What factors determine cation coordination numbers?

Over 14 000 coordination environments of 100 different cations retrieved from the Inorganic Crystal Structure Database have been analyzed. For comparison predicted coordination numbers (PCN's) have been calculated using ionic radius ratios. The observed coordination numbers are generally smaller than or equal to the PCN's and their range, for most cations, can be predicted from a knowledge of the Lewis-base strengths of available anions and the requirement that these strengths be close to the Lewis-acid strength of the cation. The occurrence of smaller coordination numbers is associated with strongly directed bonds (electronic effects) and is found for main-group elements in low oxidation states and for closed-d-shell cations of Groups 11, 12 and 13. An analysis of the results shows that to use ionic radii to predict both coordination numbers and interatomic distances it is necessary to use cation and anion radii that both vary in the same way with the cation coordination number (N). The value found for the oxygen radius is 1.12 + 0.23In(N-2)/~. The average observed coordination number is used to calculate cation Lewis-acid strengths which are shown to correlate with electronegativity.