Multireference Brillouin–Wigner coupled cluster (MR‐BWCC) theory applied to the H8 model: Comparison with CCSD(T) theory

Multireference Brillouin–Wigner coupled cluster theory is applied to the H8 model, a model in which the degree of quasidegeneracy is a function of a single geometrical parameter a. Using a 6-31G basis set, multireference Brillouin–Wigner coupled cluster theory (MR-BWCC) is applied to the H8 model as a function of a both with and without an a posteriori correction for the lack of extensivity. The resulting potential energy curve is compared with the corresponding curve obtained by the application of single reference CCSD theory (“coupled cluster singles and doubles”), and with the curve obtained after adding a perturbative estimate of the triple excitation energy component, CCSD(T). The MR-BWCCSD, CCSD, and CCSD(T) curves are also compared with the full configuration interaction (FCI) curve defining the exact solution within the chosen basis set. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

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

[2]  P. Mach,et al.  Brillouin-Wigner Expansions in Quantum Chemistry: Bloch-Like and Lippmann-Schwinger-Like Equations , 2003 .

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

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

[5]  Stephen R. Langhoff,et al.  Quantum mechanical electronic structure calculations with chemical accuracy , 1995 .

[6]  Sonia Coriani,et al.  The molecular electric quadrupole moment of N2 , 1998 .

[7]  Angela K. Wilson,et al.  Benchmark calculations with correlated molecular wave functions XII. Core correlation effects on the homonuclear diatomic molecules B2-F2 , 1997 .

[8]  P. Pyykkö,et al.  An improved value of the nuclear quadrupole moment of the 197 keV I = 52 excited state of 19F , 1997 .

[9]  I. Hubač,et al.  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 , 1997 .

[10]  Henry F. Schaefer,et al.  The shape‐driven graphical unitary group approach to the electron correlation problem. Application to the ethylene molecule , 1982 .

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

[12]  Jan M. L. Martin Coupling between the convergence behavior of basis set and electron correlation: a quantitative study , 1997 .

[13]  P. C. Hariharan,et al.  Accuracy of AH n equilibrium geometries by single determinant molecular orbital theory , 1974 .

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

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

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

[17]  Mihály Kállay,et al.  On the convergence of the coupled-cluster sequence: The H8 model , 2001 .

[18]  E. Brändas,et al.  Fundamental world of quantum chemistry : a tribute to the memory of Per-Olov Löwdin , 2003 .

[19]  Jürgen Gauss,et al.  The prediction of molecular equilibrium structures by the standard electronic wave functions , 1997 .

[20]  Sonia Coriani,et al.  On the molecular electric quadrupole moment of C2H2 , 1999 .

[21]  P. Taylor,et al.  A theoretical investigation of the equilibrium electric dipole moment of ammonia , 1998 .

[22]  Piecuch,et al.  Application of Hilbert-space coupled-cluster theory to simple (H2)2 model systems. II. Nonplanar models. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[23]  J. Paldus,et al.  Applicability of non‐degenerate many‐body perturbation theory to quasidegenerate electronic states: A model study , 1983 .

[24]  J. Paldus,et al.  Applicability of nondegenerate many-body perturbation theory to quasi-degenerate electronic states. II. A two-state model , 1985 .

[25]  Mark S. Gordon,et al.  The isomers of silacyclopropane , 1980 .

[26]  T. Dunning,et al.  The dissociation energies of NF(X 3Σ−) and NCl(X 3Σ−) , 1997 .

[27]  I. Hubač,et al.  Multireference Brillouin—Wigner Coupled-Cluster Theory: Hilbert Space Approach , 1997 .

[28]  Kirk A. Peterson,et al.  BENCHMARK CALCULATIONS WITH CORRELATED MOLECULAR WAVE FUNCTIONS. VII: BINDING ENERGY AND STRUCTURE OF THE HF DIMER , 1995 .

[29]  C. David Sherrill,et al.  A comparison of polarized double-zeta basis sets and natural orbitals for full configuration interaction benchmarks , 2003 .

[30]  P. Taylor,et al.  A purely ab initio spectroscopic quality quartic force field for acetylene , 1998 .

[31]  P. Taylor,et al.  The geometry, vibrational frequencies, and total atomization energy of ethylene. A calibration study , 1996 .

[32]  Trygve Helgaker,et al.  Basis-set convergence of correlated calculations on water , 1997 .

[33]  Jan M. L. Martin THE TOTAL ATOMIZATION ENERGY AND HEAT OF FORMATION OF HCN(G) , 1996 .

[34]  Kirk A. Peterson,et al.  Intrinsic Errors in Several ab Initio Methods: The Dissociation Energy of N2 , 1995 .

[35]  M. Head‐Gordon,et al.  Partitioning Techniques in Coupled-Cluster Theory , 2003 .

[36]  P. C. Hariharan,et al.  The influence of polarization functions on molecular orbital hydrogenation energies , 1973 .

[37]  S. Wilson,et al.  Brillouin-Wigner Expansions in Quantum Chemistry: A robust approach to the quantum many-body problem in molecules , 2003 .

[38]  Gustavo E. Scuseria,et al.  Achieving Chemical Accuracy with Coupled-Cluster Theory , 1995 .

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

[40]  Uttam Sinha Mahapatra,et al.  Development of a size-consistent state-specific multireference perturbation theory with relaxed model-space coefficients , 1999 .

[41]  Jan M. L. Martin SPECTROSCOPIC QUALITY AB INITIO POTENTIAL CURVES FOR CH, NH, OH AND HF. A CONVERGENCE STUDY , 1998 .

[42]  E. Brändas,et al.  Fundamental World of Quantum Chemistry , 2003 .

[43]  Peter R. Taylor,et al.  Benchmark quality total atomization energies of small polyatomic molecules , 1997 .

[44]  J. Olsen,et al.  Full configuration interaction benchmark calculations of first-order one-electron properties of BH and HF , 1999 .

[45]  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 .

[46]  A. Saika,et al.  A note on the convergence of multiconfigurational many‐body perturbation theory , 1985 .

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

[48]  Trygve Helgaker,et al.  A systematic ab initio study of the water dimer in hierarchies of basis sets and correlation models , 1997 .

[49]  H. Schaefer,et al.  Natural orbitals from single and double excitation configuration interaction wave functions: their use in second‐order configuration interaction and wave functions incorporating limited triple and quadruple excitations , 1992 .

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

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

[52]  J. Pople,et al.  Self‐Consistent Molecular‐Orbital Methods. IX. An Extended Gaussian‐Type Basis for Molecular‐Orbital Studies of Organic Molecules , 1971 .

[53]  J. Paldus,et al.  Cluster relations for multireference coupled‐cluster theories: A model study , 1991 .

[54]  T. Dunning,et al.  Benchmark calculations with correlated molecular wave functions. IX. The weakly bound complexes Ar–H2 and Ar–HCl , 1998 .

[55]  T. Dunning,et al.  A new ab initio potential energy curve for the helium dimer , 1999 .

[56]  T. Dunning,et al.  Ab initio characterization of the structure and energetics of the ArHF complex , 1997 .

[57]  Timothy J. Lee,et al.  The atomization energy and proton affinity of NH3. An ab initio calibration study , 1996 .

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

[59]  Jan M. L. Martin Benchmark ab initio calculations of the total atomization energies of the first-row hydrides AHn (A = LiF) , 1997 .

[60]  Jan M. L. Martin Ab initio total atomization energies of small molecules — towards the basis set limit , 1996 .

[61]  Kirk A. Peterson,et al.  The CO molecule: the role of basis set and correlation treatment in the calculation of molecular properties , 1997 .

[62]  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.

[63]  T. H. Dunning,et al.  Ab initio investigation of the N2–HF complex: Accurate structure and energetics , 1996 .

[64]  I. Lindgren,et al.  On the connectivity criteria in the open-shell coupled-cluster theory for general model spaces , 1987 .

[65]  Antara Dutta,et al.  Full configuration interaction potential energy curves for breaking bonds to hydrogen: An assessment of single-reference correlation methods , 2003 .

[66]  Trygve Helgaker,et al.  Basis set convergence of the interaction energy of hydrogen-bonded complexes , 1999 .

[67]  P. Piecuch,et al.  New Alternatives for Electronic Structure Calculations: Renormalized, Extended, and Generalized Coupled-Cluster Theories , 2003 .

[68]  Josef Paldus,et al.  APPLICABILITY OF MULTI-REFERENCE MANY-BODY PERTURBATION THEORY TO THE DETERMINATION OF POTENTIAL ENERGY SURFACES : A MODEL STUDY , 1990 .

[69]  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.

[70]  Trygve Helgaker,et al.  Basis-set convergence in correlated calculations on Ne, N2, and H2O , 1998 .

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

[72]  K. Peterson,et al.  An examination of intrinsic errors in electronic structure methods using the Environmental Molecular Sciences Laboratory computational results database and the Gaussian-2 set , 1998 .

[73]  Kirk A. Peterson,et al.  Approximating the basis set dependence of coupled cluster calculations: Evaluation of perturbation theory approximations for stable molecules , 2000 .

[74]  U. Kaldor Can nondegenerate many-body perturbation theory be applied to quasidegenerate electronic states? , 1985 .

[75]  C. David Sherrill,et al.  An assessment of the accuracy of multireference configuration interaction (MRCI) and complete-active-space second-order perturbation theory (CASPT2) for breaking bonds to hydrogen , 2003 .

[76]  T. Dunning,et al.  Benchmark calculations with correlated molecular wavefunctions. XIII. Potential energy curves for He2, Ne2 and Ar2 using correlation consistent basis sets through augmented sextuple zeta , 1999 .

[77]  Timothy J. Lee,et al.  Accurate ab initio quartic force field and vibrational frequencies of the NH4+ ion and its deuterated forms , 1996 .

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