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Title: Green’s function coupled cluster formulations utilizing extended inner excitations

Abstract

Here, we analyze new approximations of the Green’s function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i(n, m) method, where the excitation level of the inner auxiliary operators (m) used to describe the ionization potential and electron affinity effects in the N-1 and N+1 particle spaces is higher than the excitation level (n) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called “n + 1” rule in this category [or the GFCC-i(n, n + 1) method], which states that in order to maintain size-extensivity of the Green’s function matrix elements, the excitation level of inner auxiliary operators Xp(ω) and Yq(ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N2 and CO molecules in the inner and outermore » valence regimes. Lastly, in comparison with the Green’s function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.« less

Authors:
 [1];  [1]
  1. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Chemical Sciences, Geosciences & Biosciences Division; USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)
OSTI Identifier:
1489236
Report Number(s):
PNNL-SA-136088
Journal ID: ISSN 0021-9606
Grant/Contract Number:  
AC05-76RL01830
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 149; Journal Issue: 21; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ab initio; coupled cluster calculations; Coupled cluster Green function

Citation Formats

Peng, Bo, and Kowalski, Karol. Green’s function coupled cluster formulations utilizing extended inner excitations. United States: N. p., 2018. Web. doi:10.1063/1.5046529.
Peng, Bo, & Kowalski, Karol. Green’s function coupled cluster formulations utilizing extended inner excitations. United States. doi:10.1063/1.5046529.
Peng, Bo, and Kowalski, Karol. Wed . "Green’s function coupled cluster formulations utilizing extended inner excitations". United States. doi:10.1063/1.5046529. https://www.osti.gov/servlets/purl/1489236.
@article{osti_1489236,
title = {Green’s function coupled cluster formulations utilizing extended inner excitations},
author = {Peng, Bo and Kowalski, Karol},
abstractNote = {Here, we analyze new approximations of the Green’s function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i(n, m) method, where the excitation level of the inner auxiliary operators (m) used to describe the ionization potential and electron affinity effects in the N-1 and N+1 particle spaces is higher than the excitation level (n) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called “n + 1” rule in this category [or the GFCC-i(n, n + 1) method], which states that in order to maintain size-extensivity of the Green’s function matrix elements, the excitation level of inner auxiliary operators Xp(ω) and Yq(ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N2 and CO molecules in the inner and outer valence regimes. Lastly, in comparison with the Green’s function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.},
doi = {10.1063/1.5046529},
journal = {Journal of Chemical Physics},
number = 21,
volume = 149,
place = {United States},
year = {2018},
month = {12}
}

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Works referenced in this record:

Calculating X-ray Absorption Spectra of Open-Shell Molecules with the Unrestricted Algebraic-Diagrammatic Construction Scheme for the Polarization Propagator
journal, September 2014

  • Wenzel, Jan; Wormit, Michael; Dreuw, Andreas
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 10
  • DOI: 10.1021/ct5006888

Coupled cluster response functions
journal, September 1990

  • Koch, Henrik; Jo/rgensen, Poul
  • The Journal of Chemical Physics, Vol. 93, Issue 5
  • DOI: 10.1063/1.458814

Perturbative triples correction for the equation-of-motion coupled-cluster wave functions with single and double substitutions for ionized states: Theory, implementation, and examples
journal, September 2009

  • Manohar, Prashant U.; Stanton, John F.; Krylov, Anna I.
  • The Journal of Chemical Physics, Vol. 131, Issue 11
  • DOI: 10.1063/1.3231133

Many-Body Effects in Valence and Core Photoionization of Molecules
journal, January 1980


Method of moments approach and coupled cluster theory
journal, January 1991

  • Jankowski, Karol; Paldus, Josef; Piecuch, Piotr
  • Theoretica Chimica Acta, Vol. 80, Issue 4-5
  • DOI: 10.1007/bf01117411

Simulating X-ray Spectroscopies and Calculating Core-Excited States of Molecules
journal, April 2018


Second order many‐body perturbation approximations to the coupled cluster Green’s function
journal, January 1995

  • Nooijen, Marcel; Snijders, Jaap G.
  • The Journal of Chemical Physics, Vol. 102, Issue 4
  • DOI: 10.1063/1.468900

Origin of satellite structure in the valence x-ray photoelectron spectrum of CO: A theoretical study
journal, April 1977


Complete breakdown of the quasiparticle picture for inner valence electrons
journal, October 1977

  • Cederbaum, L. S.; Schirmer, J.; Domcke, W.
  • Journal of Physics B: Atomic and Molecular Physics, Vol. 10, Issue 15
  • DOI: 10.1088/0022-3700/10/15/001

Coupled-cluster representation of Green function employing modified spectral resolutions of similarity transformed Hamiltonians
journal, September 2014

  • Kowalski, K.; Bhaskaran-Nair, K.; Shelton, W. A.
  • The Journal of Chemical Physics, Vol. 141, Issue 9
  • DOI: 10.1063/1.4893527

Green’s Function Coupled-Cluster Approach: Simulating Photoelectron Spectra for Realistic Molecular Systems
journal, June 2018


One-body Green's function for atoms and molecules: theory and application
journal, February 1975


Application of an equation-of-motion coupled cluster method including higher-order corrections to potential energy surfaces of radicals
journal, November 1999

  • Saeh, Jamal C.; Stanton, John F.
  • The Journal of Chemical Physics, Vol. 111, Issue 18
  • DOI: 10.1063/1.480171

Core-level electronic spectra in ADC(2) approximation for polarization propagator: Carbon monoxide and nitrogen molecules
journal, May 2000

  • Trofimov, A. B.; Moskovskaya, T. É.; Gromov, E. V.
  • Journal of Structural Chemistry, Vol. 41, Issue 3
  • DOI: 10.1007/bf02742009

What happens when several closely lying electronic states interact through nuclear motion?
journal, March 1982


Inner-shell photoionisation in molecules: the nitrogen case
journal, October 1980

  • Krummacher, S.; Schmidt, V.; Wuilleumier, F.
  • Journal of Physics B: Atomic and Molecular Physics, Vol. 13, Issue 20
  • DOI: 10.1088/0022-3700/13/20/013

Spin-conserving and spin-flipping equation-of-motion coupled-cluster method with triple excitations
journal, August 2005

  • Slipchenko, Lyudmila V.; Krylov, Anna I.
  • The Journal of Chemical Physics, Vol. 123, Issue 8
  • DOI: 10.1063/1.2006091

Inner-shell photoionisation in molecules: the carbon monoxide case
journal, May 1983

  • Krummacher, S.; Schmidt, V.; Wuilleumier, F.
  • Journal of Physics B: Atomic and Molecular Physics, Vol. 16, Issue 10
  • DOI: 10.1088/0022-3700/16/10/010

Theoretical K ‐shell ionization spectra of N 2 and CO by a fourth‐order Green’s function method
journal, December 1987

  • Angonoa, G.; Walter, O.; Schirmer, J.
  • The Journal of Chemical Physics, Vol. 87, Issue 12
  • DOI: 10.1063/1.453424

One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms
journal, July 2017

  • Hirata, So; Doran, Alexander E.; Knowles, Peter J.
  • The Journal of Chemical Physics, Vol. 147, Issue 4
  • DOI: 10.1063/1.4994837

A new approach to approximate equation-of-motion coupled cluster with triple excitations
journal, September 2016

  • Matthews, Devin A.; Stanton, John F.
  • The Journal of Chemical Physics, Vol. 145, Issue 12
  • DOI: 10.1063/1.4962910

Molecular ionization energies and ground- and ionic-state properties using a non-Dyson electron propagator approach
journal, October 2005

  • Trofimov, A. B.; Schirmer, J.
  • The Journal of Chemical Physics, Vol. 123, Issue 14
  • DOI: 10.1063/1.2047550

Review of biorthogonal coupled cluster representations for electronic excitation
journal, July 2009


Many-body theory of core holes
journal, July 1980


The algebraic diagrammatic construction scheme for the polarization propagator for the calculation of excited states
journal, September 2014

  • Dreuw, Andreas; Wormit, Michael
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 5, Issue 1
  • DOI: 10.1002/wcms.1206

Coupled cluster Green function: Model involving single and double excitations
journal, April 2016

  • Bhaskaran-Nair, Kiran; Kowalski, Karol; Shelton, William A.
  • The Journal of Chemical Physics, Vol. 144, Issue 14
  • DOI: 10.1063/1.4944960

Calculation of properties with the coupled-cluster method
journal, January 1977

  • Monkhorst, Hendrik J.
  • International Journal of Quantum Chemistry, Vol. 12, Issue S11
  • DOI: 10.1002/qua.560120850

A table of absolute core-electron binding-energies for gaseous atoms and molecules
journal, January 1980

  • Bakke, Albert A.; Chen, Hsiang-Wen; Jolly, William L.
  • Journal of Electron Spectroscopy and Related Phenomena, Vol. 20, Issue 3
  • DOI: 10.1016/0368-2048(80)85030-4

Communication: Towards ab initio self-energy embedding theory in quantum chemistry
journal, December 2015

  • Lan, Tran Nguyen; Kananenka, Alexei A.; Zgid, Dominika
  • The Journal of Chemical Physics, Vol. 143, Issue 24
  • DOI: 10.1063/1.4938562

Ab initio electron propagator methods: Applications to nucleic acids fragments and metallophthalocyanines
journal, August 2010

  • Zakrzewski, Viatcheslav G.; Dolgounitcheva, Olga; Zakjevskii, Alexander V.
  • International Journal of Quantum Chemistry, Vol. 110, Issue 15
  • DOI: 10.1002/qua.22836

New algorithms for iterative matrix-free eigensolvers in quantum chemistry
journal, December 2014

  • Zuev, Dmitry; Vecharynski, Eugene; Yang, Chao
  • Journal of Computational Chemistry, Vol. 36, Issue 5
  • DOI: 10.1002/jcc.23800

Green's function approach to the direct perturbation calculation of the excitation energies of closed shell fermion systems
journal, January 1974

  • Paldus, J.; Čížek, J.
  • The Journal of Chemical Physics, Vol. 60, Issue 1
  • DOI: 10.1063/1.1680762

Similarity-transformed equation-of-motion vibrational coupled-cluster theory
journal, February 2018

  • Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So
  • The Journal of Chemical Physics, Vol. 148, Issue 5
  • DOI: 10.1063/1.5004151

Electronic Structure and Spectroscopy of Nucleic Acid Bases: Ionization Energies, Ionization-Induced Structural Changes, and Photoelectron Spectra
journal, November 2010

  • Bravaya, Ksenia B.; Kostko, Oleg; Dolgikh, Stanislav
  • The Journal of Physical Chemistry A, Vol. 114, Issue 46
  • DOI: 10.1021/jp1063726

General-Order Many-Body Green’s Function Method
journal, March 2015

  • Hirata, So; Hermes, Matthew R.; Simons, Jack
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 4
  • DOI: 10.1021/acs.jctc.5b00005

A simple scheme for the direct calculation of ionization potentials with coupled-cluster theory that exploits established excitation energy methods
journal, November 1999

  • Stanton, John F.; Gauss, Jürgen
  • The Journal of Chemical Physics, Vol. 111, Issue 19
  • DOI: 10.1063/1.479673

Interplay of Jahn–Teller and pseudo‐Jahn–Teller vibronic dynamics in the benzene cation
journal, August 1988

  • Köppel, H.; Cederbaum, L. S.; Domcke, W.
  • The Journal of Chemical Physics, Vol. 89, Issue 4
  • DOI: 10.1063/1.455100

Theoretical Fine Spectroscopy with SAC-CI Method: Outer- and Inner-Valence Ionization Spectra of CO and N2
journal, January 2005

  • Ehara, Masahiro; Ishida, Mayumi; Nakatsuji, Hiroshi
  • Collection of Czechoslovak Chemical Communications, Vol. 70, Issue 7
  • DOI: 10.1135/cccc20050881

Towards a full CCSDT model for electron correlation
journal, October 1985

  • Urban, Miroslav; Noga, Jozef; Cole, Samuel J.
  • The Journal of Chemical Physics, Vol. 83, Issue 8
  • DOI: 10.1063/1.449067

Equation-of-motion coupled-cluster methods for ionized states with an approximate treatment of triple excitations
journal, April 2005

  • Bomble, Yannick J.; Saeh, Jamal C.; Stanton, John F.
  • The Journal of Chemical Physics, Vol. 122, Issue 15
  • DOI: 10.1063/1.1884600

Self-consistent second-order Green’s function perturbation theory for periodic systems
journal, February 2016

  • Rusakov, Alexander A.; Zgid, Dominika
  • The Journal of Chemical Physics, Vol. 144, Issue 5
  • DOI: 10.1063/1.4940900

The GW approximation: content, successes and limitations: The GW approximation
journal, December 2017

  • Reining, Lucia
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 3
  • DOI: 10.1002/wcms.1344

Dynamical mean-field theory for correlated electrons
journal, November 2011


Quasiparticle energy spectra of isolated atoms from coupled-cluster singles and doubles (CCSD): Comparison with exact CI calculations
journal, July 2018

  • Nishi, Hirofumi; Kosugi, Taichi; Furukawa, Yoritaka
  • The Journal of Chemical Physics, Vol. 149, Issue 3
  • DOI: 10.1063/1.5029536

Band structures in coupled-cluster singles-and-doubles Green’s function (GFCCSD)
journal, May 2018

  • Furukawa, Yoritaka; Kosugi, Taichi; Nishi, Hirofumi
  • The Journal of Chemical Physics, Vol. 148, Issue 20
  • DOI: 10.1063/1.5029537

Comparison of Green’s functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD)
journal, June 2018

  • Kosugi, Taichi; Nishi, Hirofumi; Furukawa, Yoritaka
  • The Journal of Chemical Physics, Vol. 148, Issue 22
  • DOI: 10.1063/1.5029535

Vertical Ionization Energies of Adenine and 9-Methyl Adenine
journal, December 2009

  • Dolgounitcheva, O.; Zakrzewski, V. G.; Ortiz, J. V.
  • The Journal of Physical Chemistry A, Vol. 113, Issue 52
  • DOI: 10.1021/jp904392z

High-energy photoelectron C 1s and O 1s shake-up spectra of CO
journal, November 1987

  • Schirmer, J.; Angonoa, G.; Svensson, S.
  • Journal of Physics B: Atomic and Molecular Physics, Vol. 20, Issue 22
  • DOI: 10.1088/0022-3700/20/22/015

Inner valence satellite structure in high resolution X-ray excited photoelectron spectra of N 2 and CO
journal, August 1991


NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations
journal, September 2010

  • Valiev, M.; Bylaska, E. J.; Govind, N.
  • Computer Physics Communications, Vol. 181, Issue 9, p. 1477-1489
  • DOI: 10.1016/j.cpc.2010.04.018

Consequences of electron correlation for XPS binding energies: Representative case for C(1s) and O(1s) XPS of CO
journal, October 2016

  • Bagus, Paul S.; Sousa, Carme; Illas, Francesc
  • The Journal of Chemical Physics, Vol. 145, Issue 14
  • DOI: 10.1063/1.4964320

The CC3 model: An iterative coupled cluster approach including connected triples
journal, February 1997

  • Koch, Henrik; Christiansen, Ove; Jo/rgensen, Poul
  • The Journal of Chemical Physics, Vol. 106, Issue 5
  • DOI: 10.1063/1.473322

Dynamical mean-field theory from a quantum chemical perspective
journal, March 2011

  • Zgid, Dominika; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 134, Issue 9
  • DOI: 10.1063/1.3556707

Generalized Self-Energy Embedding Theory
journal, May 2017


Properties of advanced coupled-cluster Green's function
journal, July 2017


Coupled cluster approach to the single-particle Green's function
journal, March 1992

  • Nooijen, Marcel; Snijders, Jaap G.
  • International Journal of Quantum Chemistry, Vol. 44, Issue S26
  • DOI: 10.1002/qua.560440808

The two-particle-hole Tamm-Dancoff approximation (2ph-TDA) equations for closed-shell atoms and molecules
journal, June 1978

  • Schirmer, J.; Cederbaum, L. S.
  • Journal of Physics B: Atomic and Molecular Physics, Vol. 11, Issue 11
  • DOI: 10.1088/0022-3700/11/11/006

The second-order approximate coupled cluster singles and doubles model CC2
journal, September 1995


Energy-Specific Equation-of-Motion Coupled-Cluster Methods for High-Energy Excited States: Application to K -edge X-ray Absorption Spectroscopy
journal, August 2015

  • Peng, Bo; Lestrange, Patrick J.; Goings, Joshua J.
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 9
  • DOI: 10.1021/acs.jctc.5b00459

The method of moments of coupled-cluster equations and the renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approaches
journal, July 2000

  • Kowalski, Karol; Piecuch, Piotr
  • The Journal of Chemical Physics, Vol. 113, Issue 1
  • DOI: 10.1063/1.481769

Higher-order equation-of-motion coupled-cluster methods for ionization processes
journal, August 2006

  • Kamiya, Muneaki; Hirata, So
  • The Journal of Chemical Physics, Vol. 125, Issue 7
  • DOI: 10.1063/1.2244570

On the accuracy of ionization potentials calculated by Green’s functions
journal, January 1999

  • von Niessen, W.
  • The Journal of Chemical Physics, Vol. 67, Issue 9
  • DOI: 10.1063/1.435389

Asymmetric-Lanczos-Chain-Driven Implementation of Electronic Resonance Convergent Coupled-Cluster Linear Response Theory
journal, April 2012

  • Coriani, Sonia; Fransson, Thomas; Christiansen, Ove
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 5
  • DOI: 10.1021/ct200919e

The observation of “forbidden” transitions in He II photoelectron spectra
journal, January 1974


Coupled cluster Green's function method: Working equations and applications
journal, October 1993

  • Nooijen, Marcel; Snijders, Jaap G.
  • International Journal of Quantum Chemistry, Vol. 48, Issue 1
  • DOI: 10.1002/qua.560480103

Computational methods for the one-particle green's function
journal, April 1984


Strong Correlation Effects in inner Valence Ionization of N2 AND CO
journal, November 1977


Electron propagator theory: an approach to prediction and interpretation in quantum chemistry: Electron propagator theory
journal, September 2012

  • Ortiz, Joseph Vincent
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 3, Issue 2
  • DOI: 10.1002/wcms.1116