High-order excitations in state-universal and state-specific multireference coupled cluster theories: model systems.

For the first time high-order excitations (n>2) have been studied in three multireference couple cluster (MRCC) theories built on the wave operator formalism: (1) the state-universal (SU) method of Jeziorski and Monkhorst (JM) (2) the state-specific Brillouin-Wigner (BW) coupled cluster method, and (3) the state-specific MRCC approach of Mukherjee (Mk). For the H4, P4, BeH(2), and H8 models, multireference coupled cluster wave functions, with complete excitations ranging from doubles to hextuples, have been computed with a new arbitrary-order string-based code. Comparison is then made to corresponding single-reference coupled cluster and full configuration interaction (FCI) results. For the ground states the BW and Mk methods are found, in general, to provide more accurate results than the SU approach at all levels of truncation of the cluster operator. The inclusion of connected triple excitations reduces the nonparallelism error in singles and doubles MRCC energies by a factor of 2-10. In the BeH(2) and H8 models, the inclusion of all quadruple excitations yields absolute energies within 1 kcal mol(-1) of the FCI limit. While the MRCC methods are very effective in multireference regions of the potential energy surfaces, they are outperformed by single-reference CC when one electronic configuration dominates.

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

[2]  D R Yarkony,et al.  Modern electronic structure theory , 1995 .

[3]  S. Chattopadhyay,et al.  A state-specific approach to multireference coupled electron-pair approximation like methods: development and applications. , 2004, The Journal of chemical physics.

[4]  Anna I. Krylov,et al.  Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+ , 1998 .

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

[6]  P. Piecuch,et al.  Method of moments of coupled-cluster equations: The quasivariational and quadratic approximations , 2003 .

[7]  J. Pittner,et al.  The performance of the multireference Brillouin–Wigner coupled cluster singles and doubles method on the insertion of Be into H2 , 2004 .

[8]  Ludwik Adamowicz,et al.  Automated generation of coupled-cluster diagrams: implementation in the multireference state-specific coupled-cluster approach with the complete-active-space reference. , 2005, The Journal of chemical physics.

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

[10]  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.

[11]  Jing Ma,et al.  A multireference configuration interaction method based on the separated electron pair wave functions , 2006, J. Comput. Chem..

[12]  H. Schaefer,et al.  Brillouin-Wigner coupled cluster theory: Fock-space approach , 2002 .

[13]  J. Paldus,et al.  Computer generation of Feynman diagrams for perturbation theory. II. Program description , 1984 .

[14]  R. Bartlett.  How and why coupled-cluster theory became the pre-eminent method in an ab into quantum chemistry , 2005 .

[15]  P. Mach,et al.  Single-root multireference Brillouin-Wigner coupled-cluster theory: Applicability to the F2 molecule , 1998 .

[16]  Piotr Piecuch,et al.  Is the mechanism of the [2+2] cycloaddition of cyclopentyne to ethylene concerted or biradical? A completely renormalized coupled cluster study. , 2006, The journal of physical chemistry. A.

[17]  J. H. van Lenthe,et al.  Multireference coupled electron-pair approximations to the multireference coupled cluster method. The MR-CEPA1 method , 2005 .

[18]  P. Pulay,et al.  Direct inversion in the iterative subspace (DIIS) optimization of open‐shell, excited‐state, and small multiconfiguration SCF wave functions , 1986 .

[19]  Michael J. McGuire,et al.  Renormalized Coupled-Cluster Calculations of Reactive Potential Energy Surfaces: The BeFH System† , 2004 .

[20]  K. Freed,et al.  Comparison of the perturbative convergence with multireference Möller–Plesset, Epstein–Nesbet, forced degenerate and optimized zeroth order partitionings: The excited BeH2 surface , 1997 .

[21]  P. Schleyer.  Encyclopedia of computational chemistry , 1998 .

[22]  Comparison of the open‐shell state‐universal and state‐selective coupled‐cluster theories: H4 and H8 models , 1995 .

[23]  W. D. Allen,et al.  The Electronic Structure and Vibrational Spectrum of trans-HNOO , 2004 .

[24]  S. Chattopadhyay,et al.  Applications of size-consistent state-specific multi-reference coupled cluster (SS-MRCC) theory to study the potential energy curves of some interesting molecular systems , 2004 .

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

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

[27]  Karol Kowalski,et al.  Can ordinary single-reference coupled-cluster methods describe the potential energy curve of N2? The renormalized CCSDT(Q) study , 2001 .

[28]  P. Piecuch,et al.  Method of moments approach and coupled cluster theory , 1991 .

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

[30]  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.

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

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

[33]  C. David Sherrill,et al.  The Configuration Interaction Method: Advances in Highly Correlated Approaches , 1999 .

[34]  Anna I. Krylov,et al.  Size-consistent wave functions for nondynamical correlation energy: The valence active space optimized orbital coupled-cluster doubles model , 1998 .

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

[36]  Jeppe Olsen,et al.  The initial implementation and applications of a general active space coupled cluster method , 2000 .

[37]  Ludwik Adamowicz,et al.  STATE-SELECTIVE MULTIREFERENCE COUPLED-CLUSTER THEORY EMPLOYING THE SINGLE-REFERENCE FORMALISM : IMPLEMENTATION AND APPLICATION TO THE H8 MODEL SYSTEM , 1994 .

[38]  Rodney J. Bartlett,et al.  The reduced linear equation method in coupled cluster theory. , 1981 .

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

[40]  So Hirata,et al.  High-order coupled-cluster calculations through connected octuple excitations , 2000 .

[41]  T. Crawford,et al.  An Introduction to Coupled Cluster Theory for Computational Chemists , 2007 .

[42]  Josef Paldus,et al.  Simultaneous handling of dynamical and nondynamical correlation via reduced multireference coupled cluster method: Geometry and harmonic force field of ozone , 1999 .

[43]  Josef Paldus,et al.  Automation of the implementation of spin‐adapted open‐shell coupled‐cluster theories relying on the unitary group formalism , 1994 .

[44]  J. Paldus,et al.  Performance of the general-model-space state-universal coupled-cluster method. , 2004, The Journal of chemical physics.

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

[46]  Hubac,et al.  Size-consistent Brillouin-Wigner perturbation theory with an exponentially parametrized wave function: Brillouin-Wigner coupled-cluster theory. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[47]  Robert J. Gdanitz,et al.  A new version of the multireference averaged coupled‐pair functional (MR‐ACPF‐2) , 2001 .

[48]  K. Kowalski,et al.  Model study of the impact of orbital choice on the accuracy of coupled‐cluster energies. I. Single‐reference‐state formulation , 1998 .

[49]  Jürgen Gauss,et al.  Analytic second derivatives for general coupled-cluster and configuration-interaction models. , 2003, The Journal of chemical physics.

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

[51]  J. Paldus,et al.  Computer generation of Feynman diagrams for perturbation theory I. General algorithm , 1973 .

[52]  S. Wilson,et al.  On the generalized multi-reference Brillouin-Wigner coupled cluster theory , 2001 .

[53]  S. Kucharski,et al.  Can ordinary single-reference coupled-cluster methods describe potential energy surfaces with nearly spectroscopic accuracy? The renormalized coupled-cluster study of the vibrational spectrum of HF , 2001 .

[54]  State-selective multi-reference coupled-cluster theory using multi-configuration self-consistent-field orbitals. A model study on H8 , 1994 .

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

[56]  J. Cizek.  On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods , 1966 .

[57]  Ludwik Adamowicz,et al.  New approach to the state-specific multireference coupled-cluster formalism , 2000 .

[58]  R. Bartlett.  Recent advances in coupled-cluster methods , 1997 .

[59]  Peter J. Knowles,et al.  A new determinant-based full configuration interaction method , 1984 .

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

[61]  M. Musiał,et al.  Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states , 2004 .

[62]  Karol Kowalski,et al.  Extensive generalization of renormalized coupled-cluster methods. , 2005, The Journal of chemical physics.

[63]  H. Schaefer,et al.  On the single-root approach within the framework of coupled-cluster theory in Fock space , 2005 .

[64]  Mihály Kállay,et al.  A general state-selective multireference coupled-cluster algorithm , 2002 .

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

[66]  D Mukherjee,et al.  Molecular Applications of a Size-Consistent State-Specific Multireference Perturbation Theory with Relaxed Model-Space Coefficients. , 1999, The journal of physical chemistry. A.

[67]  J. Paldus,et al.  Size extensivity of a general-model-space state-universal coupled-cluster method , 2004 .

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

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

[70]  Anna I. Krylov,et al.  Excited states theory for optimized orbitals and valence optimized orbitals coupled-cluster doubles models , 2000 .

[71]  Josef Paldus,et al.  Applicability of coupled‐pair theories to quasidegenerate electronic states: A model study , 1980 .

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

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

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

[75]  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 .

[76]  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.

[77]  Josef Paldus,et al.  Orthogonally spin‐adapted state‐universal coupled‐cluster formalism: Implementation of the complete two‐reference theory including cubic and quartic coupling terms , 1994 .

[78]  J. Paldus,et al.  Reduced multireference coupled cluster method IV: open-shell systems , 2000 .

[79]  Debashis Mukherjee,et al.  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 , 1977 .

[80]  K Kowalski,et al.  Experimental and theoretical UV characterizations of acetylacetone and its isomers. , 2006, The journal of physical chemistry. A.

[81]  P. Piecuch,et al.  A comparison of the renormalized and active-space coupled-cluster methods: Potential energy curves of BH and F2 , 2001 .

[82]  Karol Kowalski,et al.  The active-space equation-of-motion coupled-cluster methods for excited electronic states: The EOMCCSDt approach , 2000 .

[83]  Karol Kowalski,et al.  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 , 2002 .

[84]  Michael J. McGuire,et al.  Recent advances in electronic structure theory: Method of moments of coupled-cluster equations and renormalized coupled-cluster approaches , 2002 .

[85]  Karol Kowalski,et al.  The active-space equation-of-motion coupled-cluster methods for excited electronic states: Full EOMCCSDt , 2001 .

[86]  J. Paldus,et al.  Truncated version of the reduced multireference coupled‐cluster method with perturbation selection of higher than pair clusters , 2000 .

[87]  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 .

[88]  D. Mukherjee,et al.  Application of cluster expansion techniques to open shells: Calculation of difference energies , 1984 .

[89]  P. Piecuch,et al.  Automated derivation and parallel computer implementation of renormalized and active-space coupled-cluster methods , 2006 .

[90]  Stephen Wilson,et al.  Multireference Brillouin–Wigner coupled cluster (MR‐BWCC) theory applied to the H8 model: Comparison with CCSD(T) theory , 2005 .

[91]  P. Piecuch,et al.  Balancing dynamic and nondynamic correlation for diradical and aromatic transition states: a renormalized coupled-cluster study of the cope rearrangement of 1,5-hexadiene. , 2005, Journal of the American Chemical Society.

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

[93]  Robert J. Gdanitz,et al.  The averaged coupled-pair functional (ACPF): A size-extensive modification of MR CI(SD) , 1988 .

[94]  S. Chattopadhyay,et al.  Development of a linear response theory based on a state-specific multireference coupled cluster formalism , 2000 .

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

[96]  Micah L. Abrams,et al.  General-order single- and multi-reference configuration interaction and coupled-cluster theory: Symmetric dissociation of water , 2005 .

[97]  K. Kowalski,et al.  Non-iterative corrections to extended coupled-cluster energies employing the generalized method of moments of coupled-cluster equations , 2005 .

[98]  So Hirata,et al.  Combined coupled-cluster and many-body perturbation theories. , 2004, The Journal of chemical physics.

[99]  C. David Sherrill,et al.  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 , 2005 .

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

[101]  J. Paldus,et al.  Singlet-Triplet Splitting in Methylene: An Accurate Description of Dynamic and Nondynamic Correlation by Reduced Multireference Coupled Cluster Method , 1998 .

[102]  Curtis L. Janssen,et al.  The automated solution of second quantization equations with applications to the coupled cluster approach , 1991 .

[103]  G. I. Gellene,et al.  σ Bond Activation by Cooperative Interaction with n s 2 Atoms: Be + n H 2 , n = 1−3 , 2000 .

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

[105]  Henry F. Schaefer,et al.  Accelerating the convergence of the coupled-cluster approach: The use of the DIIS method , 1986 .

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

[107]  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 .

[108]  J. Simons,et al.  A test of multiconfigurational coupled-cluster theory on Be(1S)+H2(X 1Σg+) → BeH2(1A1) , 1983 .

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