Linear energy relationships for the octahedral preference of Mg, Ca and transition metal ions

The geometry, atomic charges, force constants, and relative energies of the symmetric and distorted M(2+)(H(2)O)(4)(F(-))(2), M(3+)(H(2)O)(4)(F(-))(2), M(2+)(H(2)O)(3)(F(-))(2), and M(3+)(H(2)O)(3)(F(-))(2) metal complexes, M = Mg, Ca, Co, Cu, Fe, Mn, Ni, Zn, Cr, V, were calculated by using the B3LYP/TZVP density functional method in both gas phase and aqueous solution, modeled using the polarized continuum model. The deformation energy associated with moving one water ligand 12 degrees from the initial "octahedral" arrangement, in which all O-M-O, O-M-F, and F-M-F angles are either 90 degrees or 180 degrees, was calculated to examine the angular ligand flexibility. For all M(2+)(H(2)O)(4)(F(-))(2) complexes, this distortion increased the energy of the complex in proportion to the electrostatic potential-derived (ESP) charge of the metal, and in proportion to D(-10), where D is the distance from the distorted ligand to its closest neighbor. The octahedral stability was further examined by calculating the energies for the removal of a water ligand from the octahedral complex to form a square-pyramidal or trigonal-bipyramidal complex. The octahedral preference, defined as the negative of the corresponding binding energy of the ligand, was found to linearly correlate with the ESP charge of the metal in both the gas phase and aqueous solution. The obtained results indicate that quantum-mechanical covalent effects are of secondary importance for both the flexibility and the octahedral preference of M(2+)(H(2)O)(4)(F(-))(2) and M(3+)(H(2)O)(4)(F(-))(2) complexes. This conclusion and supporting data are important for the development of consistent molecular mechanical force fields of the studied metal ions.