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  • 1
    Electronic Resource
    Electronic Resource
    Does the atomic structure factor show atomic structure? (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 4346-4351 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Numerical evidence for the monotonicity of the isotropic atomic form factor, F(k), is presented. It is shown that the structural features of F(k) can be considerably enhanced by taking its Laplacian, ∇2F(k). Roots and extrema of this function can be assigned to different atomic shells. Linear relationships between the position of the roots and extrema and the atomic number Z are found for the neutral atoms with Z≤92.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460621
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  • 2
    Electronic Resource
    Electronic Resource
    On the determination of atomic shell boundaries (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 8627-8629 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Integrations of the charge density between the critical points of ∇2ρ(r) show that these points are not suitable as definitions of atomic shell boundaries. A comparison with the corresponding scheme based on D(r) favors the latter. Minima in D(r) and corresponding shell populations are tabulated for 55≤Z≤92.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460049
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  • 3
    Electronic Resource
    Electronic Resource
    Two functions of the density matrix and their relation to the chemical bond (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 3184-3193 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We examine and compare two previously introduced functions of the one-particle density matrix that are suitable to represent its off-diagonal structure in a condensed form and that have illustrative connections to the nature of the chemical bond. One of them, the Localized-Orbital Locator (LOL) [J. Molec. Struct. (THEOCHEM) 527, 51 (2000)], is based only on the noninteracting kinetic-energy density τ and the charge density ρ at a point, and gives an intuitive measure of the relative speed of electrons in its vicinity. Alternatively, LOL focuses on regions that are dominated by single localized orbitals. The other one, the Parity Function P [J. Chem. Phys. 105, 11134 (1996)], is a section through the Wigner phase-space function at zero momentum, and contains information about the phase of the interference of atomiclike orbital contributions from bound centers. In this paper, we discuss the way in which these functions condense information in the density matrix, and illustrate on a variety of examples of unusual chemical bonds how they can help to understand the nature of "covalence." © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1431271
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  • 4
    Electronic Resource
    Electronic Resource
    "Low-momentum electrons'' and the electronic structure of small molecules (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 3627-3635 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The electronic Husimi distribution η(r↘,p↘) is a "fuzzy'' density in phase space. Sections through this function with a zero momentum variable (p↘;=0), are shown to be indicative of the spatial locations of chemical bonds and "free electron pairs'' in molecules. The distribution η(r↘;0) tends to focus on the inter-nuclear regions in position space. The Laplacian ∇2rη(r↘;0), of the function may be used to enhance its diffuse features. The argument is made that the momentum-space Hessian of the Husimi function at the momentum-origin (p↘=0), includes information about the "flexibility'' of the electrons and the anisotropy of the latter. The diagonalization of this tensor supplies a pictorial map of preferred directions of electrons in the low-momentum, i.e., "valence'' region of momentum space. Examples studied in this paper include the H2, N2, CH4, H2O, C2H4 and C6H6 systems in their Hartree–Fock approximation. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.472233
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  • 5
    Electronic Resource
    Electronic Resource
    Density functionals from the extended G2 test set: Second-order gradient corrections (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 8188-8199 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In a recent paper [H. L. Schmider and A. D. Becke, J. Chem. Phys. 108, 9624 (1998)], we applied a systematic method for the determination of exchange-correlation functionals within the generalized gradient approximation (GGA) to the extended G2 test set of standard heats of formation of Curtiss et al. [J. Chem. Phys. 106, 1063 (1997)]. In the present work, we apply a similar methodology that goes beyond the GGA by taking second-order gradients and the (noninteracting) kinetic-energy density into account. The resulting improvement in the reproduction of thermochemical data brings us very close to the quality of G2 theory itself. Our lowest mean absolute error for standard heats of formation, 1.60 kcal/mol, is only marginally greater than the G2 value (1.58 kcal/mol). The corresponding largest deviation is 9.97 kcal/mol, as compared to 8.2 kcal/mol for G2 theory. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.477481
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  • 6
    Electronic Resource
    Electronic Resource
    Optimized density functionals from the extended G2 test set (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 9624-9631 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A recently suggested procedure for the systematic optimization of gradient-corrected exchange-correlation functionals [A. D. Becke, J. Chem. Phys. 107, 8554 (1997)] has been applied to the extended G2 test set [L. A. Curtiss et al., J. Chem. Phys. 106, 1063 (1997)], which consists of the standard heats of formation of 148 molecules. The limit of reproduction of the experimental data in this test set is found to be 1.78 kcal/mol mean absolute error, with a maximum of 8.89 kcal/mol error for the ozone molecule. This compares rather well with previous results for G2 theory itself (1.58 and 8.2 kcal/mol, respectively). We show that fair stability can be obtained by our optimization procedure. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.476438
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  • 7
    Electronic Resource
    Electronic Resource
    A parity function for studying the molecular electronic structure (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 11134-11142 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Sections through the molecular Wigner function with zero momentum variable are shown to provide important information about the off-diagonal regions of the spinless one-particle reduced density matrix. Since these regions are characteristic for the bonding situation in molecules, the sections are qualitatively even more affected by the presence of chemical bonds than a complementary projection, the reciprocal form factor. In this paper we discuss, on the grounds of a variety of examples, how this rather simple function may aid the understanding of the chemical bond on a one-particle level. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.472913
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  • 8
    Electronic Resource
    Electronic Resource
    One-particle density matrices along the molecular bonds in linear molecules (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 8411-8419 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The bonding in a number of σ-bonded diatomic and linear triatomic molecules is interpreted in terms of the one-particle density matrix (ODM) along the bond axis. Special attention is drawn to the off-diagonal contributions of the ODM in a two-dimensional position space representation, which are shown to be indicative of a bonding or antibonding covalent interaction between the atomic centers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462293
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  • 9
    Electronic Resource
    Electronic Resource
    Reconstruction of the one-particle density matrix from expectation values in position and momentum space (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 8986-8994 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: For the beryllium atom, it is demonstrated that coherent form factors F(k) can be insufficient for inferring the one-particle reduced density matrix (ODM). The description in terms of reciprocal form factors B(s) as the complementary momentum-space property is compared with the results for a least-squares fit to F(k) data. A virtually complete description of the true ODM may be obtained by using a combined data set, as can be shown by representing the ODM in spherically averaged form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462256
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  • 10
    Electronic Resource
    Electronic Resource
    A spherically averaged representation of the atomic one-particle reduced density matrix (1993)
    Springer
    Theoretical chemistry accounts 86 (1993), S. 115-127 
    Details
    ISSN: 1432-2234
    Keywords: One-particle reduced density matrix ; Closed-shell atoms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary A new way of representing the one-particle reduced density matrix (ODM) of closed-shell atoms in a spherically averaged manner is presented, and connections of this representation to the radial density distributionD(R) and the isotropic reciprocal form factorB(s) are shown. In this representation, certain characteristics of the angular nodal structure of the natural orbitals (NOs) are preserved. Examples of hydrogenic orbitals and near-Hartree-Fock wave functions for some closed-shell atoms are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01113518
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