Fast noniterative orbital localization for large molecules.

We use Cholesky decomposition of the density matrix in atomic orbital basis to define a new set of occupied molecular orbital coefficients. Analysis of the resulting orbitals ("Cholesky molecular orbitals") demonstrates their localized character inherited from the sparsity of the density matrix. Comparison with the results of traditional iterative localization schemes shows minor differences with respect to a number of suitable measures of locality, particularly the scaling with system size of orbital pair domains used in local correlation methods. The Cholesky procedure for generating orthonormal localized orbitals is noniterative and may be made linear scaling. Although our present implementation scales cubically, the algorithm is significantly faster than any of the conventional localization schemes. In addition, since this approach does not require starting orbitals, it will be useful in local correlation treatments on top of diagonalization-free Hartree-Fock optimization algorithms.

[1]  Christian Ochsenfeld,et al.  Locality and Sparsity of Ab Initio One-Particle Density Matrices and Localized Orbitals , 1998 .

[2]  E. Tfirst,et al.  APPLICATION OF MANY-BODY PERTURBATION THEORY IN THE LOCALIZED REPRESENTATION FOR THE ALL-TRANS CONJUGATED POLYENES , 1994 .

[3]  Matt Challacombe,et al.  A simplified density matrix minimization for linear scaling self-consistent field theory , 1999 .

[4]  R. Mcweeny.  Some Recent Advances in Density Matrix Theory , 1960 .

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

[6]  C. Kozmutza,et al.  Many-body perturbation theory for spatially extended systems , 1993 .

[7]  Thomas Bondo Pedersen,et al.  Polarizability and optical rotation calculated from the approximate coupled cluster singles and doubles CC2 linear response theory using Cholesky decompositions. , 2004, The Journal of chemical physics.

[8]  B. C. Carlson,et al.  Orthogonalization Procedures and the Localization of Wannier Functions , 1957 .

[9]  Frederick R. Manby,et al.  Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations , 2003 .

[10]  Peter Pulay,et al.  Comparison of the boys and Pipek–Mezey localizations in the local correlation approach and automatic virtual basis selection , 1993, J. Comput. Chem..

[11]  Trygve Helgaker,et al.  Direct optimization of the AO density matrix in Hartree-Fock and Kohn-Sham theories , 2000 .

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

[13]  Hans-Joachim Werner,et al.  Local treatment of electron correlation in coupled cluster theory , 1996 .

[14]  N. Marzari,et al.  Maximally localized Wannier functions for entangled energy bands , 2001, cond-mat/0108084.

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

[16]  S. F. Boys,et al.  Canonical Configurational Interaction Procedure , 1960 .

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

[18]  Joseph E. Subotnik,et al.  An efficient method for calculating maxima of homogeneous functions of orthogonal matrices: applications to localized occupied orbitals. , 2004, The Journal of chemical physics.

[19]  W. Niessen,et al.  Density localization of atomic and molecular orbitals , 1973 .

[20]  P. Surján,et al.  Ab initio numerical studies on density-matrix asymptotics in extended systems , 1983 .

[21]  Eric Schwegler,et al.  Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build , 1997 .

[22]  Janos Ladik,et al.  Numerical application of the coupled cluster theory with localized orbitals to polymers. IV. Band structure corrections in model systems and polyacetylene , 1997 .

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

[24]  Michele Parrinello,et al.  General and efficient algorithms for obtaining maximally localized Wannier functions , 2000 .

[25]  Trygve Helgaker,et al.  Direct optimization of the atomic-orbital density matrix using the conjugate-gradient method with a multilevel preconditioner , 2001 .

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

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

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

[29]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[30]  Martin,et al.  Linear system-size scaling methods for electronic-structure calculations. , 1995, Physical review. B, Condensed matter.

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

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

[33]  Satoshi Yokojima,et al.  Localized-density-matrix implementation of time-dependent density-functional theory , 2003 .

[34]  Kohn,et al.  Density functional and density matrix method scaling linearly with the number of atoms. , 1996, Physical review letters.

[35]  Christian Ochsenfeld,et al.  Linear and sublinear scaling formation of Hartree-Fock-type exchange matrices , 1998 .

[36]  M. Head‐Gordon,et al.  Fast evaluation of a linear number of local exchange matrices , 2002 .

[37]  Gustavo E. Scuseria,et al.  Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations , 1997 .

[38]  I. Røeggen,et al.  On the Beebe-Linderberg two-electron integral approximation , 1986 .

[39]  Martin Head-Gordon,et al.  Sparsity of the Density Matrix in Kohn-Sham Density Functional Theory and an Assessment of Linear System-Size Scaling Methods , 1997 .

[40]  Thomas Bondo Pedersen,et al.  Reduced scaling in electronic structure calculations using Cholesky decompositions , 2003 .