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  2. Polyhedral skeletal electron pair theory - Wikipedia

    en.wikipedia.org/wiki/Polyhedral_skeletal...

    For the special case of transition metal clusters, ligands are added to the metal centers to give the metals reasonable coordination numbers, and if any hydrogen atoms are present they are placed in bridging positions to even out the coordination numbers of the vertices. In general, closo structures with n vertices are n-vertex polyhedra.

  3. Pauling's rules - Wikipedia

    en.wikipedia.org/wiki/Pauling's_rules

    For typical ionic solids, the cations are smaller than the anions, and each cation is surrounded by coordinated anions which form a polyhedron.The sum of the ionic radii determines the cation-anion distance, while the cation-anion radius ratio + / (or /) determines the coordination number (C.N.) of the cation, as well as the shape of the coordinated polyhedron of anions.

  4. Coordination number - Wikipedia

    en.wikipedia.org/wiki/Coordination_number

    In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central ion/molecule/atom is called a ligand .

  5. Bond valence method - Wikipedia

    en.wikipedia.org/wiki/Bond_valence_method

    The association of the cation bonding electrons with the anion in the ionic model is purely formal. There is no change in physical locations of any electrons, and there is no change in the bond valence. The terms "anion" and "cation" in the bond valence model are defined in terms of the bond topology, not the chemical properties of the atoms.

  6. Cation-anion radius ratio - Wikipedia

    en.wikipedia.org/wiki/Cation-anion_radius_ratio

    This diagram is for octahedral interstices (coordination number six): 4 anions in the plane shown, 1 above the plane and 1 below. The stability limit is at r C /r A = 0.414. The radius ratio rule defines a critical radius ratio for different crystal structures, based on their coordination geometry. [1]

  7. Coordination sequence - Wikipedia

    en.wikipedia.org/wiki/Coordination_sequence

    In crystallography and the theory of infinite vertex-transitive graphs, the coordination sequence of a vertex is an integer sequence that counts how many vertices are at each possible distance from . That is, it is a sequence n 0 , n 1 , n 2 , … {\displaystyle n_{0},n_{1},n_{2},\dots } where each n i {\displaystyle n_{i}} is the number of ...

  8. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    There is no general consensus about the definition of mathematics or its epistemological status—that is, its place inside knowledge. A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. There is not even consensus on whether mathematics is an art or a science.

  9. d electron count - Wikipedia

    en.wikipedia.org/wiki/D_electron_count

    The d electron count or number of d electrons is a chemistry formalism used to describe the electron configuration of the valence electrons of a transition metal center in a coordination complex. [ 1 ] [ 2 ] The d electron count is an effective way to understand the geometry and reactivity of transition metal complexes.