Localized molecular second-order properties

Maestro, M.; Moccia, R.

doi:10.1080/00268977500100071

Cited by 27 publications

(24 citation statements)

References 15 publications

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“…We see from (19) after scalar multiplying it from the left by 'PIO and adding the corresponding equation with k and I interchanged that (20a) results automatically from (19) at least for et~13,. We conclude that we have the freedom to impose the condition ('PtO I'Pt,) = 0 (21) in order to make the 'Pt, unique.…”

Section: Introductionmentioning

confidence: 99%

“…By scalar multiplying (12) from the left by 'Pto, noting the antihermiticity of F" we find that ekl = 0, i.e., that (12) can be rewritten as (19) Equation (19) is the basic equation of coupled Hartree-Fock theory. Of course, the 'Ptl are not uniquely determined by (19) since one can add an arbitrary multiple of 'Pto to a 'PkI that satisfies (19) and it remains a solution of (19).…”

Section: Introductionmentioning

confidence: 99%

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Theory of Magnetic Susceptibilities and NMR Chemical Shifts in Terms of Localized Quantities

Kutzelnigg

1980

Israel Journal of Chemistry

675

291

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A coupled Hartree–Fock theory for diamagnetic susceptibilities χ and chemical shifts σ in terms of localized MO's and individual gauge origins for the different MO's is derived. The new coupled Hartree–Fock equations and expressions for χ and σ differ from the traditional ones by the presence of “exchange coupling terms” (ECT) and “resonance coupling terms” (RCT). For the ECT, that are expected to be very small, a simple approximation is proposed. Both the ECT and the RCT can be decomposed into “diamagnetic” and “paramagnetic” contributions. Spurious paramagnetic terms due to inappropriate choices of the gauge origin are avoided in the present scheme. The possibility to include correlation effects is discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theory of Magnetic Susceptibilities and NMR Chemical Shifts in Terms of Localized Quantities

Kutzelnigg

1980

Israel Journal of Chemistry

675

291

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“…6,7 Although atomic and bond contributions to average electric dipole polarizabilities can be reasonably defined in this way, the theoretical values depend on the molecular orbital ͑MO͒ localization scheme adopted in the calculation. Moreover, due to the fact that complete orbital localization is not actually feasible, small discrepancies are to be expected between total theoretical polarizability and corresponding sums of atomic and bond contributions.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, due to the fact that complete orbital localization is not actually feasible, small discrepancies are to be expected between total theoretical polarizability and corresponding sums of atomic and bond contributions. 6,7 Several molecular orbital approaches for the multicenter distribution of molecular polarization have been proposed, see a recent article by Nakagawa 8 for extended bibliography. A general formalism has been established by Stone.…”

Section: Introductionmentioning

confidence: 99%

Resolution of alkane molecular polarizabilities into atomic terms

Ferraro

Caputo

Lazzeretti

1998

The Journal of Chemical Physics

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Size-dependency of polarizabilities of fractal-and nonfractal-structured oligomers modeled after dendron parts in Cayley-tree-type dendrimers J. Chem. Phys. 115, 1052 (2001) Two additive schemes for resolving average molecular electric dipole polarizabilities into atomic contributions, based on the acceleration gauge for the electric dipole, are outlined. Extended calculations have been carried out for a few terms of the alkane series to test the reliability of the partition method. Gross atomic isotropic contributions evaluated for carbon, ␣ Av C Ϸ5.7 a.u., and hydrogen, ␣ Av H Ϸ2.7 a.u., are actually transferable from molecule to molecule, and can be used to predict fairly accurate average polarizabilities of higher homologous molecules in the alkane series.

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“…The results show good general agreement with other localization methods, with advantages in the ability to display group orbitals in complex molecules which most closely resemble the SCF orbitals for simple prototypes. The impetus for obtaining localized orbitals is well recognized and much has been written about the applications and uses of localized orbitals (1)(2)(3).…”

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confidence: 99%

Density matrix method for orbital localization

Caldwell

Redington

Eyring

1979

Proc. Natl. Acad. Sci. U.S.A.

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A method is presented for localizing molecular orbitals, based on diagonalizing subunits of the density matrix. First, nonbonding orbitals are found by diagonalizing the monatomic subunits; then, diatomic a or -r bonding and antibonding orbitals are obtained from the diatomic subunits for all bonded pairs of atoms; finally, the delocalized ir-orbitals for particular chromophores are found by projecting the first set out of the self-consistent field (SCF) Hamiltonian. The results show good general agreement with other localization methods, with advantages in the ability to display group orbitals in complex molecules which most closely resemble the SCF orbitals for simple prototypes. The impetus for obtaining localized orbitals is well recognized and much has been written about the applications and uses of localized orbitals (1-3).A set of localized orbitals may be obtained by a direct calculation of self-consistent field (SCF) localized molecular orbitals (4) or, given an arbitrary set of delocalized orbitals, one may construct a unitary matrix that will transform the delocalized orbitals into localized orbitals. The two most commonly used procedures for doing the latter are those of Boys (5) and Edmiston and Ruedenberg (6). Closely related methods (7, 8), improvements in efficiency (9), and general discussions of the various methods have been presented elsewhere (10-14).In this work a method is presented that is based on the density matrix formalism and can be used with either ab initio or semi-empirical programs. In the latter case the required input consists of the overlap matrix, the molecular Hamiltonian, and the first-order density matrix. METHODThe localization process is based on the diagonalization of appropriate subunits of the density matrix (15). First, the nonbonding and vacant atomic orbitals are obtained by diagonalizing the individual monatomic components, which are individually delineated by the basis orbitals for each atom. Ideally, a nonbonding orbital would be associated with the eigenvalue 2 and a vacant orbital would have the value 0. In practice it has been found convenient to take all orbitals with ni > 1.6 as nonbonding and those for which nj < 0.4 as vacant. The remaining eigenvectors are hybrids or linear combinations thereof associated with bonding to nearest neighbors.Although it is tempting to use the remaining eigenvectors as hybrids for localized bonding and antibonding orbitals, this process is defeated by the near degeneracy (ideally, 1) for such orbitals, and extensive mixing occurs. The problem is avoided by the second step.The diatomic portions for all pairs of atoms are isolated and diagonalized. Again

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Localized molecular second-order properties

Cited by 27 publications

References 15 publications

Theory of Magnetic Susceptibilities and NMR Chemical Shifts in Terms of Localized Quantities

Theory of Magnetic Susceptibilities and NMR Chemical Shifts in Terms of Localized Quantities

Resolution of alkane molecular polarizabilities into atomic terms

Density matrix method for orbital localization

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