Local orbitals by minimizing powers of the orbital variance.

It is demonstrated that a set of local orthonormal Hartree-Fock (HF) molecular orbitals can be obtained for both the occupied and virtual orbital spaces by minimizing powers of the orbital variance using the trust-region algorithm. For a power exponent equal to one, the Boys localization function is obtained. For increasing power exponents, the penalty for delocalized orbitals is increased and smaller maximum orbital spreads are encountered. Calculations on superbenzene, C(60), and a fragment of the titin protein show that for a power exponent equal to one, delocalized outlier orbitals may be encountered. These disappear when the exponent is larger than one. For a small penalty, the occupied orbitals are more local than the virtual ones. When the penalty is increased, the locality of the occupied and virtual orbitals becomes similar. In fact, when increasing the cardinal number for Dunning's correlation consistent basis sets, it is seen that for larger penalties, the virtual orbitals become more local than the occupied ones. We also show that the local virtual HF orbitals are significantly more local than the redundant projected atomic orbitals, which often have been used to span the virtual orbital space in local correlated wave function calculations. Our local molecular orbitals thus appear to be a good candidate for local correlation methods.

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

[2]  Mikael P. Johansson,et al.  A stepwise atomic, valence-molecular, and full-molecular optimisation of the Hartree-Fock/Kohn-Sham energy. , 2009, Physical chemistry chemical physics : PCCP.

[3]  M. Head‐Gordon,et al.  An accurate local model for triple substitutions in fourth order Møller–Plesset theory and in perturbative corrections to singles and doubles coupled cluster methods , 2000 .

[4]  Francesco Aquilante,et al.  Fast noniterative orbital localization for large molecules. , 2006, The Journal of chemical physics.

[5]  Martin Schütz,et al.  Low-order scaling local electron correlation methods. III. Linear scaling local perturbative triples correction (T) , 2000 .

[6]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[7]  S. F. Boys.  Localized Orbitals and Localized Adjustment Functions , 1966 .

[8]  Klaus Ruedenberg,et al.  Localized Atomic and Molecular Orbitals. II , 1965 .

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

[10]  Trygve Helgaker,et al.  Robust and Reliable Multilevel Minimization of the Kohn-Sham Energy. , 2009, Journal of chemical theory and computation.

[11]  Branislav Jansík,et al.  Maximum locality in occupied and virtual orbital spaces using a least-change strategy. , 2009, The Journal of chemical physics.

[12]  K. Ruedenberg,et al.  Localized Atomic and Molecular Orbitals. III , 1966 .

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

[14]  Wei Li,et al.  Improved design of orbital domains within the cluster-in-molecule local correlation framework: single-environment cluster-in-molecule ansatz and its application to local coupled-cluster approach with singles and doubles. , 2010, The journal of physical chemistry. A.

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

[16]  J. Pipek.  Localization measure and maximum delocalization in molecular systems , 1989 .

[17]  José-Vicente Pitarch Ruiz,et al.  The use of local orbitals in multireference calculations , 2003 .

[18]  Trygve Helgaker,et al.  An efficient density-functional-theory force evaluation for large molecular systems. , 2010, The Journal of chemical physics.

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

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

[21]  Michael Dolg,et al.  Fully automated implementation of the incremental scheme: application to CCSD energies for hydrocarbons and transition metal compounds. , 2007, The Journal of chemical physics.

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

[23]  Wei Li,et al.  Local correlation calculations using standard and renormalized coupled-cluster approaches. , 2009, The Journal of chemical physics.

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

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

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

[27]  J. Olsen,et al.  General biorthogonal projected bases as applied to second-order Møller-Plesset perturbation theory. , 2007, The Journal of chemical physics.

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

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

[30]  Georg Hetzer,et al.  Low-order scaling local correlation methods II: Splitting the Coulomb operator in linear scaling local second-order Møller–Plesset perturbation theory , 2000 .

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

[32]  Martin Head-Gordon,et al.  Fast localized orthonormal virtual orbitals which depend smoothly on nuclear coordinates. , 2005, The Journal of chemical physics.

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

[34]  F. Sauter,et al.  Quantum Theory of Atoms, Molecules and the Solid State , 1968 .

[35]  Lorenz S. Cederbaum,et al.  Block diagonalisation of Hermitian matrices , 1989 .

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

[37]  Thomas A. Halgren,et al.  Localized molecular orbitals for polyatomic molecules. I. A comparison of the Edmiston-Ruedenberg and Boys localization methods , 1974 .

[38]  Hermann Stoll,et al.  The correlation energy of crystalline silicon , 1992 .

[39]  J. Olsen,et al.  Coupled-cluster theory in a projected atomic orbital basis. , 2006, The Journal of chemical physics.