Periodicity of Single-Molecule Magnet Behaviour of Heterotetranuclear Lanthanide Complexes across the Lanthanide Series: A Compendium

Acetato-bridged palladium–lanthanide tetranuclear heterometallic complexes of the form [Pd₂Ln₂(H₂O)₂(CH₃COO)₁₀] ⋅ 2 CH₃COOH [Ln₂=Ce₂ ( 1 ), Pr₂ ( 2 ), Nd₂ ( 3 ), Sm₂ ( 4 ), Tb₂ ( 5 ), Dy₂ ( 6 ), Dy_0.2Y_1.8 ( 6′′ ), Ho₂ ( 7 ), Er₂ ( 8 ), Er_0.24Y_1.7 ( 8′′ ), Tm₂ ( 9 ), Yb₂ ( 10 ), Y₂( 11 )] were synthesised and characterised by experimental and theoretical techniques. All complexes containing Kramers lanthanide ions [Ln³⁺=Ce ( 1 ), Nd ( 3 ), Sm ( 4 ), Dy ( 6 ), DyY ( 6′′ ), Er ( 8 ), ErY ( 8′′ ), Yb ( 10 )] showed field-induced slow magnetic relaxation, characteristic of single-molecule magnetism and purely of molecular origin. In contrast, all non-Kramers lanthanide ions [Ln³⁺=Pr ( 2 ), Tb ( 5 ), Ho ( 7 ), Tm ( 9 ), Y³⁺ ( 11 ) is diamagnetic and non-lanthanide] did not show any slow magnetic relaxation. The variation in the electronic structure and accompanying consequences across the complexes representing all Kramers and non-Kramers lanthanide ions were investigated. The origin of the magnetic properties and the extent to which the axial donor–acceptor interaction involving the lanthanide ions and an electron-deficient orbital of palladium affects the observed magnetic and electronic properties across the lanthanide series are presented. Unique consistent electronic and magnetic properties of isostructural complexes spanning the lanthanide series with properties dependent on whether the ions are Kramers or non-Kramers are reported.     

Multi-step damage accumulation in irradiated crystals

This article presents a model of damage accumulation in irradiated crystals. This model is based on the assumption that the damage accumulation occurs through a series of structural transformations triggered by the destabilization of the current structure of crystals. Formal equations describing the damage accumulation build-up and experimental assessment of the model are presented and discussed in the framework of the actual knowledge of radiation effects in oxide crystals (yttria-stabilized zirconia (YSZ) and magnesium-aluminate spinel (MAS)), silicon carbide crystals and zirconia implanted nickel crystals.     

Ab initio study of the electronic structure of manganese carbide

We report electronic structure calculations on 13 states of the experimentally unknown manganese carbide (MnC) using standard multireference configuration interaction (MRCI) methods coupled with high quality basis sets. For all states considered we have constructed full potential energy curves and calculated zero point energies. The X state, correlating to ground state atoms, is of 4sigma- symmetry featuring three bonds, with a recommended dissociation energy of D0 = 70.0 kcal/mol and r(e) = 1.640 angstroms. The first and second excited states, which also correlate to ground state atoms, are of 6sigma- and 8sigma- symmetry, respectively, and lie 17.7 and 28.2 kcal/mol above the X state at the MRCI level of theory.     

Resolving a puzzling anomaly in the spin-coupled generalized valence bond description of benzene

In an earlier study of benzene, Small and Head-Gordon found that the spin-coupled generalized valence bond (SCGVB) wave function for the π system predicted a distorted (non-D_6h) geometry, one with alternating CC bond lengths. However, the variations in the energy were very small and the predictions were made using a very small basis set (STO-3G). We re-examined this prediction using a much larger basis set (aug-cc-pVTZ) to determine the dependence of the energy of benzene on the distortion angle, Δθ_CXC (Δθ_CXC = 0° corresponds to the D_6h structure). We also found a distorted geometry with the optimum Δθ_CXC being 0.31° with an energy 0.040 kcal mol⁻¹ lower than that for the D_6h structure. In the optimum geometry, adjacent CC bond lengths are 1.3861 Å and 1.4004 Å. Analysis of the SCGVB wave function led us to conclude that the cause of the unusual non-D_6h geometry predicted by the SCGVB calculations seems to be a result of the interaction between the Kekulé and Dewar components of the full SCGVB wave function. The addition of doubly ionic configurations to the SCGVB wave function leads to the prediction of a D_6h geometry for benzene and a dependence on Δθ_CXC essentially the same as that predicted by the complete active space self-consistent field wave function.     

Bonding in SCln (n = 1-6): a quantum chemical study

Following a previous study of bonding and isomerism in the SF(n) and singly chloro-substituted SF(n-1)Cl (n = 1-6) series, we describe bonding in the ground and low-lying excited states of the completely substituted series, SCl(n) (n = 1-6). All structures were characterized at least at the RCCSD(T)/aug-cc-pV(Q+d)Z level of theory. Both differences and similarities were observed between SCl(n) and our previous results on SF(n-1)Cl and SF(n). Several minimum structures that exist in SF(n) and SF(n-1)Cl are absent in SCl(n). For example, the optimized structure of SCl(2)((3)A(2)) is a transition state in C(s) symmetry, whereas the analogous states are minima in SF(n) and SF(n-1)Cl. Second, we found a continuation of a trend discovered in the SF(n-1)Cl series, where Cl substitution has a destabilizing effect that weakens bonds with respect to SF(n). This effect is much stronger in the SCl(n) series than it is in the SF(n-1)Cl series, which is why SCl(2) is the most stable observed species in the family and why SCl(4), SCl(5), and SCl(6) are unstable (SCl(n-2) + Cl(2) additions are endothermic for n = 4-6).     

Studies of intersystem crossing dynamics in acetylene

We report a new ab initio study of the acetylene T3 potential energy surface, which clarifies the nature of its energy minimum, and present computed equilibrium geometries and diabatic frequencies. This information enables the computation of harmonic vibrational overlap integrals of T3 vibrational levels with the S1 3nu3 state. The results of this calculation support the interpretation of two local perturbations of S1 3nu3, revealed in ultraviolet laser-induced fluorescence/surface electron ejection by laser excited metastables spectroscopy and Zeeman anticrossing measurements, respectively, as arising from two rotational submanifolds of a single T3 vibrational state. We present plausible assignments for this state as a guide for future experimental work.     

Looking at the complexity of two young children's understanding of number

This paper presents a qualitative study that investigated two third-grade students’ understanding of number. The children were videotaped while they worked to record everything they knew about the number, 72. Their artifacts and conversations were then analyzed using the Pirie-Kieren dynamical theory for the growth of mathematical understanding as the theoretical framework. The results of the video analysis revealed the two students’ understanding of natural numbers as being conceptually complex and existing in several different realms of the Pirie-Kieren model. Significant instances of Primitive Knowing, Image Making, Image Having, Property Noticing, Formalizing, Observing, as well as how the children's understanding existed beyond “Don’t Need” Boundaries are identified and examined in detail. Other features of the model — Structuring, Inventising, Folding Back, and Connected Understanding - are also explained and possible examples illustrating these kinds of mathematical thinking in relation to the two children's understanding of number are offered.     

Sofic groups and diophantine approximation

We prove the algebraic eigenvalue conjecture of J. Dodziuk, P. Linnell, V. Mathai, T. Schick, and S. Yates (see [2]) for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we define integer operators and prove a quantization of the operator norm below 2. To the knowledge of the author, there is no group known that is not sofic. © 2007 Wiley Periodicals, Inc.