A generalization of Filliman duality

Filliman duality expresses (the characteristic measure of) a convex polytope containing the origin as an alternating sum of simplices that share supporting hyperplanes with . The terms in the alternating sum are given by a triangulation of the polar body . The duality can lead to useful formulas for the volume of . A limiting case called Lawrence's algorithm can be used to compute the Fourier transform of .

In this note we extend Filliman duality to an involution on the space of polytopal measures on a finite-dimensional vector space, excluding polytopes that have a supporting hyperplane coplanar with the origin. As a special case, if is a convex polytope containing the origin, any realization of as a linear combination of simplices leads to a dual realization of .

     

Syntheses, characterization, and photochromic studies of spirooxazine-containing 2,2'-bipyridine ligands and their zinc(II) thiolate complexes

A series of photochromic spirooxazine-containing zinc(II) diimine bis-thiolate complexes were successfully synthesized, and their photophysical and photochromic properties were studied. The X-ray crystal structure of complex 1a has also been determined. Upon excitation by UV light at 330 nm, all the ligands and complexes exhibit photochromic behavior. The thermal bleaching kinetics of the ligands and the complexes were studied in dimethylformamide at various temperatures. The photochemical quantum yields for the photochromic reactions of the ligands and complexes were also determined.     

The molecular conformation of clonidine hydrochloride,an α-adrenergic agonist

The molecular conformation of the antihypertensive drug clonidine hydrochloride [2-(2,6-dichlorophenylimino)-2-imidazole HCl] has been shown by crystallographic studies to have a nearly perpendicular arrangement of the phenyl and imidazole rings as described by the torsion angles C₂-C₁-N₁-C₂= 76 ° and C₁-N₁-C₂-N₁ = 0 °. This conformation is not either of those suggested as the minimum energy form by CNDO/2 calculations for the protonated or free-base models. However, it is consistent with a nonplanar model proposed as the active conformer based on QSAR and spectral studies. The bonding about the imidazole carbon is similar to the guanidinium ion and the three C₂-N distances of the planar imidazole ring are nearly equal. The chloride ion forms strong hydrogen bonds with the amine hydrogen (2.3 Å) and the imidazole (N₁,) hydrogen (2.4 Å). Comparison with -adrenergic agonists shows that this conformation of clonidine fits the proposed pharmacophore model and should compete effectively for the -adrenergic receptors.Presented in part at the American Crystallographic Association Meeting, Clemson, South Carolina, January 1976.     

Anion-assisted trans-cis isomerization of palladium(II) phosphine complexes containing acetanilide functionalities through hydrogen bonding interactions

The anion-assisted shift of trans-cis isomerization equilibrium of a palladium(II) complex containing acetanilide functionalities brought about by allosteric hydrogen bonding interactions has been established by UV/Vis, 1H NMR, 31P NMR and ESI-MS studies.     

Synthesis and luminescence behaviour of novel heterodecanuclear silver(I)-rhenium(I) alkynyl complexes. X-ray crystal structures of [Ag6(mu-dppm)4[mu3-C[triple bond]CC[triple bond]C-Re(Me2bpy)(CO)3]4](PF6)2 and [Ag6(mu-dppm)4[mu3-C[triple bond]CC[triple bond]C-Re(Br2phen)(CO)3]4](PF6)2

A novel series of luminescent heterodecanuclear mixed-metal alkynyl complexes, [Ag6(mu-dppm)4[mu3-C[triple bond]CC[triple bond]C-Re(N--N)(CO)3]4](PF6)2, (N--N = tBu2bpy, Me2bpy, phen, Br2phen), have been successfully synthesized; the X-ray crystal structures of [Ag6(mu-dppm)4[mu3-C[triple bond]CC[triple bond]C-Re(Me2bpy)(CO)3]4](PF6)2 and [Ag6(mu-dppm)4[mu3-C[triple bond]CC[triple bond]C-Re(Br2phen)(CO)3]4](PF6)2 have also been determined.     

Cleavage of a PN Bond in a Urea‐Containing (Ph2P(R)PPh2)‐Bridged Dinuclear Gold(I) Thiolate Complex by Fluoride and a Mechanistic Insight

A urea‐containing, (Ph₂P(R)PPh₂)‐bridged, dinuclear, gold(I) thiolate complex, [Au₂{Ph₂PN(C₆H₄OMe‐4)PPh₂}(SC₆H₄NHCONHC₆H₅)₂] ( 1 ) was designed and synthesized and its photophysical and anion recognition properties studied. The results show that 1 has a high selectivity toward F^?. Upon addition of F^?, the yellow solution was decolorized, and drastic changes of emission and ¹H and ³¹P{¹H} NMR signals were observed. Interestingly, these changes are attributed to fluoride‐assisted P?N bond hydrolysis, instead of the expected hydrogen‐bonding interactions with the urea receptor. Similar changes were observed for two other basic anions, AcO^? and H₂PO₄^?, but to a much lesser extent; and these anions were found to bind to the urea receptor at the same time. On the other hand, Cl^? was found to only bind to the urea moiety through hydrogen‐bonding interactions. Further studies with the control complex [Au₂{Ph₂PN(C₆H₄OMe‐4)PPh₂}Cl₂] ( 2 ) indicate that F^? assists the hydrolysis process via cleavage of the P?N bond. DFT calculations were performed to study the reaction mechanism for the fluoride‐assisted P?N bond hydrolysis of 2 ; these provide a better insight into the role of fluoride in the hydrolysis.     

Boron(iii) β-diketonate-based small molecules for functional non-fullerene polymer solar cells and organic resistive memory devices

A class of acceptor–donor–acceptor chromophoric small-molecule non-fullerene acceptors, 1–4, with difluoroboron(iii) β-diketonate (BF₂bdk) as the electron-accepting moiety has been developed. Through the variation of the central donor unit and the modification on the peripheral substituents of the terminal BF₂bdk acceptor unit, their photophysical and electrochemical properties have been systematically studied. Taking advantage of their low-lying lowest unoccupied molecular orbital energy levels (from −3.65 to −3.72 eV) and relatively high electron mobility (7.49 × 10⁻⁴ cm² V⁻¹ s⁻¹), these BF₂bdk-based compounds have been employed as non-fullerene acceptors in organic solar cells with maximum power conversion efficiencies of up to 4.31%. Moreover, bistable resistive memory characteristics with charge-trapping mechanisms have been demonstrated in these BF₂bdk-based compounds. This work not only demonstrates for the first time the use of a boron(iii) β-diketonate unit in constructing non-fullerene acceptors, but also provides more insights into designing organic materials with multi-functional properties.

Boron(iii) β-diketonates have been demonstrated to serve as multi-functional materials in NFA-based OPVs and organic resistive memories.     

Syntheses and photochromic studies of dithienylethene-containing imidazolium derivatives and their reactivity towards nucleophiles

A series of dithienylethene-containing imidazolium salts with various substituents on the 2-position of the imidazolium ring has been synthesized. The photochromic properties of these compounds have been studied, and the closed forms are found to be solvatochromic due to the donor-acceptor interaction with the solvent molecules. The closed form of the imidazolium salt shows a much higher affinity towards nucleophiles over the open form of the salt. A reaction pathway has been proposed to account for this reactivity difference based on the structure-property relationship, and the possible structure of the reaction product is discussed.