One more beaded emacs

Qian-Rui Huang made a few more bead models of EMACs using several different colored beads today. Here is one of them:






This model uses five different colors of beads, one for the central metal-metal and metal-nitrogen bonds and the other four colors for four surrounding ligands. So one can easily distinguish helically coiled ligands from the central metal string. The sizes of two different kinds of beads are 12mm and 10 mm, respectively. The pitch angle generated by this choice of beads is a little bit greater than the true molecular pitch angle. Additionally, Qian-Rui has also managed to add two axial ligands with another kind of beads to mimic N-C-S ligands. So each ligand contain three beads.

Bond lengths in the beaded model

In the beaded model of fullerenes that contains only one type of beads, we don't really need to know the relationship between bond length and size of beads to construct a faithful model. But, in molecules such as EMACs, there are at least two types of bond lengths, central metal-metal bonds and ligand bonds, and two types of hybrizations, sp² and d²sp³. It is important to get the correct relation between bond lengths and diameter of beads, in order to get the right pitch angle of EMACs.

In the sp² hybridized carbon atom, we use three spherical beads to mimic carbon-carbon bonds as shown in the left of the following figure. These spherical beads are in contact with each other and the atom is located at the center of three spheres. The relation between bond length and diameter of bead is given by r=1.155a. Similarly, the metal-metal bond lengths for the d2sp3 hybridized atom, is given by r=1.414a.



In the previous post, I gave a simple formula for the pitch angle. But the a and b in the formula should stand for the central metal-metal bond length and the ligand bond length, respectively.

On the pitch angle of a beaded EMAC

I figured out a simple method to estimate the pitch angle of a beaded EMAC that consists of two types of beads, say with diameter a and b (a>b). Beads with size a are used to mimic metal-metal bonds and beads with size b are used to mimic bonds of surrounding ligands. The pitch angle θ can be shown to be approximately given by cosθ=a/(sqrt(3)b) or θ=cos^-1(a/sqrt(3)b). Thus if one use 8mm and 6mm beads to make a bead model of the EMAC compound, the pitch angle can be shown to be θ=cos^-1(8/sqrt(3)*6)= 30. By inspection, one can see that this angle is quite close to that in the beaded model Chuang made. The angle is a little larger than the experimental observation, though.

Three more photos of beaded EMAC

Three more pictures of the beaded EMAC:

Some more pictures of the giant model of the longest EMAC compoound

In the main lobby of chemistry department of National Taiwan University, there is a beautiful model of the longest EMAC compound that was first synthesized by Prof. S.-M. Peng. Here are a few pictures taken by J.-H. Huang.

Comments on using several different sizes of beads in a same beaded structure

In constructing the bead models of the EMACs (extended metal atom chains), we face a new problem, i.e. several apparently different bond lengths in this kind of molecules. Previously, we have been concentrating on the fullerenes which consist of sp²-type carbon-carbon bonds only. The variation of bond length in this type of molecules such as fullerenes is quite small, so in most of molecules we have constructed, we can use beads with same size to get quite faithful structures for them.

Here EMACs present a new situation since we have two kinds of atoms. In addition to the standard tri-valent sp² carbon and nitrogen in the surrounding ligands, we also have hexa-valent d²sp³ central metal atoms. As we all know, according the VSEPR, trivalent atoms tend to form a planar structure, but hexa-valent atoms prefer to have a locally octahedral structures, i.e. six bonds pointing to the six vertices of a octahedron. The lengths of central metal-metal bonds and the surrounding ligand bonds are quite different. For instance, in the famous tri-nuclear metal complexes [M₃(dpa)₄Cl₂] where M = Co^II, Ni^II , Co^II, and so on. The lengths of the central metal-metal bonds are about 0.23 ~ 0.25 nm. But the bond lengths of the surrounding carbon-carbon bonds are only about 0.14 nm. The bond lengths for bonds between central metal atoms and donor atoms (nitrogen) are about 0.2 nm. So it is not possible to construct this kind of molecules with only one type of beads, we have to use at least two or three types of beads to represent these bonds in order to get a faithful representation of this kind of molecules.

In the bead model Chuang made for the longest Emacs, he used two types of beads, 6mm beads for the bonds in the surrounding ligands and 8mm beads for the central metal-metal bonds and the metal-nitrogen bonds. The difficulty for making bead model for EMACs comes from the central metal-metal bonds. Unlike the typical carbon-carbon bonds, where we need to thread the fish line through every small beads (carbon-carbon bonds) twice; here we need to thread each large beads (metal-metal bonds) four times. This makes the weaving difficult. I am glad that Chuang succeeded in making it. The resulting bead model is surprisingly stable and just like a rigid rod, especially for the central metal string. This can also be understood as a beautiful realization of VSEPR for the central metal string.

One can also see that the four surrounding ligands spiraling around the central metal string beautifully. But the only problem is that the ligands spiral around the central metal string too fast. One can easily understand this because the size of smaller beads in this structure is too big. The ratio of bond length for metal-metal bond vs metal-nitrogen bond vs ligand bond is 0.24 nm : 0.20nm : 0.14 nm = 1.2: 1.0: 0.7. The size of large beads should be almost twice of that of small beads. The two sizes Chuang used is 0.8 cm: 0.6cm. I have never seen beads with a size 0.7cm in local stores in Taipei. So maybe a good option for making EMACs is to use either two types of beads with 1.2 cm and 0.8 cm or three types of beads with 1.2 cm, 1.0 cm and 0.8 cm, respectively. The pitch for the surrounding ligands may be still shorter than the true molecule, but should be closer.

Another problem for making bead model of EMACs is how to construct two axial ligands which are not in any loop of molecular graph of the corresponding EMACs. Up to now, all of the bead models we have been making have all beads belonging a particular loop. The simplest method is simply ignoring them. This is how Chuang handled it. Additionally, one can also use a small bead to stop the bead that represents axial ligand from falling off.

Some useful structural information from Jinn-Tsair Sheu, Cheng-Chen Lin, Ito Chao, Chih-Chieh Wang and Shie-Ming Peng*, "Linear trinuclear three-centred metal-metal multiple bonds: synthesis and crystal structure of [M₃(dpa)₄C1₂] [M = Ru^II or Rh^II, dpa = bis(2-pyridy1)amido anion]" Chem. Commun. 1996, 315.

Fig. 1, ORTEP view of[R^II₃(dpa)₄Cl₂] along the metal-metal bond axis.


Table 1, Structural comparison of [M₃(dpa)₄C1₂] trinuclear metal complexes

Bead model of the longest Emac (Extended Metal Atom Chain)

Extended metal atom chains (Emacs) refer a family of molecules that consist of a central metal atoms with metal-metal bonds and four surrounding ligands. My colleague Shie-Min Peng is a pioneer in this field.

The shortest emacs contain three central metal atoms such as triCobalt emacs, [Co₃(dipyridylamido)₄Cl₂]⁺, as shown in the following figure:
.
(Dimitrios A. Pantazis, Carlos A. Murillo and John E. McGrady, Dalton Trans., 2008, 608)

Originally, I don't think beads are suitable for making molecular model for this kind of molecules. But Chern Chuang proved that I was wrong. Today, right after I came back to my office, Chern gave me the first bead model of the longest emacs with 11 Nickel atoms that has ever been synthesized.

VSEPR and higher-valent systems

Based on our experience, beads are best for making trivalent systems, which should be locally flat according to the VSEPR (Valence Shell Electron Pair Repulsion) commonly used by chemists to predict 3-D structures of molecules. Molecules with unconstrained tetravalent center such as methane should be locally tetrahedral. But it is difficult to weave this kind of structures. We have only tried a few of this kind of systems.

Another situation we may like to do is constraining a tetravalent or even a pentavalent (hexavalent) bonds in a plane such as boron-boron bonds in the boron fullerenes as shown in the previous post. According to our experience, it is quite hard to keep or constrain all these bonds in a plane due to the tendency to reduce the repulsion among these bonds as required by the VSEPR.

Boron buckyball: B80

I noticed a few research articles and a news report about the Boron buckyball in Science News today. This reminds me the article (The Wonderful World of Beaded Molecules, in chinese) I wrote two years ago about the potential molecules that may have the same structures as the dual structures Chuang constructed. In that article, I suggested the possible candidates should be boron clusters. Well I was not exactly right, but I was not that far away either. In the reports I read today, the smallest boron cage seems to be B₈₀, not the structure I posted before.




The structure of B₈₀ is very similar to that of C₆₀. The main difference is that all hexagons in the C₆₀ are replaced by six equilateral triangles.


(Phys. Rev. B 80, 033410, 2009)

Here is the bead model I made for this molecule. It is quite difficult to make penta- or hexa-valent local structures with rod-like beads, though. This model is not stable.
Maybe, I should try to make another one with rice-shaped beads, But I am not sure that will help.