skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Journal Article · · Molecular Physics
 [1];  [1];  [1]
  1. Michigan State Univ., East Lansing, MI (United States). Dept. of Chemistry
+ Show Author Affiliations

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.

Research Organization:
Michigan State Univ., East Lansing, MI (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
FG02-01ER15228
OSTI ID:
1287704
Journal Information:
Molecular Physics, Vol. 113, Issue 19-20; ISSN 0026-8976
Publisher:
Taylor & FrancisCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 41 works
Citation information provided by
Web of Science

References (156)

Study of Ion Specific Interactions of Alkali Cations with Dicarboxylate Dianions journal February 2012
New coupled-cluster methods with singles, doubles, and noniterative triples for high accuracy calculations of excited electronic states journal January 2004
Two-dimensional (2+n) resonance enhanced multiphoton ionization of HCl: Photorupture channels via the FΔ21 Rydberg state and ab initio spectra journal October 2008
Left-eigenstate completely renormalized equation-of-motion coupled-cluster methods: Review of key concepts, extension to excited states of open-shell systems, and comparison with electron-attached and ionized approaches journal November 2009
Renormalized CCSD(T) and CCSD(TQ) approaches: Dissociation of the N2 triple bond journal October 2000
The closed‐shell coupled cluster single and double excitation (CCSD) model for the description of electron correlation. A comparison with configuration interaction (CISD) results journal March 1987
Perturbative corrections to coupled-cluster and equation-of-motion coupled-cluster energies: A determinantal analysis journal March 2001
Excitation energies from the coupled cluster singles and doubles linear response function (CCSDLR). Applications to Be, CH + , CO, and H 2 O journal September 1990
Coupled cluster response functions journal September 1990
Communication: Existence of the doubly excited state that mediates the photoionization of azulene journal May 2013
On the Use of the Cluster Expansion and the Technique of Diagrams in Calculations of Correlation Effects in Atoms and Molecules book January 2007
Assessment of n-Electron Valence State Perturbation Theory for Vertical Excitation Energies journal July 2013
A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples journal February 1982
Extension of renormalized coupled-cluster methods including triple excitations to excited electronic states of open-shell molecules journal June 2005
Assessment of the MP2 Method, along with Several Basis Sets, for the Computation of Interaction Energies of Biologically Relevant Hydrogen Bonded and Dispersion Bound Complexes journal August 2007
Two new classes of non-iterative coupled-cluster methods derived from the method of moments of coupled-cluster equations journal July 2006
The active-space equation-of-motion coupled-cluster methods for excited electronic states: Full EOMCCSDt journal July 2001
On the vertical excitation energy of cyclopentadiene journal September 2004
Orthogonally spin-adapted coupled-cluster equations involving singly and doubly excited clusters. Comparison of different procedures for spin-adaptation journal October 1989
Can a Single-Reference Approach Provide a Balanced Description of Ground and Excited States? A Comparison of the Completely Renormalized Equation-of-Motion Coupled-Cluster Method with Multireference Quasidegenerate Perturbation Theory near a Conical Intersection and along a Photodissociation Coordinate in Ammonia journal December 2005
Benchmarking Coupled Cluster Methods on Valence Singlet Excited States journal July 2014
Toward Enabling Large-Scale Open-Shell Equation-of-Motion Coupled Cluster Calculations: Triplet States of β-Carotene journal June 2014
High-order determinantal equation-of-motion coupled-cluster calculations for electronic excited states journal August 2000
A combination of Kohn–Sham density functional theory and multi-reference configuration interaction methods journal October 1999
Active-space coupled-cluster methods journal November 2010
Reliable modeling of the electronic spectra of realistic uranium complexes journal July 2013
Ab initio study of a biradical radiationless decay channel of the lowest excited electronic state of cytosine and its derivatives journal August 2005
The photoisomerization of 11- cis -retinal protonated schiff base in gas phase: Insight from spin-flip density functional theory journal November 2013
Correlation problems in atomic and molecular systems III. Rederivation of the coupled-pair many-electron theory using the traditional quantum chemical methodst journal July 1971
Economical triple excitation equation-of-motion coupled-cluster methods for excitation energies journal February 1995
Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model journal September 1982
Conical intersections and double excitations in time-dependent density functional theory journal March 2006
Time‐dependent coupled cluster approach: Excitation energy calculation using an orthogonally spin‐adapted formalism journal August 1986
Gaussian‐1 theory: A general procedure for prediction of molecular energies journal May 1989
Assessment of Gaussian-3 and density functional theories for a larger experimental test set journal May 2000
Perturbative corrections to the equation-of-motion spin–flip self-consistent field model: Application to bond-breaking and equilibrium properties of diradicals journal February 2002
Comparison of the completely renormalized equation-of-motion coupled-cluster and Quantum Monte Carlo results for the low-lying electronic states of methylene journal October 2010
S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures journal July 2011
Representative Benchmark Suites for Barrier Heights of Diverse Reaction Types and Assessment of Electronic Structure Methods for Thermochemical Kinetics journal December 2006
Progress in Time-Dependent Density-Functional Theory journal May 2012
Asymptotic Extrapolation Scheme for Large-Scale Calculations with Hybrid Coupled Cluster and Molecular Dynamics Simulations journal December 2006
Higher-order equation-of-motion coupled-cluster methods journal January 2004
The XΣg+1, BΔg1, and B′Σg+1 states of C2: A comparison of renormalized coupled-cluster and multireference methods with full configuration interaction benchmarks journal March 2005
Recent advances in electronic structure theory: Method of moments of coupled-cluster equations and renormalized coupled-cluster approaches journal October 2002
Photoelectron spectroscopy and the electronic structure of the uranyl tetrachloride dianion: UO 2 Cl 4 2− journal August 2012
Similarity transformed equation-of-motion coupled-cluster theory: Details, examples, and comparisons journal November 1997
“Mindless” DFT Benchmarking journal March 2009
Active Thermochemical Tables: thermochemistry for the 21st century journal January 2005
The linked singles and doubles model: An approximate theory of electron correlation based on the coupled‐cluster ansatz journal October 1982
Benchmarks for electronically excited states: Time-dependent density functional theory and density functional theory based multireference configuration interaction journal September 2008
Performance of the completely renormalized equation-of-motion coupled-cluster method in calculations of excited-state potential cuts of water journal July 2014
An exploration of electronic structure and nuclear dynamics in tropolone: II. The Ã B12 (π∗π) excited state journal April 2009
The equation-of-motion coupled-cluster method: Excitation energies of Be and CO journal December 1989
A new method for excited states: Similarity transformed equation-of-motion coupled-cluster theory journal April 1997
Coupled cluster calculations on TiO 2 nanoclusters journal August 2013
Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states journal July 2004
Absorption Spectrum of OH Radical in Water journal December 2008
Low valency in lanthanides: A theoretical study of NdF and LuF journal June 2014
Tests of Exchange-Correlation Functional Approximations Against Reliable Experimental Data for Average Bond Energies of 3d Transition Metal Compounds journal August 2013
The active-space equation-of-motion coupled-cluster methods for excited electronic states: The EOMCCSDt approach journal November 2000
Iterative and non-iterative triple excitation corrections in coupled-cluster methods for excited electronic states: the EOM-CCSDT-3 and EOM-CCSD(T̃) methods journal August 1996
Calculation of excited-state properties using general coupled-cluster and configuration-interaction models journal November 2004
n -electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants journal November 2002
State‐selective multireference coupled‐cluster theory employing the single‐reference formalism: Implementation and application to the H 8 model system journal April 1994
Benchmarking for Perturbative Triple-Excitations in EE-EOM-CC Methods journal March 2013
Photoelectron spectroscopy and theoretical studies of gaseous uranium hexachlorides in different oxidation states: UCl6q− (q = 0–2) journal April 2015
EOMCC, MRPT, and TDDFT Studies of Charge Transfer Processes in Mixed-Valence Compounds: Application to the Spiro Molecule † journal August 2010
Response functions in the CC3 iterative triple excitation model journal November 1995
A state‐selective multireference coupled‐cluster theory employing the single‐reference formalism journal August 1993
Extension of the method of moments of coupled-cluster equations to excited states: The triples and quadruples corrections to the equation-of-motion coupled-cluster singles and doubles energies journal May 2002
Correlation Problems in Atomic and Molecular Systems. IV. Extended Coupled-Pair Many-Electron Theory and Its Application to the B H 3 Molecule journal January 1972
Assessment of Gaussian-2 and density functional theories for the computation of ionization potentials and electron affinities journal July 1998
Density-Functional Theory for Time-Dependent Systems journal March 1984
Excited-state potential energy curves of CH+: a comparison of the EOMCCSDt and full EOMCCSDT results journal October 2001
Excitation energies of H2O, N2 and C2 in full configuration interaction and coupled cluster theory journal June 1996
Solvent Induced Shifts in the UV Spectrum of Amides journal May 2013
Singlet-triplet gaps in diradicals by the spin-flip approach: A benchmark study journal September 2002
Calculation of One- and Two-Photon Absorption Spectra of Thiolated Gold Nanoclusters using Time-Dependent Density Functional Theory journal August 2010
On the Origin of the Ultrafast Internal Conversion of Electronically Excited Pyrimidine Bases journal October 2005
Observation and investigation of the uranyl tetrafluoride dianion (UO2F42−) and its solvation complexes with water and acetonitrile journal January 2012
Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules journal March 1972
Large-scale parallel calculations with combined coupled cluster and molecular mechanics formalism: Excitation energies of zinc–porphyrin in aqueous solution journal June 2008
Biradical radiationless decay channel in adenine and its derivatives journal February 2007
Embedding vs Supermolecular Strategies in Evaluating the Hydrogen-Bonding-Induced Shifts of Excitation Energies journal May 2011
Electronic excitation energies of pyrimidine studied using coupled cluster response theory journal January 2001
New type of noniterative energy corrections for excited electronic states: Extension of the method of moments of coupled-cluster equations to the equation-of-motion coupled-cluster formalism journal August 2001
The state-selective coupled cluster method for quasi-degenerate electronic states journal May 1998
Coupled-cluster theory for excited electronic states: The full equation-of-motion coupled-cluster single, double, and triple excitation method journal November 2001
Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method journal November 1994
Size-consistent wave functions for bond-breaking: the equation-of-motion spin-flip model journal April 2001
Stretching of hydrogen-bonded OH in the lowest singlet excited electronic state of water dimer journal January 2006
Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies journal July 1996
Active-space coupled-cluster study of electronic states of Be3 journal August 2005
Extension of the Renormalized Coupled-Cluster Methods Exploiting Left Eigenstates of the Similarity-Transformed Hamiltonian to Open-Shell Systems:  A Benchmark Study † journal November 2007
Reaction pathways and excited states in H2O2+OH→HO2+H2O: A new ab initio investigation journal August 2007
Introduction to Active Thermochemical Tables:  Several “Key” Enthalpies of Formation Revisited † journal November 2004
A response-function approach to the direct calculation of the transition-energy in a multiple-cluster expansion formalism journal June 1979
Shifts in Excitation Energies Induced by Hydrogen Bonding: A Comparison of the Embedding and Supermolecular Time-Dependent Density Functional Theory Calculations with the Equation-of-Motion Coupled-Cluster Results book September 2011
Assessment of Gaussian-3 and density-functional theories on the G3/05 test set of experimental energies journal September 2005
The implementation of the multireference coupled‐cluster method based on the single‐reference formalism journal March 1992
Introduction of n -electron valence states for multireference perturbation theory journal June 2001
Second‐order perturbation theory with a complete active space self‐consistent field reference function journal January 1992
The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties journal May 1993
Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3 journal April 2008
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
Fully optimized contracted Gaussian basis sets for atoms Li to Kr journal August 1992
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
Second- and third-order triples and quadruples corrections to coupled-cluster singles and doubles in the ground and excited states journal June 2007
Experimental and Theoretical UV Characterizations of Acetylacetone and Its Isomers journal March 2006
A Joint Photoelectron Spectroscopy and Theoretical Study on the Electronic Structure of UCl 5 − and UCl 5 journal July 2013
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
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
Multireference coupled‐cluster method using a single‐reference formalism journal January 1991
Noniterative Coupled-Cluster Methods for Excited Electronic States book January 2006
General atomic and molecular electronic structure system journal November 1993
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
Coupled cluster approach to the single-particle Green's function journal March 1992
Probing the Electronic Structure and Chemical Bonding in Tricoordinate Uranyl Complexes UO 2 X 3 – (X = F, Cl, Br, I): Competition between Coulomb Repulsion and U–X Bonding journal May 2013
Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian journal December 2005
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
Computing coupled-cluster wave functions with arbitrary excitations journal July 2000
Highly Accurate First-Principles Benchmark Data Sets for the Parametrization and Validation of Density Functional and Other Approximate Methods. Derivation of a Robust, Generally Applicable, Double-Hybrid Functional for Thermochemistry and Thermochemical Kinetics † journal December 2008
The method of moments of coupled-cluster equations and the renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approaches journal July 2000
A generalization of the state-specific complete-active-space coupled-cluster method for calculating electronic excited states journal February 2008
Benchmarks of electronically excited states: Basis set effects on CASPT2 results journal November 2010
Biorthogonal moment expansions in coupled-cluster theory: Review of key concepts and merging the renormalized and active-space coupled-cluster methods journal June 2012
Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds journal June 1991
The equation-of-motion coupled-cluster method. Applications to open- and closed-shell reference states journal May 1993
Nested variant of the method of moments of coupled cluster equations for vertical excitation energies and excited-state potential energy surfaces journal May 2009
Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation journal January 1997
A dressing for the matrix elements of the singles and doubles equation‐of‐motion coupled‐cluster method that recovers additive separability of excitation energies journal May 1995
Electronic structure of the S 1 state in methylcobalamin: Insight from CASSCF/MC-XQDPT2, EOM-CCSD, and TD-DFT calculations journal January 2013
Coupled-cluster methods with internal and semi-internal triply excited clusters: Vibrational spectrum of the HF molecule journal October 1999
Second-order perturbation theory with a CASSCF reference function journal July 1990
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
Coupled-cluster dynamic polarizabilities including triple excitations journal June 2008
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
Coupled cluster Green's function method: Working equations and applications journal October 1993
On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell‐Type Expansion Using Quantum‐Field Theoretical Methods journal December 1966
A noniterative perturbative triples correction for the spin-flipping and spin-conserving equation-of-motion coupled-cluster methods with single and double substitutions journal November 2008
Coupled-cluster methods with internal and semi-internal triply and quadruply excited clusters: CCSDt and CCSDtq approaches journal April 1999
Optimizing Conical Intersections without Derivative Coupling Vectors:  Application to Multistate Multireference Second-Order Perturbation Theory (MS-CASPT2) † journal January 2008
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
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
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

Cited By (6)

Valence and charge-transfer optical properties for some Si n C m ( m , n ≤ 12) clusters: Comparing TD-DFT, complete-basis-limit EOMCC, and benchmarks from spectroscopy journal May 2018
Perspective: Kohn-Sham density functional theory descending a staircase journal October 2016
The ring-opening channel and the influence of Rydberg states on the excited state dynamics of furan and its derivatives journal August 2018
Accurate excited-state energetics by a combination of Monte Carlo sampling and equation-of-motion coupled-cluster computations journal March 2019
Benchmarks for Electronically Excited States with CASSCF Methods journal May 2019
Accuracy of Spin-Component-Scaled CC2 Excitation Energies and Potential Energy Surfaces journal August 2019

Linked Research (4)

Similar Records

Reliable Modeling of the Electronic Spectra of Realistic Uranium Complexes
Journal Article · Sun Jul 21 00:00:00 EDT 2013 · Journal of Chemical Physics, 139(3):Article No. 034301 · OSTI ID:1287704
+2 more
Dealing with chemical reaction pathways and electronic excitations in molecular systems via renormalized and active-space coupled-cluster methods
Journal Article · Thu Jan 22 00:00:00 EST 2015 · AIP Conference Proceedings · OSTI ID:1287704
+2 more
Excitation energies with cost-reduced variant of the active-space EOMCCSDT method: the EOMCCSDt-(3) over-bar approach
Journal Article · Tue Nov 12 00:00:00 EST 2013 · Journal of Chemical Theory and Computation, 9(11):4761-4768 · OSTI ID:1287704

Related Subjects

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