Shining light on dinitrogen cleavage: structural features, redox chemistry, and photochemistry of the key intermediate bridging dinitrogen complex

The key intermediate in dinitrogen cleavage by Mo(N[t-Bu]Ar)3, 1 (Ar = 3,5-C6H3Me2), has been characterized by a pair of single crystal X-ray structures. For the first time, the X-ray crystal structure of (mu-N2)[Mo(N[t-Bu]Ar)3]2, 2, and the product of homolytic fragmentation of the NN bond, NMo(N[t-Bu]Ar)3, are reported. The structural features of 2 are compared with previously reported EXAFS data. Moreover, contrasts are drawn between theoretical predictions concerning the structural and magnetic properties of 2 and those reported herein. In particular, it is shown that 2 exists as a triplet (S = 1) at 20 degrees C. Further insight into the bonding across the MoNNMo core of the molecule is obtained by the synthesis and structural characterization of the one- and two-electron oxidized congeners, (mu-N2)[Mo(N[t-Bu]Ar)3]2[B(Ar(F))4], 2[B(Ar(F))4] (Ar(F) = 3,5-C6H3(CF3)2) and (mu-N2)[Mo(N[t-Bu]Ar)3]2[B(Ar(F))4]2, 2[B(Ar(F))4]2, respectively. Bonding in these three molecules is discussed in view of X-ray crystallography, Raman spectroscopy, electronic absorption spectroscopy, and density functional theory. Combining X-ray crystallography data with Raman spectroscopy studies allows the NN bond polarization energy and NN internuclear distance to be correlated in three states of charge across the MoNNMo core. For 2[B(Ar(F))4], bonding is symmetric about the mu-N2 ligand and the NN polarization is Raman active; therefore, 2[B(Ar(F))4] meets the criteria of a Robin-Day class III mixed-valent compound. The redox couples that interrelate 2, 2(+), and 2(2+) are studied by cyclic voltammetry and spectroelectrochemistry. Insights into the electronic structure of 2 led to the discovery of a photochemical reaction that forms NMo(N[t-Bu]Ar)3 and Mo(N[t-Bu]Ar)3 through competing NN bond cleavage and N2 extrusion reaction pathways. The primary quantum yield was determined to be Phi(p) = 0.05, and transient absorption experiments show that the photochemical reaction is complete in less than 10 ns.     

Optical micromanipulation

Optical micromanipulation has engendered some major studies across all of the natural sciences at the mesoscopic scale. Though over thirty-five years old, the field is finding new applications and has lost none of its dynamic or innovative character: a trapped object presents a system that enables a calibrated minuscule force (piconewtons or less) to be exerted at will, enabling precision displacements right down to the angstrom level to be observed. The study of the motion of single biological molecular motors has been revolutionised and new studies in the physical sciences have been realised. From the chemistry and microfluidic viewpoint, optical forces may remotely actuate micro-components and perform micro-reactions. Overall, optical traps are becoming a key part of a wider "optical toolkit". We present a tutorial review of this technique, its fundamental principles and a flavour of some of the recent advances made.     

A Depolarized Dynamic Light Scattering Method to Calculate Translational and Rotational Diffusion Coefficients of Nanorods

A new analysis of depolarized dynamic light scattering data is presented, which allows the unambiguous determination of rotational and translational diffusions coefficients of nanorods in suspension. By visualizing data scaling, purely translational diffusive motions can be isolated from vertically polarized scattering, allowing the unique determination of rotational diffusion from the depolarized scattering. The method is applied to nanorods with four different aspect ratios, and compared with theoretical predictions. Diffusion coefficients obtained show good agreement with calculations based on the direct measurements of rod length and diameter. Where the theories are shown to be valid, the method allows the measurement of statistically meaningful particle sizes and aspect ratios.     

The Weak Gravity Conjecture and emergence from an ultraviolet cutoff

We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale \(e G_N^{-1/2}\) with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for nonabelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scales at which loop corrections from the tower of charged particles to the gauge boson and graviton propagators become important are parametrically identical. This suggests a picture in which gauge fields emerge from the quantum gravity scale by integrating out a tower of charged matter fields. We derive a converse statement: if a gauge theory becomes strongly coupled at or below the quantum gravity scale, the WGC follows. We sketch some phenomenological consequences of the UV cutoffs we derive.     

The Measurement of Volume: Why Do Young Children Measure Inaccurately?

A total of 257 children in grades 2–5 were individually interviewed to find the grade level at which they demonstrated transitive reasoning and unit iteration in the measurement of volume. In the transitivity task, the children were asked if a larger, empty container could be used to compare the quantity of popcorn kernels (about 350 cc) in two containers that looked very different. The unit‐iteration task was similar except that children were asked if a small cup could be used to compare similar quantities of rice in two containers. It was found that a majority of children (51%) demonstrated transitive reasoning by third grade and that a majority (56%) demonstrated unit iteration by fourth grade. A conclusion reached is that the standard of the National Council of Teachers of Mathematics (2000) expecting children to understand units of measurement by grade 2 is unrealistic. Better principles of teaching are also suggested to encourage children to think logically.     

Exploring the similarities between potential smoothing and simulated annealing

Simulated annealing and potential function smoothing are two widely used approaches for global energy optimization of molecular systems. Potential smoothing as implemented in the diffusion equation method has been applied to study partitioning of the potential energy surface (PES) for N‐Acetyl‐Ala‐Ala‐N‐Methylamide (CDAP) and the clustering of conformations on deformed surfaces. A deformable version of the united‐atom OPLS force field is described, and used to locate all local minima and conformational transition states on the CDAP surface. It is shown that the smoothing process clusters conformations in a manner consistent with the inherent structure of the undeformed PES. Smoothing deforms the original surface in three ways: structural shifting of individual minima, merging of adjacent minima, and energy crossings between unrelated minima. A master equation approach and explicit molecular dynamics trajectories are used to uncover similar features in the equilibrium probability distribution of CDAP minima as a function of temperature. Qualitative and quantitative correlations between the simulated annealing and potential smoothing approaches to enhanced conformational sampling are established. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 531–552, 2000     

Extracting angular correlations from the rare decay \bar Bd \to \bar K*^0 μ + μ − at LHCb

$ \bar Bd \to \bar K*^0 $ μ ⁺ μ ^? is a rare flavor-changing neutral-current decay. It proceeds via a b → s quark transition and is sensitive to many classes of new physics model. In this article the theoretical framework relevant to making a measurement at LHCb, the precision flavor experiment at the Large Hadron Collider, will be introduced. Progress made towards using a full angular analysis to extract A _FB, the forward-backward asymmetry of the μ pair, will be covered and its implications for the precision of the A _FB zero-crossing-point measurement discussed.