Nonorthogonal localized molecular orbitals in electronic structure theory

The concept of nonorthogonal localized molecular orbital (NOLMO) is investigated in this paper. Given a set of the commonly used canonical molecular orbitals, a direct minimization algorithm is proposed to obtain both the orthogonal localized molecular orbitals (OLMO) and NOLMO by using the Boys criterion and conjugate gradient minimization. To avoid the multiple-minimum problem, the absolute energy minimization principle of Yang is employed to obtain initial guesses. Contrary to the early conclusion drawn by Lipscomb and co-workers who claimed that OLMOs and the corresponding NOLMOs are more or less the same, we found that NOLMOs are about 10%–30% more localized than OLMOs. More importantly, the so-called “delocalization tail” that plagues OLMOs is not present in NOLMOs, showing that NOLMOs are more compact and less oscillatory and capable of providing greater transferability in describing the electronic structure of molecules. We also found that main lobes of NOLMOs are slightly larger in size than thos...

[1]  E. Davidson.  Selection of the Proper Canonical Roothaan-Hartree-Fock Orbitals for Particular Applications. I. Theory , 1972 .

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

[3]  Robert G. Parr,et al.  Density Functional Theory of Electronic Structure , 1996 .

[4]  Uwe Stephan,et al.  Order-N projection method for first-principles computations of electronic quantities and Wannier functions , 1998 .

[5]  Weitao Yang.  Absolute-energy-minimum principles for linear-scaling electronic-structure calculations , 1997 .

[6]  Williams,et al.  N-scaling algorithm for density-functional calculations of metals and insulators. , 1994, Physical review. B, Condensed matter.

[7]  Wang,et al.  Simple quantum-mechanical model of covalent bonding using a tight-binding basis. , 1992, Physical review. B, Condensed matter.

[8]  William H. Press,et al.  Numerical recipes , 1990 .

[9]  Aoki,et al.  Bond-order potentials: Theory and implementation. , 1996, Physical review. B, Condensed matter.

[10]  P. Giannozzi,et al.  Towards Very Large-Scale Electronic-Structure Calculations , 1992 .

[11]  Martin,et al.  Unconstrained minimization approach for electronic computations that scales linearly with system size. , 1993, Physical review. B, Condensed matter.

[12]  S. L. Dixon,et al.  Semiempirical molecular orbital calculations with linear system size scaling , 1996 .

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

[14]  M. Krol,et al.  Theoretical investigations of the nature of intramolecular interactions: I. Expansion of the molecular energy in terms of non-orthogonal, strictly local, molecular orbitals with application to ethane , 1986 .

[15]  R. Parr,et al.  Density-functional theory of the electronic structure of molecules. , 1995, Annual review of physical chemistry.

[16]  Stechel,et al.  Order-N methods in self-consistent density-functional calculations. , 1994, Physical review. B, Condensed matter.

[17]  Harel Weinstein,et al.  Localized Molecular Orbitals , 1971 .

[18]  P. Schleyer.  Encyclopedia of computational chemistry , 1998 .

[19]  Williams Ar,et al.  Localized orbital theory of electronic structure: A simple application. , 1995 .

[20]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[21]  Galli,et al.  Large scale electronic structure calculations. , 1992, Physical review letters.

[22]  Daw.  Model for energetics of solids based on the density matrix. , 1993, Physical review. B, Condensed matter.

[23]  Yang,et al.  Direct calculation of electron density in density-functional theory: Implementation for benzene and a tetrapeptide. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[24]  Cornelis Altona,et al.  Calculation and properties of non-orthogonal, strictly local molecular orbitals , 1985 .

[25]  T. Gilbert.  Multiconfiguration Self-Consistent-Field Theory for Localized Orbitals. I. The Orbital Equations , 1972 .

[26]  Kress,et al.  Linear-scaling tight binding from a truncated-moment approach. , 1996, Physical review. B, Condensed matter.

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

[28]  Peter Pulay,et al.  Efficient elimination of basis set superposition errors by the local correlation method: Accurate ab initio studies of the water dimer , 1993 .

[29]  S. L. Dixon,et al.  Fast, accurate semiempirical molecular orbital calculations for macromolecules , 1997 .

[30]  Galli,et al.  Electronic-structure calculations and molecular-dynamics simulations with linear system-size scaling. , 1994, Physical review. B, Condensed matter.

[31]  R. Dreizler,et al.  Density-Functional Theory , 1990 .

[32]  Colombo,et al.  Efficient linear scaling algorithm for tight-binding molecular dynamics. , 1994, Physical review letters.

[33]  Car,et al.  Orbital formulation for electronic-structure calculations with linear system-size scaling. , 1993, Physical review. B, Condensed matter.

[34]  R. Parr.  Density-functional theory of atoms and molecules , 1989 .

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

[36]  N. Marzari,et al.  Maximally localized generalized Wannier functions for composite energy bands , 1997, cond-mat/9707145.

[37]  I. Mayer.  Non-orthogonal localized orbitals to study delocalization effects , 1982 .

[38]  Weitao Yang.  A local projection method for the linear combination of atomic orbital implementation of density‐functional theory , 1991 .

[39]  Yang,et al.  Direct calculation of electron density in density-functional theory. , 1991, Physical review letters.

[40]  H. Stoll,et al.  THE HARTREE-FOCK THEORY OF LOCAL REGIONS IN MOLECULES , 1978 .

[41]  V. Fock,et al.  Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems , 1930 .

[42]  Yixiang Cao,et al.  Correlated ab Initio Electronic Structure Calculations for Large Molecules , 1999 .

[43]  G. Musso,et al.  Localized orbitals and short‐range molecular interactions. I. Theory , 1974 .

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

[45]  P. Claverie,et al.  Fully localized bond orbitals and the correlation problem , 1968 .

[46]  A. St.-Amant,et al.  Using a fitted electronic density to improve the efficiency of a linear combination of Gaussian-type orbitals calculation , 1997 .

[47]  W. Lipscomb,et al.  Variationally deorthogonalized localized molecular orbitals , 1979 .

[48]  E. Mehler,et al.  Self-consistent, nonorthogonal group function approximation for polyatomic systems. I. Closed shells , 1977 .

[49]  Walter Kohn,et al.  Density functional/Wannier function theory for systems of very many atoms , 1993 .

[50]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[51]  J. Carpenter,et al.  Some remarks on nonorthogonal orbitals in quantum chemistry , 1988 .

[52]  T. Arias,et al.  Iterative minimization techniques for ab initio total energy calculations: molecular dynamics and co , 1992 .

[53]  Hernández,et al.  Self-consistent first-principles technique with linear scaling. , 1995, Physical review. B, Condensed matter.

[54]  Hermann Stoll,et al.  On the use of local basis sets for localized molecular orbitals , 1980 .

[55]  Encyclopedia of Computational Chemistry P. von R. Schleyer, Editor-in-Chief. John Wiley and Sons, Inc., Chichester, U.K. 1998. xxix + 3429 pp. 21 x 27.5 cm. ISBN 0-471-96588-X. $2550.00. , 1999 .

[56]  Soler,et al.  Self-consistent order-N density-functional calculations for very large systems. , 1996, Physical review. B, Condensed matter.

[57]  Gustavo E. Scuseria,et al.  Semiempirical methods with conjugate gradient density matrix search to replace diagonalization for molecular systems containing thousands of atoms , 1997 .

[58]  Li,et al.  Density-matrix electronic-structure method with linear system-size scaling. , 1993, Physical review. B, Condensed matter.

[59]  Galli,et al.  Large scsle quantum simulations: C60 Impacts on a semiconducting surface. , 1994, Physical review letters.

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

[61]  Kim,et al.  Total-energy global optimizations using nonorthogonal localized orbitals. , 1995, Physical review. B, Condensed matter.

[62]  Weitao Yang,et al.  A density‐matrix divide‐and‐conquer approach for electronic structure calculations of large molecules , 1995 .

[63]  P. Anderson.  Self-Consistent Pseudopotentials and Ultralocalized Functions for Energy Bands , 1968 .

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

[65]  A. St.-Amant,et al.  Linear scaling for the charge density fitting procedure of the linear combination of Gaussian-type orbitals density functional method , 1996 .

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