Localization of molecular orbitals on fragments

A non‐iterative algorithm for the localization of molecular orbitals (MOs) from complete active space self consistent field (CASSCF) and for single‐determinantal wave functions on predefined moieties is given. The localized fragment orbitals can be used to analyze chemical reactions between fragments and also the binding of fragments in the product molecule with a fragments‐in‐molecules approach by using a valence bond expansion of the CASSCF wave function. The algorithm is an example of the orthogonal Procrustes problem, which is a matrix optimization problem using the singular value decomposition. It is based on the similarity of the set of MOs for the moieties to the localized MOs of the molecule; the similarity is expressed by overlap matrices between the original fragment MOs and the localized MOs. For CASSCF wave functions, localization is done independently in the space of occupied orbitals and active orbitals, whereas, the space of virtual orbitals is mostly uninteresting. Localization of Hartree–Fock or Kohn–Sham density functional theory orbitals is not straightforward; rather, it needs careful consideration, because in this case some virtual orbitals are needed but the space of virtual orbitals depends on the basis sets used and causes considerable problems due to the diffuse character of most virtual orbitals. © 2012 Wiley Periodicals, Inc.

[1]  Mark S. Gordon,et al.  High-valent transition-metal alkylidene complexes : effect of ligand and substituent modification , 1992 .

[2]  L. Cheung,et al.  Dimerization of carbene to ethylene , 1978 .

[3]  Michael W. Schmidt,et al.  Are atoms intrinsic to molecular electronic wavefunctions? III. Analysis of FORS configurations , 1982 .

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

[5]  N. Handy,et al.  Implications of unitary invariance for gradient theory , 1992 .

[6]  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 .

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

[8]  Expansion of molecular orbital wave functions into valence bond wave functions. A simplified procedure , 1978 .

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

[10]  C Z Wang,et al.  Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals. , 2004, The Journal of chemical physics.

[11]  V. Bachler,et al.  The photochemistry of 1,3-butadiene rationalized by means of theoretical resonance structures and their weights , 2000, Chemistry.

[12]  Sason Shaik,et al.  What happens to molecules as they react? A valence bond approach to reactivity , 1981 .

[13]  Michael W. Schmidt,et al.  Concerted dihydrogen exchange between ethane and ethylene. SCF and FORS calculations of the barrier , 1982 .

[14]  Kimihiko Hirao,et al.  Theoretical study of the π→π* excited states of linear polyenes: The energy gap between 11Bu+ and 21Ag− states and their character , 1998 .

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

[16]  G. Scuseria,et al.  Scaling reduction of the perturbative triples correction (T) to coupled cluster theory via Laplace transform formalism , 2000 .

[17]  Emily A. Carter,et al.  Local correlation in the virtual space in multireference singles and doubles configuration interaction , 2003 .

[18]  R. Levine.  Molecular Reaction Dynamics: Frontmatter , 2005 .

[19]  Philippe Y. Ayala,et al.  Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems , 1999 .

[20]  L. Curtiss,et al.  Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint , 1988 .

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

[22]  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 .

[23]  P. Hiberty.  The Diradical Character of 1,3‐Dipoles , 1983 .

[24]  Michael W. Schmidt,et al.  The construction and interpretation of MCSCF wavefunctions. , 1998, Annual review of physical chemistry.

[25]  R. Ahlrichs,et al.  Population analysis based on occupation numbers of modified atomic orbitals (MAOs) , 1976 .

[26]  Haesun Park,et al.  A Procrustes problem on the Stiefel manifold , 1999, Numerische Mathematik.

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

[28]  Klaus Ruedenberg,et al.  Electronic rearrangements during chemical reactions. II. Planar dissociation of ethylene , 1979 .

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

[30]  B. Roos,et al.  A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach , 1980 .

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

[32]  Frank Weinhold,et al.  Natural hybrid orbitals , 1980 .

[33]  F. Matthias Bickelhaupt,et al.  A chemist's guide to valence bond theory , 2009, J. Comput. Chem..

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

[35]  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.

[36]  M. Böhm.  A simple extension of the external magnasco-perico localization procedure to the virtual MO-Space , 1981 .

[37]  K. Fukui,et al.  Molecular orbital calculations of the electronic structure of borazane , 1974 .

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

[39]  M. Gordon,et al.  Principal Resonance Contributors to High-Valent, Transition-Metal Alkylidene Complexes , 1991 .

[40]  R. Everson.  Orthogonal, but not Orthonormal, Procrustes Problems , 1999 .

[41]  P. Karafiloglou.  Chemical structures from multi-electron density operators , 1990 .

[42]  Gus Hancock,et al.  Molecular reaction dynamics , 2003 .

[43]  Ky Fan,et al.  Imbedding Conditions for Hermitian and Normal Matrices , 1957, Canadian Journal of Mathematics.

[44]  P. Karafiloglou,et al.  Understanding molecular orbital wave functions in terms of resonance structures , 1991 .

[45]  B. Parlett,et al.  Matrices with prescribed Ritz values , 2008 .

[47]  J. Malrieu,et al.  The effect of electronic correlation on molecular wavefunctions , 1986 .

[48]  Martin Head-Gordon,et al.  Closely approximating second-order Mo/ller–Plesset perturbation theory with a local triatomics in molecules model , 2000 .

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