Terminating high-spin bands in 101Rh

High spin states of ¹⁰¹Rh have been populated using the reaction ⁷⁰Zn+³⁶S at 130 MeV. γ-rays were detected with the EUROGAM2 array. New high-spin bands have been observed in this nucleus up to 45/2⁻, 57/2⁻ and 65/2⁺ states. They have been interpreted using the Nilsson-Strutinsky cranking formalism as terminating configurations. Two of the bands were observed up to the predicted terminating states which are built up from g_9/2 protons as well as d_5/2, g_7/2 and h_11/2 neutrons relative to a ⁹⁰Zr core. Received: 30 October 1998     

Obtaining local reciprocal lattice vectors from finite‐element analysis

Finite‐element analysis is frequently used by engineers at synchrotron beamlines to calculate the elastic deformation of a single crystal undergoing mechanical bending or thermal load. ANSYS^® Workbench? software is widely used for such simulations. However, although ANSYS^® Workbench? software provides useful information on the displacements, strains and stresses within the crystal, it does not yield the local reciprocal lattice vectors that would be required for X‐ray diffraction calculations. To bridge this gap, a method based on the shape functions and interpolation procedures of the software itself has been developed. An application to the double‐crystal bent Laue monochromator being designed for the I12 (JEEP) wiggler beamline at the Diamond Light Source is presented.     

Building Blocks for High-Efficiency Organic Photovoltaics: Interplay of Molecular,Crystal, and Electronic Properties in Post-Fullerene ITIC Ensembles

Accurate single-crystal X-ray diffraction data offer a unique opportunity to compare and contrast the atomistic details of bulk heterojunction photovoltaic small-molecule acceptor structure and packing, as well as provide an essential starting point for computational electronic structure and charge transport analysis. Herein, we report diffraction-derived crystal structures and computational analyses on the n-type semiconductors which enable some of the highest efficiency organic solar cells produced to date, 3,9-bis(2-methylene-(3-(1,1-dicyanomethylene)-indanone))-5,5,11,11-tetrakis(4-hexylphenyl)-dithieno[2,3-d:2′,3′-d′]-s-indaceno[1,2-b:5,6-b′]dithiophene ( ITIC ) and seven derivatives (including three new crystal structures: 3,9-bis(2-methylene-(3-(1,1-dicyanomethylene)-indanone))-5,5,11,11-tetrakis(4-propylphenyl)-dithieno[2,3-d:2′,3′-d′]-s-indaceno[1,2-b:5,6-b′]dithiophene ( ITIC-C3 ), 3,9-bis(2-methylene-(3-(1,1-dicyanomethylene)-indanone))-5,5,11,11-tetrakis(3-hexylphenyl)-dithieno[2,3-d:2′,3′-d′]-s-indaceno[1,2-b:5,6-b′]dithiophene ( m -ITIC-C6 ), and 3,9-bis(2-methylene-((3-(1,1-dicyanomethylene)-6,7-difluoro)-indanone))-5,5,11,11-tetrakis(4-butylphenyl)-dithieno[2,3-d:2′,3′-d′]-s-indaceno[1,2-b:5,6-b′]dithiophene ( ITIC-C4-4F ). IDTT acceptors typically pack in a face-to-face fashion with π–π distances ranging from 3.28–3.95 Å. Additionally, edge-to-face packing is observed with S⋯π interactions as short as 3.21–3.24 Å. Moreover, ITIC end group identities and side chain substituents influence the nature and strength of noncovalent interactions (e. g. H-bonding, π–π) and thus correlate with the observed packing motif, electronic structure, and charge transport properties of the crystals. Density functional theory (DFT) calculations reveal relatively large nearest-neighbor intermolecular π-π electronic couplings (5.85–56.8 meV) and correlate the nature of the band structure with the dispersion interactions in the single crystals and core–end group polarization effects. Overall, this combined experimental and theoretical work reveals key insights into crystal engineering strategies for indacenodithienothiophene (IDTT) acceptors, as well as general design rules for high-efficiency post-fullerene small molecule acceptors.     

Heavy-Atom Tunneling in Semibullvalenes: How Driving Force,Substituents, and Environment Influence the Tunneling Rates

The Cope rearrangement of selectively deuterated isotopomers of 1,5-dimethylsemibullvalene 2 a and 3,7-dicyano-1,5-dimethylsemibullvalene 2 b were studied in cryogenic matrices. In both semibullvalenes the Cope rearrangement is governed by heavy-atom tunneling. The driving force for the rearrangements is the small difference in the zero-point vibrational energies of the isotopomers. To evaluate the effect of the driving force on the tunneling probability in 2 a and 2 b , two different pairs of isotopomers were studied for each of the semibullvalenes. The reaction rates for the rearrangement of 2 b in cryogenic matrices were found to be smaller than the ones of 2 a under similar conditions, whereas differences in the driving force do not influence the rates. Small curvature tunneling (SCT) calculations suggest that the reduced tunneling rate of 2 b compared to that of 2 a results from a change in the shape of the potential energy barrier. The tunneling probability of the semibullvalenes strongly depends on the matrix environment; however, for 2 a in a qualitatively different way than for 2 b .     

Highly Enantioselective,Organocatalytic, and Scalable Synthesis of a Rare cis,cis-Tricyclic Diterpenoid

A highly enantioselective, organocatalytic, and scalable synthesis of a very unusual cis-decalin-cis-hydrindane tricyclic diterpenoid system has been achieved. Despite the prevalent pharmacological space that the related trans,trans and trans,cis-systems occupy, there have been no reports of an asymmetric synthesis of the cis,cis systems in the literature until now. We demonstrate the flexibility of our approach not only through access to a diverse range of products, all of which are attained in exceptionally high selectivities, but also by showing their easy conversion to the corresponding trans,cis-system and other derivatives.     

A Global Optimization Algorithm using Lagrangian Underestimates and the Interval Newton Method

Convex relaxations can be used to obtain lower bounds on the optimal objective function value of nonconvex quadratically constrained quadratic programs. However, for some problems, significantly better bounds can be obtained by minimizing the restricted Lagrangian function for a given estimate of the Lagrange multipliers. The difficulty in utilizing Lagrangian duality within a global optimization context is that the restricted Lagrangian is often nonconvex. Minimizing a convex underestimate of the restricted Lagrangian overcomes this difficulty and facilitates the use of Lagrangian duality within a global optimization framework. A branch-and-bound algorithm is presented that relies on these Lagrangian underestimates to provide lower bounds and on the interval Newton method to facilitate convergence in the neighborhood of the global solution. Computational results show that the algorithm compares favorably to the Reformulation–Linearization Technique for problems with a favorable structure.     

Interpolation by positive definite functions on locally compact groups with application to SO (3)

In this research a method for interpolation on arbitrary locally compact groups is developed. The method is based on positive definite functions definable on spaces with group multiplication. To be able to use these functions two steps are necessary. First, positive semidefinite functions are determined using Bochners theorem on commutative groups respectively representation theory in the non commutative case. Then transformations are given to get positive definite out of positive semidefinite functions. For the compact group 50(3) the result is explicitly calculated and implemented in the case of three and five dimensional representations, and is applied to the approximation of energy functions of molecule interactions in 3-space.     

Littlewood–Paley Theory for Triangle Buildings

For the natural two-parameter filtration \(\left( {\mathcal {F}_\lambda }: {\lambda \in P}\right) \) on the boundary of a triangle building, we define a maximal function and a square function and show their boundedness on \(L^p(\Omega _0)\) for \(p \in (1, \infty )\). At the end, we consider \(L^p(\Omega _0)\) boundedness of martingale transforms. If the building is of \({\text {GL}}(3, \mathbb {Q}_p)\), then \(\Omega _0\) can be identified with p-adic Heisenberg group.