Universal state-selective corrections to multi-reference coupled-cluster theories with single and double excitations.

The recently proposed universal state-selective (USS) corrections [K. Kowalski, J. Chem. Phys. 134, 194107 (2011)] to approximate multi-reference coupled-cluster (MRCC) energies can be commonly applied to any type of MRCC theory based on the Jeziorski-Monkhorst [B. Jeziorski and H. J. Monkhorst, Phys. Rev. A 24, 1668 (1981)] exponential ansatz. In this paper we report on the performance of a simple USS correction to the Brillouin-Wigner and Mukherjee's MRCC approaches employing single and double excitations (USS-BW-MRCCSD and USS-Mk-MRCCSD). It is shown that the USS-BW-MRCCSD correction, which employs the manifold of single and double excitations, can be related to a posteriori corrections utilized in routine BW-MRCCSD calculations. In several benchmark calculations we compare the USS-BW-MRCCSD and USS-Mk-MRCCSD results with the results obtained with the full configuration interaction method.

[1]  S. Wilson,et al.  On the use of Brillouin-Wigner perturbation theory for many-body systems , 2000 .

[2]  S. Hirata Tensor Contraction Engine: Abstraction and Automated Parallel Implementation of Configuration-Interaction, Coupled-Cluster, and Many-Body Perturbation Theories , 2003 .

[3]  So Hirata,et al.  Perturbative corrections to coupled-cluster and equation-of-motion coupled-cluster energies: A determinantal analysis , 2001 .

[4]  Jürgen Gauss,et al.  Triple excitations in state-specific multireference coupled cluster theory: application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems. , 2008, The Journal of chemical physics.

[5]  Sanghamitra Das,et al.  Full implementation and benchmark studies of Mukherjee's state-specific multireference coupled-cluster ansatz. , 2010, The Journal of chemical physics.

[6]  C. Bloch,et al.  Sur la théorie des perturbations des états liés , 1958 .

[7]  J. Pittner,et al.  Multireference Brillouin-Wigner coupled cluster method with singles, doubles, and triples: efficient implementation and comparison with approximate approaches. , 2008, The Journal of chemical physics.

[8]  R. Bartlett,et al.  Coupled‐cluster method for an incomplete model space , 1992 .

[9]  Piotr Piecuch,et al.  Single-reference, size-extensive, non-iterative coupled-cluster approaches to bond breaking and biradicals , 2006 .

[10]  U. Kaldor,et al.  Hilbert space coupled-cluster method in an incomplete model space , 1992 .

[11]  Mihály Kállay,et al.  Approximate treatment of higher excitations in coupled-cluster theory. , 2005, The Journal of chemical physics.

[12]  Martin Head-Gordon,et al.  A second-order correction to singles and doubles coupled-cluster methods based on a perturbative expansion of a similarity-transformed Hamiltonian , 2000 .

[13]  Karol Kowalski,et al.  Extension of the method of moments of coupled-cluster equations to a multireference wave operator formalism ☆ , 2001 .

[14]  Carlos E. Soliverez,et al.  General theory of effective Hamiltonians , 1981 .

[15]  John F. Stanton,et al.  Perturbative treatment of the similarity transformed Hamiltonian in equation‐of‐motion coupled‐cluster approximations , 1995 .

[16]  H. Monkhorst,et al.  Coupled-cluster method for multideterminantal reference states , 1981 .

[17]  Josef Paldus,et al.  Reduced multireference CCSD method: An effective approach to quasidegenerate states , 1997 .

[18]  Piecuch,et al.  Application of Hilbert-space coupled-cluster theory to simple (H2)2 model systems: Planar models. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[19]  Josef Paldus,et al.  Spin‐adapted multireference coupled‐cluster approach: Linear approximation for two closed‐shell‐type reference configurations , 1988 .

[20]  Andrew C Simmonett,et al.  A companion perturbation theory for state-specific multireference coupled cluster methods. , 2009, Physical chemistry chemical physics : PCCP.

[21]  J. M. Junquera-Hernández,et al.  Full configuration interaction calculation of Be3. , 2004, The Journal of chemical physics.

[22]  U. Kaldor,et al.  Degeneracy breaking in the Hilbert‐space coupled cluster method , 1993 .

[23]  P. Piecuch,et al.  Complete set of solutions of the generalized Bloch equation , 2000 .

[24]  Kiran Bhaskaran-Nair,et al.  Multireference state-specific Mukherjee's coupled cluster method with noniterative triexcitations using uncoupled approximation. , 2011, The Journal of chemical physics.

[25]  Andrew C. Simmonett,et al.  Capture of hydroxymethylene and its fast disappearance through tunnelling , 2008, Nature.

[26]  J. Pople,et al.  Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules , 1972 .

[27]  J. Paldus,et al.  Multi-reference state-universal coupled-cluster approaches to electronically excited states. , 2011, The Journal of chemical physics.

[28]  So Hirata,et al.  Symbolic Algebra in Quantum Chemistry , 2006 .

[29]  Mihály Kállay,et al.  Coupled-cluster methods including noniterative corrections for quadruple excitations. , 2005, The Journal of chemical physics.

[30]  Petr Nachtigall,et al.  Assessment of the single-root multireference Brillouin–Wigner coupled- cluster method: Test calculations on CH2, SiH2, and twisted ethylene , 1999 .

[31]  Karol Kowalski,et al.  Renormalized CCSD(T) and CCSD(TQ) approaches: Dissociation of the N2 triple bond , 2000 .

[32]  J. Paldus,et al.  Partially linearized, fully size-extensive, and reduced multireference coupled-cluster methods. II. Applications and performance. , 2008, The Journal of chemical physics.

[33]  Uttam Sinha Mahapatra,et al.  State-Specific Multi-Reference Coupled Cluster Formulations: Two Paradigms , 1998 .

[34]  J. Paldus,et al.  A multireference coupled-cluster study of electronic excitations in furan and pyrrole. , 2010, The journal of physical chemistry. A.

[35]  P. Piecuch,et al.  Active-space coupled-cluster study of electronic states of Be3. , 2005, The Journal of chemical physics.

[36]  Rodney J. Bartlett,et al.  Hilbert space multireference coupled-cluster methods. I: The single and double excitation model , 1991 .

[37]  Karol Kowalski,et al.  A universal state-selective approach to multireference coupled-cluster non-iterative corrections. , 2011, The Journal of chemical physics.

[38]  J. Pittner,et al.  Multireference Brillouin-Wigner coupled clusters method with noniterative perturbative connected triples. , 2006, The Journal of chemical physics.

[39]  Uttam Sinha Mahapatra,et al.  A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications , 1999 .

[40]  Ivan Hubač,et al.  Multireference Brillouin-Wigner Coupled-Cluster Theory. Single-root approach. , 1998 .

[41]  T. H. Dunning Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[42]  Anna I. Krylov,et al.  Second order perturbation corrections to singles and doubles coupled-cluster methods: General theory and application to the valence optimized doubles model , 2000 .

[43]  Jiří Pittner,et al.  Continuous transition between Brillouin-Wigner and Rayleigh-Schrödinger perturbation theory, generalized Bloch equation, and Hilbert space multireference coupled cluster , 2003 .

[44]  Michael Hanrath,et al.  An exponential multireference wave-function Ansatz. , 2005, The Journal of chemical physics.

[45]  Rodney J. Bartlett,et al.  Noniterative energy corrections through fifth-order to the coupled cluster singles and doubles method , 1998 .

[46]  Josef Paldus,et al.  General-model-space state-universal coupled-cluster theory: Connectivity conditions and explicit equations , 2003 .

[47]  Uttam Sinha Mahapatra,et al.  A state-specific multi-reference coupled cluster formalism with molecular applications , 1998 .

[48]  Karol Kowalski,et al.  The method of moments of coupled-cluster equations and the renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approaches , 2000 .

[49]  Sriram Krishnamoorthy,et al.  Massively parallel implementation of the multireference Brillouin–Wigner CCSD method , 2011 .

[50]  Francesco A Evangelista,et al.  Perturbative triples corrections in state-specific multireference coupled cluster theory. , 2010, The Journal of chemical physics.

[51]  Andrew G. Taube,et al.  Improving upon CCSD(T): LambdaCCSD(T). I. Potential energy surfaces. , 2008, The Journal of chemical physics.

[52]  Rodney J. Bartlett,et al.  Coupled‐cluster theory and its equation‐of‐motion extensions , 2012 .

[53]  Edoardo Aprà,et al.  Parallel Implementation of Multireference Coupled-Cluster Theories Based on the Reference-Level Parallelism. , 2012, Journal of chemical theory and computation.

[54]  H. Weidenmüller,et al.  Perturbation theory for the effective interaction in nuclei , 1973 .

[55]  Francesco A Evangelista,et al.  High-order excitations in state-universal and state-specific multireference coupled cluster theories: model systems. , 2006, The Journal of chemical physics.

[56]  Kiran Bhaskaran-Nair,et al.  Multireference state-specific Mukherjee's coupled cluster method with noniterative triexcitations. , 2008, The Journal of chemical physics.

[57]  Martin Head-Gordon,et al.  A second-order perturbative correction to the coupled-cluster singles and doubles method: CCSD(2) , 2001 .

[58]  P. Durand,et al.  Direct determination of effective Hamiltonians by wave-operator methods. I. General formalism , 1983 .

[59]  Ivan Hubač,et al.  Size-extensivity correction for the state-specific multireference Brillouin–Wigner coupled-cluster theory , 2000 .

[60]  J. Paldus,et al.  Reduced multireference couple cluster method. II. Application to potential energy surfaces of HF, F2, and H2O , 1998 .

[61]  Rodney J. Bartlett,et al.  Sixth-order energy corrections with converged coupled cluster singles and doubles amplitudes , 1998 .

[62]  John F. Stanton,et al.  A simple correction to final state energies of doublet radicals described by equation-of-motion coupled cluster theory in the singles and doubles approximation , 1997 .

[63]  Kiran Bhaskaran-Nair,et al.  Multireference Mukherjee's coupled cluster method with triexcitations in the linked formulation: Efficient implementation and applications. , 2010, The Journal of chemical physics.

[64]  Leszek Meissner,et al.  A coupled‐cluster method for quasidegenerate states , 1988 .

[65]  So Hirata,et al.  Erratum: “Perturbative corrections to coupled-cluster and equation-of-motion coupled-cluster energies: A determinantal analysis” [J. Chem. Phys. 114, 3919 (2001)] , 2001 .

[66]  Karol Kowalski,et al.  New classes of non-iterative energy corrections to multi-reference coupled-cluster energies , 2004 .

[67]  J. Stanton Why CCSD(T) works: a different perspective , 1997 .

[68]  Josef Paldus,et al.  General-model-space state-universal coupled-cluster methods for excited states: diagonal noniterative triple corrections. , 2006, The Journal of chemical physics.

[69]  Karol Kowalski,et al.  Complete set of solutions of multireference coupled-cluster equations: The state-universal formalism , 2000 .

[70]  Josef Paldus,et al.  The general-model-space state-universal coupled-cluster method exemplified by the LiH molecule , 2003 .

[71]  Francesco A Evangelista,et al.  Coupling term derivation and general implementation of state-specific multireference coupled cluster theories. , 2007, The Journal of chemical physics.

[72]  Josef Paldus,et al.  Orthogonally spin-adapted multi-reference Hilbert space coupled-cluster formalism: diagrammatic formulation , 1992 .

[73]  Liguo Kong,et al.  Connection between a few Jeziorski‐Monkhorst ansatz‐based methods , 2009 .

[74]  J. Paldus,et al.  Full potential energy curve for N2 by the reduced multireference coupled-cluster method. , 2008, The Journal of chemical physics.

[75]  Rodney J. Bartlett,et al.  A Hilbert space multi-reference coupled-cluster study of the H4 model system , 1991 .

[76]  Leszek Meissner,et al.  Davidson-type corrections for quasidegenerate states , 1985 .

[77]  P. Piecuch,et al.  The state-universal multi-reference coupled-cluster theory with perturbative description of core-virtual excitations , 2001 .

[78]  John F. Stanton,et al.  INVESTIGATION OF AN ASYMMETRIC TRIPLE-EXCITATION CORRECTION FOR COUPLED-CLUSTER ENERGIES , 1998 .

[79]  Uttam Sinha Mahapatra,et al.  Potential energy surface studies via a single root multireference coupled cluster theory. , 2010, The Journal of chemical physics.

[80]  J. M. Junquera-Hernández,et al.  Full configuration interaction calculation of singlet excited states of Be3. , 2004, The Journal of chemical physics.

[81]  Michael Hanrath,et al.  Initial applications of an exponential multi-reference wavefunction ansatz , 2006 .

[82]  Ajith Perera,et al.  Multireference coupled-cluster theory: the easy way. , 2011, The Journal of chemical physics.

[83]  Josef Paldus,et al.  Multireference general-model-space state-universal and state-specific coupled-cluster approaches to excited states. , 2010, The Journal of chemical physics.

[84]  Rodney J. Bartlett,et al.  The multi-reference Hilbert space coupled-cluster study of the Li2 molecule. Application in a complete model space , 1991 .

[85]  J. Pittner,et al.  Towards the multireference Brillouin-Wigner coupled-clusters method with iterative connected triples: MR BWCCSDT-alpha approximation. , 2005, The Journal of chemical physics.

[86]  Martin Head-Gordon,et al.  A perturbative correction to the quadratic coupled-cluster doubles method for higher excitations , 2002 .

[87]  Rodney J. Bartlett,et al.  Full configuration-interaction and state of the art correlation calculations on water in a valence double-zeta basis with polarization functions , 1996 .

[88]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .

[89]  J. Paldus,et al.  Multi-reference Brillouin–Wigner coupled-cluster method with a general model space , 2005 .

[90]  Josef Paldus,et al.  N-reference, M-state coupled-cluster method: Merging the state-universal and reduced multireference coupled-cluster theories , 2003 .

[91]  Andrew G. Taube,et al.  Improving upon CCSD(T): LambdaCCSD(T). II. Stationary formulation and derivatives. , 2008, The Journal of chemical physics.

[92]  Michael Hanrath,et al.  An exponential multi-reference wavefunction ansatz: connectivity analysis and application to N2 , 2008 .

[93]  H. Weidenmüller,et al.  The effective interaction in nuclei and its perturbation expansion: An algebraic approach , 1972 .

[94]  Piotr Piecuch,et al.  Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian. , 2005, The Journal of chemical physics.

[95]  J. Paldus,et al.  DISSOCIATION OF N2 TRIPLE BOND : A REDUCED MULTIREFERENCE CCSD STUDY , 1998 .

[96]  R. Bartlett The coupled-cluster revolution , 2010 .

[97]  Rodney J. Bartlett,et al.  Hilbert space multireference coupled-cluster methods. II: A model study on H8 , 1992 .

[98]  Josef Paldus,et al.  Reduced multireference coupled cluster method: Ro-vibrational spectra of N2 , 2000 .

[99]  Ron Shepard,et al.  C2V Insertion pathway for BeH2: A test problem for the coupled‐cluster single and double excitation model , 1983 .

[100]  T. H. Dunning Gaussian Basis Functions for Use in Molecular Calculations. III. Contraction of (10s6p) Atomic Basis Sets for the First‐Row Atoms , 1970 .

[101]  Tjerk P. Straatsma,et al.  NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations , 2010, Comput. Phys. Commun..

[102]  I. Hubač Size-Extensive Brillouin-Wigner Perturbation Theory. Size-Extensive Brillouin-Wigner Coupled Cluster Theory , 1996 .

[103]  J. Paldus,et al.  Spin-Adapted Multi-Reference Coupled Cluster Formalism Including Non-Linear Terms and its Application to the H4 Model System , 1989 .

[104]  Rodney J. Bartlett,et al.  A multireference coupled‐cluster study of the ground state and lowest excited states of cyclobutadiene , 1994 .