A unitary multiconfigurational coupled‐cluster method: Theory and applications

A unitary wave operator exp(G) is used to relate a multiconfigurational reference function Φ to the full, potentially exact, electronic eigenfunction Ψ=exp(G)Φ. If the reference function Φ is of a generalized complete‐active‐space (CAS) form, then the energy, computed as 〈Φ‖exp(−G)H exp(G)‖Φ〉 is size extensive; here H is the full N‐electron Hamiltonian. The Hausdorff expansion of exp(−G)H exp(G) is truncated at second order as part of our development. The parameters which appear in the cluster operator G are determined by making this second‐order energy stationary. Applications to the widely studied H2O (at the double zeta basis level) and lowest and first excited 1A1 states of BeH2 are performed in order to test this method on problems where ‘‘exact’’ results are known.

[1]  J. Hinze,et al.  The Unitary group for the evaluation of electronic energy matrix elements , 1981 .

[2]  Ajit Banerjee,et al.  Applications of multiconfigurational coupled‐cluster theory , 1982 .

[3]  B. Roos,et al.  A Comparison of the Super-CI and the Newton-Raphson Scheme in the Complete Active Space SCF Method , 1980 .

[4]  S. J. Cole,et al.  Erratum: Towards a full CCSDT model for electron correlation [J. Chem. Phys. 83, 4041 (1985)] , 1986 .

[5]  H. Primas.  GENERALIZED PERTURBATION THEORY IN OPERATOR FORM , 1963 .

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

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

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

[9]  M. Hoffmann,et al.  Influence of molecular geometry on valence space for quasidegenerate many-body perturbation theory , 1987 .

[10]  H. Schaefer,et al.  The treatment of triple excitations within the coupled cluster description of molecular electronic structure , 1985 .

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

[12]  V. Kvasnicka.  Quasidegenerate coupled-cluster approach with hermitian model Hamiltonian , 1983 .

[13]  A. Szabo,et al.  Modern quantum chemistry , 1982 .

[14]  Claus Ehrhardt,et al.  The coupled pair functional (CPF). A size consistent modification of the CI(SD) based on an energy functional , 1985 .

[15]  H. Schaefer,et al.  Generalization of analytic configuration interaction (CI) gradient techniques for potential energy hypersurfaces, including a solution to the coupled perturbed Hartree–Fock equations for multiconfiguration SCF molecular wave functions , 1982 .

[16]  H. Schaefer,et al.  A theory of self‐consistent electron pairs. Computational methods and preliminary applications , 1976 .

[17]  E. Dalgaard.  Expansion and completeness theorems for operator manifolds , 1979 .

[18]  D. Mukherjee,et al.  A non-perturbative open-shell theory for atomic and molecular systems: Application to transbutadiene , 1975 .

[19]  K. Freed.  Theoretical foundations of purely semiempirical quantum chemistry , 1974 .

[20]  R. Offermann.  Degenerate many fermion theory in expS form: (II). Comparison with perturbation theory☆ , 1976 .

[21]  Klaus Ruedenberg,et al.  MCSCF optimization through combined use of natural orbitals and the brillouin–levy–berthier theorem , 1979 .

[22]  R. Bartlett,et al.  Towards a full CCSDT model for electron correlation. CCSDT-n models , 1987 .

[23]  Hans-Joachim Werner,et al.  The self‐consistent electron pairs method for multiconfiguration reference state functions , 1982 .

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

[25]  R. Yaris.  Cluster Expansions and the Unitary Group , 1965 .

[26]  F. B. Brown,et al.  Multireference configuration interaction treatment of potential energy surfaces: symmetric dissociation of H2O in a double-zeta basis , 1984 .

[27]  H. Kümmel.  Compound pair states in imperfect Fermi gases , 1961 .

[28]  G. D. Purvis,et al.  Comparison of MBPT and coupled-cluster methods with full CI. Importance of triplet excitation and infinite summations☆ , 1983 .

[29]  I. Lindgren,et al.  A Numerical Coupled-Cluster Procedure Applied to the Closed-Shell Atoms Be and Ne , 1980 .

[30]  A. Banerjee,et al.  Multiconfiguration wavefunctions for excited states. Selection of optimal configurations: The b 1Σ+ and d 1Σ+ states of NH , 1977 .

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

[32]  P. Wormer,et al.  Relationship between configuration interaction and coupled cluster approaches , 1982 .

[33]  Raymond J. Seeger,et al.  Lectures in Theoretical Physics , 1962 .

[34]  H. Monkhorst,et al.  Analytic connection between configuration–interaction and coupled‐cluster solutions , 1978 .

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

[36]  P. Payne.  Matrix element factorization in the unitary group approach for configuration interaction calculations , 1982 .

[37]  S. Salomonson,et al.  Many-Body Perturbation Theory of the Effective Electron-Electron Interaction for Open-Shell Atoms , 1980 .

[38]  M. Robb,et al.  A size consistent unitary group approach Multi-reference linear coupled cluster theory , 1983 .

[39]  P. Joergensen,et al.  Second Quantization-based Methods in Quantum Chemistry , 1981 .

[40]  H. Schaefer.  Methods of Electronic Structure Theory , 1977 .

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