All 36 exactly solvable solutions of eigenvalues for nuclear electric quadrupole interaction Hamiltonian and equivalent rigid asymmetric rotor with expanded characteristic equation listing

This paper derives all 36 analytical solutions of the energy eigenvalues for nuclear electric quadrupole interaction Hamiltonian and equivalent rigid asymmetric rotor for polynomial degrees 1 through 4 using classical algebraic theory. By the use of double-parameterization the full general solution sets are illustrated in a compact, symmetric, structural, and usable form that is valid for asymmetry parameter $\eta \in \left({- \infty , + \infty}\right)$ . These results are useful for code developers in the area of Perturbed Angular Correlation (PAC), Nuclear Quadrupole Resonance (NQR) and rotational spectroscopy who want to offer exact solutions whenever possible, rather that resorting to numerical solutions. In addition, by using standard linear algebra methods, the characteristic equations of all integer and half-integer spins I from 0 to 15, inclusive are represented in a compact and naturally parameterized form that illustrates structure and symmetries. This extends Nielson’s?[1] listing of characteristic equations for integer spins out to I?=?15, inclusive.     

Tb3N@C84: an improbable, egg-shaped endohedral fullerene that violates the isolated pentagon rule

The structure of isomer 2 of Tb3N@C84 has been determined through single-crystal X-ray diffraction on Tb3N@C84.NiII(OEP).2(C6H6). The carbon cage has a distinct egg shape due to the presence of a single pair of fused pentagons at one apex of the molecule. Thus, although 24 IPR structures are available to the C84 cage, Nature utilizes one of the 51 568 isomeric structures that do not conform to the IPR for this unusual molecule. The Tb3N portion of isomer 2 of Tb3N@C84 is strictly planar. One Tb atom is nestled within the fold of the fused pentagons, while the other Tb atoms are disordered over four pairs of sites.     

Preparation and structure of CeSc2N@C80: an icosahedral carbon cage enclosing an acentric CeSc2N unit with buried f electron spin

Herein, we report the preparation, purification, and characterization of a mixed trimetallic nitride endohedral metallofullerene, CeSc(2)N@C(80). Single-crystal X-ray diffraction shows that CeSc(2)N@C(80) consists of a four-atom asymmetric top (CeSc(2)N) inside a C(80) (I(h)()) carbon cage. Unlike the situation in most endohedrals of the M(3)N@C(2)(n)() type, the nitride ion is not located at the center of the carbon cage but is offset by 0.36 A in order to accommodate the large Ce(III) ion. The cage carbon atoms near the endohedral Ce and Sc atoms exhibit significantly larger pyramidal angles than the other carbon atoms on the C(80) cage. Surprisingly, at ambient temperature, the (13)C NMR spectrum exhibits isotropic motional averaging yielding only two signals (3 to 1 intensity ratio) for the icosahedral C(80) cage carbons. At the same temperature, the (45)Sc NMR exhibits a relatively narrow, symmetric signal (2700 Hz) with a small temperature-dependent Curie shift. A rotation energy barrier (E(a) = 79 meV) was derived from the (45)Sc NMR line-width analysis. Finally, the XPS spectrum for CeSc(2)N@C(80) confirms a +3 oxidation state for cerium, Ce(3+)(4f(1)5d(0)).This oxidation state and the Curie shift are consistent with a weakly paramagnetic system with a single buried f electron spin.     

Incorporating a flexible crown ether into neutral discrete self-assemblies driven by metal coordination

Driven by metal coordination, a flexible crown ether was self-assembled into neutral discrete complexes with two organoplatinum acceptors. Specifically, a [1 + 1]-assembled structure was separated from self-assemblies with different stoichiometries by vapor diffusion of acetone into their dichloromethane solution. The formation of these crown ether-incorporated self-assemblies was confirmed by NMR, elemental analysis, and X-ray single-crystal analysis.     

Strong cooperative enhancement of two-photon absorption in double-strand conjugated porphyrin ladder arrays

We present the two-photon absorption (2PA) spectra of a series of conjugated porphyrin oligomers containing N = 2, 4, 8, and ca. 13 monomer units, meso-meso connected with butadiyne linkers. We demonstrate that, in the coplanar double-strand arrays, self-assembled upon addition of 4,4'-bipyridyl, the conjugation length increases dramatically, leading to very strong cooperative enhancement of 2PA. We analyze the scaling of 2PA in both the double-strand and rotationally free single-strand arrays and show how the effective conjugation length in both cases is linked to the observed 2PA properties. By introducing a "conjugation signature" for the 2PA strength, we show that, in double-strand arrangement, the conjugation embraces the whole molecule up to the tetramer level, whereas in single-strand arrangement, it is always less than N, except for N = 2, but keeps increasing until N = 8. Our finding of extremely strong 2PA cross section, sigma2 approximately 105 GM, in double-strand oligomers peaking at 1.3 mum can find use for signal processing in fiber-optic devices.     

Reversible extrusion and uptake of HCl molecules by crystalline solids involving coordination bond cleavage and formation

Yellow crystalline salts (3-XpyH)2[CuCl4] (3-XpyH = 3-halopyridinium, X = Cl, Br) lose HCl upon exposure to air in an open vessel, yielding quantitatively blue crystalline coordination compounds [CuCl2(3-Xpy)2]. The reaction is prevented if the vessel is sealed, but can be driven forward under such conditions by providing a trapping agent for HCl, such as an aqueous solution of AgNO3. The reaction requires cleavage of Cu-Cl and N-H bonds and formation of Cu-N bonds. The metal coordination geometry also changes from distorted tetrahedral to square planar. Remarkably, the reaction is fully reversible upon exposure of the blue coordination compound to vapor from a concentrated aqueous solution of HCl, and the initial yellow crystalline salt results. The structural changes occurring in these reactions have been followed by X-ray powder diffraction, including Rietveld refinement, of the crystal structures.     

A closed molecular cube and an open book: two different products from assembly of the same metal salt and bridging ligand

Reaction of the bis-bidentate bridging ligand L1 with Co(ClO4)2 or Zn(BF4)2 affords a mixture of complexes [M8(L1)12]X16 and [M6(L1)9]X12 having the same metal : ligand ratio: the former is a molecular cube with a metal ion at each vertex and a bridging ligand spanning each edge, whereas the latter has a metal framework like that of an 'open book' containing cross-linked double helical metal-ligand subunits.     

Effect of surface acoustic waves on the catalytic decomposition of ethanol employing a comb transducer for ultrasonic generation

The effect of surface acoustic waves, generated on a silver catalyst using a comb transducer, on the catalytic decomposition of ethanol is examined. The comb transducer employs purely mechanical means for surface acoustic wave (SAW) transduction. Unlike interdigital SAW transducers on piezoelectric substrates, the complicating effects of heat generation due to electromechanical coupling, high electric fields between adjacent electrodes, and acoustoelectric currents are avoided. The ethanol decomposition reactions are carried out at 473 K. The rates of acetaldehyde and ethylene production are retarded when acoustic waves are applied. The rates recover to varying degrees when acoustic excitation ceases.     

Synthesis of a library of xylogluco-oligosaccharides for active-site mapping of xyloglucan endo-transglycosylase

Complex oligosaccharides containing alpha-D-xylosyl-(1-->6)-beta-D-glucosyl residues and unsubstituted beta-(1-->4)-linked D-glucosyl units were readily synthesized using enzymatic coupling catalyzed by the Cel7B E197A glycosynthase from Humicola insolens. Constituting this library required four key steps: (1) preparing unprotected building blocks by chemical synthesis or enzymatic degradation of xyloglucan polymers; (2) generating the donor synthon in the enzymatic coupling by temporarily introducing a lactosyl motif on the 4-OH of the terminal glucosyl units of the xylogluco-oligosaccharides; (3) synthesizing the corresponding alpha-fluorides, followed by their de-O-acetylation and the glycosynthase-catalyzed condensation of these donors onto various acceptors; and (4) enzymatically releasing lactose or galactose from the reaction product, affording the target molecules in good overall yields. These complex oligosaccharides proved useful for mapping the active site of a key enzyme in plant cell wall biosynthesis and modification: the xyloglucan endo-transglycosylase (XET). We also report some preliminary enzymatic results regarding the efficiency of these compounds.     

Minimally radiating sources for personal audio

In order to reduce annoyance from the audio output of personal devices, it is necessary to maintain the sound level at the user position while minimizing the levels elsewhere. If the dark zone, within which the sound is to be minimized, extends over the whole far field of the source, the problem reduces to that of minimizing the radiated sound power while maintaining the pressure level at the user position. It is shown analytically that the optimum two-source array then has a hypercardioid directivity and gives about 7 dB reduction in radiated sound power, compared with a monopole producing the same on-axis pressure. The performance of other linear arrays is studied using monopole simulations for the motivating example of a mobile phone. The trade-off is investigated between the performance in reducing radiated noise, and the electrical power required to drive the array for different numbers of elements. It is shown for both simulations and experiments conducted on a small array of loudspeakers under anechoic conditions, that both two and three element arrays provide a reasonable compromise between these competing requirements. The implementation of the two-source array in a coupled enclosure is also shown to reduce the electrical power requirements.