Structure and strength of complexes
As has been noted above, actinide ions in their common solution oxidation states (3+ to 6+) are all hard Lewis acids, and their bonds with aqueous ligands are predominantly ionic. Several decades ago it was observed that for a given ligand, the strength of actinide complexes increased with the “effective” cationic electrostatic charge of the actinide ions (Rao, Choppin 1984):
AnO2+ < An3+ < AnO22+ < An4+ 2.5
The effective cationic charges of both the actinyl(V) and actinyl(VI) ions, larger than their overall, formal charge, suggest that the oxygen atoms of both O = An5/6 = O cations retain a partial negative charge and the bonds between the actinide cations and the ligands in the equatorial plane are
Table 2.6 Nominal, overall and effective cationic charge of actinides

considerably stronger than would be indicated by their formal charge of +1/+2. The values of the effective charge, determined experimentally (Choppin, Rao, 1984) have been confirmed by theoretical calculations (Walch, Ellis, 1976; Matsika, Pitzer, 2000), providing theoretical foundations for the observed behavior of actinides (Choppin, Jensen, 2006) (Table 2.6).
The thermodynamic bond strengths of actinideligand complexes are determined primarily by electrostatic attraction of metal and ligand modified by steric constraints; aside from the dioxocations, directed valence effects are generally not evident in actinide coordination compounds. The electrostatic attraction between an actinide cation and a ligand is proportional to the product of the effective charges of the metal and ligand divided by the actinideligand distance (Choppin, Jensen, 2006). The steric constraints may arise from the properties of the actinide cation (ion size and presence or absence of actinyl oxygen atoms) or of the ligand (number and spatial relationship of donor atoms, size of the chelate rings, and flexibility of ligand conformations).
If the interactions of ligands with both the actinide cation and proton are governed by the same (electrostatic) interactions, some properties of their metal complexes, such as the stability constant, stoichiometry or structure can often be predicted from the chemistry of their chemical analogs (related ligands or other metal ions of similar properties). Linear free energy correlations of structurallysimilar complexes can be used to understand differences in coordination geometries for actinide complexes in solutions (Choppin, 1996; Choppin, Jensen, 2006; Paulenova, Clark, 2009). One can predict the relative strength of the metal complexes by comparison of the ligand affinity for a proton and metal cation. Gibbs free energy of a reaction is proportional to its equilibrium constant K:
AG = 2.3RTlogK 2.6
where R is the universal gas constant and T is the absolute temperature. The logarithmic constants for complex stability constant and the protonation of ligand can be used for correlating and interpreting observed values. Obviously, the ligand protonation constant can be expressed as a constant
of the reverse process, ligand dissociation, and log kH will be replaced with pKa.
The next three thermodynamic correlations (Figs 2.32.5) are based on the assumption that the interactions between the ligand and cation are primarily electrostatic in nature. When the coordination chemistry of complexes is the same, linear correlations between stability constants are apparent. A comprehensive database of ligand pKa values (Smith, Martell, 2006)
EpKA 2.5 Correlation between log pi and the sum of the protonation constants (XpKA) for a variety of complexes with the uranyl cation. 
was used in correlations below. Thermodynamic data for gluconate and oxalate ligands were measured at WSU (Paulenova, Clark, 2009).
A nearly ideal correlation between the 1 : 1 stability constants for the neptunyl and uranyl cations with a variety of organic and inorganic ligands confirms the same coordination geometry for both the dioxolinear structures of felements, and can be used (with caution) to predict the stability constants if one of constant for this pair is known.
Though the different structures of the An3+/4+ cations and An5+/6+dioxocations should impose restrictions on the correlation of thermodynamic data, it is noteworthy that data for the actinyl cation (U(VI), Np(V)) complexes generally correlates well with corresponding data for complexes of amino — carboxylates with the simple, spherical cations (Paulenova, Clark, 2009). Although the coordination geometry for the dioxocations differs from the spherical cations, the correlation between the first stability constants (log) for NTA (nitrilotriacetic) and EDTA (ethylenediamineN, N,N’,N’tetra acetic) acids with a variety of metal cations is consistent for both NTA and EDTA. As displayed in Fig. 2.4., the formally monovalent cation NpO2+ lies halfway between the monovalent and divalent spherical cations, and the correlation is satisfactory also for uranyl cation.
The correlation between log p1 and the sum of the protonation constants (XpKa) for neptunyl complexes with different carboxylate ligands is displayed in Fig. 2.5. The hydroxymonocarboxylates are correlated worse than aminocarboxylates, and lie between dicarboxylate (oxalate) and other carboxylate ligands. This is presumed to result from the strong donor effect of the oxygens present in the molecules of hydroxycarboxylates.