Coordination Number Calculator

The coordination number counts the atoms, ions or ligand donor atoms bonded directly to a central centre. In molecular coordination chemistry it equals the number of donor atoms in the first sphere, so hexaamminecobalt(III) has a coordination number of 6 and tetrachloridocuprate(II) has 4; in an extended solid it counts nearest neighbours, giving 6 for sodium in rock salt, 8 for caesium in caesium chloride and 12 in cubic close packing. Values from 2 to 12 occur, with 4 and 6 dominating first-row transition metal chemistry and higher numbers of 8 or 9 appearing among the larger lanthanide and actinide ions. Each number carries a characteristic polyhedron and angle set: linear at 180 degrees, tetrahedral at 109.5, square planar and octahedral at 90, trigonal bipyramidal at 90 and 120, and square antiprismatic near 70.5 and 99.6. Adding the two ionic radii gives a first estimate of the metal to donor distance. A size argument gives the first-pass prediction. When the central ion is too small for its cavity the surrounding anions come into contact and repel, so each geometry has a minimum radius ratio, with the familiar cut-offs at 0.155, 0.225, 0.414 and 0.732 separating coordination numbers 2, 3, 4, 6 and 8. Size alone is not decisive, however. Electronic factors intervene, and d8 ions such as platinum(II) and palladium(II) adopt square planar four-coordination rather than tetrahedral because of the large crystal field stabilisation available. Bulky ligands such as triphenylphosphine suppress coordination numbers sterically, while small ligands such as carbon monoxide and cyanide permit high ones. Pressure can change the answer outright: sodium chloride converts from the six-coordinate rock salt structure to the eight-coordinate caesium chloride type above roughly 30 gigapascals. Experimental determination relies on single-crystal X-ray diffraction, on EXAFS for solutions and amorphous solids, and on neutron diffraction where light atoms must be located.

Coordination number as a concept is inseparable from Alfred Werner, who proposed his coordination theory in 1893 while at the University of Zurich, reportedly writing it out after waking with the idea. Faced with cobalt ammine compounds such as CoCl3 with six, five or four ammonia molecules, Werner argued that a metal has a primary valence satisfied by charge and a secondary valence, fixed in number and directed in space, satisfied by ligands. He predicted that a six-coordinate centre should be octahedral rather than planar or prismatic and confirmed it by counting the isomers actually isolable, then supported the model with electrical conductivity measurements made with Arturo Miolati that showed how many ions each complex released. His rival Sophus Mads Jorgensen in Copenhagen defended a chain formulation until the evidence became decisive, and Werner received the 1913 Nobel Prize in Chemistry. The solid-state meaning of the term arrived with crystallography. William Henry Bragg and William Lawrence Bragg determined the structure of sodium chloride in 1913 and found no discrete molecules at all, only each ion surrounded by six of the other, which forced chemists to describe ionic solids in terms of nearest-neighbour counts. Victor Goldschmidt in Oslo assembled ionic radii and correlated them with coordination in his crystal chemistry papers from 1926, and Linus Pauling formalised the size argument in his 1929 rules for complex ionic crystals. Spectroscopic determination of coordination numbers in non-crystalline environments became possible after Dale Sayers, Edward Stern and Farrel Lytle showed in 1971 how to extract structural information from extended X-ray absorption fine structure.