Chemical applications of topology and group theory. XXI: Chirality in transitive skeletons and qualitative completeness [1]

This paper unifies the following ideas for the study of chirality polynomials in transitive skeletons: (1) Generalization of chirality to permutation groups not corresponding to three-dimensional symmetry point groups leading to the concepts of signed permutation groups and their signed subgroups; (2) Determination of the total dimension of the chiral ligand partitions through the Frobenius reciprocity theorem; (3) Determination of signed permutation groups, not necessarily corresponding to three-dimensional point groups, of which a given ligand partition is a maximum symmetry chiral ligand partition by the Ruch-Schönhofer partial ordering, thereby allowing the determination of corresponding chirality polynomials depending only upon differences between ligand parameters; such permutation groups having the point group as a signed subgroup relate to qualitative completeness. In the case of transitive permutation groups on four sites, the tetrahedron and polarized square each have only one chiral ligand partition, but the allene and polarized rectangle skeletons each have two chiral ligand partitions related to their being signed subgroups of the tetrahedron and polarized square, respectively. The single transitive permutation group on five sites, the polarized pentagon, has a degenerate chiral ligand partition related to its being a signed subgroup of a metacyclic group with 20 elements. The octahedron has two chiral ligand partitions, both of degree six; a qualitatively complete chirality polynomial is therefore homogeneous of degree six. The cyclopropane (or trigonal prism or trigonal antiprism) skeleton is a signed subgroup of both the octahedron and a twist group of order 36; two of its six chiral ligand partitions come from the octahedron and two more from the twist group. The polarized hexagon is a signed subgroup of the same twist group but not of the octahedron and thus has a different set of six chiral ligand partitions than the cyclopropane skeleton. Two of its six chiral ligand partitions come from the above twist group of order 36 and two more from a signed permutation group of order 48 derived from the P₃[P ₂] wreath product group with a different assignment of positive and negative operations than the octahedron.     

Chemical applications of topology and group Theory. XXIV: Chiralization of chemically significant polyhedra [1]

Permutation group-theoretical methods are used to study the chiralization of achiral polyhedral skeletons with v vertices by successive ligand replacement. Starting from the fully symmetrical ligand partition (), such chiralization processes may be characterized either by the minimum number of ligand replacement steps m, or the minimum number of different kinds of ligandsi, required to destroy all improper rotations. These parameters are trivially related to the lowest degree chiral ligand partition(s) as determined by the subduction of the skeleton point group G into the corresponding symmetric groupS by the procedure of Ruch and Schönhofer. Two different chiralization pathways with different values ofm andi are found for the octahedron, cube, hexagonal bipyramid, and icosahedron. Many less symmetrical chemically significant polyhedra have the degree 2 ligand partition (v - 2, 2) as the lowest degree chiral ligand partition and thus have only one chiralization pathway. Such polyhedra include the bicapped tetrahedron, trigonal prism, capped octahedron, bisdisphenoid, square antiprism, 4, 4, 4-tricapped trigonal prism, 4-capped square antiprism, 4,4-bicapped square antiprism, and the cuboctahedron.     

Synthesis and spectral properties of substituted 4-chlorooxazoloquinolines

Summary The treatment of a mixture of linearly and angularly annelated 2-substituted oxazolo[4,5-f]quinolones (5a–c) and oxazolo[5,4-g]quinolones (6a–c) and similarly the treatment of 2-substituted oxazolo[5,4-f]quinolones (7a–c) and oxazolo[4,5-g]quinolones (8b,c) with POCl₃ afforded substituted 4-chlorooxazolo[4,5-f]quinolines (9a–c) and 2-substituted 4-chlorooxazolo[5,4-f]quinolines (10b,c), respectively. Spectral characteristics of the synthesized derivatives (¹H and¹³C NMR, IR, UV, and MS) are discussed.Dedicated to Prof.Fritz Sauter on the occasion of his 65th birthday     

Synthese arylsubstituierter 2-Pyrimidinamine,Dihydro-2-pyrimidinamine und Pyrimido[1,2-a]pyrimidine durch Reaktion von Guanidin mit Chalkonen

4- and 4-methoxy-, 4-hydroxy- and 2-hydroxychalcone4 e,k,f andg, respectively, are transformed by action of guanidine in benzene to yield 4-(4-methoxyphenyl)-6-phenyl-2-pyrimidinamine (6 e=6 k) and hydroxyphenylpyrimidinamines6 f andg, respectively. In contrast, 4- and 4-chlor-, 4-brom- and 4-phenylchalcone4 h,l–n resp. react with guanidine under analogous conditions to give 4,6-diaryl-1,4-dihydro-2-pyrimidinamines5 h,l–n. The bases5 h,l–n also tend to aromatize, but they can be stabilized by transformation into salts5 h,l–n · HCl with hydrochloric acid. Heating of5 n inDMF under atmospheric oxygen yields 4-(4-biphenyl)-6-phenyl-2-pyrimidinamine (6 n). Action of guanidine on 4-nitrochalcone4 o in chloroform affords 2-amino-4-nitrophenyl-6-phenyl-tetrahydro-4-pyrimidinol8 o, which is transformed by hydrochloric acid into 6-nitrophenyl-dihydropyrimidinamine-hydrochloride5 o · HCl. Treating of the latter with sodiummethylat in methanol yields the very stable dihydropyrimidinamine5 o. Action of guanidine on 4-chlor- and 4-bromchalcone4 h andm respectively (in addition to5 h andm) yields 2,4,6,8-tetraaryl-1,4-dihydro-2H-pyrimido[1,2-a]pyrimidines7 h andm, respectively.

Herrn Prof. Dr.Erwin Schauenstein mit den besten Wünschen zum 65. Geburtstag gewidmet.     

Near-Infrared-Absorbing Chiral Open [60]Fullerenes

Though [60]fullerene is an achiral molecular nanocarbon with I_h symmetry, it could attain an inherent chirality depending upon a functionalization pattern. The conventional chiral induction of C₆₀ relies mainly upon a multiple addition affording a mixture of achiral and chiral isomers while their chiral function would be largely offset by the existence of pseudo-mirror plane(s). These are major obstacles to proceed further study on fullerene chirality and yet leave its understanding elusive. Herein, we showcase a carbene-mediated synthesis of C₁-symmetric chiral open [60]fullerenes showing an intense far-red to near-infrared absorption. The large dissymmetry factor of |g_abs|=0.12 was achieved at λ=820 nm for circular dichroism in benzonitrile. This is, in general, unachievable by other small chiral organic molecules, demonstrating the potential usage of open [60]fullerenes as novel types of chiral chromophores.     

On the expansion of hole in main chain polymers determined by positron annihilation

The temperature dependence of positron annihilation characteristics, ₃ andI ₃, has been studied on sample of poly(butadiene), poly(isobutylene) and poly(chloroprene). The temperature range was between 15 and 470 K. The rate of expansion of holes or free-volume in all samples was deduced belowT _g as well aboveT _g as appr. 3·10^–3 K^–1 and 2·10^–2 K^–1, respectively. These values are very close to the rate of the mean squared displacement of scatterer<r ²>observed in neutron scattering experiments. A possibility to use an inverse value of free-volume,V _f ^–1 for study of viscoelastic state of polymers is demonstrated.     

Zur Synthese und Struktur derp-Indazolchinone und ihrer Methylierungsprodukte Untersuchungen über Chinone, 8. Mitt.

Summary Thep-benzoquinones5e-j react with diazomethane (after dehydrogenation) to 6-anilino-2e, dimethylamino-2h, phenylthio-2i, and methylthioindazolquinone2j. Methylation with dimethylsulfate of these as well as of the already known indazolquinones 6-toluidino-2f, 6-methylanilino-2g, 5-tert.butyl-2m, 5,6-methyl- (isomer mixture)2l,n, and benz-indazolquinone2o yield the 1-and 2-N-methyl derivatives3 and4. The structure of the 2-methyl derivatives is established by reaction of the corresponding benzoquinones with 3-methylsydnon in the case of4e,4g. UV/VIS-, IR- and¹H-NMR-spectroscopy (in CDCl₃ andDMSO) were used for structure determination. Comparison of the UV/VIS-spectra of2–4 shows that the indazolquinones are existing as 2 H-4,7-diones. For the structure elucidation of the 1- rs. 2-methylderivatives (whichh can be attributed to the methylation products) NMR-spectroscopy is well suited even without knowing the second isomer (solvent-effect). The course of the reaction of quinones with diazomethane and of the methylation reactions of the indazolquinones is discussed.

Herrn Univ.-Prof. Dr. G. Zigeuner zum 70. Geburtstag gewidmet     

Strong Coupling of Chiral Frenkel Exciton for Intense,Bisignate Circularly Polarized Luminescence

We show that chiral Frenkel excitons yield intense circularly polarized luminescence with an intrinsic dissymmetry factor in emission g_lum as high as 0.08. This outstanding value is measured through thin films of cyanine J-aggregates that form twisted bundles. Our measurements, obtained by a Mueller polarization analysis, are artifact-free and reveal a quasi-perfect correlation between the dissymmetry factors in absorption, g_abs, and in emission g_lum. We interpret the bisignate dissymmetry factors as the signature of a strong coupling between chiral Frenkel excitons longitudinally excited along the bundles. We further resolve by polarimetry analysis the split in energy between the excited states with a Davydov splitting as small as 28 meV. We finally show the anti-Kasha nature of the chiral emission bands with opposite optical chirality. These mirror-imaged emissive chiroptical features emerge from the structural rigidity of the bundles that preserves the ground- and excited-state chirality.     

Icosahedral hybrid orbitals

A set of twelve equivalent icosahedral hybrid orbitals pointing from the centre to the corners of a regular icosahedron has been obtained. Such hybrids can be used to explain the geometry of twelve-coordinate complexes of a rare-earth atom. Using group theoretical considerations, it is shown that these hybrids can be constructed by linear combination of one s, three p, five d and three f-orbitals. Bearing in mind that the twelve hybrids have identical shape but are oriented differently in space, their mathematical expressions have been obtained by applying geometrical transformations to the sp³d⁵f³ hybrid pointing along the positive z-axis. In order to obtain elegant mathematical expressions, the x, y and z axes have been chosen to be coincident with three orthogonal binary axes of the icosahedron.     

Highly-Active Chiral Organic Photovoltaic Catalysts with Suppressed Charge Recombination

Recombination of free charges in organic semiconductors reduces the available photo-induced charge-carriers and restricts photovoltaic efficiency. In this work, the chiral organic semiconductors (Y6-R and Y6-S with enantiopure R- and S- chiral alkyl sidechains) are designed and synthesized, which show effective aggregation-induced chirality through mainchain packing with chiral conformations in non-centrosymmetric space groups with tilt chirality. Based on the analysis of spin-injection, magnetic-hysteresis loop, and thermodynamics and dynamics of the excited state, we suggest that the aggregation-induced chirality can generate spin-polarization, which suppresses charge recombination and offers more available charge-carriers within Y6-R and Y6-S relative to the achiral counterpart (Y6). Then the chiral Y6-R and Y6-S show enhanced catalytic activity with optimal average hydrogen evolution rates of 205 and 217 mmol h⁻¹ g⁻¹, respectively, 60–70 % higher than Y6, when they are employed as nanoparticle photocatalysts in photocatalytic hydrogen evolution under simulated solar light, AM1.5G, 100 mW cm⁻².     

Ground-state energies of mono-, di-, tri- and tetranegative ions of porphins and their metal complexes

From a range of porphin and metal porphin molecules, mono-, di-, tri- and tetranegative ions can be formed in solution. The disproportionation energies of these ions, measured byHush andClack [6] in dimethylformamide, show similar patterns. For the mononegative and trinegative ions, the disproportion of energies are of comparable magnitudes, but the disproportionation energy of the dinegative ion is 0.3 – 0.4 eV more positive. If it is assumed that the electrons are successively filling the lowest vacant orbital (e _g inD _4h ) these results can be rationalized. In particular, if it is assumed that the dinegative ion is spin-paired, with ground-state electronic symmetryB _1g inD _4h , the average difference of 0.3 – 0.4 eV mentioned above should approximate to twice the exchange integral in the antibondinge _g orbital. Calculation of this integral for a number of porphin structures gives good agreement with experiment.

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Zusammenfassung Von einer Reihe von Porphin- und Metallporphinmolekülen können ein-, zwei-, drei- und vierfach negativ geladene Ionen in Lösung hergestellt werden. Die Disproportionierungsenergien dieser Ionen, vonHush undClack [6] in Dimethylformamid gemessen, zeigen ähnliche Struktur. Für die ein- und dreifach negativ geladenen Ionen ist die Disproportionierungsenergie etwa gleich, dagegen für das zweifach negativ geladene Ion 0,3 – 0,4 eV positiver. Wenn man annimmt, daß die Elektronen nacheinander das tiefste unbesetzte Orbital (e _g inD _4h) auffüllen, können diese Ergebnisse erklärt werden. Wenn man insbesondere annimmt, daß das zweifach negativ geladene Ion als Grundzustand einen Singulettzustand der SymmetrieB _1g inD _4h besitzt, ist die oben erwähnte mittlere Differenz von 0,3 – 0,4 eV angenähert doppelt so groß wie das Austauschintegral im antibindendene _g-Orbital. Berechnung dieses Integrals für eine Anzahl Porphinstrukturen ergibt gute Übereinstimmung mit dem Experiment.

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Résumé Une série de porphines et porphines métallés forment des ions mono-, di, tri- et tétranégatifs en solution. Les énergies de disproportionation dans dimethylformamide, présentant de similitudes [6], sont comparables pour les ions mono- et trinégatifs, mais 0,3 – 0,4 eV plus positif pour l'ion dinégatif. Ces résultats sont compréhensibles dans un schéma où les électrons occupent successivement l'orbitale vide la plus basse (e _g en symétrieD _4h ). En particulier, si l'on adopte l'état fondamentalB _1g (enD _4h) aux spins antiparallèles, pour l'ion dinégatif, les 0,3 – 0,4 eV valent approximativement deux fois l'intégrale d'échange pour l'orbitalee _g antiliante. Le calcul de cette intégrale pour une série de porphines s'accorde bien à l'expérience.

     

Boundary conditions in the theory of the relaxation field

The perturbationf _ji ^' generated by an external field in the distribution function is derived by integration of the Onsager-Fuoss equation of continuity. The solution isf _ji ^' (r)=C(I+Ah₁+Bh₂) whereCI is a particular integral andh ₁ andh ₂ are solutions of the homogeneous equation. The physical significance of the boundary conditions which evaluate the constantsA andB is discussed. It is then shown that the conditionf _ji ^' () 0 requiresB=0 and that the condition lim(f _ji ^' /n²) 0 at zero concentration is satisfied if and only ifA=–1.     

The electronic and molecular structure of carbon clusters: C8 and C10

Summary The equilibrium geometries of C₈ and C₁₀ have been determined from electronic structure calculations, using a variety of correlated methods and large basis sets of atomic natural orbitals. For C₈, a cyclic form withC _4h symmetry (¹ A _g) and a linear, cumulene-like form (³ _g ^– ) are isoenergetic candidates for the electronic ground state. For C₁₀, the ground-state equilibrium structure is definitely monocyclic. Three different cyclic structures have been considered here, i.e. cumulenicD _10h , distorted-cumulenicD _5h and acetylenicD _5h . These are all essentially isoenergetic, and are about 50 kcal/mol below the linear³ _g ^– state. The choice of basis sets and methods used has a strong impact on the predicted ground-state structures.Dedicated to Prof. Klaus Ruedenberg     

Density functional study on electronic and optical properties of C (or N)-doped cubic cerium dioxide

Density functional calculations were performed on electronic and optical properties of C (or N)-doped cubic cerium dioxide (CeO₂). When O is replaced by C (or N) in CeO₂, obvious band-gap (E_g) reduction is observed. Meanwhile, it is interesting to find that the substitutional doping of C (or N) in CeO₂ obviously increases the O 2p–Ce 4f transition intensity and also the refractive index. The increase in the O 2p–Ce 4f transition intensity on going from undoped, N-doped and C-doped CeO₂ was related to the covalent character of the Ce–O bond. Compared with the undoped CeO₂, the C (or N)-doped CeO₂, with steep absorption peaks at lower energy, can be used for visible-light absorption applications.     

Einfluß der Polarität und Viskosität des Lösungsmittels auf die Deaktivierung des S1-Zustandes von Donator-Akzeptor-substituiertentrans-Stilbenen

The dependence of the fluorescence constantsk _f ⁿ and the adiabatic twisting constantsk _tpof the S₁-State upon the solvent polarity, the capacity of hydrogen-bonding, as well as the solvent viscosity, were investigated for donor-acceptor substitutedtrans-stilbenes [4-dimethylamino-4-cyano-stilbene (1 g), 4-dimethylamino-4-diphenylphosphinyl-stilbene (1 b), 4-dimethylamino-4-brom-stilbene (1 h) and 4-dimethylamino-4-methoxistilbene (1 k)] by using the multiparameter model. An increase of the solvent polarity results in the decrease of the fluorescence ratek _f ⁿ for all these compounds. The specific interaction between the strongly polar stilbenes such as1 g and1 b and a solvent leads to additional decrease ink _f ⁿ but in the case of a relatively weak polar compound1 k to its growth. The linear combination of universal and specific solvent-solute interactions yields distinct relations fork _tp. Both interactions have an influence onk _tpfor1 g,1 b, and1 k to an equal degree. The twisting observed for1 g and1 b due to the interaction with solvent is hindered, however it is being supported for1 k. The influence of the investigated small range of viscosity onk _tpat simultaneous variable solvent polarity (pure solvent) is only visible for the weak polar1 k. In the other cases the effect of solvent-polarity is predominant.The viscosity dependence ofk _tpwas also experimentally proved for1 g,1 b and1 k by applying the obtained different dimethylformamid-acetonitril mixtures. According previous results the radiationless deactivation process is caused by twisting around ethyl-bonding, thereforek _tpevidently decreases with an increase of viscosity.

     

Synthesis and characterization of novel optically active poly(ester‐imide)s with high Tg and good thermal stability

A series of novel optically active poly(ester‐imide)s (ter‐PEIs) with high glass transition temperature (T_g), good thermal stability, and solubility were successfully designed and synthesized by direct polycondensation reactions, using p‐hydroxybenzoic acid (PHB), 4,4’‐dihydroxybenzophenone, and a chiral diacid, N,N'‐(pyromellitoyl)‐bis‐L‐phenylalanine diacid as monomers. The resulting terpolymers were characterized by¹H‐NMR, FTIR, element analysis, thermogravimetric analysis, different scanning calorimeter and wide‐angle x‐ray diffraction, etc. The ter‐PEIs are amorphous polymers with good heat resistance and high T_gs. They are soluble in many common polar organic solvents and show optically rotation property. The specific rotation values of the ter‐PEIs increase with the molar ratio of the chiral diacid, and the rigid PHB monomer is beneficial to increase the T_gs of the polymers. Copyright © 2013 John Wiley & Sons, Ltd.     

Modeling the Proton Transport in Orthoperiodic and Orthotelluric Acids and Their Salts

Orthoperiodic and orthotelluric acids, their salts MIO₆H₄ (M = Li, Rb, Cs) and CsH₅TeO₆, and dimers of the salt · acid type are calculated within density functional theory B3LYP and basis set LanL2DZ complemented by the polarizationd,p-functions. According to calculations, the salt · acid dimerization is energetically favorable for compounds MIO₆H₄ · H₅IO₆ (M = Rb, Cs) and CsIO₆H₄ · H₆TeO₆. The dimerization energy is equal to 138–146 kJ mol^–1. With relatively small activation energies equal to 4 kJ mol^–1 (M = Li) and 11 kJ mol^–1 (M = Rb, Cs), possible is rotation of octahedron IO₆ relative to the M atom in monomers of salt molecules. The proton transfer along an octahedron occurs with activation energies of 63–84 kJ mol^–1. The activation energy for the proton transfer between neighboring octahedrons of the type salt · acid acid · salt equals 8–17 kJ mol^–1. Quantum-chemical calculations nicely conform to x-ray diffraction and electrochemical data.     

Determination of the bond-angle distribution in vitreous B2O3 by B double rotation (DOR) NMR spectroscopy

The B–O–B bond angle distributions for both ring and non-ring boron sites in vitreous B₂O₃ have been determined by ¹¹B double rotation (DOR) NMR and multiple-quantum (MQ) DOR NMR. The [B₃O₆] boroxol rings are observed to have a mean internal B–O–B angle of 120.0±0.7° with a small standard deviation, σ_R=3.2±0.4°, indicating that the rings are near-perfect planar, hexagonal structures. The rings are linked predominantly by non-ring [BO₃] units, which share oxygens with the boroxol ring, with a mean B_ring–O–B_non-ring angle of 135.1±0.6° and σ_NR=6.7±0.4°. In addition, the fraction of boron atoms, f, which reside in the boroxol rings has been measured for this sample as f=0.73±0.01.     

Quantum Chemical Calculation of Conformations and Rotation Barriers of Functional Groups in Arylsulfonyl Halides

The semiempirical PM3 method is used to calculate the potential functions of internal rotation of the functional groups –SO₂Cl, –NO₂, –CH₃, –OCH₃, and –NH₂ of benzenesulfonyl halide molecules (PhSO₂Hal, Hal = F, Cl, Br, I) and twelve substituted derivatives of benzenesulfonyl chloride. Molecular conformations have been determined and internal rotation barriers of the functional groups have been calculated. For meta- and para-substituted benzenesulfonyl chlorides, the projection of the S–Hal bond is perpendicular to the plane of the benzene ring. The rotation barriers of the –SO₂Hal group of benzenesulfonyl halides increase in the series Hal = F, Cl, Br, I. The rotation barriers of the –SO₂Cl group of benzenesulfonyl chloride with meta- and para-substituents slightly increase with the electron-donor properties of the substituent. The rotation barriers of the functional groups of ortho-substituted benzenesulfonyl chlorides are 3 or 4 times as high as those of the meta- and para-isomers. For para-substituted benzenesulfonyl chlorides, the rotation barriers of the functional groups increase in the order –CH₃, –NO₂, –SO₂Cl, –OCH₃, –NH₂.     

Contracted well-tempered Gaussian basis sets in SCF calculations on the ground and excited electronic states of neutral and ionized diatomic molecules containing first-row atoms

Summary Calculations were done on ground and excited states of C₂, C ₂ ⁺ , C ₂ ^– , N₂, N ₂ ⁺ , O₂, O ₂ ⁺ , O ₂ ^– , CO, CO⁺, CO²⁺, and CO^– using contracted well-tempered basis sets. The (14s 10p) basis sets were augmented with threed, one or twof, and oneg functions. Total energies, orbital energies, and spectroscopic constants were compared with the best available computational data.