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Title: Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies

Abstract

When vertical energies are excited for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. We demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating themore » utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. Finally, we show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.« less

Authors:
 [1];  [1];  [1]
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  1. Michigan State Univ., East Lansing, MI (United States). Dept. of Chemistry
Publication Date:
Research Org.:
Michigan State Univ., East Lansing, MI (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1287704
Grant/Contract Number:  
FG02-01ER15228
Resource Type:
Accepted Manuscript
Journal Name:
Molecular Physics
Additional Journal Information:
Journal Volume: 113; Journal Issue: 19-20; Journal ID: ISSN 0026-8976
Publisher:
Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; equation-of-motion coupled-cluster methods; completely renormalized approaches; non-iterative triples corrections; electronically excited states; benchmarking quantum chemistry methods

Citation Formats

Piecuch, Piotr, Hansen, Jared A., and Ajala, Adeayo O. Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies. United States: N. p., 2015. Web. doi:10.1080/00268976.2015.1076901.
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Piecuch, Piotr, Hansen, Jared A., & Ajala, Adeayo O. Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies. United States. https://doi.org/10.1080/00268976.2015.1076901
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Piecuch, Piotr, Hansen, Jared A., and Ajala, Adeayo O. Tue . "Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies". United States. https://doi.org/10.1080/00268976.2015.1076901. https://www.osti.gov/servlets/purl/1287704.
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@article{osti_1287704,
title = {Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies},
author = {Piecuch, Piotr and Hansen, Jared A. and Ajala, Adeayo O.},
abstractNote = {When vertical energies are excited for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. We demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. Finally, we show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.},
doi = {10.1080/00268976.2015.1076901},
journal = {Molecular Physics},
number = 19-20,
volume = 113,
place = {United States},
year = {Tue Sep 15 00:00:00 EDT 2015},
month = {Tue Sep 15 00:00:00 EDT 2015}
}
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  • Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 96, Issue 5
  • DOI: 10.1063/1.461878

Introduction of n -electron valence states for multireference perturbation theory
journal, June 2001

  • Angeli, C.; Cimiraglia, R.; Evangelisti, S.
  • The Journal of Chemical Physics, Vol. 114, Issue 23
  • DOI: 10.1063/1.1361246

Second‐order perturbation theory with a complete active space self‐consistent field reference function
journal, January 1992

  • Andersson, Kerstin; Malmqvist, Per‐Åke; Roos, Björn O.
  • The Journal of Chemical Physics, Vol. 96, Issue 2
  • DOI: 10.1063/1.462209

Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3
journal, April 2008

  • Schreiber, Marko; Silva-Junior, Mario R.; Sauer, Stephan P. A.
  • The Journal of Chemical Physics, Vol. 128, Issue 13
  • DOI: 10.1063/1.2889385

Role of Many-Body Effects in Describing Low-Lying Excited States of π-Conjugated Chromophores: High-Level Equation-of-Motion Coupled-Cluster Studies of Fused Porphyrin Systems
journal, June 2011

  • Kowalski, K.; Olson, R. M.; Krishnamoorthy, S.
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 7
  • DOI: 10.1021/ct200217y

Fully optimized contracted Gaussian basis sets for atoms Li to Kr
journal, August 1992

  • Schäfer, Ansgar; Horn, Hans; Ahlrichs, Reinhart
  • The Journal of Chemical Physics, Vol. 97, Issue 4
  • DOI: 10.1063/1.463096

Single-reference, size-extensive, non-iterative coupled-cluster approaches to bond breaking and biradicals
journal, February 2006

Anharmonic vibrational state calculations in the electronic excited states studied by time-dependent density functional theory
journal, February 2007

Multireference perturbation configuration interaction V. Third-order energy contributions in the M�ller?Plesset and Epstein?Nesbet partitions
journal, May 2002

  • Angeli, Celestino; Cimiraglia, Renzo
  • Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 107, Issue 5
  • DOI: 10.1007/s00214-002-0336-z

Second- and third-order triples and quadruples corrections to coupled-cluster singles and doubles in the ground and excited states
journal, June 2007

  • Shiozaki, Toru; Hirao, Kimihiko; Hirata, So
  • The Journal of Chemical Physics, Vol. 126, Issue 24
  • DOI: 10.1063/1.2741262

Experimental and Theoretical UV Characterizations of Acetylacetone and Its Isomers
journal, March 2006

  • Coussan, S.; Ferro, Y.; Trivella, A.
  • The Journal of Physical Chemistry A, Vol. 110, Issue 11
  • DOI: 10.1021/jp056834r

A Joint Photoelectron Spectroscopy and Theoretical Study on the Electronic Structure of UCl 5 − and UCl 5
journal, July 2013

  • Su, Jing; Dau, Phuong Diem; Xu, Chao-Fei
  • Chemistry - An Asian Journal, Vol. 8, Issue 10
  • DOI: 10.1002/asia.201300627

Vibrationally Resolved Decay Width of Interatomic Coulombic Decay in HeNe
journal, December 2013

Performance of the EOMIP-CCSD(2) Method for Determining the Structure and Properties of Doublet Radicals: A Benchmark Investigation
journal, September 2013

  • Dutta, Achintya Kumar; Vaval, Nayana; Pal, Sourav
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 10
  • DOI: 10.1021/ct400316m

In Search of the Relationship between Multiple Solutions Characterizing Coupled-Cluster Theories
book, October 2000

Basis set effects on coupled cluster benchmarks of electronically excited states: CC3, CCSDR(3) and CC2
journal, February 2010

  • Silva-Junior, Mario R.; Sauer, Stephan P. A.; Schreiber, Marko
  • Molecular Physics, Vol. 108, Issue 3-4
  • DOI: 10.1080/00268970903549047

Multireference coupled‐cluster method using a single‐reference formalism
journal, January 1991

  • Oliphant, Nevin; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 94, Issue 2
  • DOI: 10.1063/1.460031

Noniterative Coupled-Cluster Methods for Excited Electronic States
book, January 2006

  • Piecuch, Piotr; Loch, Marta; Lodriguito, Maricris
  • Recent Advances in the Theory of Chemical and Physical Systems
  • DOI: 10.1007/1-4020-4528-X_3

General atomic and molecular electronic structure system
journal, November 1993

  • Schmidt, Michael W.; Baldridge, Kim K.; Boatz, Jerry A.
  • Journal of Computational Chemistry, Vol. 14, Issue 11, p. 1347-1363
  • DOI: 10.1002/jcc.540141112

Benchmarks for Electronically Excited States: A Comparison of Noniterative and Iterative Triples Corrections in Linear Response Coupled Cluster Methods: CCSDR(3) versus CC3
journal, February 2009

  • Sauer, Stephan P. A.; Schreiber, Marko; Silva-Junior, Mario R.
  • Journal of Chemical Theory and Computation, Vol. 5, Issue 3
  • DOI: 10.1021/ct800256j

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

Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian
journal, December 2005

  • Piecuch, Piotr; Włoch, Marta
  • The Journal of Chemical Physics, Vol. 123, Issue 22
  • DOI: 10.1063/1.2137318

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

Hybrid coupled cluster and molecular dynamics approach: Application to the excitation spectrum of cytosine in the native DNA environment
journal, December 2006

  • Valiev, Marat; Kowalski, Karol
  • The Journal of Chemical Physics, Vol. 125, Issue 21
  • DOI: 10.1063/1.2403847

Computing coupled-cluster wave functions with arbitrary excitations
journal, July 2000

  • Kállay, Mihály; Surján, Péter R.
  • The Journal of Chemical Physics, Vol. 113, Issue 4
  • DOI: 10.1063/1.481925

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

A generalization of the state-specific complete-active-space coupled-cluster method for calculating electronic excited states
journal, February 2008

  • Lyakh, Dmitry I.; Ivanov, Vladimir V.; Adamowicz, Ludwik
  • The Journal of Chemical Physics, Vol. 128, Issue 7
  • DOI: 10.1063/1.2828548

Benchmarks of electronically excited states: Basis set effects on CASPT2 results
journal, November 2010

  • Silva-Junior, Mario R.; Schreiber, Marko; Sauer, Stephan P. A.
  • The Journal of Chemical Physics, Vol. 133, Issue 17
  • DOI: 10.1063/1.3499598

Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds
journal, June 1991

  • Curtiss, Larry A.; Raghavachari, Krishnan; Trucks, Gary W.
  • The Journal of Chemical Physics, Vol. 94, Issue 11
  • DOI: 10.1063/1.460205

The equation-of-motion coupled-cluster method. Applications to open- and closed-shell reference states
journal, May 1993

Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation
journal, January 1997

  • Curtiss, Larry A.; Raghavachari, Krishnan; Redfern, Paul C.
  • The Journal of Chemical Physics, Vol. 106, Issue 3
  • DOI: 10.1063/1.473182

Multimode Molecular Dynamics Beyond the Born-Oppenheimer Approximation
book, January 2007

Electronic structure of the S 1 state in methylcobalamin: Insight from CASSCF/MC-XQDPT2, EOM-CCSD, and TD-DFT calculations
journal, January 2013

  • Kornobis, Karina; Kumar, Neeraj; Lodowski, Piotr
  • Journal of Computational Chemistry, Vol. 34, Issue 12
  • DOI: 10.1002/jcc.23204

Coupled-cluster methods with internal and semi-internal triply excited clusters: Vibrational spectrum of the HF molecule
journal, October 1999

  • Piecuch, Piotr; Kucharski, Stanisław A.; Špirko, Vladimir
  • The Journal of Chemical Physics, Vol. 111, Issue 15
  • DOI: 10.1063/1.479968

Second-order perturbation theory with a CASSCF reference function
journal, July 1990

  • Andersson, Kerstin.; Malmqvist, Per Aake.; Roos, Bjoern O.
  • The Journal of Physical Chemistry, Vol. 94, Issue 14
  • DOI: 10.1021/j100377a012

Efficient computer implementation of the renormalized coupled-cluster methods: The R-CCSD[T], R-CCSD(T), CR-CCSD[T], and CR-CCSD(T) approaches
journal, December 2002

  • Piecuch, Piotr; Kucharski, Stanisław A.; Kowalski, Karol
  • Computer Physics Communications, Vol. 149, Issue 2
  • DOI: 10.1016/S0010-4655(02)00598-2

Coupled-cluster dynamic polarizabilities including triple excitations
journal, June 2008

  • Hammond, Jeff R.; de Jong, Wibe A.; Kowalski, Karol
  • The Journal of Chemical Physics, Vol. 128, Issue 22
  • DOI: 10.1063/1.2929840

Excited-State Studies of Polyacenes: A Comparative Picture Using EOMCCSD, CR-EOMCCSD(T), Range-Separated (LR/RT)-TDDFT, TD-PM3, and TD-ZINDO
journal, October 2011

  • Lopata, K.; Reslan, R.; Kowalska, M.
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 11
  • DOI: 10.1021/ct2005165

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

Coupled-cluster methods with internal and semi-internal triply and quadruply excited clusters: CCSDt and CCSDtq approaches
journal, April 1999

  • Piecuch, Piotr; Kucharski, Stanisław A.; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 110, Issue 13
  • DOI: 10.1063/1.478517

Optimizing Conical Intersections without Derivative Coupling Vectors:  Application to Multistate Multireference Second-Order Perturbation Theory (MS-CASPT2) †
journal, January 2008

  • Levine, Benjamin G.; Coe, Joshua D.; Martínez, Todd J.
  • The Journal of Physical Chemistry B, Vol. 112, Issue 2
  • DOI: 10.1021/jp0761618

Similarity transformed equation of motion coupled cluster theory revisited: a benchmark study of valence excited states
journal, October 2013

Theoretical Studies on the Photoelectron and Absorption Spectra of MnO 4 – and TcO 4 –
journal, August 2013

  • Su, Jing; Xu, Wen-Hua; Xu, Chao-Fei
  • Inorganic Chemistry, Vol. 52, Issue 17
  • DOI: 10.1021/ic4009625

Excitons in potassium bromide: A study using embedded time-dependent density functional theory and equation-of-motion coupled cluster methods
journal, March 2009

Active-space completely-renormalized equation-of-motion coupled-cluster formalism: Excited-state studies of green fluorescent protein, free-base porphyrin, and oligoporphyrin dimer
journal, April 2010

  • Kowalski, Karol; Krishnamoorthy, Sriram; Villa, Oreste
  • The Journal of Chemical Physics, Vol. 132, Issue 15
  • DOI: 10.1063/1.3385315

N-electron valence state perturbation theory: a fast implementation of the strongly contracted variant
journal, December 2001

Some aspects of the time-dependent coupled-cluster approach to dynamic response functions
journal, September 1983

Excitation energies of BH, CH2 and Ne in full configuration interaction and the hierarchy CCS, CC2, CCSD and CC3 of coupled cluster models
journal, September 1995

Advances in electronic structure theory
book, January 2005

Vibrationally Resolved Decay Width of Interatomic Coulombic Decay in HeNe
text, January 2013

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