Adam J. Bridgeman

Density functional study of the vibrational frequencies of α-Keggin heteropolyanions

Abstract The structures and vibrational spectra of the α-Keggin heteropolyanions [ PMo 12 O 40 ] 3− , [ PW 12 O 40 ] 3− , [ AsMo 12 O 40 ] 3− , [ SiMo 12 O 40 ] 4− , [ GeMo 12 O 40 ] 4− , [ AlMo 12 O 40 ] 5− and [GaMo12O40]5− have been calculated using density functional theory. The calculations represent the first non-empirical study of the vibrational frequencies of this important class of polyoxometalates. The agreement between the previously reported vibrational spectra and the calculated values is, in general, good. A number of previously reported assignments have been confirmed or clarified. The calculations are extremely computationally demanding requiring precise energies and geometries and cannot presently be considered a standard task for the study of these large, heavy element cluster anions. Characteristic group frequencies for the type I polyoxometalates with isopolyanions with the Lindqvist structure and heteropolyanions with the α-Keggin structure have been identified and the effect of the heteroatom on these frequencies studied. The vibrational analyses confirm the high symmetry for these anions suggested by previous geometry calculations.

The Mayer bond order as a tool in inorganic chemistry

The bonding in molecules is most often described using the classical chemical ideas of covalency (bond multiplicity) and ionicity (atomic charges). The Mayer bond order is a natural extension of the Wiberg bond order, which has proved extremely useful in bonding analysis using semi-empirical computational methods, and the Mulliken population analysis to ab initio theories. The usefulness of the Mayer bond order has been tested in a number of inorganic molecules including sulfur–nitrogen rings, halogen–oxide molecules and transition metal dichloride molecules. The basis set dependence of the Mayer bond order is tested through the case studies presented. It is shown that the bond order can be fully or partially decomposed into the contributions from symmetry types for many interactions of interest to the inorganic chemist. The power of this approach is shown by examining the bonding in a variety of systems and is illustrated by detailed studies of the role of the ring size and electron count on the bonding in S–N rings, the role of hypervalency in the relative stabilities of mixed hydrogen and halogen peroxide isomers and the importance of s–d hybridization in the 3d transition metal dichloride molecules.

Structural and Vibrational Study of [Mo7O24]6− and [W7O24]6−

Density functional methods have been used to investigate the structure and the vibrational modes of [M7O24]6- isopolyanions of molybdenum and tungsten. Relativistic effects have been considered through the zeroth-order regular approximation (ZORA) and interactions with an aqueous environment modeled by the COSMO approach. A structural study of the two compounds has been performed, and the geometrical parameters obtained are in good agreement with experimental data. However, when the solvent is introduced in the model, deviations are found, especially for some tungsten-oxygen bonds which involve pseudoterminal oxygens. Thus, different computational strategies have been tested to reject any reliance on the COSMO model and the optimization algorithms. The variations compared to solid-state bond lengths appear to be due to the solvent. Infrared and Raman spectra have been also calculated in the gas phase and in water leading, for the first time, to a detailed assignment of the vibrational frequencies. The vibrational contributions of the aminopyridinium counterion [C5H7N2]+ have been isolated, improving the assignment of experimental spectra. Inclusion of solvent causes a shift toward lower frequencies and an increase in the intensity of the peaks. Spectra obtained using pseudo-gas-phase calculations reproduce the experimental data most satisfactorily, especially when the experiments are performed on the solid state.

Density functional study of the vibrational frequencies of Lindqvist polyanions

Abstract The structures and vibrational spectra of the Lindqvist polyanions [Mo6O19]2−, [W6O19]2−, [Mo6O19]3−, [VMo5O19]3− and [VMo5O19]4− have been calculated using density functional theory. The agreement between the previously reported vibrational spectra and the calculated values is extremely good. For [Mo6O19]2−, a detailed comparison between the performance of commonly used functionals and basis sets and between Hartree–Fock and density functional methods has been performed. Whilst all density functional methods perform adequately, the Hartree–Fock method overestimates the strength of the metal–oxygen bonding and this is reflected in poor reproduction of the stretching frequencies. The results suggest that the local density approximation with Slater type orbitals and relativistic corrections is best able to model both the structure and vibrational spectra of these polyanions when treated as pseudo-gas phase species. The calculations are extremely computationally demanding requiring precise energies and geometries and cannot presently be considered a standard task for the study of these large, heavy element cluster anions. The vibrational analyses confirm the high symmetry for these anions suggested by previous geometry calculations.

THE GROUND STATE OF A TETRAGONALLY COMPRESSED COPPER(II) COMPLEX

Abstract Electronic spectra, non-local density functional and cellular ligand-field calculations have been used to characterize the ligand fields and ground states of two potentially Jahn–Teller compressed CuN 6 octahedra containing rigid tridentate ligands. The calculations predict that one of the systems has genuinely tetragonally compressed octahedral coordination with a high barrier to elongation. This is caused by large substituents on the ligands that prevent both dynamic effects and the adoption of the more familiar elongated shape.

Multiple bonding in homonuclear Group 13 ethene analogues

Abstract The nature and strength of the bonding in the neutral (MR 2 ) 2 and reduced (MR 2 ) 2 n − ( n =0, 1, 2) complexes of the Group 13 elements (M=B, Al, Ga or In) have been investigated using non-local density functional theory. The reduced systems are found to be genuinely multiply bonded and estimates of the π-bond strengths suggest that these weaken considerably down the group and are compared with those between Group 14 elements. Formation of the doubly reduced complexes is disfavored for the heavier elements by the repulsion between the negatively charged centers and the weakness of the MM π-interaction. Calculations on Li 2 [M 2 R 4 ] derivatives, however, suggest that strong solvation is the key to the successful syntheses of these systems. trans -Bending of the [M 2 R 4 ] 2− anions is investigated and is predicted to increase down the group. A careful treatment of the electronic causes of this bending is reported, and differs from previous analyses of the non-classical shapes of isoelectronic Group 14 molecules.

The study, evaluation, and improvement of university student self-efficacy

In this review of 64 articles published since the year 2000, a strong association between self-efficacy and student learning outcomes was apparent. Self-efficacy is also related to other factors such as value, self-regulation and metacognition, locus of control, intrinsic motivation, and strategy learning use. The review revealed that university student self-efficacy is higher under certain conditions than others, and that it can be improved. Examples of teaching strategies that may be used to improve self-efficacy are outlined. In screening articles for inclusion in the review, several conflicting definitions of self-efficacy arose. Clarification on the meaning and scope of the self-efficacy term is provided. The interpretation of the results of some studies reviewed was limited by design or analysis issues. Suggestions for addressing these issues in future research and evaluation work is given.

Temperature dependence of the electronic ground states of two mononuclear, six-coordinate copper(II) centres

Powdered [Cu(L2NH2)2][ClO4]2 (1; L2NH2 = 2,6-bis{hydrazonomethyl}pyridine) and [Cu(L2OH)2][ClO4]2 (2; L2OH = 2,6-bis{oximomethyl}pyridine) exhibit EPR spectra that are consistent with {dz2}1 Cu(II) centres at 295 K. These slowly transform upon cooling to 5 K, to show g-values that more closely resemble {dy2−z2}1, pseudo-Jahn–Teller elongated structures. Single crystal X-ray structures of 1·2(CH3)2CO and 22(CH3)2CO show the expected six-coordinate Cu(II) centres, with Cu–N bond lengths that are consistent with a {dz2}1 configuration according to DF calculations. Importantly, the structure of 2 is temperature-dependent between 100–300 K, its Cu–N bond lengths varying in a manner consistent with the EPR data. The EPR spectra, and TLS analyses of the crystal structures, strongly imply that these changes are not a consequence of dynamic Jahn–Teller disorder. These results contrast with [Cu(L2Me)2]2+ (L2Me = 2,6-bis{N-methylcarbaldimino}pyridine) and other [Cu(L2R)2]2+ complexes with small alkyl or aryl ‘R’ substituents, which adopt the more usual {dy2−z2}1 ground states at all temperatures.

Stereochemical effects on the spin-state transition shown by salts of [FeL2]2+ [L = 2,6-di(pyrazol-1-yl)pyridine]

The syntheses of [Fe(L1H)2]X2 (L1H = 2,6-di(pyrazol-1-yl)pyridine [L1H]; X− = BF4−, PF6−) are described. Solvent-free [Fe(L1H)2][BF4]2 shows an approximately D2d-symmetric metal centre in the crystal, and undergoes an unusual abrupt spin-state transition centered at 261 K in the solid, or at 248 K in acetone solution. A solvated phase [Fe(L1H)2][BF4]2·2.9CH3NO2·0.25H2O can be grown at 240 K, which undergoes an irreversible spin-state transition between 260 and 265 K. In contrast, solid [Fe(L1H)2][PF6]2 adopts an unusual C2-symmetric coordination geometry, reflecting a ca. 28° twist of one L1H ligand with respect to each other. This salt is high-spin in the range 10–330 K. DFT calculations have rationalised this unusual structure as a Jahn–Teller distortion of the 5E ground state of the six-coordinate Fe(II) ion. This distortion is favoured by the restricted bite-angle of the L1H ligands.

Main group monocarbonyls

Abstract Non-local density functional calculations are used to investigate the properties and bonding of the monocarbonyl complexes of the s- and p-block main group elements of the first five periods. There is good agreement between the calculated properties and those of experimentally observed monocarbonyls. Predictions of the vibrational frequencies and stabilities of, as yet, unknown complexes are given. A bonding model involving synergistic M←CO σ-donation and M→CO π-backbonding analogous to that used for transition metal carbonyls is described. It is used to describe the variations in the properties of these systems within the groups and periods of the main group elements. The limitations of this description when applied to electron-poor and electron-rich main group MCO molecules are outlined. The bonding in the s-block monocarbonyls is dominated by the repulsive σ-interaction between the metal s-electrons and the CO lone pair. In the monocarbonyls of electronegative elements, there is significant involvement of the filled π-level on CO.