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  • 1
    Electronic Resource
    Electronic Resource
    The Laplacian of the charge density and its relationship to the shell structure of atoms and ions (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 4367-4374 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Laplacian of the spherically averaged charge density ∇2ρ¯(r) has been computed from nonrelativistic SCF wave functions for the neutral atoms from hydrogen to uranium, and the singly positive ions, from helium to barium and lutetium to radium, in order to examine the shell structure. ∇2ρ¯(r) exhibits a number of extremal points and zeros with the absolute value of the function becoming smaller at each successive extremal point. The zeros, in particular the odd numbered zeros, are shown to exhibit good correlation with the Bohr theory of an atom while the extremal points correlate to a lesser extent. At most five shells are seen in the studied atomic cases based on the fact that the odd numbered zeros are the topological feature of ∇2ρ¯(r) most indicative of a shell.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453796
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  • 2
    Electronic Resource
    Electronic Resource
    Topographical features of the Laplacian of the momentum density of atoms and ions most indicative of shell structure (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 6520-6527 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Laplacian of the spherically averaged momentum density, ∇2Π¯(p), is computed from nonrelativistic self-consistent-field wave functions for the neutral atoms from hydrogen to uranium, and the singly positive ions, from helium to barium and lutetium to radium. In particular, the topography of ∇2Π¯(p) reveals that there are seven distinct types of behavior for the studied atomic and ionic cases, based on the number of zeros and extrema present and the value of ∇2Π¯(p) at the origin. Shell structure within ∇2Π¯(p) is shown to be exhibited by the zeros that occur as ∇2Π¯(p) crosses from negative values to positive values. These zeros have been found to be the topographical feature most intimately related to the radii predicted by the Bohr theory of an atom. At most four shells per atom or ion are revealed based on this criterion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456318
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  • 3
    Electronic Resource
    Electronic Resource
    The nonmonotonic behavior of and the presence of slow and fast maxima in the momentum densities of atoms and ions (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 4054-4058 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The spherically averaged momentum densities Π¯(p) for the ground states of the 92 neutral atoms from hydrogen to uranium, and of the 73 singly positive ions from helium to barium and from lutetium to radium, constructed from nonrelativistic SCF wave functions, are examined. From these investigations, it is noted that the general shape of Π¯(p) of an atomic system is clearly determined by the orbitals of the two outermost shells. Two distinct types of maxima that make Π¯(p) nonmonotonic have been investigated: (i) a slow type, which typically occurs for pε(0.0,0.6](h-dash-bar)a−10, and (ii) a fast type, not previously reported in the literature, which either is very small and barely noticeable, or is huge (as compared to those of the slow type), and which occurs for pε[0.7, 1.6](h-dash-bar)a−10 . The results indicate that while maxima of the slow type result from occupied p orbitals of the outermost shell when that shell possesses no occupied d orbitals, maxima of the fast type are the result of both d and p occupied orbitals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449069
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  • 4
    Electronic Resource
    Electronic Resource
    Modeling Lanthanide Complexes: Towards the Theoretical Design of Light Conversion Molecular Devices (1997)
    Springer
    Molecular engineering 7 (1997), S. 293-308 
    Details
    ISSN: 1572-8951
    Keywords: Sparkle model ; lanthanide complexes ; INDO/S-CI ; energy transfer ; luminescence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Theoretical techniques have been developed and/or improved to predict the molecular structure of lanthanide complexes which were used to calculate their electronic properties, in particular, their electronic spectra and energy levels necessary to calculate the rates of energy transfer from the ligands to the metal ion. The molecular structure has been obtained by the SMLC/AM1 (Sparkle Model for the Calculation of Lanthanide Complexes – Austin Model 1) model where the lanthanide ion is simulated by a sparkle implemented into the AM1 Hamiltonian used to perform a HF-SCF (Hartree-Fock Self-Consistent Field) calculation. The previous implementation of the SMLC/AM1 model (sparkle/1) involving only two parameters has been generalized to be consistent with the AM1 Hamiltonian and the new model (sparkle/2) significantly improved the prediction of molecular structures of Eu(III) complexes. For the electronic spectra and energy level calculations of the lanthanide complexes the model replaces the metal ion by a point charge with the ligands held in their positions as determined by the SMLC/AM1 model, and uses a INDO/S-CI (intermediate neglect of differential overlap/spectroscopic-configuration interaction) model. A preliminary study of the solvent effects on the absorption spectra of the free ligand is also presented. For the ligand-lanthanide ion energy transfer Fermi's golden rule is used with the multipolar and exchange mechanisms being implemented and tested for several complexes. These theoretical techniques have been applied to several complexes yielding very good results when compared to experimental data as well as predictions for the molecular and electronic structures and the relative contributions of the mechanisms for the energy transfer rates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008227001656
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  • 5
    Electronic Resource
    Electronic Resource
    Momentum space properties of atomsResearch supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERCC). (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 811-820 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A systematic investigation of momentum densities Π(p), Compton profiles J(q), and internally folded densities B(r) has been made for the ground states of the atoms from H to Kr. The data are presented in reduced form by means of the characteristic momentum p* = q* and length r* = 1/p*, where p* = [J(0)/2πΠ(0)]½. The results indicate that p* and J(0) contain the gross qualitative behavior of the atomic properties in momentum space. They also show that subtle effects over and above the gross scale and size are mostly periodic.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560230305
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  • 6
    Electronic Resource
    Electronic Resource
    Partial-wave analysis of the momentum densities of 14 electron diatomicsBased in part on the Ph.D. dissertation of A. M. S. (1984)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 26 (1984), S. 385-392 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The differences between the anisotropic momentum densities of the isoelectronic molecules N2, CO, and BF are examined by the partial-wave decomposition technique. It is shown that in momentum space a qualitative manifestation of the different bonding situations in these diatomics occurs in the leading anisotropic component of the partial-wave expansion of the momentum density, and a quantitative manifestation in the anisotropy of the kinetic energy tensor. It is found that the isotropic momentum density is monotonically decreasing in these three molecules.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560260836
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  • 7
    Electronic Resource
    Electronic Resource
    Momentum space properties of various orbital basis sets used in quantum chemical calculations (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 419-429 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Momentum expectation values (pk), values of the momentum density P(p) at selected points, and coefficients in the MacLaurin and asymptotic expansions of P(p) are used to test the quality of various orbital basis sets previously used for the atomic helium Hartree-Fock problem. The wellknown position-space defects of Gaussian-type orbital expansions are shown to have their momentum-space counterparts. Expansions of even-tempered Slater-type orbitals are found to be rather accurate. The exponentially damped rational function is found to be the outstanding two-parameter unconventional orbital.
    Additional Material: 12 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560210207
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  • 8
    Electronic Resource
    Electronic Resource
    The nodal structure of the momentum distributions of moleculesResearch supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERCC) and by the U.S. National Science Foundation (grant dmr 79-0721). (1984)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 25 (1984), S. 1035-1044 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The nodal structure of molecular momentum distributions is studied by considering the simplest case of the ground state of the hydrogen molecular ion. By examining the exact expansion of the H2+ momentum distribution, it is shown that an infinite sequence of nodes does exist along the pz axis (z axis parallel to the bond axis) but not nodal planes perpendicular to the pz axis (as is found for the simplest LCAO function). The nodes are those points where nonplanar nodal surfaces cross the pz axis. It is also shown that molecular systems with more than one electron cannot, in the ground state, have nodal surfaces in their momentum distributions. Implications for the directional Compton profiles J(q) are discussed.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560250608
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  • 9
    Electronic Resource
    Electronic Resource
    Appraisal of computer hardware and software for quantum-chemical calculations (1984)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 26 (1984), S. 619-638 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Various computers with different hardware configurations and operating systems are tested for speed, Fortran compiler efficiency of optimization, and library accuracy. Three different benchmarking schemes were used: (i) the PRECIS program, designed to reveal the floating-point characteristics and library accuracy of the machine in which it is run; (ii) the benchmark program FORCE, which is a stand-alone version of link 702 of Gaussian 80; and (iii) two previously published “crystallographic” benchmarks that check the speed of computation of nested DO loops. The results indicate that the quality of the compiler and its interaction with the operating system have as much impact on the overall performance of the system as the various hardware improvements.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560260855
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  • 10
    Electronic Resource
    Electronic Resource
    Basis set quality. II. Information theoretic appraisal of various s- orbitalsBased in part on the Ph.D. dissertation of one of us (A.M.S.). (1983)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 24 (1983), S. 527-550 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The expectation values 〈rk〉 (-2 ≤ k ≤ 4, k = 10), values of the charge density ρ(r) at selected points, and coefficients in the MacLaurin expansion of ρ(r) are used to test the quality of 71 orbital basis sets used for the atomic helium Hartree-Fock problem. These tests in position space are complementary to the momentum space tests previously carried out [Int. J. Quantum Chem. 21, 419 (1982)]. Information theoretic measures with respect to either or both position and momentum space properties are subsequently defined and the orbitals are ranked accordingly. These measures indicate that, for a given orbital, momentum space properties are more poorly predicted than position space ones. Moreover an improvement in the virial ratio does not necessarily lead to a more balanced orbital with respect to position and momentum space properties. Basis sets containing Slater-type orbitals are again found to be rather accurate. The exponentially damped rational function is confirmed to be the outstanding two-parameter unconventional orbital.
    Additional Material: 27 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560240603
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