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Coupled-Cluster Valence-Bond Singles and Doubles for Strongly Correlated Systems: Block-Tensor Based Implementation and Application to Oligoacenes

Journal Article · · Journal of Chemical Theory and Computation
 [1];  [2];  [2];  [2]
  1. Univ. of California, Berkeley, CA (United States). Dept. of Chemistry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Division
  2. Univ. of California, Berkeley, CA (United States). Dept. of Chemistry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Division
+ Show Author Affiliations
Here, we demonstrate a block-tensor based implementation of coupled-cluster valence-bond singles and doubles (CCVB-SD) [Small, D. W.; Head-Gordon M. J. Chem. Phys. 2012, 137, 114103] which is a simple modification to restricted CCSD (RCCSD) that provides a qualitatively correct description of valence correlations even in strongly correlated systems. We derive the Λ-equation of CCVB-SD and the corresponding unrelaxed density matrices. The resulting production-level implementation is applied to oligoacenes, correlating up to 318 electrons in 318 orbitals. CCVB-SD shows a qualitative agreement with exact methods for short acenes and reaches the bulk limit of oligoacenes in terms of natural orbital occupation numbers, whereas RCCSD shows nonvariational behavior even for relatively short acenes. A significant reduction in polyradicaloid character is found when correlating all valence electrons instead of only the π-electrons.
Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1478342
Journal Information:
Journal of Chemical Theory and Computation, Journal Name: Journal of Chemical Theory and Computation Journal Issue: 2 Vol. 13; ISSN 1549-9618
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (182)

The Multiradical Character of One- and Two-Dimensional Graphene Nanoribbons journal January 2013
A Stable π-Conjugated Singlet Biradical journal June 2016
Kekulé versus Lewis: When Aromaticity Prevents Electron Pairing and Imposes Polyradical Character journal October 2014
New implementation of high-level correlated methods using a general block tensor library for high-performance electronic structure calculations journal July 2013
Connection between a few Jeziorski-Monkhorst ansatz-based methods journal January 2009
Applicability of coupled-pair theories to quasidegenerate electronic states: A model study journal November 1980
A linear response, coupled-cluster theory for excitation energy journal March 1984
Coupled-cluster method with optimized reference state journal March 1984
Orthogonally spin-adapted coupled-cluster equations involving singly and doubly excited clusters. Comparison of different procedures for spin-adaptation journal October 1989
Coupled-Cluster approaches with an approximate account of triply and quadruply excited clusters: Implementation of the orthogonally spin-adaptedCCD +ST(CCD),CCSD +T(CCSD), andACPQ +ST(ACPQ) formalisms journal July 1995
State-specific multireference coupled-cluster theory: State-specific multireference coupled-cluster theory
  • Köhn, Andreas; Hanauer, Matthias; Mück, Leonie Anna
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 3, Issue 2 https://doi.org/10.1002/wcms.1120
journal October 2012
PNO-CI and CEPA studies of electron correlation effects: II. Potential curves and dipole moment functions of the OH radical journal January 1974
Use of a unitary wavefunction in the calculation of static electronic properties journal January 1984
Orthogonally spin-adapted multi-reference Hilbert space coupled-cluster formalism: diagrammatic formulation journal January 1992
A Hilbert space multi-reference coupled-cluster study of the H4 model system journal January 1991
Coupled cluster approaches with an approximate account of triexcitations and the optimized inner projection technique: I. General orthogonally spin-adapted formalism journal January 1990
Valence bond corrected single reference coupled cluster approach: I. General formalism journal September 1994
Valence bond corrected single reference coupled cluster approach: II. Application to PPP model systems journal September 1994
Valence bond corrected single reference coupled cluster approach: III. Simple model of bond breaking or formation journal September 1994
Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states journal July 2004
A comparison of singlet and triplet states for one- and two-dimensional graphene nanoribbons using multireference theory journal June 2014
The effective interaction in nuclei and its perturbation expansion: An algebraic approach journal September 1972
Variational principles and linked-cluster exp S expansions for static and dynamic many-body problems journal December 1983
Convergence acceleration of iterative sequences. the case of scf iteration journal July 1980
An efficient and accurate approximation to double substitution coupled cluster wavefunctions journal May 1981
A new determinant-based full configuration interaction method journal November 1984
Further tests of the approximate double substitution coupled-cluster method journal June 1987
The expectation value coupled-cluster method and analytical energy derivatives journal September 1988
The unitary coupled-cluster approach and molecular properties. Applications of the UCC(4) method journal May 1989
Complete active space coupled-cluster method. Extension of single-reference coupled-cluster method using the CASSCF wavefunction journal January 1994
Simplified methods for equation-of-motion coupled-cluster excited state calculations journal January 1996
A determinant based full configuration interaction program journal April 1989
On the connectivity criteria in the open-shell coupled-cluster theory for general model spaces journal July 1987
A second-order correction to singles and doubles coupled-cluster methods based on a perturbative expansion of a similarity-transformed Hamiltonian journal June 2000
The quadratic coupled cluster doubles model journal November 2000
Size-consistent wave functions for bond-breaking: the equation-of-motion spin-flip model journal April 2001
A comparison of the renormalized and active-space coupled-cluster methods: Potential energy curves of BH and F2 journal August 2001
A perturbative correction to the quadratic coupled-cluster doubles method for higher excitations journal February 2002
Characterizing unpaired electrons from the one-particle density matrix journal April 2003
Alternative coupled-cluster ansätze II. The unitary coupled-cluster method journal February 1989
A fifth-order perturbation comparison of electron correlation theories journal May 1989
An extended coupled-cluster functional for molecular properties: study of an analytical and numerical approach journal October 1998
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
The Usefulness of Exponential Wave Function Expansions Employing One- and Two-Body Cluster Operators in Electronic Structure Theory: The Extended and Generalized Coupled-Cluster Methods journal December 2006
State-specific Brillouin–Wigner multireference coupled cluster study of the F2 molecule: assessment of the a posteriori size-extensivity correction journal July 2001
The density-matrix renormalization group in the age of matrix product states journal January 2011
Extended coupled-cluster approach for magnetizabilities of small molecules journal April 2004
A strategy for obtaining a more accurate transition state estimate using the growing string method journal January 2010
Many – Body Methods in Chemistry and Physics book January 2009
Can Single-Reference Coupled Cluster Theory Describe Static Correlation? journal June 2015
Electronically Excited States of Higher Acenes up to Nonacene: A Density Functional Theory/Multireference Configuration Interaction Study journal December 2015
Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes journal May 2016
Large-Scale Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Methods journal April 2016
Spin-Flip Equation-of-Motion Coupled-Cluster Electronic Structure Method for a Description of Excited States, Bond Breaking, Diradicals, and Triradicals journal February 2006
Water-Splitting Chemistry of Photosystem II journal November 2006
Manganese Clusters with Relevance to Photosystem II journal September 2004
Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications journal December 2011
Multireference Nature of Chemistry: The Coupled-Cluster View journal December 2011
Quantum Chemical Studies of Mechanisms for Metalloenzymes journal January 2014
Full Configuration Interaction Excitations of Ethene and Butadiene: Resolution of an Ancient Question journal September 2012
Taming the First-Row Diatomics: A Full Configuration Interaction Quantum Monte Carlo Study journal October 2012
More π Electrons Make a Difference: Emergence of Many Radicals on Graphene Nanoribbons Studied by Ab Initio DMRG Theory journal December 2012
Reliable Transition State Searches Integrated with the Growing String Method journal June 2013
Coupled Cluster Valence Bond Method: Efficient Computer Implementation and Application to Multiple Bond Dissociations and Strong Correlations in the Acenes journal April 2014
Oligoacenes:  Theoretical Prediction of Open-Shell Singlet Diradical Ground States journal June 2004
Toward Tetraradicaloid: The Effect of Fusion Mode on Radical Character and Chemical Reactivity journal January 2016
Higher Order π-Conjugated Polycyclic Hydrocarbons with Open-Shell Singlet Ground State: Nonazethrene versus Nonacene journal August 2016
State-Specific Brillouin−Wigner Multireference Coupled Cluster Study of the Singlet−Triplet Separation in the Tetramethyleneethane Diradical journal March 2001
Quadratic Coupled-Cluster Doubles:  Implementation and Assessment of Perfect Pairing Optimized Geometries † journal August 2002
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
Singlet−Triplet Energy Gaps for Diradicals from Fractional-Spin Density-Functional Theory journal January 2011
Strong Correlation in Acene Sheets from the Active-Space Variational Two-Electron Reduced Density Matrix Method: Effects of Symmetry and Size journal June 2011
Towards an exact description of electronic wavefunctions in real solids journal December 2012
Entangled quantum electronic wavefunctions of the Mn4CaO5 cluster in photosystem II journal June 2013
Low-energy spectrum of iron–sulfur clusters directly from many-particle quantum mechanics journal August 2014
Electronic structures of [n]-cyclacenes (n = 6–12) and short, hydrogen-capped, carbon nanotubes journal January 2010
Post-modern valence bond theory for strongly correlated electron spins journal January 2011
Modern valence bond theory journal January 1997
Renormalized CCSD(T) and CCSD(TQ) approaches: Dissociation of the N2 triple bond journal October 2000
Benchmark variational coupled cluster doubles results journal November 2000
Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points journal December 2000
A climbing image nudged elastic band method for finding saddle points and minimum energy paths journal December 2000
A general state-selective multireference coupled-cluster algorithm journal July 2002
Singlet-triplet gaps in diradicals by the spin-flip approach: A benchmark study journal September 2002
Continuous transition between Brillouin–Wigner and Rayleigh–Schrödinger perturbation theory, generalized Bloch equation, and Hilbert space multireference coupled cluster journal June 2003
Benchmark theoretical study of the ionization threshold of benzene and oligoacenes journal August 2003
New coupled-cluster methods with singles, doubles, and noniterative triples for high accuracy calculations of excited electronic states journal January 2004
A growing string method for determining transition states: Comparison to the nudged elastic band and string methods journal May 2004
Automated generation of coupled-cluster diagrams: Implementation in the multireference state-specific coupled-cluster approach with the complete-active-space reference journal January 2005
An exponential multireference wave-function Ansatz journal August 2005
Coupled-cluster method tailored by configuration interaction journal August 2005
Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian journal December 2005
High-order excitations in state-universal and state-specific multireference coupled cluster theories: Model systems journal October 2006
Addition by subtraction in coupled-cluster theory: A reconsideration of the CC and CI interface and the nCC hierarchy journal November 2006
The radical character of the acenes: A density matrix renormalization group study journal October 2007
Block correlated coupled cluster theory with a complete active-space self-consistent-field reference function: The formulation and test applications for single bond breaking journal November 2007
Improving upon CCSD(T): ΛCCSD(T). I. Potential energy surfaces journal January 2008
Block correlated coupled cluster method with a complete-active-space self-consistent-field reference function: The formula for general active spaces and its applications for multibond breaking systems journal June 2008
Tractable spin-pure methods for bond breaking: Local many-electron spin-vector sets and an approximate valence bond model journal February 2009
The perfect quadruples model for electron correlation in a valence active space journal February 2009
Rethinking linearized coupled-cluster theory journal April 2009
Transition state-finding strategies for use with the growing string method journal June 2009
An explicitly spin-free compact open-shell coupled cluster theory using a multireference combinatoric exponential ansatz: Formal development and pilot applications journal July 2009
Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space journal January 2009
A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linear acenes journal December 2009
Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo journal January 2010
A tractable and accurate electronic structure method for static correlations: The perfect hextuples model journal July 2010
Benchmark studies of variational, unitary and extended coupled cluster methods journal December 2010
An orbital-invariant internally contracted multireference coupled cluster approach journal March 2011
The formulation and performance of a perturbative correction to the perfect quadruples model journal April 2011
A state-specific partially internally contracted multireference coupled cluster approach journal June 2011
Pilot applications of internally contracted multireference coupled cluster theory, and how to choose the cluster operator properly journal May 2011
Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory journal September 2011
Density functional theory with fractional orbital occupations journal April 2012
PNO–CI (pair natural orbital configuration interaction) and CEPA–PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. I. Outline of the method for closed‐shell states journal February 1975
Correlation problems in atomic and molecular systems. V. Spin‐adapted coupled cluster many‐electron theory journal July 1977
A coupled cluster polarization propagator method applied to CH + journal August 1986
The full CCSDT model for molecular electronic structure journal June 1987
A unitary multiconfigurational coupled‐cluster method: Theory and applications journal January 1988
Coupled‐cluster method truncated at quadruples journal November 1991
Hilbert space multireference coupled‐cluster methods. II. A model study on H 8 journal September 1992
Externally corrected singles and doubles coupled cluster methods for open-shell systems journal July 1997
A fusion of the closed-shell coupled cluster singles and doubles method and valence-bond theory for bond breaking journal September 2012
Single-root multireference Brillouin-Wigner coupled-cluster theory: Applicability to the F2 molecule journal April 1998
Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+ journal September 1998
Size-consistent wave functions for nondynamical correlation energy: The valence active space optimized orbital coupled-cluster doubles model journal December 1998
Ab initio quantum chemistry using the density matrix renormalization group journal March 1999
A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications journal April 1999
Property calculations using perturbed orbitals via state-specific multireference coupled-cluster and perturbation theories journal September 1999
Communication: The distinguishable cluster approximation journal July 2013
Development of a linear response theory based on a state-specific multireference coupled cluster formalism journal May 2000
Size-extensivity correction for the state-specific multireference Brillouin–Wigner coupled-cluster theory journal May 2000
New approach to the state-specific multireference coupled-cluster formalism journal June 2000
The method of moments of coupled-cluster equations and the renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approaches journal July 2000
Communication: The distinguishable cluster approximation. II. The role of orbital relaxation journal August 2014
The distinguishable cluster approach from a screened Coulomb formalism journal January 2016
Assessing the distinguishable cluster approximation based on the triple bond-breaking in the nitrogen molecule journal March 2016
Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy journal April 2016
Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations journal September 2016
Recoupling the singlet- and triplet-pairing channels in single-reference coupled cluster theory journal October 2016
Cost-effective description of strong correlation: Efficient implementations of the perfect quadruples and perfect hextuples models journal October 2016
Nature of ground and electronic excited states of higher acenes journal August 2016
Non-iterative corrections to extended coupled-cluster energies employing the generalized method of moments of coupled-cluster equations journal August 2005
Quasiparticle Fock-space coupled-cluster theory journal November 2010
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package journal September 2014
Accuracy of two-particle N -representability conditions for describing different spin states and the singlet–triplet gap in the linear acene series journal September 2015
Applications of a non-perturbative many-body formalism to general open-shell atomic and molecular problems: calculation of the ground and the lowest π-π* singlet and triplet energies and the first ionization potential of trans-butadiene journal April 1977
A state-specific multi-reference coupled cluster formalism with molecular applications journal May 1998
Recent advances in electronic structure theory: Method of moments of coupled-cluster equations and renormalized coupled-cluster approaches journal October 2002
Linked-Diagram and Coupled-Cluster Expansions for Multi-Configurational, Complete and Incomplete Model Spaces journal October 1985
Intermediate Hamiltonians as a new class of effective Hamiltonians journal April 1985
A valence-universal coupled-cluster single- and double-excitations method for atoms. III. Solvability problems in the presence of intruder states journal April 1994
On the use of Brillouin-Wigner perturbation theory for many-body systems journal January 2000
The density-matrix renormalization group: a short introduction journal July 2011
Quantum Theory of Many-Particle Systems. III. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects journal March 1955
Orthogonally-spin-adapted coupled-cluster theory for closed-shell systems including triexcited clusters journal July 1979
Coupled-cluster method for multideterminantal reference states journal October 1981
Symmetry-adapted coupled-pair approach to the many-electron correlation problem. III. Approximate coupled-pair approaches for the Be atom journal November 1981
Approximate account of the connected quadruply excited clusters in the coupled-pair many-electron theory journal November 1984
Coupled-cluster method in Fock space. I. General formalism journal August 1985
Coupled-cluster method in Fock space. II. Brueckner-Hartree-Fock method journal August 1985
Bivariational coupled-cluster approach for the study of static electronic properties / e m p h > journal October 1986
Coupled-cluster method in Fock space. III. On similarity transformation of operators in Fock space journal March 1988
Coupled-cluster method in Fock space. IV. Calculation of expectation values and transition moments journal March 1988
Intruder states and incomplete model spaces in multireference coupled-cluster theory: The 2 p 2 states of Be journal December 1988
Coupled-cluster approaches with an approximate account of triexcitations and the optimized-inner-projection technique. III. Lower bounds to the ground-state correlation energy of cyclic-polyene model systems journal November 1990
Size-consistent Brillouin-Wigner perturbation theory with an exponentially parametrized wave function: Brillouin-Wigner coupled-cluster theory journal December 1994
Approximate account of connected quadruply excited clusters in single-reference coupled-cluster theory via cluster analysis of the projected unrestricted Hartree-Fock wave function journal August 1996
Coupled-cluster approach to electron correlation in one dimension: Cyclic polyene model in delocalized basis journal October 1984
Coupled-cluster approaches with an approximate account of triexcitations and the optimized-inner-projection technique. II. Coupled-cluster results for cyclic-polyene model systems journal August 1990
Density-matrix algorithms for quantum renormalization groups journal October 1993
Accurate Ab Initio Calculation of Ionization Potentials of the First-Row Transition Metals with the Configuration-Interaction Quantum Monte Carlo Technique journal January 2015
Density matrix formulation for quantum renormalization groups journal November 1992
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions journal January 1996
Coupled-cluster theory in quantum chemistry journal February 2007
Antiferromagnetic order and spin dynamics in iron-based superconductors journal August 2015
Matplotlib: A 2D Graphics Environment journal January 2007
Comparison of the Brillouin-Wigner Coupled Cluster Theory with the Standard Coupled Cluster Theory. Cancellation of Disconnected Terms in the Brillouin-Wigner Coupled Cluster Theory journal January 1997
Externally Corrected Coupled-Cluster Approaches: Energy versus Amplitude Corrected CCSD journal January 2003
The Description of Chemical Bonding From AB Initio Calculations journal October 1978
Equation-of-Motion Coupled-Cluster Methods for Open-Shell and Electronically Excited Species: The Hitchhiker's Guide to Fock Space journal May 2008
The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances journal June 2002

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