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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 .
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.
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]
If the structure is not known, the average bond valence, S a can be calculated from the atomic valence, V, if the coordination number, N, of the atom is known using Eq. 3. = / (Eq. 3) If the coordination number is not known, a typical coordination number for the atom can be used instead.
Co(CO) 3 (NO) is a stable 18-electron complex in part due to the bonding of the NO ligand in its linear form. The donation of the lone pair on the nitrogen makes this complex ML 4 X, containing 18 electrons. The traditional coordination number here would be 4, while the CBC more accurately describes the bonding with a LBN of 5.
The coordination geometry depends on the number, not the type, of ligands bonded to the metal centre as well as their locations. The number of atoms bonded is the coordination number . The geometrical pattern can be described as a polyhedron where the vertices of the polyhedron are the centres of the coordinating atoms in the ligands.
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.
where: β > α are the two greatest valence angles of coordination center; θ = cos −1 (− 1 ⁄ 3) ≈ 109.5° is a tetrahedral angle. Extreme values of τ 4 and τ 4 ′ denote exactly the same geometries, however τ 4 ′ is always less or equal to τ 4 so the deviation from ideal tetrahedral geometry is more visible.