Trims and extensions of quadratic APN functions

Designs, Codes and Cryptography - In this work, we study functions that can be obtained by restricting a vectorial Boolean function $$F :\mathbb {F}_{2}^n \rightarrow \mathbb {F}_{2}^n$$ to an...     

Dispersion coefficients for first hyperpolarizabilities using coupled cluster quadratic response theory

The frequency dependence of third-order properties can in the normal dispersion region be expanded in a Taylor series in the frequency arguments. The dispersion coefficients thus obtained provide an efficient way of expressing the dispersion of frequency-dependent properties and are transferable between different optical processes. We derive analytic expressions for the dispersion coefficients of third-order properties in coupled cluster quadratic response theory and report an implementation for the three coupled cluster models CCS, CC2, and CCSD. Calculations are performed for the first hyperpolarizability of the NH₃ molecule. The convergence of the dispersion expansion with the order of the coefficients is examined and we find good convergence up to about half the frequency at which the first pole in the hyperpolarizability occurs. Padé approximants improve the convergence dramatically and extend the application range of the dispersion expansion to frequencies close to the first pole. The sensitivity of the dispersion coefficients on the dynamic correlation treatment and on the choice of the one-electron basis set is investigated. The results demonstrate that, contrary to presumptions in the literature, the dispersion coefficients are sensitive to basis set effects and correlation treatment similar to the static hyperpolarizabilities. Received: 26 March 1998 / Accepted: 21 July 1998 / Published online: 19 October 1998     

Interplay of structural dynamics and electronic effects in an engineered assembly of pentacene in a metal–organic framework

Charge carrier mobility is an important figure of merit to evaluate organic semiconductor (OSC) materials. In aggregated OSCs, this quantity is determined by inter-chromophoric electronic and vibrational coupling. These key parameters sensitively depend on structural properties, including the density of defects. We have employed a new type of crystalline assembly strategy to engineer the arrangement of the OSC pentacene in a structure not realized as crystals to date. Our approach is based on metal–organic frameworks (MOFs), in which suitably substituted pentacenes act as ditopic linkers and assemble into highly ordered π-stacks with long-range order. Layer-by-layer fabrication of the MOF yields arrays of electronically coupled pentacene chains, running parallel to the substrate surface. Detailed photophysical studies reveal strong, anisotropic inter-pentacene electronic coupling, leading to efficient charge delocalization. Despite a high degree of structural order and pronounced dispersion of the 1D-bands for the static arrangement, our experimental results demonstrate hopping-like charge transport with an activation energy of 64 meV dominating the band transport over a wide range of temperatures. A thorough combined quantum mechanical and molecular dynamics investigation identifies frustrated localized rotations of the pentacene cores as the reason for the breakdown of band transport and paves the way for a crystal engineering strategy of molecular OSCs that independently varies the arrangement of the molecular cores and their vibrational degrees of freedom.

Pentacene assembled into 1D arrays using a metal–organic framework (MOF) approach. This cofacial packing motif, which is not present in pentacene bulk, shows an interesting interplay of band-like and hopping-type transport.     

Ab initio calculation of the vibrational and electronic spectra of trans- and cis-azobenzene

We report accurate geometries and harmonic force fields for trans- and cis-azobenzene determined by second-order M?ller-Plesset perturbation theory. For the trans isomer, the planar structure with C(2h) symmetry, found in a recent gas electron diffraction experiment, is verified. The calculated vibrational spectra are compared with experimental data and density functional calculations. Important vibrational frequencies are localized and discussed. For both isomers, we report UV spectra calculated using the second-order approximate coupled-cluster singles-and-doubles model CC2 with accurate basis sets. Vertical excitation energies and oscillator strengths have been determined for the lowest singlet n(pi)* and (pi)(pi)* transitions. The results are compared with the available experimental data and second-order polarization propagator (SOPPA) and density functional (DFT) calculations. For both isomers, the CC2 results for the excitation energies into the S(1) and S(2) states agree within 0.1 eV with experimental gas-phase measurements.     

Synthese von (5,10)-(7,8)-Bisepoxiden aus α- und β-4-Phenyl-1,2,4-triazolin-3,5-dion-Addukten von Vitamin D3 und Röntgenstrukturanalyse eines der Benzoylderivate

Oxidation of the α- and β-4-phenyl-1,2,4-triazolin-3,5-dione adducts of vitamin D₃ (2 and1) withMCPBA yields two diastereomeric mixtures of the (5,10)-(7,8)-dioxiranes3 a,3 b,3 c and4 a,4 b respectively. The corresponding benzoates5 a,5 b,6 a and6 b were prepared and the X-ray crystal structure of5 b was determined. This analysis proved5 b to be the (5R, 1 OS)-(7R, 8R)-dioxirane of the β-resp. (6S)-4-phenyl-1,2,4-triazolin-3,5-dione adduct1 of vitamin D₃.     

A Sterically Hindered Phosphonic Acid with a Hydrogen‐Bonded Cage Structure: [4‐tert‐Bu‐2,6‐Mes2‐C6H2P(O)(OH)2·H2O]4

The synthesis and molecular structure of the novel phosphonic acid 4‐tert‐Bu‐2,6‐Mes₂‐C₆H₂P(O)(OH)₂ ( 1 ) is reported. Compound 1 crystallizes in form of its monohydrate as a hydrogen‐bonded cluster ( 1·H₂O )₄ comprizing four phosphonic acid molecules (O···O 2.383(3)‐3.006(4) Å). Additionally, sterically hindered terphenyl‐substituted phosphorus compounds of the type 4‐tert‐Bu‐2,6‐Mes₂‐C₆H₂PR(O)(OH) ( 5 , R = H; 7 , R = O₂CC₆H₄‐3‐Cl; 9 , R = OEt) were prepared, which all show dimeric hydrogen‐bonded structures with O···O distances in the range 2.489(2)–2.519(3) Å. Attempts at oxidizing 5 using H₂O₂, KMnO₄, O₃, or Me₃NO in order to give 1 failed. Crystallization of 5 in the presence of Me₃NO gave the novel hydrogen bonded aggregate 4‐tert‐Bu‐2,6‐Mes₂‐C₆H₂PH(O)(OH)·ONMe₃ ( 6 ) showing an O–H···O distance of 2.560(4) Å.