The method of moments of coupled-cluster equations and the renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approaches

This paper is the first in a series of papers on the new approach to the many-electron correlation problem, termed the method of moments of coupled-cluster equations (MMCC). A hierarchy of MMCC approximations, including the renormalized and completely renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) methods, which can be viewed as generalizations of the well-known perturbative coupled-cluster CCSD[T], CCSD(T), CCSD(TQf), and CCSDT(Qf) schemes, is introduced. In this initial study, an emphasis is placed on the ability of the MMCC approach to describe bond breaking and large effects due to connected triples and quadruples by modifying the standard noniterative CC approaches, such as the popular CCSD(T) method. The performance of selected MMCC approaches, including the renormalized and completely renormalized CCSD[T], CCSD(T), and CCSD(TQ) schemes, is illustrated by the results of pilot calculations for the HF and H2O molecules.

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

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

[3]  P. Löwdin,et al.  New Horizons of Quantum Chemistry , 1983 .

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

[5]  M. Head‐Gordon,et al.  A fifth-order perturbation comparison of electron correlation theories , 1989 .

[6]  Krishnan Raghavachari,et al.  An augmented coupled cluster method and its application to the first‐row homonuclear diatomics , 1985 .

[7]  Josef Paldus,et al.  Coupled cluster approaches with an approximate account of triexcitations and the optimized inner projection technique , 1990, Physical review. B, Condensed matter.

[8]  Clifford E. Dykstra,et al.  Advanced theories and computational approaches to the electronic structure of molecules , 1984 .

[9]  Ludwik Adamowicz,et al.  The implementation of the multireference coupled‐cluster method based on the single‐reference formalism , 1992 .

[10]  Piecuch,et al.  Approximate account of connected quadruply excited clusters in single-reference coupled-cluster theory via cluster analysis of the projected unrestricted Hartree-Fock wave function. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[11]  Approximate coupled-cluster methods employing split cluster amplitudes: Implementation of an almost-linear coupled-cluster formalism , 1998 .

[12]  R. Bartlett,et al.  Coupled-cluster methods that include connected quadruple excitations, T4: CCSDTQ-1 and Q(CCSDT) , 1989 .

[13]  R. Bartlett,et al.  An efficient way to include connected quadruple contributions into the coupled cluster method , 1998 .

[14]  R. Bartlett,et al.  The full CCSDT model for molecular electronic structure , 1987 .

[15]  Ludwik Adamowicz,et al.  A state-selective multireference coupled-cluster theory employing the single-reference formalism , 1993 .

[16]  R. Bartlett.  Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules , 1981 .

[17]  P. Piecuch,et al.  Coupled‐Cluster approaches with an approximate account of triply and quadruply excited clusters: Implementation of the orthogonally spin‐adapted CCD + ST(CCD), CCSD + T(CCSD), and ACPQ + ST(ACPQ) formalisms , 1995 .

[18]  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 .

[19]  L. Kantorovich,et al.  Approximate methods of higher analysis , 1960 .

[20]  E. Allgower,et al.  Numerical Continuation Methods , 1990 .

[21]  K. Kowalski,et al.  Physical and mathematical content of coupled-cluster equations. III. Model studies of dissociation processes for various reference states , 1999 .

[22]  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 .

[23]  Josef Paldus,et al.  Time-Independent Diagrammatic Approach to Perturbation Theory of Fermion Systems , 1975 .

[24]  Josef Paldus,et al.  Coupled Cluster Theory , 1992 .

[25]  R. Bartlett,et al.  The description of N2 and F2 potential energy surfaces using multireference coupled cluster theory , 1987 .

[26]  Rodney J. Bartlett,et al.  Fifth-Order Many-Body Perturbation Theory and Its Relationship to Various Coupled-Cluster Approaches* , 1986 .

[27]  Josef Paldus,et al.  Orthogonally spin-adapted coupled-cluster equations involving singly and doubly excited clusters. Comparison of different procedures for spin-adaptation , 1989 .

[28]  N. Handy,et al.  Full CI calculations on BH, H2O, NH3, and HF , 1983 .

[29]  P. Piecuch,et al.  Improved computational strategy for the state‐selective coupled‐cluster theory with semi‐internal triexcited clusters: Potential energy surface of the HF molecule , 1995 .

[30]  Josef Paldus,et al.  Correlation problems in atomic and molecular systems. V. Spin‐adapted coupled cluster many‐electron theory , 1977 .

[31]  K. Kowalski,et al.  Physical and mathematical content of coupled-cluster equations. IV. Impact of approximations to the cluster operator on the structure of solutions , 1999 .

[32]  R. Bartlett,et al.  The coupled‐cluster single, double, triple, and quadruple excitation method , 1992 .

[33]  Josef Paldus,et al.  Approximate account of the connected quadruply excited clusters in the coupled-pair many-electron theory , 1984 .

[34]  F. Coester,et al.  Short-range correlations in nuclear wave functions , 1960 .

[35]  Rodney J. Bartlett,et al.  Coupled-cluster methods with internal and semi-internal triply and quadruply excited clusters: CCSDt and CCSDtq approaches , 1999 .

[36]  Josef Paldus,et al.  Correlation Problems in Atomic and Molecular Systems. IV. Extended Coupled-Pair Many-Electron Theory and Its Application to the B H 3 Molecule , 1972 .

[37]  R. Bartlett,et al.  Recursive intermediate factorization and complete computational linearization of the coupled-cluster single, double, triple, and quadruple excitation equations , 1991 .

[38]  John D. Watts,et al.  Non-iterative fifth-order triple and quadruple excitation energy corrections in correlated methods , 1990 .

[39]  N. Oliphant,et al.  Coupled‐cluster method truncated at quadruples , 1991 .

[40]  R. Bartlett,et al.  Erratum: A coupled cluster approach with triple excitations [J. Chem. Phys. 81, 5906 (1984)] , 1985 .

[41]  L. Stolarczyk.  Complete active space coupled-cluster method. Extension of single-reference coupled-cluster method using the CASSCF wavefunction , 1994 .

[42]  P. Piecuch,et al.  STATE-SELECTIVE MULTI-REFERENCE COUPLED-CLUSTER THEORY EMPLOYING THE SINGLE-REFERENCE FORMALISM : APPLICATION TO AN EXCITED STATE OF H8 , 1995 .

[43]  Rodney J. Bartlett,et al.  Convergence of the coupled-cluster singles, doubles and triples method , 1988 .

[44]  D. Rutkowska,et al.  An investigation of the reliability of the Galerkin-Petrov method , 1978 .

[45]  Henry F. Schaefer,et al.  A new implementation of the full CCSDT model for molecular electronic structure , 1988 .

[46]  John F. Stanton,et al.  The ACES II program system , 1992 .

[47]  S. J. Cole,et al.  Comparison of MBPT and coupled cluster methods with full CI. II. Polarized basis sets , 1987 .

[48]  Josef Paldus,et al.  Correlation problems in atomic and molecular systems III. Rederivation of the coupled-pair many-electron theory using the traditional quantum chemical methodst†‡§ , 1971 .

[49]  P. Wormer,et al.  Coupled-pair theories and Davidson-type corrections for quasidegenerate states: the H4 model revisited , 1988 .

[50]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[51]  M. Nooijen,et al.  The coupled-cluster correction to multi-reference configuration interaction method: application to excited states , 2000 .

[52]  P. Piecuch,et al.  Molecular quadrupole moment functions of HF and N2. I. Ab initio linear‐response coupled‐cluster results , 1996 .

[53]  Jürgen Gauss,et al.  Coupled‐cluster methods with noniterative triple excitations for restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients , 1993 .

[54]  P. Piecuch,et al.  State‐selective multireference coupled‐cluster theory: In pursuit of property calculation , 1996 .

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

[56]  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 .

[57]  B. G. Adams,et al.  Application of graphical methods of spin algebras to limited CI approaches. I. Closed shell case , 1977 .

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

[59]  Nicholas C. Handy,et al.  Exact solution (within a double-zeta basis set) of the schrodinger electronic equation for water , 1981 .

[60]  M. Head‐Gordon,et al.  Fifth order Moeller-Plesset perturbation theory: comparison of existing correlation methods and implementation of new methods correct to fifth order , 1990 .

[61]  Josef Paldus,et al.  On the solution of coupled-cluster equations in the fully correlated limit of cyclic polyene model , 1991 .

[62]  R. Bartlett,et al.  Triple excitations in coupled‐cluster theory: Energies and analytical derivatives , 1993 .

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

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

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

[66]  J. Paldus,et al.  Externally corrected singles and doubles coupled cluster methods for open-shell systems , 1997 .

[67]  R. Bartlett,et al.  Performance of single-reference coupled-cluster methods for quasidegenerate problems: The H4 model , 1991 .

[68]  S. Kucharski,et al.  Coupled-cluster methods with internal and semi-internal triply excited clusters: Vibrational spectrum of the HF molecule , 1999 .

[69]  Josef Paldus,et al.  A Critical Assessment of Coupled Cluster Method in Quantum Chemistry , 2007 .

[70]  P. Piecuch,et al.  BREAKING BONDS WITH THE STATE-SELECTIVE MULTIREFERENCE COUPLED-CLUSTER METHOD EMPLOYING THE SINGLE-REFERENCE FORMALISM , 1995 .

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