A Selenium‐Nitrogen Chain with Selenium in Different Oxidation States

The reaction of tBuNH₂ with a mixture of SeCl₂ and SeOCl₂ in a 6:2:1 molar ratio produces the novel selenium‐nitrogen chain ClSeN(tBu)Se(O)Cl ( 4 ), in which the selenium atoms are in two different oxidation states, Se^II and Se^IV. The crystal structure of 4 is compared with that of the related Se^II/Se^II system ClSeN(tBu)SeCl ( 1 ) and differences are attributed to hyperconjugative effects. The energetics of the formation of 4 via two different routes are elucidated by PBE0/def2‐TZVPP calculations.     

Synthesis and redox behaviour of the chalcogenocarbonyl dianions [(E)C(PPh(2)S)(2)](2-): formation and structures of chalcogen-chalcogen bonded dimers and a novel selone

The lithium salts of the chalcogenocarbonyl dianions [(E)C(PPh₂S)₂]^2? (E=S ( 4 b ), Se ( 4 c )) were produced through the reactions between Li₂[C(PPh₂S)₂] and elemental chalcogens in the presence of tetramethylethylenediamine (TMEDA). The solid‐state structure of {[Li(TMEDA)]₂[(Se)C(PPh₂S)₂]}—[{Li(TMEDA)}₂ 4 c ]—was shown to be bicyclic with the Li⁺ cations bis‐S,Se‐chelated by the dianionic ligand. One‐electron oxidation of the dianions 4 b and 4 c with iodine afforded the diamagnetic complexes {[Li(TMEDA)]₂[(SPh₂P)₂CEEC(PPh₂S)₂]} ([Li(TMEDA)]₂ 7 b (E=S), [Li(TMEDA)]₂ 7 c (E=Se)), which are formally dimers of the radical anions [(E)C(PPh₂S)₂]^{? .} (E=S ( 5 b ), Se ( 5 c )) with elongated central E? E bonds. Two‐electron oxidation of the selenium‐containing dianion 4 c with I₂ yielded the LiI adduct of a neutral selone {[Li(TMEDA)][I(Se)C(PPh₂S)₂]}—[{LiI(TMEDA)} 6 c ]—whereas the analogous reaction with 4 b resulted in the formation of 7 b followed by protonation to give {[Li(TMEDA)][(SPh₂P)₂CSS(H)C(PPh₂S)₂]}—[Li(TMEDA)] 8 b . Attempts to identify the transient radicals 5 b and 5 c by EPR spectroscopy in conjunction with DFT calculations of the electronic structures of these paramagnetic species and their dimers are also described. The crystal structures of [{Li(TMEDA)}₂ 4 c ], [{LiI(TMEDA)} 6 c ] ? C₇H₈, [Li(TMEDA)]₂ 7 b? (CH₂Cl₂)_0.33, [Li(THF)₂]₂ 7 b , [Li(TMEDA)]₂ 7 c , [Li(TMEDA)] 8 b? (CH₂Cl₂)₂ and [Li([12]crown‐4)₂] 8 b were determined and salient structural features are discussed.     

Cobalt complexes of a selenium diimide and a tellurium diimide dimer

[CoCl₂{N,N′-Te₂(N^tBu)₄}] (1) was obtained in good yields by the reaction of equimolar amounts of (^tBu)NTe(μ-N^tBu)₂TeN(^tBu) and CoCl₂ in toluene under an argon atmosphere. The crystal structure of 1·CH₂Cl₂ showed that the dimeric tellurium diimide ligand is N,N′-chelated to cobalt. The related reaction of Se(N^tBu)₂ and CoCl₂ affords a green product tentatively identified as a 1:1 adduct [CoCl₂{N,N′-Se(N^tBu)₂}] (CHN analysis). However, recrystallization from thf produces the ion-separated complex [Co₂(μ-Cl)₃{N,N′-Se(N^tBu)₂}₂(thf)₂][CoCl₃{NH₂(^tBu)}]·1½thf (2·1½thf), in which the monomeric selenium diimide ligand is N,N′-chelated to cobalt in the cation. A pathway for the formation of 2 from [CoCl₂{N,N′-Se(N^tBu)₂}] in thf is proposed.     

A Lower Bound for the Determinantal Complexity of a Hypersurface

We prove that the determinantal complexity of a hypersurface of degree \(d > 2\) is bounded below by one more than the codimension of the singular locus, provided that this codimension is at least 5. As a result, we obtain that the determinantal complexity of the \(3 \times 3\) permanent is 7. We also prove that for \(n> 3\), there is no nonsingular hypersurface in \({\mathbb {P}}^n\) of degree d that has an expression as a determinant of a \(d \times d\) matrix of linear forms, while on the other hand for \(n \le 3\), a general determinantal expression is nonsingular. Finally, we answer a question of Ressayre by showing that the determinantal complexity of the unique (singular) cubic surface containing a single line is 5.     

Derivatives of molecular surface area and volume: simple and exact analytical formulas

The computational effort of biomolecular simulations can be significantly reduced by means of implicit solvent models in which the energy generally contains a correction depending on the surface area and/or the volume of the molecule. In this article, we present simple derivation of exact, easy-to-use analytical formulas for these quantities and their derivatives with respect to atomic coordinates. In addition, we provide an efficient, linear-scaling algorithm for the construction of the power diagram required for practical implementation of these formulas. Our approach is implemented in a C++ header-only template library.     

Ultrasonic wave fluctuations through tissue: an experimental pilot study

The fundamental role of the assumption of plane wave ultrasonic propagation in attenuation and scattering measurements on soft tissues is discussed. The evidence for and against the validity of the assumption is shown to be inconclusive. An experimental procedure for direct assessment, by measurement of the ultrasonic amplitude and phase fluctuations occurring after an interrogating plane wave has passed through a tissue specimen, is described. The phase measurements impose significant demands on the mechanical precision, temperature stability and electronic timing capabilities of the measurement system. Measurements are reported on two specimens of fresh beef liver. One exhibited significant fluctuations of amplitude and phase which were reduced by 50% when the effects of thickness variations in the specimen were removed. The other specimen exhibited relatively small fluctuations. The feasibility of making such measurements has been demonstrated and the detailed features of the experimental procedure-which requires considerable care-have been outlined. Although more measurements are needed for definitive conclusions, these will require the development of a reliable technique for determining the presence of gaseous microbubbles in tissue in vitro. The preliminary conclusion that some samples of liver may exhibit low levels of wavefront disruption is consistent with recent evidence in the literature.