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  • 1
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    Berlin ; Heidelberg : Springer
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  • 2
    ISSN: 1432-2234
    Keywords: Character formula ; general ; for multiplet states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Starting from the symmetry groupG × SU(2) for the special case of negligible spin-orbit coupling, a general character formula is derived for them-tuplet representation, which is realized in the space of state functions ofn-electron systems in fields with symmetryG. Apart from the characters of the initial representation for the single electron space function, the formula only contains the number of particlesn and the multiplicitym.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-2234
    Keywords: Character formula ; general ; for multiplet states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Starting from the symmetry groupG × SU(2) for the special case of negligible spin-orbit coupling, a general character formula is derived for them-tuplet representation, which is realized in the space of state functions ofn-electron systems in fields with symmetryG. Apart from the characters of the initial representation for the single electron space function, the formula only contains the number of particlesn and the multiplicitym.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 49 (1978), S. 199-210 
    ISSN: 1432-2234
    Keywords: Symmetry adapted orbitals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The overlap matrix of symmetric molecules is diagonalized for arbitrary orbitals as far as this is possible by group theoretical methods. The remaining invariant matrix elements are expressed in coordinate and numeration independent way by “physical” orbital factors and purely geometric factors arising from group algebra only.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 49 (1978), S. 211-222 
    ISSN: 1432-2234
    Keywords: Force constants ; Symmetry coordinates ; Normal vibrations ; Tetrahedral molecule
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The matrix of force constants of a symmetric molecule is reduced to its invariants (nearly diagonal form). For the case of distance dependent potentials these invariants are expressed by the derivations of the potentials and geometric factors. For the purpose of parametrization the inversions of these formulae are derived. The general equilibrium condition and the elimination of the translational and rotational coordinates are discussed. The example of the tetrahedral AB4 structure is worked out.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 73 (1988), S. 247-277 
    ISSN: 1432-2234
    Keywords: Polycentric molecules ; Permutational representations ; Symmetry adaption ; Irreducible tensors ; Wigner-Eckart theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The reducible representations of the point groups are generally studied because of their relevance to molecular orbital and vibration theory. Triple correlations within the polyhedra are described by group-theoretical invariants that are related to the permutation representations and termed polyhedral isoscalar factors. These invariants are applied in theorems on matrix elements referring to the symmetry-adapted bases at different centres. Further invariants or geometrical weight factors inter-relate different types of reduced matrix elements of irreducible tensors (generalization of the Wigner-Eckart theorem to the polycentric case). As a demonstration a complete tabulation is given for the point group C 4υ.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 44 (1977), S. 279-291 
    ISSN: 1432-2234
    Keywords: Symmetry-adaption formula ; LCAO, symmetry adapted ; Symmetry coordinates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The aim of this paper is to give an algebraic formula for symmetry-adapted linear combinations avoiding intuitive or laborious projection operator techniques. By utilization of the tabulated Clebsch-Gordan coefficients and surface harmonics of the point-groups the symmetry-adapted linear combinations are given in formula (4). A five-step algorithm is proposed and the example of a tetrahedron worked out. The relation to methods using site symmetry is discussed.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 49 (1978), S. 187-198 
    ISSN: 1432-2234
    Keywords: Symmetry-adaption ; Racah algebra ; Coordination polyhedra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Stimulated by the invention of an algebraic formula for the coefficients of symmetry-adapted linear combinations in a previous paper [1], the representations induced by the edge vectors of a symmetric, molecular polyhedron AmBnCp... are studied in detail. The following objects are defined (in brackets the analogous, common objects): Complete systems of standard functions (spherical harmonics), polyhedral vector coupling coefficients (3jm-symbols), polyhedral Racah coefficients (6j-symbols), polyhedral isoscalar factors (isoscalar factors). The algebraic properties and evaluation methods of these coefficients are discussed in order to be used in subsequent papers on quantities depending on symmetry-adapted orbitals and symmetry coordinates.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 54 (1980), S. 323-332 
    ISSN: 1432-2234
    Keywords: Multi-centre integrals ; Gauss-Laguerre orbitals ; Talmi-Transformation ; Generalized gradient operator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The multi-centre integrals of the orbital system Δ n Y lm (∇) exp (−r 2) are evaluated using the Talmi transformation of nuclear shell theory. The integrals are simpler than those of the systems r 2n Y lm(r) exp (−r 2), x l y m z n exp (−r 2), (∂/∂x) l (∂/∂y) m (∂/∂z) n exp (−r 2) and the spherical oscillator functions. The integral types investigated are: overlap, electric dipole transition (momentum operator), kinetic energy, three-centre nuclear attraction, four-centre electronic repulsion, three-centre spin-orbit coupling, and magnetic dipole transition (three-centre integrals of the angular momentum operator).
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  • 10
    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 electrostatic interaction for arbitrary symmetry (including non-simply reducible point groups), different coupling schemes, and several open shells is discussed from a common viewpoint using the particle-number representation (second quantization). The different coupling schemes simply arise from a different interpretation of the relevant symmetry group. Using the adjective CFPS of the preceding paper, the interaction within several open shells can be calculated. In the case of one-center expansions like ligand field theory the many-particle matrix elements are directly expressed by the radial Slater integrals using isoscalar factors. An example of the formalism is worked out. By the way the unitary transformations between strong and weak field coupling schemes are expressed recursively in the number of particles.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
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