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  • 1
    Keywords: Germany ; MODEL ; SYSTEMS ; ENERGY ; PERTURBATION-THEORY ; MOTION ; CHEMISTRY ; ELECTRON-DENSITY ; ATOMS ; FUNCTIONAL THEORY ; METALS ; time-dependent density functional theory ; EXCHANGE-CORRELATION POTENTIALS ; HARMONIC CONFINEMENT ; IMPERFECTIONS ; IMPURITIES ; Linear response theory ; Moshinsky atom
    Abstract: After a brief introduction to the use of the idempotent Dirac first-order density matrix (DM), its time-dependent generalization is considered. Special attention is focused on the equation of motion for the time-dependent DM, which is characterized by the one-body potential V (r, t) of time-dependent density functional theory. It is then shown how the force - del V (r, t) can be extracted explicitly from this equation of motion. Following a linear-response treatment in which a weak potential V (r, t) is switched on to an initially uniform electron gas, the non-linear example of the two-electron spin-compensated Moshinsky atom is a further focal point. We demonstrate explicitly how the correlated DM for this model can be constructed from the idempotent Dirac DM, in this time-dependent example
    Type of Publication: Journal article published
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical chemistry 1 (1987), S. 1-14 
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Macromolecules (such as polymethelyene and DNA) are large and flexible, and can present themselves in 3-space in topologically interesting ways. The branch of topology known asknot theory is the mathematical study of flexible graphs in 3-space. Knot theory can be used to quantify and compare the various configurations of large molecules, and to study the various spatial isomers of molecules which have complicated molecular graphs.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract A mathematical analysis of the Bjerrum function is carried out. This function arises from the Stepwise Equilibrium Model, which is used to describe successive complex formation in systems consisting of free metal ion, free ligand, and all theML i complexes that can form in solution. The appropriate root of the Bjerrum polynomial allows the determination of the concentrations of all species present in solution, given the initial concentrations of metal and of ligand, and the equilibrium constants governing the system. It is proved that there is only one positive root of the Bjerrum polynomial, and thus that only a single equilibrium state can exist. It is also shown that the positive root of the Bjerrum polynomial can be reliably obtained by Newton's method, but only if the initialization point is properly chosen, and that the initial concentrationL of ligand is the optimum such point. Finding this root is a calculation that typically must be carried out at each iteration in nonlinear least squares procedures for determining equilibrium constants. Finally, the necessary mathematical analysis is carried out to determine the optimum initial concentrations of metal and lgand which maximize the resulting concentration of a particularML i complex.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical chemistry 1 (1987), S. 281-307 
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The individual rings in benzenoid systems are studied via a new structural index, called Clar's ring character. The new index, which is based onselected Kekulé valence structures, differs significantly in a number of cases from similar ring characterizations based onall Kekulé valence structures. It is related to previously introduced quantities based on MO functions, but it can be obtained simply (i.e. without the need of a computer). We have illustrated the new ring index for several families of compounds, and report a number of regularities for a homologous series of molecules.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The electronic structure of a π-network polymer with random numbers of two types of monomer units is considered in a “conjugated circuit” resonance-theoretic framework. A transfer-matrix technique for computing relevant ensemble-average energies is described and applied to a few example simple benzenoid systems. A type of long-range ordering is noted to be relevant, and some of its implications are discussed.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Permutation group-theoretical methods are used to study the chiralization of achiral polyhedral skeletons with v vertices by successive ligand replacement. Starting from the fully symmetrical ligand partition (ν), such chiralization processes may be characterized either by the minimum number of ligand replacement steps m, or the minimum number of different kinds of ligandsi, required to destroy all improper rotations. These parameters are trivially related to the lowest degree chiral ligand partition(s) as determined by the subduction of the skeleton point group G into the corresponding symmetric groupS ν by the procedure of Ruch and Schönhofer. Two different chiralization pathways with different values ofm andi are found for the octahedron, cube, hexagonal bipyramid, and icosahedron. Many less symmetrical chemically significant polyhedra have the degree 2 ligand partition (v - 2, 2) as the lowest degree chiral ligand partition and thus have only one chiralization pathway. Such polyhedra include the bicapped tetrahedron, trigonal prism, capped octahedron, bisdisphenoid, square antiprism, 4, 4, 4-tricapped trigonal prism, 4-capped square antiprism, 4,4-bicapped square antiprism, and the cuboctahedron.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Some novel physical ideas and mathematical techniques are described, useful in the development of effective Hamiltonian methods for studying molecular environmental effects.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The quantum chemical and mathematical background and some new approaches to the modeling of solvent effects are described.
    Type of Medium: Electronic Resource
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  • 9
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The reformulation of the single determinantal, closed shell wavefunction into an antisymmetrized product of nonorthogonal group functions (NOGF) is reviewed. It is shown that by introducing the idea of a “reciprocal” group function, i.e. a group function defined as a product of reciprocal orbitals, the resulting expressions for one- and two-electron operators are formally identical with the equations obtained using strong-orthogonal group functions. Orbital equations are given for the NOGF wavefunction which are derived by formulating a variation principle in terms of group energy functionals, where the presence of the other groups is expressed in terms of Coulomb and exchange operators in the group's Hamiltonian, To ensure that the group's orbitals do not violate the Pauli exclusion principle, a coupling or screening operator is introduced into the variational equations. The effectiveness of the coupling operator is discussed and it is demonstrated that it fully screens the group's orbitals from collapsing or distorting into forbidden regions of function space. To provide techniques for modelling and analyzing intermolecular interactions, the procedure for calculating the NGOF wavefunction can be reformulated into a series of steps which allows the components of the interaction energy, i.e. Coulomb, exchange, polarization and charge transfer, to be evaluated. This approach leads to considerable simplification and reduces the computational effort required to determine the wavefunction. The decomposition is used to analyze many-body effects in linear water chains and a model of a helical hydrogen bonding. The basis set superposition error (BSSE) in the NOGF approximation is discussed and methods for its evaluation are given, and it is shown that the BSSE is inherently less in the NOGF wavefunction than in the corresponding HF-SCF wavefunction. In the final parts of the paper, additional methods are given which further reduce computation time when both interacting fragments and their immediate environment must be considered at the quantum chemical level. These techniques are then applied to a study of the effect of environment on ion pair formation and proton transfer. The results of these studies demonstrate the remarkably strong modulating effect of molecules hydrogen bonded to the interacting pair.
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract We review a computationally efficient approach, based jointly on the Random Phase Approximation (RPA) and on localized molecular orbitals, for calculating and analyzing electronic excitations in terms of the nature of the chromophore and its interaction with its molecular surroundings. The method is applied to two typical chromophoric systems using ab initio extended-basis calculations: the non-conjugated but electronically coupled ethylenic double bonds in norbornadiene (NBD, bicyclo[2.2.1]hepta-2,5-diene) and the chirally perturbed carbonyl chromophore inequatorial 4-methyladamantanone (EMAO). The analyses are a posteriori in nature but provide insights into the spectroscopic properties of medium-sized molecules.
    Type of Medium: Electronic Resource
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