Theory of helicenic hydrocarbons. Part 3: Enumeration of extremal helicenes

The enumeration of extremal helicenes is equivalent to the counting of distinct positions a lagoon can be introduced into the extremal benzenoids. The topic is treated algebraically, and numerical results are reported. Symmetry plays an important role in the algebraical treatment.     

Isomers of polycyclic conjugated hydrocarbons with six-membered and seven-membered rings

Summary Monoheptapolyhexes are polygonal systems with exactly one heptagon and otherwise hexagons. General formulations with emphasis on the C _n H _s formula, and the first enumerations of C _n H _s isomers are reported for these systems. Also a more general class of systems is treated in some detail, viz. P₇₍₆₎, which consists of hexagons and/or heptagons. The maximum numbers of heptagons for given C _n H _s formulas are studied, and the possible C _n H _s formulas are specified.

---

Isomere von polycyclischen konjugierten Kohlenwasserstoffen mit 6- und 7-gliedrigen Ringen

Zusammenfassung Monoheptapolyhexe sind polygonale Systeme mit genau einem Siebeneck und ansonsten nur Sechsecken. Es wird der allgemeine Formelapparat mit Betonung auf C _n H _s und die Auswertung bezüglich der Anzahl von C _n H _s -Isomeren für diese Systeme berichtet. Ebenso wird über eine generellere Klasse von Systemen, nämlich P₇₍₆₎ berichtet, die aus Sechsecken und/oder Siebenecken besteht. Die Maximalanzahl von Siebenecken für gegebene C _n H _s -Formeln wird untersucht und mögliche C _n H _s -Formeln werden angegeben.

     

Enumeration of the isomers of phenylenes

Summary The [h]phenylene C_6h H_2h+4 isomers are enumerated up toh=12. The numbers are compared with old and new data for C _n H₅ isomers of benzenoids, fluoranthenoids and biphenylenoids.

---

Anzahl möglicher Isomerer von Phenylenen

Zusammenfassung Die Anzahl der [h]Phenylen-Isomeren C_6h H_2h+4 wurde bish=12 ausgewertet. Die Zahlen wurden mit alten und neuen Daten für C _n H _s -Isomere von Benzenoiden, Fluoranthenoiden und Biphenyloiden verglichen.

     

取代冠醚的异构体计数

采用图论方法对取代冠醚的构造、构型以及手性构型和非手性构型进行计数。为了便于计数，取代冠醚的构型、手性构型和非手性构型的计数采用平面模型，并利用Ｐｏｌｙａ计数定理求出其计数母函数，最后使用计算机计算，结果列表给出。     

Enumeration of Isomers of Acyclic Saturated Hydroxyl Ethers

In this paper, we present generating functions for counting constitutional isomers and stereo isomers of acyclic saturated compounds consisting of O, C and H for the first time, and obtain the numbers of constitutional isomers and stereo isomers of acyclic saturated hydroxyl ethers. The numerical results are tabulated.     

Chemical relevance of a pure combinatorial problem: Isomers of conjugated polyenes

A correspondence is pointed out between the triangulation of convex polygons on the one hand and the enumeration of isomers of conjugated polyenes on the other.     

Theory of helicenic hydrocarbons. Part 4: Further enumerations

A complete generation and enumeration of helicenes through fifteen hexagons was executed. The systems are classified according to neo (normal/essentially disconnected/non-Kekuléan), the color excess ( values), and the C _n H _s isomers. Furthermore, the soft and hard helicenes are distinguished. The method of combinatorial constructions (without use of computers) is demonstrated for some classes of helicenes with ten hexagons.     

Enumeration of Kekulé structures for some coronoid hydrocarbons: “Waffles”

Summary Primitive coronoids of hexagonal symmetry (D _6h orC _6h ) are referred to as waffles. Some theorems about unbranched catacondensed benzenoids are presented and used to derive a general combinatorial formula for the number of Kekulé structures (K) for waffles. The symmetry-adapted method of fragmentation is employed. SeveralK formulas for special classes of waffles are also reported.

---

Die Anzahl von Kekulé-Strukturen für einige aromatische Coronoid-Kohlenwasserstoffe: Waffel-Strukturen

Zusammenfassung Einfache Coronoide von hexagonaler Symmetrie (D _6h oderC ₆ h) werden als Waffel bezeichnet. Einige Theoreme bezüglich unverzweigter catakondensierter Benzenoide werden angegeben und zur Ableitung einer generellen Formel für die Anzahl von Kekulé-Strukturen (K) für Waffel benutzt. Es wird die symmetrie-adaptierte Methode zur Fragmentierung angewendet. Außerdem werden einigeK-Formeln für spezielle Klassen von Waffeln angegeben.

     

烃同分异构体的计数

能否系统精确地解决高中化学学习中的同分异构体计数问题?本文在高中数学化学的背景知识之上,引入生成函数以及Pólya计数定理,在不考虑立体异构的前提下,从烷基的同分异构体计数入手,逐步推导烷烃、一烯烃、一炔烃苯的衍生物、二取代烷烃以及二烯烃的同分异构体计数的公式,并将计算结果与手工枚举进行对比,进一步证明其正确性。我们还归纳性地发掘了同分异构体计数的渐进特征并提出了以上烃类同分异构体计数的近似公式。对比国外的成果,本文尽力避免引入过多的数学概念,降低门槛,适合高中生阅读,加深对于烃结构的理解,培养计算思维;对比国内相同主题的研究,本文的推导形式清晰简洁,拓展性较强。     

Enumeration of Isomers of Alkylcyclobutadienes by Means of Alkyl 1,1,1-Triradicals

Previous studies have shown that alkyl 1,1-biradicals could be used to enumerate the constitutional isomers of alkenes [1] and cyclopropanes [2]. In this study, an algorithm of using alkyl 1,1,1-triradicals to enumerate the constitutional isomers of alkylcyclobutadienes is described. An alkylcyclobutadiene molecule is considered to be formed by four alkyl 1,1,1-triradicals by pairing two of the electrons with two of the adjacent alkyl 1,1,1-triradicals, and the remaining unpaired electron with one of the other adjacent alkyl 1,1,1-triradical. This enumeration algorithm showed that the constitutional isomers of the methanol series enumerated by Henze and Blair [3] can be used for enumerating the constitutional isomer of unsaturated cyclic compounds.     

Theory of helicenic hydrocarbons. Part 5: Irreducible helicenes and their enumeration

An irreducible helicene is a helicene from which no hexagon can be deleted if it shall remain to be a helicene. The generation of irreducible helicenes from primitive coronoids is treated, and algebraic expressions are deduced for their numbers. Symmetry plays an important role in this treatment. Numerical results obtained with the aid of computer programming are reported.     

Theory of helicenic hydrocarbons. Part 6: Concealed non-kekuléans

As a contribution to the enumeration of concealed non-Kekuléan helicenes, a construction method is applied to the caseh=14, whereh is the number of hexagons; computerized enumerations are given forh=14 and 15.     

Isomer combinatorics for acyclic conjugated polyenes: enumeration and beyond

A combinatorial approach to fully conjugated acyclic polyenes (C _N H _{N +2}) is considered with a view to the extension of standard enumeration techniques to treat a widened range of chemically interesting features. As a first step, enumerations are made respecting: placement of single and double bonds, the occurrence of cis/trans isomers, and the degree (and type) of “radicality” of such conjugated networks. As a further extension, several structural (graph-theoretic) invariants averaged over various types of isomer classes and sub-classes are made, and then these invariants are utilized to estimate several physicochemical properties averaged over these same classes or sub-classes. The properties currently so considered are heats of formation, indices of refraction, and magnetic susceptibilities. Finally, the asymptotic behaviors of isomer counts and isomer properties in the many-atom limit is elaborated. Received: 10 August 1998 / Accepted: 17 November 1998 / Published online: 16 March 1999     

Theory of helicenic hydrocarbons. Part 2: Chemical formulas

The formulas C _n H _s (n; s) for helicenic hydrocarbons are treated. The restrictions onn ands are specified comprehensively in terms of inequalities. General expressions are given for the C _n H _s formulas of extremal helicenes and some of their subclasses: circumextremal- and circular helicenes. Sequences of formulas for extremal helicenes, viz. (n ₀; s₀), (n ₁; s₁), ..., (n _k; s_k), ..., are defined. Here (n ₀;s ₀) is said to represent ground-form helicenes, while (n _k; s_k) for k > 0 pertain to higher members. A higher member with the formula (n _k; s_k) is an extremal helicene which can be obtained byk-fold complete sedimentation of a ground form. This process corresponds to circumscribing of benzenoids. A formula index, viz.x as a function ofn ands, distinguishes different classes of helicenes and can be used to identify the formulas for ground forms and higher members. The possible C _n H _s formulas for helicenes and their indices are tabulated. Finally the numbers of edges in C _n H _s isomers are discussed.     

Diamond hydrocarbons revisited: partitioned formula tables of diamondoids

Isomeric diamondoids with the same number $n$ of adamantane units (or cells), which share the same molecular formula $\text{ C}_\mathrm{Q}(\text{ CH})_\mathrm{T}(\text{ CH}_{2})_\mathrm{S}$ , can be divided into valence isomers by partitioning the number $C $ of their carbon atoms according to whether they are Quaternary, Tertiary, or Secondary: $C =Q +T +S$ . Each [ $n$ ]diamondoid has a dualist (or inner dual) with $n$ vertices (situated at centers of adamantane units), and edges connecting vertices of adjacent adamantane units sharing a chair-shaped hexagon of carbon atoms. Such a dualist is characterized by a quadruplet of indices (denoted as p, s, t, q for primary, secondary, tertiary, or quaternary) specifying again the connectivity of each vertex by assimilating it with a virtual carbon atom. The diamond lattice is self-dual. Dualists help in classifying diamondoids as catamantanes with acyclic dualists, perimantanes with dualists having chair-shaped six-membered rings, or coronamantanes with dualists having only higher-membered rings. In turn, catamantanes can be either regular when they have formulas $\text{ C}_{4n+6}\text{ H}_{4n+12}$ , or irregular when the numbers of carbon and hydrogen atoms are lower than the above values for the given numbers $n$ of adamantane units. Regular catamantanes can have branched or non-branched dualists and they are isomeric when having the same $n$ . Partitioned formulas reflect the branching patterns, encoded in their dualists. Partition formulas and codes are presented for all possible diamondoids with up to 7 adamantane units. A remarkable symmetry is observed for the table of partition periodic table of regular catamantanes with up to 7 adamantane units. Isomeric irregular catamantanes with six or more adamantane units may be valence-isomeric (or homomeric, sharing both the molecular and the partitioned formulas), or heteromeric when they have different partitioned formulas.     

硫化锌纳米空心球：合成及光学性质研究

Cubic ZnS hollow nanospheres have been prepared by a simple and template-free solvothermal method. The reaction was accomplished between Zn powder and the in-situ prepared S8. The results of X-ray diffraction (XRD), field-emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM) show that the ZnS hollow spheres are composed of ultrafine nanoparticles. The average diameters of the hollow nanospheres are about 100 nm. Their photoluminescence (PL) spectra indicate that they have excellent optical properties.     

Enumeration of Kekulé structures in benzenoid hydrocarbons: “flounders”

Combinatorial formulas for Kekulé structure counts (K) of a class of benzenoids referred to as flounders are derived. They represent a generalization of the previously studied pentagon-shaped benzenoids. A special case of theK formula reproduces the well-known Catalan numbers.received by the Publisher 20 September 1989Part VI in the series Pentagon-Shaped Benzenoids. For parts I–V, see refs. [12–161].     

柔软的球状和长方体状氧化硅中空结构的制备研究

采用自组装形成的芘纳米结构作为模板,成功地制备了柔软的球状和长方体状氧化硅中空结构.当不同量的芘在十六烷基三甲基溴化铵(CTAB)溶液中自组装时,产生的自组装结构展现出明显的从球状到长方体状的形貌变化.这些结构被用作氧化硅前驱体溶胶-凝胶反应的模板,获得了球状和长方体状氧化硅/芘复合结构.通过乙醇除去模板后,生成了柔软的球状(直径约为400nm)和长方体状(长为0.5—2.5μm)的氧化硅中空结构.这些结果展现了采用有机纳米结构作为模板来合成无机中空结构的优势:合成简便、结构多样以及结构形貌的灵活可控.     

Self-assembly of Hollow PNIPAM Microgels to Form Discontinuously Hollow Fibers

A new kind of hollow hydrogel microfiber with discontinuous hollow structure was prepared by an ice-segregation-induced self-assembly process. Monodisperse thermo-responsive hollow poly（N-isopropylacrylamide）（PNIPAM） microgels were first synthesized by seed precipitation polymerization using colloidal Si O2 nanoparticles as seeds, followed by removing the silica cores of the formed Si O2/PNIPAM core/shell composite microgels with hydrofluoric acid. Then, the discontinuously hollow hydrogel microfibers were produced by unidirectional freezing of 1 wt% hollow PNIPAM microgel aqueous dispersion in liquid nitrogen bath, followed by freeze-drying to remove the formed ice crystals. Many orderly arrayed dents were observed on the surfaces of the hydrogel microfibers by field-emission scanning electron microscopy, indicating that they are constructed by closely packed monodisperse hollow PNIPAM microgels. The effect of freezing method and the hollow microgel concentration in the aqueous dispersion on the morphological structure of the hollow hydrogel microfibers was investigated.     

化学结构正规编码及其信息处理功能

自从计算机在化学领域中应用以来,化学结构的正规编码已广泛用来作为一种化学文献的信息索引,它还在开发化学智能系统中发挥着重要作用。正规编码生成是以化学结构图的拓扑性质为基础的。本文首先概述编码的基本原理及其生成的方法,随后分析这种编码在当今文献数据库、化学反应数据库、分子设计以及合成反应路线规划等化学信息系统中的功能。