Ping-Pong Valence Sphere Model

Valence sphere models, a qualitative chemical bond model that includes the influence of the electron pair repulsion among valence electron pairs and attraction between positive atomic core and negative electron pairs, can be constructed with Ping-Pong balls easily. Here, I made three pairs of linked ping-pong balls and used them to create a tetrahedral sp³-hybridized AX₄ system and a octahedral d²sp³ hybridized AX₆ system.

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.

Two EMACs

Qian-Rui made these two bead models of EMACs, one with 3 metal cores and the other with 9 cores, last year. The ratio of two types of beads is so small such that the surrounding ligands stop to spiral around the central metal string.

Bead model of the longest EMAC

Qian-Rui made this bead model of the longest EMAC (Extended Metal Atom Chain) for Prof. J. McGrady (Univ. of Oxford) who is an expert on the electronic structures of this class of molecules and is going to visit our department today. In making this model, Qian-Rui chose 10mm beads for both metal-metal and metal-ligand bonds, and 8mm beads for chemical bonds of surrounding ligands. The pitch of the surrounding ligands is slightly larger than the true molecular structure of this molecule. Only a single nylon cord with about 7 meter long is used for this model.





Here is a photo for the giant structure of this molecule hung in the main lobby of our department.

Pentanuclear EMAC

There is a whole family of EMACs with different chain lengths and different metal atoms.
Qian-Rui made this first bead model of EMAC with five metal atoms.


The sizes of beads are 8mm and 6mm, respectively.

Effect of bead sizes on the pitch angle of EMACs

Here I'd to show a few photos of EMACs to how the ratio of two kind of bead sizes on the pitch angles.

1. Correct pitch angle by using 8mm and 6mm beads.


2. Ligands spiral around the central metal string too fast if we use the same kind of beads for both ligands and metal string.


3. No pitch angle if we use 10mm and 14mm beads.

Alternative weaving path of EMACs

Qian-Rui told me that it is easier to use the following weaving path for creating beaded EMACs. The one-end weaving is quite odd to me. This one uses one-end weaving for the pyridyl-groups at chain ends only.

Weaving path for EMACs with 1,8-naphthyridine ligands

A simple weaving path for EMACs that contain 1,8-naphthyridine (萘啶) ligands:



I am not sure if Chern Chuang followed this path when he made the first beaded EMAC. Unlike EMACs with pyridyl-ligands, here one can use the same type of two-end weaving technique we used for making bead models of fullerenes.

Structure of nonanickel EMACs

Weaving path of EMACs

Qian-Rui told me the ingenious weaving path of EMACs he used. I made a schematic plot to show his weave path in the following figure. This path has a major difference from the ones we used for fullerenes before. I.e. one used only one end of fishing thread to weave pyridyl groups (hexagons, green) in the ligands. In doing so, he can weave the whole structure with only one long minimal fishing thread.

Bead model of tris(bipyridine)ruthenium(II) ion

I mentioned in previous post that I tried to make a beaded model of tris(bipyridine)ruthenium(II) ion (structure is shown below), but didn't succeed.



Somehow, Qian-Rui solved the problem and just showed me the bead model he made for this molecular ion.


This model clearly shows the difference between the planar structural formula and the real 3D structure of a molecule. Chemists are quite used to draw molecules on a paper, but think actually in 3D space. The rationale is the valence shell electron pair repulsion (VSEPR) taught in most general chemistry courses.

Soliton excitation in EMACs

Since right- and left-handed EMACs are mirror images of each other, these two conformatoins should have exactly the same energy. In other words, an infinitely long EMAC has a doubly degenerate ground states. At the absolute temperature T=0, an EMAC can stay either in the left- or right-handed conformation. But at T>0, one may have conformational fluctuations to other excited structures above the ground state. If the barrier to turn left-handed conformation to right-handed conformation is small, soliton excitation may become energetically favorable. An infinitely long EMAC with soliton (or domain wall) consists of three parts: a semi-infinitely long left- and right-handed structures on two sides of polymer and a soliton (a domain wall) with finite lengths in between. It is not easy to determine the size and creation energy of a soliton in an EMAC polymer, though.

Base on my experience with beaded EMACs, it is quite easy to make a soliton in the beaded model as shown in the following picture. So it is reasonable to assume that soliton excitation should be easy in the real, infinitely long EMAC polymers.

Two mor pictures of beaded EMAC

Two more pictures I took at Starbucks Chubei, Hsinchu, yesterday.

Some thoughts on beaded EMACs

Two weeks passed since Chern showed me the first beaded EMAC. Qian-Rui and Chern have further demonstrated that beads can be applied to many more EMACs with different chain lengths and ligands.
I thought, maybe there are more different types of molecules, especially coordination compounds, that can be made with beads. I tried to imagine other molecules I can think of. I tried tris(bipyridine)ruthenium(II) ion tonight. But it didn't work. Right now, I couldn't find any other molecules that can be constructed with beads easily.
It is also quite surprising to me that my group (especially, Qian-Rui Huang and me) has been working on the transport properties of EMACs for a few years. Additionally there is a giant physical model of the longest EMAC compound hung in the main lobby of our deparment, which I've seen almost everyday. But I didn't realize earlier that this class of molecules can be built so faithfully with beads that we have been playing with for four years already.

Two more beaded EMACs

The other two beaded EMACs Qian-Rui made early last week are here. The sizes of beads seem to be 12mm and 8 mm. The pitch angle of the resulting four ligands is so small, so we can almost view them as in parallel with the central metal string in this case. Here Qian-Rui has also managed to add two axial ligands corresponding to the -NCS to two ends of these two molecules.

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.