Direct selected multireference configuration interaction calculations for large systems using localized orbitals.

A selected multireference configuration interaction (CI) method and the corresponding code are presented. It is based on a procedure of localization that permits to obtain well localized occupied and virtual orbitals. Due to the local character of the electron correlation, using local orbitals allows one to neglect long range interactions. In a first step, three topological matrices are constructed, which determine whether two orbitals must be considered as interacting or not. Two of them concern the truncation of the determinant basis, one for occupied/virtual, the second one for dispersive interactions. The third one concerns the truncation of the list of two electron integrals. This approach permits a fine analysis of each kind of approximation and induces a huge reduction of the CI size and of the computational time. The procedure is tested on linear polyene aldehyde chains, dissociation potential energy curve, and reaction energy of a pesticide-Ca(2+) complex and finally on transition energies of a large iron system presenting a light-induced excited spin-state trapping effect.

[1]  Péter G. Szalay,et al.  New Versions of Approximately Extensive Corrected Multireference Configuration Interaction Methods , 1996 .

[2]  Peter Pulay,et al.  Local configuration interaction: An efficient approach for larger molecules , 1985 .

[3]  Jing Ma,et al.  Linear scaling local correlation approach for solving the coupled cluster equations of large systems , 2002, J. Comput. Chem..

[4]  N. H. Beebe,et al.  Simplifications in the generation and transformation of two‐electron integrals in molecular calculations , 1977 .

[5]  Christian Ochsenfeld,et al.  Rigorous integral screening for electron correlation methods. , 2005, The Journal of chemical physics.

[6]  C. Bauschlicher,et al.  Benchmark full configuration-interaction calculations on HF and NH2 , 1986 .

[7]  R. Lindh,et al.  Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals. , 2007, The Journal of chemical physics.

[8]  Stefano Evangelisti,et al.  Reduction of the CI dimension based on the use of local orbitals: Application to conjugated systems and excited states , 2006 .

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

[10]  Per-Olof Widmark,et al.  Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions , 1995 .

[11]  S. F. Boys.  Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another , 1960 .

[12]  Stefano Evangelisti,et al.  Direct generation of local orbitals for multireference treatment and subsequent uses for the calculation of the correlation energy , 2002 .

[13]  Rodney J. Bartlett,et al.  Approximately extensive modifications of the multireference configuration interaction method: A theoretical and practical analysis , 1995 .

[14]  J. Whitten.  Localized orbital interactions: d‐electron exchange and correlation , 2003 .

[15]  Paul G. Mezey,et al.  A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions , 1989 .

[16]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[17]  L. Seijo,et al.  The abinitio model potential method. Cowan–Griffin relativistic core potentials and valence basis sets from Li (Z = 3) to La (Z = 57) , 1992 .

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

[19]  Pesticide interaction with environmentally important cations: A theoretical study of atrazine , 2011 .

[20]  Peter Pulay,et al.  Fourth‐order Mo/ller–Plessett perturbation theory in the local correlation treatment. I. Method , 1987 .

[21]  Rodney J. Bartlett,et al.  Multi-reference averaged quadratic coupled-cluster method: a size-extensive modification of multi-reference CI , 1993 .

[22]  E. Carter,et al.  Size extensive modification of local multireference configuration interaction. , 2004, The Journal of chemical physics.

[23]  Emily A Carter,et al.  Valence Excited States in Large Molecules via Local Multireference Singles and Doubles Configuration Interaction. , 2011, Journal of chemical theory and computation.

[24]  Peter Pulay,et al.  The local correlation treatment. II. Implementation and tests , 1988 .

[25]  B. Kirtman,et al.  Local space approximation for configuration interaction and coupled cluster wave functions , 1986 .

[26]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[27]  Robert J. Gdanitz,et al.  The averaged coupled-pair functional (ACPF): A size-extensive modification of MR CI(SD) , 1988 .

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

[29]  Restoring the size consistency of multireference configuration interactions through class dressings: applications to ground and excited states. , 2008, The Journal of chemical physics.

[30]  Per-ke Malmqvist,et al.  Inclusion of dynamic σ-π polarization in π-electronab initio calculations , 1992 .

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

[32]  M. Halcrow,et al.  Stereochemical effects on the spin-state transition shown by salts of [FeL2]2+ [L = 2,6-di(pyrazol-1-yl)pyridine] , 2002 .

[33]  Frank Neese,et al.  A spectroscopy oriented configuration interaction procedure , 2003 .

[34]  Marco Häser,et al.  Improvements on the direct SCF method , 1989 .

[35]  B. Roos,et al.  Molcas: a program package for computational chemistry. , 2003 .

[36]  Roland Lindh,et al.  Linear scaling multireference singles and doubles configuration interaction. , 2008, The Journal of chemical physics.

[37]  Hans-Joachim Werner,et al.  Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD) , 2001 .

[38]  Benoît Bories,et al.  Selected excitation for CAS‐SDCI calculations , 2007, J. Comput. Chem..

[39]  P Pulay,et al.  Local Treatment of Electron Correlation , 1993 .

[40]  Robert J. Buenker,et al.  Applicability of the multi-reference double-excitation CI (MRD-CI) method to the calculation of electronic wavefunctions and comparison with related techniques , 1978 .

[41]  Emily A Carter,et al.  Cholesky decomposition within local multireference singles and doubles configuration interaction. , 2010, The Journal of chemical physics.

[42]  Stefano Evangelisti,et al.  Local orbitals for the study of the π→π* excitation in polyenes , 2005 .

[43]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[44]  Stefano Evangelisti,et al.  Correlated description of multiple bonds using localized active orbitals , 2001 .

[45]  Nadia Ben Amor,et al.  Size-consistent self-consistent configuration interaction from a complete active space , 1998 .

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

[47]  S. Goedecker.  Linear scaling electronic structure methods , 1999 .

[48]  Peter Pulay,et al.  Localizability of dynamic electron correlation , 1983 .

[49]  Peter Pulay,et al.  Orbital-invariant formulation and second-order gradient evaluation in Møller-Plesset perturbation theory , 1986 .

[50]  Guntram Rauhut,et al.  Analytical energy gradients for local second-order Mo/ller–Plesset perturbation theory , 1998 .

[51]  Kerstin Andersson,et al.  Second-order perturbation theory with a CASSCF reference function , 1990 .

[52]  Jean-Paul Malrieu,et al.  Specific CI calculation of energy differences: Transition energies and bond energies , 1993 .

[53]  A. D. McLean,et al.  Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z=11–18 , 1980 .

[54]  Georg Hetzer,et al.  Low-order scaling local electron correlation methods. I. Linear scaling local MP2 , 1999 .

[55]  Philippe Y. Ayala,et al.  Linear scaling coupled cluster and perturbation theories in the atomic orbital basis , 1999 .

[56]  Jean-Philippe Blaudeau,et al.  Extension of Gaussian-2 (G2) theory to molecules containing third-row atoms K and Ca , 1995 .

[57]  Frederick R Manby,et al.  Analytical energy gradients for local second-order Møller-Plesset perturbation theory using density fitting approximations. , 2004, The Journal of chemical physics.

[58]  Stefano Evangelisti,et al.  Localized molecular orbitals for excited states n→π * (CO) excitation , 2003 .

[59]  E. Carter,et al.  Density fitting of two-electron integrals in local multireference single and double excitation configuration interaction calculations , 2010 .

[60]  P. Ruttink,et al.  Size consistent multireference single and double excitation configuration interaction calculations. The multireference coupled electron‐pair approximation , 1991 .

[61]  Mark S. Gordon,et al.  Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements , 1982 .

[62]  Jörg Kussmann,et al.  Linear-scaling atomic orbital-based second-order Møller-Plesset perturbation theory by rigorous integral screening criteria. , 2009, The Journal of chemical physics.

[63]  E. Davidson.  The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices , 1975 .