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  • 1
    Online-Ressource
    Online-Ressource
    Berlin, Heidelberg : Springer Berlin Heidelberg
    Schlagwort(e): Chemistry ; Physical chemistry ; Chemistry ; Chemistry, Physical organic ; Chemistry ; Physical Chemistry
    Beschreibung / Inhaltsverzeichnis: Summary of the Wigner-Racah algebra of non-simply-reducible point groups with non-ambivalent classes -- Representations induced by polyhedral edges -- Bicentric matrices -- The matrix elements of s.-a. molecular orbitals -- Polyhedral coefficients referring to edges -- Triangular coefficients -- Triangular invariants -- Symmetry-adapted geminals and densities -- Pseudo-tetrahedral coefficients -- Two-particle interaction -- Complete bases of irreducible representations -- Transformation properties and structure of the multi-centre integrals -- Multi-centre integrals and molecular symmetry -- Ab initio determination of the polycentric invariants -- Wolfsberg-Helmholtz and Mulliken approximations -- Floating orbitals -- Overlap- and structural matrices, orthonormalization -- Many-electron systems -- Sketch of the VB picture -- Prospect of crystals -- Case study: Tetrahedral structures -- Case study: Matrix elements
    Materialart: Online-Ressource
    Seiten: 1 Online-Ressource (VI, 140 p. 2 illus)
    Ausgabe: Springer eBook Collection. Physics and Astronomy
    ISBN: 9783540393498 , 9783540115892
    Serie: Lecture Notes in Physics 167
    Sprache: Englisch
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 49 (1978), S. 199-210 
    ISSN: 1432-2234
    Schlagwort(e): Symmetry adapted orbitals
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 73 (1988), S. 247-277 
    ISSN: 1432-2234
    Schlagwort(e): Polycentric molecules ; Permutational representations ; Symmetry adaption ; Irreducible tensors ; Wigner-Eckart theorem
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 49 (1978), S. 187-198 
    ISSN: 1432-2234
    Schlagwort(e): Symmetry-adaption ; Racah algebra ; Coordination polyhedra
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
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  • 5
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 49 (1978), S. 211-222 
    ISSN: 1432-2234
    Schlagwort(e): Force constants ; Symmetry coordinates ; Normal vibrations ; Tetrahedral molecule
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
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  • 6
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 34 (1974), S. 245-250 
    ISSN: 1432-2234
    Schlagwort(e): Character formula ; general ; for multiplet states
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    Standort Signatur Einschränkungen Verfügbarkeit
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  • 7
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 34 (1974), S. 245-250 
    ISSN: 1432-2234
    Schlagwort(e): Character formula ; general ; for multiplet states
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
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  • 8
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 44 (1977), S. 279-291 
    ISSN: 1432-2234
    Schlagwort(e): Symmetry-adaption formula ; LCAO, symmetry adapted ; Symmetry coordinates
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
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  • 9
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 54 (1980), S. 323-332 
    ISSN: 1432-2234
    Schlagwort(e): Multi-centre integrals ; Gauss-Laguerre orbitals ; Talmi-Transformation ; Generalized gradient operator
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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).
    Materialart: Digitale Medien
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  • 10
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 18 (1980), S. 753-773 
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Zusätzliches Material: 3 Tab.
    Materialart: Digitale Medien
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