New Cyclophanes as Initiator Cores for the Construction of Dendritic Receptors: Host-guest complexation in aqueous solutions and structures of solid-state inclusion compounds

Cyclophanes 3 and 4 were prepared as initiator cores for the construction of dendrophanes (dendritic cydophanes) 1 and 2 , respectively, which mimic recognition sites buried in globular proteins. The tetra-oxy[6.1.6.1]paracyclophane 3 was prepared by a short three-step route (Scheme 1) and possesses a cavity binding site shaped by two diphenylmethane units suitable for the inclusion of flat aromatic substrates such as benzene and naphthalene derivatives as was shown by ¹H-NMR binding titrations in basic D₂O phosphate buffer (Table 1). The larger cyclophane 4 , shaped by two wider naphthyl(phenyl)methane spacers, was prepared in a longer, ten-step synthesis (Scheme 2) which included as a key intermediate the tetrabromocyclophane 5 . ¹H-NMR Binding studies in basic borate buffer in D₂O/CD₃OD demonstrated that 4 is an efficient steroid receptor. In a series of steroids (Table 1), complexation strength decreased with increasing substrate polarity and increasing number of polar substituents; in addition, electrostatic repulsion between carboxylate residues of host and guest also affected the binding affinity strongly. The conformationally flexible tetrabromocyclophane 5 displayed a pronounced tendency to form solid-state inclusion compounds of defined stoichiometry, which were analyzed by X-ray crystallography (Fig. 2). 1,2-Dichloroethane formed a cavity inclusion complex 5a with 1:1 stoichiometry, while in the 1:3 inclusion compound 5b with benzene, one guest is fully buried in the macrocyclic cavity and two others are positioned in channels between the Cyclophanes in the crystal lattice. In the 1:2 inclusion compound 5c , two toluene molecules penetrate with their aromatic rings the macrocyclic cavity from opposite sides in an antiparallel fashion. On the other hand, p-xylene (= 1,4-dimethylbenzene) in the 1:1 compound 5d is sandwiched between the cyclophane molecules with its two Me groups penetrating the cavities of the two macrocycles. In the 1:2 inclusion compound 5e with tetralin (= 1,2,3,4-tetrahydronaphthalene), both host and guest are statically disordered. The shape of the macrocycle in 5a – e depends strongly on the nature of the guest (Fig. 4). Characteristic for these compounds is the pronounced tendency of 5 to undergo regular stacking and to form channels for guest inclusion; these channels can infinitely extend across the macrocyclic cavities (Fig. 6) or in the crystal lattice between neighboring cyclophane stacks (Fig. 5). Also, the crystal lattice of 5c displays a remarkable zig-zag pattern of short Br…?O contacts between neighboring macrocycles (Fig. 7).     

Extensions of Szegö's theory of orthogonal polynomials,III

Let {ø _n (dμ)} be a system of orthonormal polynomials on the unit circle with respect to a measuredμ. Szegö's theory is concerned with the asymptotic behavior ofø _n (dμ) when logμ′∈L ¹. In what follows we will discuss the asymptotic behavior of the ratioø _n (dμ ₂)/ø _n (dμ ₁) on the unit circle whendμ ₁ anddμ ₂ are close in a sense (e.g.,dμ ₂=gdμ ₁, where g≥0 is such thatQ(e ^it )g(t) andQ(e ^it )/g(t) are bounded for a suitable polynomialQ) and μ ₁ ^′ >0 almost everywhere or (a somewhat weaker requirement) lim _n→∞Φ _n (dμ ₁,0)=0 for the monic polynomial Φ _n . The asymptotic behavior of the same fraction outside the unit circle was discussed in an earlier paper.     

A phase cell approach to Yang-Mills theory

In this paper the basic local stability result is obtained, in a form valid in both small field and large field regions. To achieve this, some modifications are made in both the action and the renormalization group transformation. Though there is some sacrifice of elegance in these modifications, the establishment of this local stability estimate yields the most basic ingredient of the phase cell cluster expansion, good estimates for all the actions.Incidental to the estimates of this paper we establish some results on lattice geometry, interesting in their own right. A bound on the minimum area of a loop of lengthl, ind dimensions, is obtained asl ²/8(1–1/d). This, a best possible bound, was obtained for us by A. Blass. We also construct a radial maximal tree for the lattice ind dimensions. We hope to stimulate someone to find a better construction of radial trees.This work was supported in part by the National Science Foundation under Grant No. PHY 85-02074     

Collision-induced and infrared multiphoton dissociation studies on M(acetone)2 + (M=Al,Fe, Co,Cu, ScO) in the gas phase

In this paper we report an extension of our earlier study on the structure of Alfacetone)₂ ⁺ Collision-induced dissociation (CID) on MfacetoneXacetone-d₆)⁺ for M = Al, Fe, Co, and Cu yields primarily, if not exclusively, nearly equal amounts of acetone and acetone-d₆. Likewise, infrared multiphoton dissociation (IRMPD) at 10.6 μm yields, exclusively, nearly equal losses of the labeled and unlabeled acetones. These results suggest that the two acetone ligands bind in an equivalent fashion. Sc⁺ was also studied, which proved to be the most interesting. Sc⁺ reacts with acetone to form primarily ScO⁺, which undergoes higher order reactions leading to several products including ScO(acetone)₂ ⁺. IRMPD on this ion produces ScO(acetone-d₆)(CD₂CO)⁺, while its perdeuterated analog also produces ScO(acetone-d₆)⁺ in addition to ScO(acetone-d₆(CD₂CO)⁺. The IRMPD results are supplemented by studying the primary and higher order reactions of Sc⁺ with acetone, as well as the CID of ScO(acetone)₂ ⁺. Finally, a qualitative assessment of the infrared photodissociation cross sections is given. It is found that the relative photodissociation cross sections follow the orders Co(acetone-d₆)₂ ⁺ > Co(acetone)(acetone-d₆) > Co(acetone)₂ ⁺ and Co(acetone-d₆)⁺ > Co(acetone)⁺.