Feynman integrals ofp-adic argument in the momentum space. II. Explicit expressions

A procedure for obtaining explicit expressions for Feynman integrals ofp-adic argument in momentum space is described, and the connection with Feynman amplitudes over a finite field and chromatic polynomials is indicated. Simple explicit expressions are given for the results of integration over the region of large and small momenta.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 3, pp. 371–392, September, 1995.     

One‐Step Synthesis of a [20]Silafullerane with an Endohedral Chloride Ion

Silicon analogues of the most prominent carbon nanostructures, namely, hollow spheroidals such as C₆₀ and the fullerene family, have been unknown to date. Herein we show that discrete Si₂₀ dodecahedra, stabilized by an endohedral guest and valence saturation, are accessible in preparative yields through a chloride‐induced disproportionation reaction of hexachlorodisilane in the presence of tri(n‐butyl)amine. X‐ray crystallography revealed that each silicon dodecahedron contains an endohedral chloride ion that imparts a net negative charge. Eight chloro substituents and twelve trichlorosilyl groups are attached to the surface of each cluster in a strictly regioregular arrangement, a thermodynamically preferred substitution pattern according to quantum‐chemical assessment. Our results demonstrate that the wet‐chemical self‐assembly of a complex, monodisperse Si nanostructure is possible under mild conditions starting from simple Si₂ building blocks.     

Boron‐Containing Polycyclic Aromatic Hydrocarbons: Facile Synthesis of Stable,Redox‐Active Luminophores

Herein we show that replacing the two meso carbon atoms of the polycyclic aromatic hydrocarbon (PAH) bisanthene by boron atoms transforms a near‐infrared dye into an efficient blue luminophore. This observation impressively illustrates the impact of boron doping on the frontier orbitals of PAHs. To take full advantage of this tool for the targeted design of organic electronic materials, the underlying structure–property relationships need to be further elucidated. We therefore developed a modular synthesis sequence based on a Peterson olefination, a stilbene‐type photocyclization, and an Si–B exchange reaction to substantially broaden the palette of accessible polycyclic aromatic organoboranes and to permit a direct comparison with their PAH congeners.     

Unsymmetrically substituted 9,10-dihydro-9,10-diboraanthracenes as versatile building blocks for boron-doped π-conjugated systems

The targeted hydrolysis of the 9,10-dihydro-9,10-diboraanthracene adduct (Me(2)S)HB(C(6)H(4))(2)BH(SMe(2)) (1) with 0.5 equiv of H(2)O leads to formation of the borinic acid anhydride [(Me(2)S)HB(C(6)H(4))(2)B](2)O (2) and thereby provides access to the field of unsymmetrically substituted 9,10-dihydro-9,10-diboraanthracenes. Compound 2 reacts with tBuC≡CH to give the corresponding vinyl derivative in an essentially quantitative conversion. Subsequent cleavage of the B-O-B bridge by LiAlH(4) with formation of hydridoborate functionalities is possible but is accompanied by partial B-C(vinyl) bond degradation. This situation changes when the related mesityl derivative [MesB(C(6)H(4))(2)B](2)O (7) is employed, which can be synthesized from BrB(C(6)H(4))(2)BBr (6) by treatment with 1 equiv of MesMgBr and subsequent hydrolysis. The reaction of 7 with LiAlH(4) in tetrahydrofuran (THF) furnishes Li[MesB(C(6)H(4))(2)BH(2)] (8); hydride elimination with Me(3)SiCl leads to formation of the THF adduct MesB(C(6)H(4))(2)BH(THF) (9·THF). Alternatively, 7 can be transformed into the bromoborane MesB(C(6)H(4))(2)BBr (10) by treatment with BBr(3). A Br/H-exchange reaction between 10 and Et(3)SiH yields the donor-free borane MesB(C(6)H(4))(2)BH (9), which forms B-H-B bridged dimers (9)(2) in the solid state. The vinyl borane MesB(C(6)H(4))(2)BC(H)=C(H)Mes (14) is accessible from MesC≡CH and either 9·THF or 9. Compared with the related compound Mes(2)BC(H)=C(H)Mes, the electronic absorption and emission spectra of 14 reveal bathochromic shifts of Δλ(abs)=17 nm and Δλ(em)=74 nm, which can be attributed to the rigid, fully delocalized π framework of the [MesB(C(6)H(4))(2)B] chromophore.     

9-H-9-Borafluorene dimethyl sulfide adduct: a product of a unique ring-contraction reaction and a useful hydroboration reagent

The dimethyl sulfide adduct 2(DMS) is a crystalline storage form of the unstable hydroboration reagent 9-H-9-borafluorene (2); 2(DMS) is available by the addition of DMS to either in situ generated [2](2) or 1,2-(2,2'-biphenylylene)diborane(6) (7).     

One tool to bring them all: Au-catalyzed synthesis of B,O- and B,N-doped PAHs from boronic and borinic acids

The isoelectronic replacement of C C bonds with ⁻B N⁺ bonds in polycyclic aromatic hydrocarbons (PAHs) is a widely used tool to prepare novel optoelectronic materials. Far less well explored are corresponding B,O-doped PAHs, although they have a similarly high application potential. We herein report on the modular synthesis of B,N- and B,O-doped PAHs through the [Au(PPh₃)NTf₂]-catalyzed 6-endo-dig cyclization of BN–H and BO–H bonds across suitably positioned C C bonds in the key step. Readily available, easy-to-handle o-alkynylaryl boronic and borinic acids serve as starting materials, which are either cyclized directly or first converted into the corresponding aminoboranes and then cyclized. The reaction even tolerates bulky mesityl substituents on boron, which later kinetically protect the formed B,N/O-PAHs from hydrolysis or oxidation. Our approach is also applicable for the synthesis of rare doubly B,N/O-doped PAHs. Specifically, we prepared 1,2-B,E-naphthalenes and -anthracenes, 1,5-B₂-2,6-E₂-anthracenes (E = N, O) as well as B,O₂-containing and unprecedented B,N,O-containing phenalenyls. Selected examples of these compounds have been structurally characterized by X-ray crystallography; their optoelectronic properties have been studied by cyclic voltammetry, electron spectroscopy, and quantum-chemical calculations. Using a new unsubstituted (B,O)₂-perylene as the substrate for late-stage functionalization, we finally show that the introduction of two pinacolatoboryl (Bpin) substituents is possible in high yield and with perfect regioselectivity via an Ir-catalyzed C–H borylation approach.

Singly and doubly B,E-doped PAHs were synthesized using a protocol that starts from easy-to-handle boronic and borinic acids and offers the possibility to choose between the preparation of B,O- and B,N-PAHs in the final reaction step.     

Toward quantifying the electrostatic transduction mechanism in carbon nanotube molecular sensors

Despite the great promise of carbon nanotube field-effect transistors (CNT FETs) for applications in chemical and biochemical detection, a quantitative understanding of sensor responses is lacking. To explore the role of electrostatics in sensor transduction, experiments were conducted with a set of highly similar compounds designed to adsorb onto the CNT FET via a pyrene linker group and take on a set of known charge states under ambient conditions. Acidic and basic species were observed to induce threshold voltage shifts of opposite sign, consistent with gating of the CNT FET by local charges due to protonation or deprotonation of the pyrene compounds by interfacial water. The magnitude of the gate voltage shift was controlled by the distance between the charged group and the CNT. Additionally, functionalization with an uncharged pyrene compound showed a threshold shift ascribed to its molecular dipole moment. This work illustrates a method for producing CNT FETs with controlled values of the turnoff gate voltage, and more generally, these results will inform the development of quantitative models for the response of CNT FET chemical and biochemical sensors.     

On existence of quantum diffusion of 2-D electrons at the surface

A quantum diffusion of 2-D electrons at a metal substrate has been shown to arise because of surface-bulk interaction via hybridization provided that the surface Fermi momentum has been smaller than the bulk one. The diffusion coefficient D has been found to depend nonmonotonously on sample dimensions L. An initial decrease in D has turned into an increase for sufficiently large L. The minimum in D has nonanalytically depended on the hybridization constant: $\text{D}{}_{\mathrm{<mtext>min</mtext>}}\text{～g}{}^{\mathrm{<mtext>4</mtext><mtext>3</mtext>}}$. The effects predicted have resulted from the instability of the zero-component nonlinear σ-model with respect to inclusion of certain symmetry — breaking terms which have proved to increase under RG transformations.     

Solvent-free methylthiomethyllithium [LiCH2SMe]infinity: solid state structure and thermal decomposition

Solvent-free [LiCH2SMe]infinity forms a layer structure consisting of four- (Li2C2), five- (Li2CS2), and six-membered (Li2C2S2) rings in the solid state; the compound violently explodes upon heating to T=160+/-5 degrees C under an argon atmosphere.