(e, 3e) test on e-e correlations in helium

The angular variations of the five-fold differential cross section obtained by using different wave functions of helium are compared with experimental data. It is found that in the coplanar geometry two kinematical arrangements, (i) equal energy sharing between the two ejected electrons with one of them ejected along the momentum transfer direction and the other along varying direction and (ii) the Bethe ridge condition with fixed sum of ejected electron energies and varying angle between them, are very sensitive to e-e correlations contained in the target wave function. This comparison has been used to show that open-shell class of wave functions better incorporate e-e correlations than the closed-shell class.     

Through-shell alkyllithium additions and borane reductions

The through-shell borane reduction and methyllithium addition to benzaldehyde (1), benzocyclobutenone (2), and benzocyclobutenedione (3) incarcerated inside a hemicarcerand (4) with four tetramethylenedioxy bridges are reported. All guests could be reduced and methylated. Selective monoreduction and monomethylation were observed for 3. In the methyllithium addition to 4[symbol: see text]3, the initially formed lithium alcoholate underwent a Moore rearrangement. The reactivity of the incarcerated guests toward methyllithium increased in the order 1 < 2 < 3 and toward borane in the order 1 < 2 approximately equal 3. Guest reactivity was correlated with the inner-phase location of the reacting carbonyl group in the preferred guest inner-phase orientation. The latter was determined from the X-ray structures of 4[symbol: see text]1, 4[symbol: see text]2, and 4[symbol: see text]3, from molecular mechanical calculations, and from the hemicarcerand-induced upfield shift of the guest proton resonances. In the methyllithium and n-butyllithium addition to 4[symbol: see text]1 and 4[symbol: see text]3 at elevated temperatures, selective cleavage of a host's spanner or tetramethylenedioxy bridge, respectively, was observed. The cleavage of one spanner also took place in the methyllithium addition to the 1-methyl-2-pyrrolidinone hemicarceplex. These scission reactions are initiated by the initially formed lithium alcoholates, which show enhanced basicity and nucleophilicity in the inner phase as compared to the bulk phase. Mechanisms for the host scission reactions are discussed.     

Mapping the potential energy surface of the tolylcarbene rearrangement in the inner phase of a hemicarcerand

Photolysis of p-tolyldiazirine (6) in the inner phase of a hemicarcerand with four butane-1,4-dioxy linker groups (5) in C(6)D(5)CD(3) at 77 K yields the 5-methylcycloheptatetraene hemicarceplex 5 circle 3b in 41% together with innermolecular reaction products resulting from an insertion of transient p-tolylcarbene (1b) into an acetal C-H or linker C-O bond of 5 and from the addition of 1b to an aryl unit of 5. The yield of incarcerated 3b increased up to 67% if 6 is photolyzed inside a hemicarcerand with deuterated spanners and butane-1,4-dioxy linker groups (d(48)-5). Hemicarceplex 5 circle 3b is not formed if the photolysis is carried out in CDCl(3). Incarcerated 3b is stable at room temperature in the absence of oxygen and is characterized by 1D and 2D NMR spectroscopy. In the presence of oxygen, 3b reacts quantitatively to yield toluene and CO(2). Upon heating solutions of d(48)-5 circle 3b in C(6)D(5)CD(3), 3b rearranges to 1b and m-tolylcarbene (18). Both tolylcarbenes immediately react with the surrounding host. From a product analysis and the measured rate constants for the thermal decomposition of d(48)-5 circle 3b in the temperature range 70-102 degrees C, the activation parameters for the 3b to 1b and 3b to 18 rearrangements are calculated (3b to 1b: DeltaG(373)++ = 27.3 +/- 1.4 kcal/mol, DeltaH(373)++ = 26.4 +/- 1.0 kcal/mol, TDeltaS(373)++ = -0.9 +/- 1.0 kcal/mol; 3b to 18: DeltaG(373)++ = 27.8 +/- 1.4 kcal/mol, DeltaH(373)++ = 19.7 +/- 1.0 kcal/mol, TDeltaS(373)++ = 8.1 +/- 1.0 kcal/mol). These values are compared with those calculated by Geise and Hadad at the B3LYP/6-311+G** level of theory (Geise, C. M.; Hadad, C. M. J. Org. Chem. 2002, 67, 2532-2540). The slightly higher inner phase activation free energy of the 3b to 18 rearrangement is explained through steric constraints imposed by the surrounding hemicarcerand on the transition state. The enthalpy-entropy compensation observed for the 3b to 18 rearrangement is discussed and interpreted as a result of a hemicarcerand and solvent reorganization along the reaction coordinate. It is taken as indirect evidence for the intermediacy of 2-methylbicyclo[4.1.0]hepta-2,4,6-triene in the 3b to 18 rearrangement.     

Thermodynamically controlled synthesis of a chiral tetra-cavitand nanocapsule and mechanism of enantiomerization

The dynamic covalent synthesis, structure and conformational dynamics of a chiral polyimine nanocapsule 1a are reported. Reaction of four tetraformyl cavitands and eight H(2)N(CH(2))(2)NH(2) yields quantitatively 1a, which has a compact, asymmetrically folded, pseudo-C(2)-symmetric structure, as determined by X-ray crystallography, and encapsulates four CHCl(3) and three CH(3)OH guests in the solid state. In solution, 1a enantiomerizes by passing over a barrier of ΔG(298)(double dagger) = 21.5 ± 0.7 kcal mol(-1) via a refolding process.     

Transient innermolecular carbene-hemicarcerand complex of fluorophenylcarbene

Laser flash photolysis of fluorophenyldiazirine incarcerated in hemicarcerand 2 affords incarcerated fluorophenylcarbene [2⊙3], which forms a metastable, innermolecular π-complex with aryl moieties of 2. This carbene complex can be observed spectroscopically. Extensive computational studies provide insights into the structure, spectroscopy, energetics, and kinetics of the 2⊙3 carbene complex.     

Templated dynamic cryptophane formation in water

Several dynamic hexaimine cryptophanes, that are built up from two triformylcyclotribenzylene cavitands and three diamino linkers and spontaneously assemble in water in the presence of a suitable templating guest, are reported. X-ray structure, kinetics and thermodynamics of assembly and molecular recognition properties are discussed.     

Scheduling precedence graphs of bounded height

The existence of a schedule for a partially ordered set of unit length tasks on m identical processors is known to be NP-complete (J. D. Ullman, NP-complete scheduling problems, J. Comput. System Sci., 10 (1975), 384–393). The problem remains NP-complete even if we restrict the precedence graph to be of height bounded by a constant. (J. K. Lenkstra and A. H. G. Rinnooy Kan, Complexity of scheduling under precedence constraints, Operations Res., 26 (1978), 22–35; D. Dolev and M. K. Warmuth, “Scheduling Flat Graphs,” IBM Research Report RJ 3398, 1982). In these NP-completeness proofs the upper bound on the number of available processors varies with the problem instance. We present a polynomial algorithm for the case where the upper bound on the number of available processors and the height of the precedence graph are both constants.