Comparison of the observed and calculated vibrational frequencies of all-trans-octatetraene indicates that the density functional theory (DFT) using Becke's exchange and Lee-Yang-Parr's correlation functionals is as accurate as the Hartree-Fock (HF)-based scaled quantum mechanical force field approach in predicting fundamental vibrational frequencies. As the DFT calculation does not use any empirical parameters pertaining to the subject molecule and its computational cost scales more favorably than that of the HF theory, it is a more promising approach to molecular vibrational problems and should replace the empirical normal coordinate analysis for assisting vibrational assignments.

<p>Crystallographic and spectroscopic studies have been performed of structures, coordination and chemical bonding for series of trivalent metal ions solvated by two oxygen-coordinating solvents, water and dimethyl sulfoxide (DMSO). The hydrated scandium(III) and lanthanoid(III) ions, La to Lu, are surrounded by tricapped trigonal prisms of aqua ligands in the isomorphous series of trifluoromethanesulfonates, [M(H₂O)_n](CF₃SO₃)₃. For the smallest ions, M = Er, Tm, Yb, Lu, Sc, the hydration numbers decrease, <i>n</i> = 8.96(5), 8.8(1), 8.7(1), 8.5(1), 8.0(1), respectively, with decreasing size of the ion. The crystal structures at ambient temperature indicate randomly distributed vacancies of the capping oxygen atoms, and ²H solid-state NMR of the diamagnetic [M(H₂O)_n](CF₃SO₃)₃, M = Sc, Lu, Y and La compounds revealed increasing mobility of the water ligands in the coordination sphere with increasing temperature, also for the fully nonahydrated La^III and Y^III ions. The stretching force constants of the Ln-O bonds, evaluated from vibrational spectroscopy, increased from 0.81 to 1.16 N cm^-1 for the Ln-6O trigonal prism in a smooth correlation with the bond distances from La to Lu. For the capping Ln-3O bonds the increase from 0.49 to 0.65 N cm^-1 reflects the increased ligand-ligand repulsion with decreasing ion size. This is also the reason for the water deficiency of the Er, Tm, Yb, Lu and Sc salts, and for [Sc(H₂O)_8.0](CF₃SO₃)₃ the repulsion induced a phase transition at about 185 K that, by low temperature crystallography, was found to distort the coordination of water molecules toward a monocapped trigonal prism around the scandium(III) ion.</p><p>All crystal structures of the octakis(dimethyl sulfoxide)lanthanoid(III) iodides comprise discrete [Ln(dmso)₈]³⁺ complexes surrounded by iodide ions. The lanthanum(III) and praseodymium(III) compounds crystallize in the orthorhombic space group <i>Pbca</i> with more efficient packing than for the heavier and smaller ions in the lanthanoid series, which crystallize in the monoclinic space group <i>P2</i>₁/<i>n</i>. The group 13 metal ions, aluminium(III), gallium(III), indium(III), thallium(III), and also scandium(III) of group 3, form crystalline hexakis(dimethyl sulfoxide) solvates in the space group <i>R</i> 3, with octahedral MO₆ coordination entities, which are increasingly compressed along one threefold axis for increasing ionic size. EXAFS measurements on the solvated ions display similar M-O bond distances in dimethyl sulfoxide solution as in the solid solvates. For all the solid dimethyl sulfoxide solvates the strength and nature of the metal-oxygen bond has been evaluated by normal coordinate analysis of vibrational spectra, and correlated with the S-O stretching vibrational mode.</p><p>Distortions from regular octahedral six coordination are discussed for the hydrated isoelectronic soft mercury(II) and thallium(III) ions in the solid bisaquamercury(II) and trisaquatallium(III) trifluoromethanesulfonates, in terms of pseudo Jahn-Teller effects (PJTE). Mercury(II), generally more strongly influenced by PJTE distortions, displays a 2 + 4 Hg-O coordination forming chains that are held together in sheets by hydrogen bonds and in layers by van der Waals interactions, which explain the fragile structure of the crystals.</p>

Crystallographic and spectroscopic studies have been performed of structures, coordination and chemical bonding for series of trivalent metal ions solvated by two oxygen-coordinating solvents, water and dimethyl sulfoxide (DMSO). The hydrated scandium(III) and lanthanoid(III) ions, La to Lu, are surrounded by tricapped trigonal prisms of aqua ligands in the isomorphous series of trifluoromethanesulfonates, [M(H2O)n](CF3SO3)3. For the smallest ions, M = Er, Tm, Yb, Lu, Sc, the hydration numbers decrease, n = 8.96(5), 8.8(1), 8.7(1), 8.5(1), 8.0(1), respectively, with decreasing size of the ion. The crystal structures at ambient temperature indicate randomly distributed vacancies of the capping oxygen atoms, and 2H solid-state NMR of the diamagnetic [M(H2O)n](CF3SO3)3, M = Sc, Lu, Y and La compounds revealed increasing mobility of the water ligands in the coordination sphere with increasing temperature, also for the fully nonahydrated LaIII and YIII ions. The stretching force constants of the Ln-O bonds, evaluated from vibrational spectroscopy, increased from 0.81 to 1.16 N cm-1 for the Ln-6O trigonal prism in a smooth correlation with the bond distances from La to Lu. For the capping Ln-3O bonds the increase from 0.49 to 0.65 N cm-1 reflects the increased ligand-ligand repulsion with decreasing ion size. This is also the reason for the water deficiency of the Er, Tm, Yb, Lu and Sc salts, and for [Sc(H2O)8.0](CF3SO3)3 the repulsion induced a phase transition at about 185 K that, by low temperature crystallography, was found to distort the coordination of water molecules toward a monocapped trigonal prism around the scandium(III) ion. All crystal structures of the octakis(dimethyl sulfoxide)lanthanoid(III) iodides comprise discrete [Ln(dmso)8]3+ complexes surrounded by iodide ions. The lanthanum(III) and praseodymium(III) compounds crystallize in the orthorhombic space group Pbca with more efficient packing than for the heavier and smaller ions in the lanthanoid series, which crystallize in the monoclinic space group P21/n. The group 13 metal ions, aluminium(III), gallium(III), indium(III), thallium(III), and also scandium(III) of group 3, form crystalline hexakis(dimethyl sulfoxide) solvates in the space group R 3, with octahedral MO6 coordination entities, which are increasingly compressed along one threefold axis for increasing ionic size. EXAFS measurements on the solvated ions display similar M-O bond distances in dimethyl sulfoxide solution as in the solid solvates. For all the solid dimethyl sulfoxide solvates the strength and nature of the metal-oxygen bond has been evaluated by normal coordinate analysis of vibrational spectra, and correlated with the S-O stretching vibrational mode. Distortions from regular octahedral six coordination are discussed for the hydrated isoelectronic soft mercury(II) and thallium(III) ions in the solid bisaquamercury(II) and trisaquatallium(III) trifluoromethanesulfonates, in terms of pseudo Jahn-Teller effects (PJTE). Mercury(II), generally more strongly influenced by PJTE distortions, displays a 2 + 4 Hg-O coordination forming chains that are held together in sheets by hydrogen bonds and in layers by van der Waals interactions, which explain the fragile structure of the crystals.