Ligands containing the 1-methyl-3-hydroxy-2(1H)-pyridinone group (Me-3,2-HOPO) are powerful plutonium-(IV) sequestering agents. The Ce(IV) complexes of bidentate and tetradentate HOPO ligands have been quantitatively studied as models for this sequestration. The complexes Ce(L-1)(4), Ce(L-2)(4), Ce(L-3)(2), and Ce(L-4)(2) (L-1 = Me-3,2-HOPO; L-2 = PR-Me-3,2-HOPO; L-3 = 5LI-Me-3,2-HOPO; L-4 = 5LIO-Me-3,2-HOPO) were prepared in THF solution from Ce(acac)(4) and the corresponding ligand. The complex Ce(L-4)(2) was also prepared in aqueous solution by air oxidation of the Ce(III) complex [Ce(L-4)(2)](-). Single-crystal X-ray diffraction analyses are reported for Ce(L-1)(4). 2CHCl(3) [P (1) over bar (no. 2), Z = 2, a = 9.2604(2) Angstrom, b = 12.1992(2) Angstrom, c 15.9400(2) Angstrom, alpha = 73.732(1)degrees, beta = 85.041(1)degrees, gamma = 74.454(1)degrees],Ce(L-3)(2). 2CH(3)OH [P2(1)/c (no. 14), Z = 4, a = 11.7002(2) Angstrom, b = 23.0033(4) Angstrom. c = 15.7155(2) Angstrom, beta = 96.149(1)degrees], Ce(L-4)(2). 2CH(3)OH [P (1) over bar (no. 2), Z = 2, a = 11.4347(2) Angstrom, b = 13.8008(2) Angstrom, c = 15.2844(3) Angstrom, alpha = 101.554(1)degrees, beta = 105.691(1)degrees, gamma = 106.746(1)degrees], and Ce(L-4)(2). 4H(2)O [P2(1)/c (no. 14), Z = 4, a = 11.8782(1) Angstrom, b = 22.6860(3) Angstrom, c = 15.2638(1) Angstrom, beta = 96.956(1)degrees]. A new criterion, the shape measure S. has been introduced to describe and compare the geometry of such complexes. It is defined as S = min[((1/m)Sigma(i=1)(m)(delta(i) - theta(i))(2))(1/2)], where m is the number of edges, delta(i) is the observed dihedral angle along the ith edge of delta (angle between normals of adjacent faces), theta(i) is the same angle of the corresponding ideal polytopal shape theta, and min is the minimum of all possible values. For these complexes the shape measure shows that the coordination geometry is strongly influenced by small changes in the ligand backbone or solvent. Solution thermodynamic studies determined overall formation constants (log beta) for Ce(L-2)(4), Ce(L-3)(2), and Ce(L-4)(2) of 40.9, 41.9, and 41.6, respectively. A thermodynamic cycle has been used to calculate these values from the corresponding formation constants of Ce(III) complexes and standard electrode potentials. From the formation constants and from the protonation constants of the ligands, extraordinarily high phl values for Ce(IV) are generated by these tetradentate Ligands (37.5 for Ce(L-3)(2) and 37.0 for Ce(L-4)(2)). The corresponding constants for Pu(TV) are expected to be substantially the same.