Coordination Principle GLY 4200 Fall, 2018

Electrostatic Attraction Anions and cations cluster together because they are attracted electrostatically The clusters form coordination arrays

Ionic Bonding The coordinated ions always cluster about the coordinating ion in such a way that their centers lie at the apices of a polyhedron For bonding that is non-ionic, the same general principles hold

Coordination Number The number of coordinated ions around a central ion is known as the coordination number (CN) This usually refers to anions around a cation, but is occasionally used for cations around anion. The ions may, in a first approximation, be thought of as hard spheres. Ideally, the anions around a cation will be arranged so that the spheres just touch. As we will see in lab, the first coordination shell (nearest neighbors) will be arranged in a pattern which depends on the relative size of the anion and cation.

Radius Ratio The radius ratio is the ratio of the cation radius (note: this is Rc) to the anion radius (Ra) or (R+/R-) Since anions are almost always larger than cations, the ratio is between zero and one

Fit Perfect Cation large, pushes anions apart Cation small, rattles around (unstable) If the fit is perfect, that is, if the cation is just large enough to fit when the anions are touching the ratios will be the minimum value given below for each range.

Common Configurations Rc/Ra CN Configuration <0.155 II linear 0.155-0.225 III trigonal 0.225-0.414 IV tetragonal 0.414-0.732 square planar VI octahedral 0.732-1.000 VIII cubic

Linear These numbers are derivable (except for the linear case) but only two derivations are straight-forward.

Trigonal Planar

Tetrahedral

Square Planar Square Planar – Octahedral Both sides of the triangle are = 1 1**2 + 1**2 = Z**2 ∴ Z**2 = 2 Z = 2**0.5 = 1.414 Z = ½ + ½ + x (where x = diameter of cation) x = 0.414 RC = 0.212 (0.212)/0.5 = 0.414 = RC/RA This is the minimum size the cation must be – if it were smaller it would rattle around – this is forbidden by the “no rattling – around” rule.

Octahedral

Cubic Cubic – Dimension of each side is 1.0 1**2 + 1**2 = 2 = diagonal measurement of each side Vertical = 1 1**2 + (1.414)**2 = 3 Z =Body diagonal = 3**0.5 = 1.732 Z – 1 = x = 0.732

Radius Ratio Computation Although the ratios thus derived are for exact fits, larger cations occasionally will fit in a smaller structure. That is, the observed coordination number will be smaller than the predicted CN. Example: Ca & O RC/RA = 0.82 Predicted CN = VIII Observed = VI