Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy.

We explore the concept of seniority number (defined as the number of unpaired electrons in a determinant) when applied to the problem of electron correlation in atomic and molecular systems. Although seniority is a good quantum number only for certain model Hamiltonians (such as the pairing Hamiltonian), we show that it provides a useful partitioning of the electronic full configuration interaction (FCI) wave function into rapidly convergent Hilbert subspaces whose weight diminishes as its seniority number increases. The primary focus of this study is the adequate description of static correlation effects. The examples considered are the ground states of the helium, beryllium, and neon atoms, the symmetric dissociation of the N(2) and CO(2) molecules, as well as the symmetric dissociation of an H(8) hydrogen chain. It is found that the symmetry constraints that are normally placed on the spatial orbitals greatly affect the convergence rate of the FCI expansion. The energy relevance of the seniority zero sector (determinants with all paired electrons) increases dramatically if orbitals of broken spatial symmetry (as those commonly used for Hubbard Hamiltonian studies) are allowed in the wave function construction.

[1]  T. Yanai,et al.  High-performance ab initio density matrix renormalization group method: applicability to large-scale multireference problems for metal compounds. , 2009, The Journal of chemical physics.

[2]  Hiroshi Nakatsuji,et al.  Structure of the exact wave function , 2000 .

[3]  S. Xantheas,et al.  Exploiting regularity in systematic sequences of wavefunctions which approach the full CI limit , 1992 .

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

[5]  N. Sherman,et al.  Exact eigenstates of the pairing-force Hamiltonian , 1964 .

[6]  K. Ruedenberg,et al.  Electron pairs, localized orbitals and electron correlation , 2002 .

[7]  E. Davidson,et al.  The electron affinity of oxygen: A systematic configuration interaction approach , 1989 .

[8]  Klaus Ruedenberg,et al.  Split-localized orbitals can yield stronger configuration interaction convergence than natural orbitals , 2003 .

[9]  G. Scuseria,et al.  Strong correlations via constrained-pairing mean-field theory. , 2009, The Journal of chemical physics.

[10]  Jürgen Gauss,et al.  State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve. , 2004, The Journal of chemical physics.

[11]  K. Ruedenberg,et al.  A priori Identification of Configurational Deadwood , 2009 .

[12]  Micah L. Abrams,et al.  On the orbital dependence of compact, weight-selected configuration interaction and coupled-cluster wave functions , 2005 .

[13]  D. G. Hopper,et al.  An improved MCSCF method , 2009 .

[14]  K. Ruedenberg,et al.  Correlation energy extrapolation by intrinsic scaling. I. Method and application to the neon atom. , 2004, The Journal of chemical physics.

[15]  R. Richardson Application to the exact theory of the pairing model to some even isotopes of lead , 1963 .

[16]  Ernest R. Davidson,et al.  Configuration interaction calculations on the nitrogen molecule , 1974 .

[17]  D. Klein,et al.  Chemical sub-structural cluster expansions for molecular properties. , 1999, SAR and QSAR in environmental research.

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

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

[20]  D. B. Cook,et al.  Doubly-occupied orbital MCSCF methods , 1975 .

[21]  L. Cooper,et al.  Theory of superconductivity , 1957 .

[22]  J. P. Malrieu,et al.  Iterative perturbation calculations of ground and excited state energies from multiconfigurational zeroth‐order wavefunctions , 1973 .

[23]  J. Tennyson,et al.  High-Accuracy ab Initio Rotation-Vibration Transitions for Water , 2003, Science.

[24]  R. Bartlett,et al.  Monte Carlo configuration interaction predictions for the electronic spectra of Ne, CH2, C2, N2, and H2O compared to full configuration interaction calculations. , 2008, The Journal of chemical physics.

[25]  Gabriel Kotliar,et al.  Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory , 2004 .

[26]  Garnet Kin-Lic Chan,et al.  Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group. , 2006, The Journal of chemical physics.

[27]  R. Bartlett,et al.  Coupled-cluster theory in quantum chemistry , 2007 .

[28]  Ernest R. Davidson,et al.  Studies in Configuration Interaction: The First-Row Diatomic Hydrides , 1969 .

[29]  J. Ivanic Direct configuration interaction and multiconfigurational self-consistent-field method for multiple active spaces with variable occupations. I. Method , 2003 .

[30]  C. David Sherrill,et al.  Natural orbitals as substitutes for optimized orbitals in complete active space wavefunctions , 2004 .

[31]  Piotr Piecuch,et al.  Intriguing accuracies of the exponential wave function expansions exploiting finite two-body correlation operators in calculations for many-electron systems , 2006 .

[32]  A. J. Coleman THE STRUCTURE OF FERMION DENSITY MATRICES , 1963 .

[33]  John A. Pople,et al.  Nobel Lecture: Quantum chemical models , 1999 .

[34]  Garnet Kin-Lic Chan,et al.  Dynamical mean-field theory from a quantum chemical perspective. , 2010, The Journal of chemical physics.

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

[36]  Thomas M Henderson,et al.  Projected quasiparticle theory for molecular electronic structure. , 2011, The Journal of chemical physics.

[37]  William A. Goddard,et al.  The Description of Chemical Bonding From AB Initio Calculations , 1978 .

[38]  Klaus Ruedenberg,et al.  Identification of deadwood in configuration spaces through general direct configuration interaction , 2001 .

[39]  Piotr Piecuch,et al.  Single-reference, size-extensive, non-iterative coupled-cluster approaches to bond breaking and biradicals , 2006 .

[40]  Martin Head-Gordon,et al.  The perfect quadruples model for electron correlation in a valence active space. , 2009, The Journal of chemical physics.

[41]  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 .

[42]  Feng Xu,et al.  Geminal model chemistry. IV. Variational and size consistent pure spin states. , 2007, The Journal of chemical physics.

[43]  K. Ruedenberg,et al.  Ab initio potential energy curve of F2. IV. Transition from the covalent to the van der Waals region: competition between multipolar and correlation forces. , 2009, The Journal of chemical physics.

[44]  J. V. Ortiz,et al.  The AGP wavefunction and its relation to other descriptions of electronic structure , 2009 .

[45]  David Feller,et al.  A survey of factors contributing to accurate theoretical predictions of atomization energies and molecular structures. , 2008, The Journal of chemical physics.

[46]  K. Wilson The renormalization group: Critical phenomena and the Kondo problem , 1975 .

[47]  Thom H. Dunning,et al.  Gaussian basis sets for use in correlated molecular calculations. V. Core-valence basis sets for boron through neon , 1995 .

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

[49]  G. Scuseria,et al.  Constrained-pairing mean-field theory. IV. Inclusion of corresponding pair constraints and connection to unrestricted Hartree-Fock theory. , 2010, The Journal of chemical physics.

[50]  Francesco A Evangelista,et al.  High-order excitations in state-universal and state-specific multireference coupled cluster theories: model systems. , 2006, The Journal of chemical physics.

[51]  P. Schuck,et al.  Self-consistent random phase approximation: Application to the Hubbard model for finite number of sites , 2004, cond-mat/0407223.

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

[53]  J. Hubbard Electron correlations in narrow energy bands , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[54]  Takashi Tsuchimochi,et al.  Constrained-pairing mean-field theory. II. Exact treatment of dissociations to nondegenerate orbitals. , 2009, The Journal of chemical physics.

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

[56]  Robert J Harrison,et al.  The lowest energy states of the group-IIIA-group-VA heteronuclear diatomics: BN, BP, AlN, and AlP from full configuration interaction calculations. , 2006, The Journal of chemical physics.

[57]  M. Gordon,et al.  Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum. , 2007, The Journal of chemical physics.

[58]  L. Kier,et al.  A molecular orbital valence bond study of 3-methyl sydnone and 3-methyl pseudosydnone , 1990 .

[59]  Anton V. Sinitskiy,et al.  Strong correlation in hydrogen chains and lattices using the variational two-electron reduced density matrix method. , 2010, The Journal of chemical physics.

[60]  Marcel Nooijen,et al.  The density matrix renormalization group self-consistent field method: orbital optimization with the density matrix renormalization group method in the active space. , 2008, The Journal of chemical physics.

[61]  M. Gordon,et al.  Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method. , 2007, The Journal of chemical physics.

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

[63]  P. Knowles,et al.  An efficient internally contracted multiconfiguration–reference configuration interaction method , 1988 .

[64]  G. Scuseria,et al.  Constrained-pairing mean-field theory. III. Inclusion of density functional exchange and correlation effects via alternative densities. , 2010, The Journal of chemical physics.

[65]  J. Egido,et al.  Generalized BCS ansatz for pairing correlations in superconducting grains , 2003 .

[66]  R. Shepard The Multiconfiguration Self‐Consistent Field Method , 2007 .

[67]  Ali Alavi,et al.  Communications: Survival of the fittest: accelerating convergence in full configuration-interaction quantum Monte Carlo. , 2010, The Journal of chemical physics.

[68]  R. Richardson A restricted class of exact eigenstates of the pairing-force Hamiltonian , 1963 .

[69]  S. Pittel,et al.  Colloquium: Exactly solvable Richardson-Gaudin models for many-body quantum systems , 2004, nucl-th/0405011.

[70]  Robert J. Buenker,et al.  Energy extrapolation in CI calculations , 1975 .

[71]  David A Mazziotti,et al.  Multireference self-consistent-field energies without the many-electron wave function through a variational low-rank two-electron reduced-density-matrix method. , 2007, The Journal of chemical physics.

[72]  Fa Wang,et al.  The Electron-Pairing Mechanism of Iron-Based Superconductors , 2011, Science.

[73]  Klaus Ruedenberg,et al.  Localized Atomic and Molecular Orbitals , 1963 .

[74]  A. Franceschetti,et al.  An optimized configuration interaction method for calculating electronic excitations in nanostructures , 2008 .

[75]  R. L. Roy,et al.  Orbital invariant single-reference coupled electron pair approximation with extensive renormalized triples correction , 2006 .

[76]  C. Sherrill Frontiers in electronic structure theory. , 2010, The Journal of chemical physics.

[77]  J. M. Eisenberg,et al.  Quantum Mechanics of Many Degrees of Freedom , 1988 .

[78]  R. Richardson Exact Eigenstates of the Pairing‐Force Hamiltonian. II , 1965 .

[79]  T. H. Dunning Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[80]  Francesco A Evangelista,et al.  Perturbative triples corrections in state-specific multireference coupled cluster theory. , 2010, The Journal of chemical physics.

[81]  E. Davidson,et al.  Ab initio multireference CI determinations of the electron affinity of carbon and oxygen , 1985 .

[82]  K. Ruedenberg,et al.  Correlation energy extrapolation by intrinsic scaling. IV. Accurate binding energies of the homonuclear diatomic molecules carbon, nitrogen, oxygen, and fluorine. , 2005, The Journal of chemical physics.

[83]  A. Varandas Extrapolation to the complete-basis-set limit and the implications of avoided crossings: The X 1Sigma(g)+, B 1Delta(g), and B' 1Sigma(g)+ states of C2. , 2008, The Journal of chemical physics.

[84]  J. R. Schrieffer,et al.  Theory of superconductivity , 1957 .

[85]  K. Ruedenberg,et al.  Accurate ab initio potential energy curve of O2. II. Core-valence correlations, relativistic contributions, and vibration-rotation spectrum. , 2010, The Journal of chemical physics.

[86]  K. Wilson The renormalization group and critical phenomena , 1983 .

[87]  Robert J. Harrison,et al.  Approximating full configuration interaction with selected configuration interaction and perturbation theory , 1991 .

[88]  K. Ruedenberg,et al.  Accurate ab initio potential energy curve of O2. I. Nonrelativistic full configuration interaction valence correlation by the correlation energy extrapolation by intrinsic scaling method. , 2010, The Journal of chemical physics.

[89]  A. J. Coleman Structure of Fermion Density Matrices. II. Antisymmetrized Geminal Powers , 1965 .

[90]  Martin Head-Gordon,et al.  Tractable spin-pure methods for bond breaking: Local many-electron spin-vector sets and an approximate valence bond model. , 2009, The Journal of chemical physics.

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

[92]  P. Knowles,et al.  A linked electron pair functional. , 2010, The Journal of chemical physics.

[93]  Chris Hooley,et al.  The strong-correlations puzzle , 2009 .

[94]  M. Hall,et al.  GENERALIZED MOLECULAR ORBITAL THEORY II , 1997 .

[95]  Isaiah Shavitt,et al.  The history and evolution of configuration interaction , 1998 .

[96]  David A Mazziotti,et al.  Active-space two-electron reduced-density-matrix method: complete active-space calculations without diagonalization of the N-electron Hamiltonian. , 2008, The Journal of chemical physics.

[97]  Anna I. Krylov,et al.  Spin-flip configuration interaction: an electronic structure model that is both variational and size-consistent , 2001 .

[98]  M. Strayer,et al.  The Nuclear Many-Body Problem , 2004 .

[99]  Micah L. Abrams,et al.  Important configurations in configuration interaction and coupled-cluster wave functions , 2005 .

[100]  V. Tyuterev,et al.  Are ab initio quantum chemistry methods able to predict vibrational states up to the dissociation limit for multi-electron molecules close to spectroscopic accuracy? , 2011, Physical chemistry chemical physics : PCCP.

[101]  Sandro Sorella,et al.  Geminal wave functions with Jastrow correlation: A first application to atoms , 2003 .

[102]  Konrad Patkowski,et al.  On the Elusive Twelfth Vibrational State of Beryllium Dimer , 2009, Science.

[103]  G. Ortiz,et al.  Breached pairing in trapped three-color atomic Fermi gases , 2008, 0812.2395.

[104]  B. Roos The Complete Active Space Self‐Consistent Field Method and its Applications in Electronic Structure Calculations , 2007 .

[105]  John Edward Lennard-Jones,et al.  The molecular orbital theory of chemical valency XVI. A theory of paired-electrons in polyatomic molecules , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[106]  P. Schuck,et al.  Class of exactly solvable pairing models. , 2001, Physical review letters.

[107]  Ron Shepard,et al.  Optimization of nonlinear wave function parameters , 2006 .

[108]  G. Scuseria,et al.  Constrained-pairing mean-field theory. V. Triplet pairing formalism. , 2011, The Journal of chemical physics.

[109]  K. Ruedenberg,et al.  Correlation energy extrapolation by intrinsic scaling. II. The water and the nitrogen molecule. , 2004, The Journal of chemical physics.

[110]  Gerardo Rodríguez Ortíz,et al.  BCS-to-BEC crossover from the exact BCS solution , 2005, cond-mat/0503664.

[111]  Ramon Carbo,et al.  A general multiconfiguration paired excitation self-consistent field theory (MC PE SCF) , 1977 .