The role of the lone pair of electrons of Pb(II) in determining the coordination geometry is analyzed from crystallographic studies and ab initio molecular orbital optimizations. Of particular interest are factors that contribute to the disposition of ligands around the lead with geometries that are (1) holodirected, in which the bonds to ligand atoms are distributed throughout the surface of an encompassing globe, and (2) hemidirect ed, in which the bonds to ligand atoms are directed throughout only part of an encompassing globe, i.e., there is an identifiable void in the distribution of bonds to the ligands. The preferred coordination numbers for lead were found to be 4 for Pb(IV) and 4 and 6 for Pb(II). All Pb(IV) structures in the CSD have a holodirected coordination geometry. Pb(II) compounds are hemidirected for low coordination numbers (2−5) and holodirected for high coordination numbers (9, 10), but for intermediate coordination numbers (6−8), examples of either type of stereochemistry are found. Ab initio molecular orbital studies of gas-phase Pb(II) complexes show that a hemidirected geometry is favored if the ligand coordination number is low, the ligands are hard, and there are attractive interactions between the ligands. In such complexes, the lone pair orbital has p character and fewer electrons are transferred from the ligands to the bonding orbitals of Pb(II), resulting in bonds that are more ionic. A holodirected geometry is favored when the coordination number is high and the ligands are soft and bulky or show strong interligand repulsion. The lone pair orbital has little or no p character when the geometry is holodirected, and the bonds are more covalent than in the hemidirected structures. The energy cost of converting a hemidirected to a constrained holodirected structure is of the order 8−12 kcal/mol in the absence of strong interligand interactions.

The coordination geometry of divalent calcium ions has been investigated by analyses of the crystal structures of small molecules containing this cation that are found in the Cambridge Structural Database, protein crystal structures in the Protein Databank, and by ab initio molecular orbital calculations on hydrated structures of the form Ca‚mH 2 O, in which there are n water molecules in the first coordination shell and m water molecules in the second coordination shell (hydrogen bonded to water molecules in the first shell). Calcium ions in crystal structures generally bind to oxygen atoms in ligands (rather than any other element), and their preferred coordination numbers range from 6 to 8. In protein crystal structures the tendency of calcium to bind water molecules is less than for magnesium (1.5 versus 2.2 water molecules on the average per metal ion site, respectively). The ratio of bidentate to monodentate binding of calcium ions to carboxylate groups is similar for small molecules and protein structures in that no bidentate binding occurs if the coordination number of Ca 2+ is 6, but its occurrence rises to near 20% for coordination numbers 7 and 8. Complexes of the form Ca[H 2 O] 5 2+ ‚H 2 O and Ca[H 2 O] 4 2+ ‚2H 2 O were found (by ab initio molecular orbital calculations in Vacuo) to be significantly higher in energy than Ca[H 2 O] 6 2+ (by 8.2 and 15.0 kcal/mol, respectively). For Ca 2+ surrounded by seven or eight water molecules, the differences in energy between Ca[H 2 O] 6 2+ ‚H 2 O and Ca[H 2 O] 7 2+ and among Ca[H 2 O] 6 2+ ‚2H 2 O, Ca[H 2 O] 7 2+ ‚H 2 O, and Ca[H 2 O] 8 2+are extremely small when diffuse functions are included in the basis set. Thus, the net energy penalty for changing the number of water molecules in the first coordination shell between 6 and 8 is small. Molecular orbital calculations also indicate that the effect of a calcium ion on the H-O-H angle to bound water is less (at normal coordination numbers) than that of magnesium, zinc, or beryllium.

Divalent manganese, magnesium, and zinc fill unique roles in biological systems, despite many apparently similar chemical properties. A comparison of the liganding properties of divalent manganese, magnesium, and zinc has been made on the basis of data on crystal structures (from the Cambridge Structural Database and the Protein Databank) and molecular orbital and density functional calculations. The distribution of coordination numbers for divalent manganese in crystal structure determinations, and the identities of ligands, have been determined from analyses of data derived from the structural databases. Enthalpy and free energy changes for processes such as loss of water or ionization of water from hydrated cations have been evaluated from computational studies. The energy penalty for changing the hexahydrate of divalent manganese to a pentahydrate with one water molecule in the second coordination shell is intermediate between the high value for magnesium and the low value for zinc. The preferred coordination number of divalent manganese is six, as it is for magnesium, while the preferred coordination is less definite for zinc and ranges from 4 to 6. Magnesium generally binds to oxygen ligands, and divalent manganese behaves similarly, although it is more receptive of nitrogen ligands, while zinc prefers nitrogen and sulfur, especially if the coordination number is low. The slightly lower discrimination between nitrogen and oxygen of divalent manganese, compared to magnesium, was apparent both in the energetics of competition of these cations for water and ammonia and from ligand binding profiles in the crystallographic databases.

The coordination geometry of divalent zinc cations has been investigated by analyses of the crystal structures of small molecules containing this cation that are found in the Cambridge Structural Database and by ab initio molecular orbital calculations on hydrated structures of the form [ 2 ]"2+ 2 , in which there are n water molecules in the first coordination shell and m water molecules in the second coordination shell. Zinc ions in crystal structures are more commonly found to bind nitrogen and sulfur atoms, in addition to oxygen, while magnesium ions have a tendency to bind oxygen atoms. While most magnesium ion complexes have a metal ion coordination number of six, zinc ion complexes show coordination numbers that are generally four, five, and six. The higher of these coordination numbers for zinc (six) is primarily found when oxygen (or, to a lesser extent, nitrogen) is bound, and the lowest when sulfur is bound. Ab initio molecular orbital studies of aquated zinc ions show that the total molecular energies of the three gas-phase complexes [ 2 ]62+, Zn[H20]s2+'H20, and [ 2 ]42+•2 2 differ by less than 0.4 kcal/mol. This is in contrast to the corresponding results for magnesium and beryllium, where we have previously shown that Mg[H20]e2+ is approximately 9 and 4 kcal/mol lower in energy than Mg[ 2 ]42+•2 2 and Mg[H20]52+lH20, respectively, while Be[H20]42+,2H20 is 22 kcal/mol lower in energy than Be[H20]62+, and no stable form with five water molecules in the first coordination sphere of a beryllium ion could be found. Thus the energy penalty for changing the local environment (coordination number) of divalent zinc ions surrounded by water is significantly less than that for the corresponding magnesium and beryllium ions. This is in line with the modes of utilization of these cations in enzyme systems, where magnesium ions play a more structural role than do zinc ions which, when bound to oxygen or nitrogen, tend to be involved in catalytic processes, possibly involving coordination number changes. The effects of Be2+, Mg2+, and Zn2+ ions on water molecules bound in the first coordination sphere have been assessed by use of values of the -O-H angle from the ab initio molecular orbital studies. It is found that this angle is increased from 105.5°in an isolated water molecule to average values of 106.7°for magnesium, 107.1°for zinc, and 108.8°for beryllium complexes. These values are even larger when other water molecules in the second hydration sphere that are hydrogen bonded to water molecules in the first hydration sphere are taken into account in the calculations, but the overall trend remains the same. This order of the effect of these cations presumably expresses the extent of polarization of water molecules by each metal cation.