground state correlations and electron scattering. ACTA ACUST UNITED AC 1976. [DOI: 10.1007/bf01437702] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Chen TT, Simons J, Jordan K. Analysis of the equation-of-motion theory of electron affinities and ionization potentials. Chem Phys 1976. [DOI: 10.1016/0301-0104(76)80033-x] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Simons J. Energy‐Shift Theory of Low‐Lying Excited Electronic States of Molecules. J Chem Phys 1972. [DOI: 10.1063/1.1678845] [Citation(s) in RCA: 51] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Linderberg J, Jo/rgensen P, Oddershede J, Ratner M. Self‐Consistent Polarization Propagator Approximation as a Modified Random Phase Method. J Chem Phys 1972. [DOI: 10.1063/1.1677174] [Citation(s) in RCA: 60] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Johnson RE, Dreizler RM, Klein A. Methods for Calculating Ground-State Correlations of Vibrational Nuclei. ACTA ACUST UNITED AC 1969. [DOI: 10.1103/physrev.186.1289] [Citation(s) in RCA: 34] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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