Cyclic Diamondoid Structures with Shared Vertices, Edges, or 6-membered Rings

Diamondoid structures with shared vertices, edges, or 6-membered rings can theoretically be curved into toroidal structures whose calculated energy provides information about steric strain. Diamondoid hydrocarbons sharing one vertex between two adamantane units are called [n]spiromantanes, where n indicates the number of adamantane units. When a pair of adamantane units shares one CC bond, the resulting assembly is called one-edge-[n]mantane, specifying (by letters in square brackets) which bonds are shared by the adamantane units. Two adjacent edges may be shared by a pair of adamantane units, and the assembly is called two-edge-[n]mantane, again specifying by letters in square brackets the shared bonds. Catamantanes or perimantanes sharing a 6-membered ring of carbon atoms may form larger rings in an assembly which is called [n]cyclomantane; in the case of catamantanes, the structure of the diamondoid is specified by codes of the dualists. Finally, nanotubes derived from hexagonal diamond, as well as corresponding toroidal structures, are discussed

Science, Technology, and Medicine have Progressed Immensely during the Last Five Centuries, yet Mankind Is Threatened by Self-Destruction

During the last 5900 years, creative human minds have dispelled false beliefs about our universe, as well as chemical, physical, and biomedical phenomena. Life expectancies in most inhabited parts of our world have increased appreciably. A brief survey of those who contributed to the progress of science, technology, and understanding is presented. Yet, primitive instincts and ambitions still dominate our world, and conflicts threaten to destroy life on this planet by way of nuclear weapons. Societies are ruled by politicians and militaries, for scientists are “on tap, but not on top”. The contrast between reason-based progress and instinct-based aggression is mind-boggling

Chemical Graphs. XL.1 Three Relations Between the Fibonacci Sequence and the Numbers of Kekule Structures for Non-branched cata-Condensed Polycyclic Aromatic Hydrocarbons

Fo·r benze.notd or non-benzenoid ca:ta1fusenes having a non- ibranched string 01f cata-co.ndensed rings, the numbers K of Kekule structures (perfect matching·s) can be expressed vi<t the recurrence relationship (1); as a coa.-ollary when each annelated .segment has exactly two ring.s, the numbers O\u27f Kelm.le structures form the Fiibonacci sequence. Coro.nary 2 presents a second re.lationshi:p with Fiibonacci numbers. Algebraic expressions for the number of Kekule struc- 1tures in non-brainched cata.fusenes 1n terms of hexago.n numbers iJn each linearly condensed segment can be obtained. The numbers of terms in .such .a,,lgebraic expressivns lead to a new numerical triangle (Table I) which is related to Pascal\u27s triangle, and which pwvides a third link with the F ~bonacci numbers expressed either by relation (7) or by the equivalent relation (10)

Chemical Graphs. XL.1 Three Relations Between the Fibonacci Sequence and the Numbers of Kekule Structures for Non-branched cata-Condensed Polycyclic Aromatic Hydrocarbons

Fo·r benze.notd or non-benzenoid ca:ta1fusenes having a non- ibranched string 01f cata-co.ndensed rings, the numbers K of Kekule structures (perfect matching·s) can be expressed vi<t the recurrence relationship (1); as a coa.-ollary when each annelated .segment has exactly two ring.s, the numbers O\u27f Kelm.le structures form the Fiibonacci sequence. Coro.nary 2 presents a second re.lationshi:p with Fiibonacci numbers. Algebraic expressions for the number of Kekule struc- 1tures in non-brainched cata.fusenes 1n terms of hexago.n numbers iJn each linearly condensed segment can be obtained. The numbers of terms in .such .a,,lgebraic expressivns lead to a new numerical triangle (Table I) which is related to Pascal\u27s triangle, and which pwvides a third link with the F ~bonacci numbers expressed either by relation (7) or by the equivalent relation (10)

Lowering the Intra- and Intermolecular Degeneracy of Topological Invariants

A review is presented of the recent progress in designing local vertex invariants with low intramolecular degeneracy and the derived topological indices with low intermolecular degeneracy; in other words, an attempt is made to assign to graph vertices real (i.e. non-integer) numerical invariants which are different for non-equivalent vertices and similarly to assign to nonisomorphic molecular graphs distinct real-number topological indices