Spin-contamination of coupled-cluster wave functions

The propensity of approximate solutions of the electronic Schrodinger equation to break spin-symmetry is directly related to the quality of the approximate wave function, and thus can be used as a diagnostic tool. The quasi-variational nature of the (valence) optimized orbitals coupled-cluster doubles methods, (V)OO-CCD, enables a discussion of the stability of coupled-cluster wave functions in terms of both spin-contamination and a corresponding energy lowering relative to the pure spin solutions. The spin-contamination of (V)OO-CCD models has been studied for bond-breaking processes and diradicals. The main findings are: (i) The OO-CCD method is stable for a relatively large range of nuclear distortions and is capable of eliminating even very large spin-contamination of the unrestricted Hartree–Fock solution given that the molecular electronic configuration remains essentially single-reference. When a spin-contaminated solution arises, the energy splitting rapidly becomes large and 〈Ŝ2〉 approaches the H...

[1]  Lionel Salem,et al.  The Electronic Properties of Diradicals , 1972 .

[2]  N. Handy,et al.  Spin contamination in single-determinant wavefunctions , 1991 .

[3]  H. Fukutome.  Unrestricted Hartree–Fock theory and its applications to molecules and chemical reactions , 1981 .

[4]  R. K. Nesbet,et al.  Self‐Consistent Orbitals for Radicals , 1954 .

[5]  G. Scuseria,et al.  The optimization of molecular orbitals for coupled cluster wavefunctions , 1987 .

[6]  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 .

[7]  M. Klobukowski,et al.  Self-consistent field : theory and applications , 1990 .

[8]  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.

[9]  H. Schlegel,et al.  Moeller-Plesset perturbation theory with spin projection , 1988 .

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

[11]  P. Löwdin,et al.  Some Studies of the General Hartree-Fock Method , 1992 .

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

[13]  Michael W. Schmidt,et al.  Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model , 1982 .

[14]  R. Bartlett,et al.  Multiplicity of many-body wavefunctions using unrestricted Hartree-Fock reference functions , 1988 .

[15]  Wei Chen,et al.  Evaluation of S2 for correlated wave functions and spin projection of unrestricted Mo/ller–Plesset perturbation theory , 1994 .

[16]  Peter Pulay,et al.  The unrestricted natural orbital–complete active space (UNO–CAS) method: An inexpensive alternative to the complete active space–self‐consistent‐field (CAS–SCF) method , 1989 .

[17]  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 .

[18]  J. Pople,et al.  Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals , 1969 .

[19]  J. Calais.  Gap Equations and Instabilities for Extended Systems , 1985 .

[20]  P. Pulay,et al.  Half‐projected Hartree–Fock natural orbitals for defining CAS–SCF active spaces , 1993 .

[21]  Joseph G. Hoffman,et al.  Quantum Theory of Atoms, Molecules and the Solid State: A Tribute to John C. Slater , 1967 .

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

[23]  J. Baker.  Møller-Plesset perturbation theory with the AUHF wavefunction , 1988 .

[24]  P. Pulay,et al.  The unrestricted natural orbital-restricted active space method: methodology and implementation , 1998 .

[25]  V. Fock,et al.  Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems , 1930 .

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

[27]  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 .

[28]  Y. Smeyers,et al.  Half‐Projected and Projected Hartree‐Fock Calculations for Singlet Ground States. i. four‐Electron Atomic Systems , 1973 .

[29]  I. Mayer.  The Spin-Projected Extended Hartree-Fock Method , 1980 .

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

[31]  P. Löwdin,et al.  Some comments on the general Hartree—Fock method , 1993 .

[32]  Jon Baker,et al.  Q‐Chem 2.0: a high‐performance ab initio electronic structure program package , 2000, J. Comput. Chem..

[33]  P. Löwdin.  Quantum Theory of Many-Particle Systems. III. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects , 1955 .

[34]  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 .

[35]  John F. Stanton,et al.  On the extent of spin contamination in open‐shell coupled‐cluster wave functions , 1994 .

[36]  J. A. Gaunt.  A Theory of Hartree's Atomic Fields , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[37]  David H. Magers,et al.  Isomers and excitation energies of C4 , 1986 .

[38]  G. W. Pratt,et al.  Discussion on The Hartree-Fock Approximation , 1963 .

[39]  B. Roos,et al.  A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach , 1980 .