A new set of bookmarks

A new set of bookmarks designed by Qian-Rui's girl friend:

Helically coiled carbon nanotube derived from T140

I made one more HCCNT that was derived from parent torus, T140.

The inner part should be weaved first. Here I keep the relative position of these heptagons unchanged.

The next step is to determine the HSP (Horizontal Shift Parameter) on the outer part of the torus. The pitch of the HCCNT will depend on the magnitude of HSP. For detail, check the papers mentioned in previous post.

Helically coiled carbon nanotube derived from torus 120

I made another HCCNT (Helically coiled carbon nanotube) derived from the parent molecule, carbon nanotorus with 120 carbon atoms yesterday.

The construction of this carbon helix is quite straightforward. First we should know that this structure can be decomposed into six strips. To simplify the weaving process, one should start from the inner part of HCCNT.

To make a helical tube, one still need to finish the remaining two strips. Particularly, we need to be careful about the relative position between two neighbored pentagons. The systematic way to generate a whole family of HCCNTs from a parent TCNT is based on the concept of horizontal shift parameters (HSP). By applying a suitable HSP, one can create a whole family of HCCNTs.
The details of structural rules of HCCNTs can be found in the following three papers we published:

Chuang, C.; Fan, Y.-C.; Jin, B.-Y.* Generalized Classification of Toroidal and Helical Carbon Nanotubes J. Chem. Info. Model. 2009, 49, 361-368.
Chuang, C; Jin, B.-Y.* Hypothetical toroidal, cylindrical, helical analogs of C60 J. Mol. Graph. Model. 2009, 28, 220-225.
Chuang, C.; Fan, Y.-C.; Jin, B.-Y. On the Possible Geometries of Helically Coiled Carbon Nanotubes J. Mol. Struct. 2012, 1008, 1-7.


In fact, Chern made a bead model of the same structure a few years ago. But in the Bridges conference held in Pecs, Hungary, I met Laura Shea and gave that model to her as a souvenir. Since then, both Chern and I didn't make any new model of helically coiled carbon nanotubes.

Workshops in Japan

I am going to Japan to give a few workshops this Saturday. The tentative schedule for this trip:

June 2-5: Fukuoka University 
June 6: Okayama University
June 7: Shiga University, Hikone
June 8-11: Nagoya

Prismane

Prismane with 3-, 4-, and 5-fold rotational symmetry:

The hydrated diacetates of rhenium

The cover of the inorganic chemistry by J. E. House shows the structure of the hydrated diacetates of molybdenum(II), chromium(II), and rhenium. One can make a very good bead valence sphere model of this molecule containing a metal-metal bond.

「科學的藝術、藝術的科學」 for NTU Newsletter

I wrote a few words in Chinese for the NTU Newsletter yesterday.

科學的藝術、藝術的科學
一線千珠串出繽紛多彩的奈米世界
臺灣大學化學系 金必耀

Principles for the Development of a Complete Mind:
Study the science of art.
Study the art of science.
Develop your senses - especially learn how to see.
Realize that everything connects to everything else.
Leonardo da Vinci

化學是一門研究微觀物質組成、結構、性質與其變化的科學;幾何是一門有關大小、形狀與空間關係的數學;而藝術則是人類透過情感的反應與探索所創造出的結果。我的實驗室在過去數年，無意間發現科學與藝術一個意想不到的交會，即傳統串珠工藝可連結到微觀的奈米世界的各種結構，進一步再由繽紛多彩的奈米分子世界回饋到串珠立體幾何藝術的創作。

串珠工藝有很長遠的歷史，遠古人類就已經開始使用珠子與線，製作出項鍊、手環、吊飾等各種形狀的飾物。僅需要珠子與線，透過適當的編織程序，不但可做出各種有趣的立體串珠結構，還可以用來建構正確的微觀分子與奈米結構，而且化學鍵的飽和性與方向性自然地反應在串珠分子模型中。粗略地了解微觀分子構造，可以不用進行任何量子力學的計算，不用解薛丁格方程式，不用談到原子軌域，因為建構串珠模型就好像是進行一個分子類比計算，計算的結果便是分子中的價電子密度的近似分佈。

我們的工作以芙類分子與石墨烯結構為主：包含碳六十、碳七十、與其他籠形芙類分子串珠模型；還有含有五七邊形的甜甜圈形狀的環形碳管、螺旋碳管、與三葉結碳管（圖一）；以環形碳管的內側為建構單元，還可發展出具有特殊拓樸結構的高孔洞芙類分子；更為精采的結構是無限延伸的週期最小曲面，這些結構還可細分成單度、雙度與三度週期最小曲面，三度週期最小曲面中的 P、D、G（圖二）、I-WP 等曲面是我們整個探索過程中最精美的一段歷程。除了芙類分子等三價體系，串珠也可用來建構其他類型的微觀結構，如烷類分子、金屬串分子、柏拉圖體、阿基米德體、Sierpinski 碎形結構等。

製作串珠分子模型可幫助我們更清楚地了解到分子的鍵結排列方式，如何影響分子在三維空間的結構，強化對分子結構與化學鍵的概念，更重要的是由奈米世界所啟發出來的許多串珠結構本身，就是一個精美的藝術品，不但可以怡情養性，甚至啟發一些科學想法。科學的藝術作品除了能讓人讚佩其優美之外，隱含於其中的數學與科學原理，更能讓人進一步沈思自然的奧妙。

圖一: 三葉結碳管

圖二: 螺旋型（Gyroid）三度週期最小曲面

Two more resonance structures of C60

As I mentioned before, two chemists, Vukicevic and Randic, gave a complete enumeration of all possible resonance forms in their paper, Detailed Atlas of Kekulé Structures of the Buckminsterfullerene, in "The Mathematics and Topology of Fullerenes". According to them, there are 158 irreducible Kekule structures for C₆₀. Following the Schlegel diagrams listed in the paper, one can easily make a bead model for any resonance structure.

I found these two intriguing resonance forms, No. 108 and 111, of C₆₀ quite accidentally yesterday. Although I knew the existence of No. 108 for a long time, I didn't know No. 111 before. I also suspect they might be the only two resonance structures which have patterns of parallel stripes along the latitude coordinates. Particularly, the Kekule structure 108 has a 5-fold rotational symmetry axis with two pentagons located at two poles and the Kekule structure 111 has a 3-fold rotational symmetry instead.

Bead valence sphere model of penta-prismane

The structure of a penta-prismane is similar to that of a cubane. Instead of 4-fold rotational symmetry, one has a five-fold rotational symmetry. So the shape of penta-prismane is just like a pentagonal prism.

Bead valence sphere model of tetra-t-butyl tetrahedrane

The tetrahedrane derivative with four tert-butyl substituents, tetra-t-butyl tetrahedrane, was synthesized by the Austrian chemist,Günther Maier, in 1978. Here is the bead valence sphere model of this interesting molecule I made this afternoon. I think the hardest part to make molecules with many sp3 centers how to control the force evenly in the whole weaving process.

An old photo from Paul Hildebrandt

I got a nice picture of D. Shechtman with Zometoy from Paul Hildebrandt, President of Zometool Inc:

(NIST, 1985)

Zometool models at the Quasicrystal international conference

The newest Nobel laureate in Chemistry, D. Shechtman, was invited to Taiwan to participate a quasicrystal international conference held in the National Taipei University of Technology (May 7-9), a university very close to the National Taiwan University where I am working.
Yuan-Chia, Qian-Rui, and Hsin-Yu moved the two large zometool models, a 3D quasicrystal consisting of two types of golden rhombohedra (prolate and oblate) and a six-layer carbon onion (C20, C80, C180, C320, C500, and C720), to the conference's lobby area. Most participants seem to enjoy these two types of quasicrystal models, cluster and tiling, a lot.

Prof. Shechtman took a picture of me in front of the zometool model of carbon onion.

I also gave Prof. Shechtman a bead model of high-genus fullerene, a topologically nontrivial quasicrystal :-), as a gift.

Two hyperbolic graphitic surfaces

I made a bead model of hyperbolic graphitic surface by connecting 10 tetrahedral C₈₄ units (the model on the right, the one on the left is the C168). The skeleton of this model is similar to that of an adamantane of the smallest unit of diamond.

Workshop in Rome (ICCE & ECRICE)

I was invited to give a workshop, An exploration of molecular shape through mathematical beading, in the 22th International Conference on Chemical Education (ICCE) and 11th European Conference on Research in Chemical Education (ECRICE) which will be held in Rome, 15-20 July 2012. Check the website here www.iccecrice2012.org for the detailed schedule.

AN EXPLORATION OF MOLECULAR SHAPE THROUGH MATHEMATICAL BEADING
Chern Chuang, Chia-Chin Tsoo, Bih-Yaw Jin
Department of Chemistry, National Taiwan University, Taipei, Taiwan;
National Center for High-Performance Computing, Hsin-Chu, Taiwan; R.O.C.
E-mail: byjin@ntu.edu.tw

A few years ago, we discovered that beading an old and traditional craft could be applied systematically to construct faithful three-dimensional molecular shapes of fullerenes and various kinds of complicated graphitic materials including Platonic solids, C60, higher fullerenes, carbon nanotubes, nanotori, nanohelices, high-genus fullerenes, singly-, and triply-periodic minimal surfaces.1-3 Unlike the standard molecular physical model, chemical bonds are represented by beads explicitly, while atoms are not shown in a bead model. The hard-sphere repulsion among beads in a bead model effectively mimic the repulsion between different chemical bonds in a molecule. Thus, the molecular shape of fullerenes can be faithfully modelled by beading technique.

In this workshop, we will show participants how to construct systematically molecular models of fullerenes with beads and how to interpret correctly microscopic meaning of these bead models. Particularly, participants will learn simple beading techniques and build bead models of a dodecahedron and a truncated icosahedron, which are C20 and C60 respectively.

1. Chuang, C.; Jin, B.-Y.; Tsoo, C.-C.; Tang, N. Y.-Wa; Cheung, M. P. S.; Cuccia, L. A., J. Chem. Edu 2012 , 89, 414–416.
2. Chuang, C.; Jin, B.-Y.; Tsoo, C.-C., Proceedings of Bridges: Mathematics, Music, Art, Architecture, Culture, 2011, 523-526.
3. The beaded molecules blog: http://thebeadedmolecules.blogspot.com/.

Comments from Prof. Henry Bent

I mailed the reprint of my paper with Prof. Cuccia, "Molecular Modeling of Fullerenes with Beads" (J. Chem. Edu 2012 , 89 (3), 414–416) to Prof. Henry Bent two months ago. He is the person who proposed the tangent sphere model in the 60s. He made the following comments on the beaded molecules:

"... contributions to the literature on molecular modeling such sophisticated molecules with so elegantly simple methods: beads and string, that's all!"
"The saturation and directional character of chemical affinity falls out naturally from your bead models without any need to refer, e.g., to Schrödinger's equation and atomic orbitals when constructing approximate electron density profiles, even for molecules as complicated as the fullerenes." 

Workshops in Japan

Prof. Sonoda of Kyushu university invited me to Japan next month to have a few lectures and workshops in a few different places of Japan. Prof. Sonoda also invited Mr. Kazunori Horibe when I give a workshop in Nagoya Child and Family Center.