Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal.

We present a new, non-variational orbital-optimization scheme for the antisymmetric product of one-reference orbital geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [L. Bytautas, T. M. Henderson, C. A. Jimenez-Hoyos, J. K. Ellis, and G. E. Scuseria, J. Chem. Phys. 135, 044119 (2011)]. A numerical analysis is performed for the C2 and LiF molecules, for the CH2 singlet diradical as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases.

[1]  Gustavo E. Scuseria,et al.  Quasiparticle Coupled Cluster Theory for Pairing Interactions , 2014, 1403.6818.

[2]  D. Silver.  Natural Orbital Expansion of Interacting Geminals , 1969 .

[3]  D. L. Cooper,et al.  Correlation and Localization , 1999 .

[4]  C. M. Moser,et al.  L'interaction de configuration comme méthode de calcul des orbitales moléculaires du champ self-consistent , 1956 .

[5]  Uğur Bozkaya,et al.  Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory. , 2011, The Journal of chemical physics.

[6]  Péter R. Surján,et al.  The interaction of chemical bonds. IV. Interbond charge transfer by a coupled‐cluster‐type formalism , 1995 .

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

[8]  Laimutis Bytautas,et al.  Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy. , 2011, The Journal of chemical physics.

[9]  L. Stella,et al.  Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study , 2011, 1110.1746.

[10]  P. Surján,et al.  Interaction of chemical bonds. V. Perturbative corrections to geminal‐type wave functions , 2000 .

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

[12]  Klaas J. H. Giesbertz,et al.  Are natural orbitals useful for generating an efficient expansion of the wave function , 2013, 1309.2449.

[13]  R. Mcweeny,et al.  The density matrix in may-electron quantum mechanics III. Generalized product functions for beryllium and four-electron ions , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[14]  Paul W. Ayers,et al.  The influence of orbital rotation on the energy of closed-shell wavefunctions , 2014 .

[15]  K. Peterson.  Accurate multireference configuration interaction calculations on the lowest 1Σ+ and 3Π electronic states of C2, CN+, BN, and BO+ , 1995 .

[16]  J. A. Coxon.  The radial Hamiltonian operator for LiH X1Σ , 1992 .

[17]  F. Grein,et al.  Multiconfiguration wavefunctions obtained by application of the generalized Brillouin theorem , 1971 .

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

[19]  M. Reiher,et al.  Entanglement Measures for Single- and Multireference Correlation Effects. , 2012, The journal of physical chemistry letters.

[20]  W. Goddard,et al.  Generalized valence bond wavefunctions for the low lying states of methylene , 1972 .

[21]  W. Kutzelnigg.  Separation of strong (bond-breaking) from weak (dynamical) correlation , 2012 .

[22]  Werner Kutzelnigg,et al.  Direct Determination of Natural Orbitals and Natural Expansion Coefficients of Many‐Electron Wavefunctions. I. Natural Orbitals in the Geminal Product Approximation , 1964 .

[23]  Paul W. Ayers,et al.  A size-consistent approach to strongly correlated systems using a generalized antisymmetrized product of nonorthogonal geminals , 2013 .

[24]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[25]  Gustavo E. Scuseria,et al.  Seniority zero pair coupled cluster doubles theory. , 2014, The Journal of chemical physics.

[26]  Bernard Levy,et al.  Generalized brillouin theorem for multiconfigurational SCF theories , 1968 .

[27]  Francesco A Evangelista,et al.  Alternative single-reference coupled cluster approaches for multireference problems: the simpler, the better. , 2011, The Journal of chemical physics.

[28]  P. Durand,et al.  Transposition of the Theories Describing Superconducting Systems to Molecular Systems. Method of Biorbitals , 1965 .

[29]  Edina Rosta,et al.  Two-body zeroth order hamiltonians in multireference perturbation theory: The APSG reference state , 2002 .

[30]  Paul W. Ayers,et al.  The density matrix renormalization group for ab initio quantum chemistry , 2013, The European Physical Journal D.

[31]  W. Kutzelnigg.  On the validity of the electron pair approximation for the Beryllium ground state , 1965 .

[32]  M. Reiher,et al.  Quantum entanglement in carbon-carbon, carbon-phosphorus and silicon-silicon bonds. , 2014, Physical chemistry chemical physics : PCCP.

[33]  Patrick Bultinck,et al.  A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals. , 2013, Journal of chemical theory and computation.

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

[35]  F. Grein,et al.  Convergence behavior of some multiconfiguration methods , 1976 .

[36]  Vitaly A. Rassolov,et al.  A geminal model chemistry , 2002 .

[37]  Paul W. Ayers,et al.  Efficient description of strongly correlated electrons with mean-field cost , 2014, 1401.8019.

[38]  Toon Verstraelen,et al.  Assessing the accuracy of new geminal-based approaches. , 2014, The journal of physical chemistry. A.

[39]  A. D. McLean,et al.  Symmetry breaking in molecular calculations and the reliable prediction of equilibrium geometries. The formyloxyl radical as an example , 1985 .

[40]  W. Goddard,et al.  Generalized valence bond description of bonding in low-lying states of molecules , 1973 .

[41]  C. S. Sharma,et al.  The generalised Brillouin theorem , 1981 .

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

[43]  P. Limacher,et al.  Simple and inexpensive perturbative correction schemes for antisymmetric products of nonorthogonal geminals. , 2014, Physical chemistry chemical physics : PCCP.

[44]  Péter R. Surján,et al.  AN INTRODUCTION TO THE THEORY OF GEMINALS , 1999 .

[45]  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.

[46]  P. Surján,et al.  Strongly orthogonal geminals: size-extensive and variational reference states , 2012, Journal of Mathematical Chemistry.

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

[48]  David Feller.  The role of databases in support of computational chemistry calculations , 1996 .

[49]  P. Surján,et al.  Generalized Møller-Plesset Partitioning in Multiconfiguration Perturbation Theory. , 2010, Journal of chemical theory and computation.

[50]  G. Náray‐Szabó.  All-pair wavefunction for many-electron states with the highest multiplicity , 1973 .

[51]  G. Scuseria,et al.  On Pair Functions for Strong Correlations. , 2013, Journal of chemical theory and computation.

[52]  K. Ruedenberg,et al.  Electron Correlation and Augmented Separated‐Pair Expansion , 1968 .

[53]  G. Náray‐Szabó.  All‐pair wave function and reduced variational equation for electronic systems , 1975 .

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

[55]  Frank Weinhold,et al.  Reduced Density Matrices of Atoms and Molecules. I. The 2 Matrix of Double‐Occupancy, Configuration‐Interaction Wavefunctions for Singlet States , 1967 .

[56]  U. Kaldor.  Calculation of Extended Hartree‐Fock Wavefunctions , 1968 .

[57]  Trygve Helgaker,et al.  Molecular Electronic-Structure Theory: Helgaker/Molecular Electronic-Structure Theory , 2000 .

[58]  Jun Li,et al.  Basis Set Exchange: A Community Database for Computational Sciences , 2007, J. Chem. Inf. Model..

[59]  John F. Stanton,et al.  Applications of Post‐Hartree—Fock Methods: A Tutorial , 2007 .

[60]  W. Marsden.  I and J , 2012 .

[61]  U. Kaldor.  Spin-Extended Wave Functions for First-Row Atoms , 1968 .

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

[63]  Nan Lin,et al.  Dynamical mean-field theory for quantum chemistry. , 2010, Physical review letters.

[64]  J. Olsen,et al.  Orbital-optimized coupled-cluster theory does not reproduce the full configuration-interaction limit. , 2005, The Journal of chemical physics.

[65]  B. A. Hess,et al.  QC-DMRG study of the ionic-neutral curve crossing of LiF , 2002 .

[66]  G. Granucci,et al.  The electronic mean field configuration interaction method: II – Improving guess geminals , 2007 .

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

[68]  M. Ratner.  Molecular electronic-structure theory , 2000 .

[69]  D. Silver.  Bilinear Orbital Expansion of Geminal‐Product Correlated Wavefunctions , 1970 .

[70]  A. Varandas,et al.  Accurate ab initio potential energy curves for the classic Li-F ionic-covalent interaction by extrapolation to the complete basis set limit and modeling of the radial nonadiabatic coupling. , 2009, The Journal of chemical physics.

[71]  P. Cassam-Chenaï.  The electronic mean-field configuration interaction method. I. Theory and integral formulas. , 2006, The Journal of chemical physics.

[72]  Luis Lain,et al.  Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions. , 2013, The Journal of chemical physics.

[73]  Robert G. Parr,et al.  Theory of Separated Electron Pairs , 1958 .

[74]  T. Crawford,et al.  Some surprising failures of Brueckner coupled cluster theory , 2000 .

[75]  Péter R. Surján,et al.  THE INTERACTION OF CHEMICAL BONDS. III: PERTURBED STRICTLY LOCALIZED GEMINALS IN LMO BASIS , 1994 .