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.

Another dodecahedrane

I made one more valence sphere model (VSM) of dodecadrane (C₂₀H₂₀) yesterday. Although this model looks simple compared to other bead models I have made, I still feel satisfied every time I made a bead model of this molecule.

Styrofoam ball/rubber band model of ethylene

I posted a bead model of ethylene made by Qing Pang, a high-school student in TFG school. I don't like the way double bond is handled in her model because the channel (hole) orientations of two beads that used to model double bond is perpendicular to the bond orientation. I would prefer to have a bead valence model in which channel of each bead lies exactly along a particular bond. In the sense, to describe a double bond by beads, we need to use the banana bond representation of double bond proposed by Linus Pauling. This also means that, to construct a correct bead valence bond model of a double bond, we have to use a bead with a curved channel with an angle about 71 degree. I don't think one can get commercial beads which have channels with this particular angle.

But to illustrate the idea of banana bond, here I try to make a styrofoam ball/rubber band model of ethylene by carefully puncturing a channel with approximately this angle (see the styrofoam ball in the center). The resulting styrofoam model of ethylene looks just great!

It is straightforward to construct valence sphere model of acetylene with five styrofoam balls. Three of these balls represent triple bond and the remaining two balls represent single C-H bonds. Using the elementary geometry, one can show that the angle of the curved channel for the ball representing triple bond is about 38 degrees.

More bead/rubber band models

I found that it is much easier to use commercial beads to make the so called styrofoam/rubber band models of L. C. King. According to Prof. H. A. Bent, every student of chemistry should make a set of this kind of models for learning the concept of chemical bond. Here, I will show how to make valence sphere models using 25mm wooden beads and rubber band with 8mm small plastic beads as endcaps.

1. To make the valence sphere model of a methane which has the tetrahedral shape, we can connect two wooden beads (two-bead unit) first as shown in the following picture:

Then cross two two-bead units with each other to get a tetrahedral methane:

2. We can easily generalize the procedure to molecules with six valencies. First make another two-bead units with rubber bands, then cross it around the tetrahedral four-bead unit we just made. Then one should get an octahedral arrangement of six beads as shown in the following picture:

3. One can also try to make a five-bead unit which represents the valence sphere model of a molecule with dsp³ hybridization.

4. Valence sphere models for molecules with more than one center such as the ethane can easily be made too. Here is my procedure for making the valence sphere model of an ethane molecule: first I connect a three-bead unit and two two-bead units as shown in the following picture.

Then, connect these three units at suitable positions, one should get the valence sphere model for the ethane.

workshop for ICCE/ECRICE

I had a workshop for joint meeting of the 22nd International Conference on Chemistry Education and the European Conference for Research in Chemical Education yesterday in Rome, Italy. My collaborator and I prepared materials for 40 people. But only around 10 people participated the event.

Before participants to make their bead models in this hands-on workshop, I gave a 30-min introductory talk about what can done with beads and particularly the connection of the bead model to the valence sphere model (VSM). I tried to emphasize that bead model is the best method to realize the VSM for both fullerenes and other molecules with sp3, dsp3 and d2sp3 hybridization.

Bead VSM of cubane

I just made a bead VSM (valence sphere model) of cubane (C₈H₈) by myself. The structure looks neat to me. Every valence electron pair is faithfully represented by a big bead, purple for CC bond and pink for CH bond. Small beads which have no chemical meaning are used to bind the pink beads to the central carbon cube. I didn't distinguish CC bonds from CH bonds. In principle, electron pairs responsible for these two types of chemical bonds should have different momenta. So they should have different sizes of charge clouds.

Bead VSM of methane, ammonium, water, and hydrogen fluoride

There is no doubt that tetravalent molecules such as methane occupy an important place in the chemical bond theory.
In 1865, German chemist August Wilhelm von Hofmann made the first stick-and-ball molecular models of methane in lecture at the Royal Institution of Great Britain. It is planar!

Then, 1872, van't Hoff, then a graduate student, learned of a possible tetrahedral arrangement of the valence bonds of carbon, proposed by the Russian chemist Alexander Butlerov in 1862. He later made a set of 3-D paper models of tetrahedral molecules.

Following Prof. H. Bent's recipes, Qing Pang (龐晴) of TFGH (北一女) made several bead valence sphere models (bead VSM) for tetravalent molecules with the formula AX_nE_m, where n+m=4, n is the number of bond electron pairs and m is the number of lone electron pairs. Here she didn't use the Windsor's knot to end the Nylon thread, instead she used simply tiny beads to cap the terminal beads of this kind of tree-like structures. Also, she use blue beads to represent bond electron pairs and yellow beads long electron pairs. You can see bead model exactly realizes the valence sphere model of Bent. I will show other bead VSM (made by Qing Pang) of molecules with several centers later.

Tangent sphere model of ethane

Using beads, one can make a faithful representation of the so-called valence sphere model (VSM) or tangent sphere model for a molecule proposed by Prof. Henry Bent in the 60s. In this model, each valence electron pair in a molecule is represented by a sphere. Its diameter is determined by the de Broglie wavelength of the corresponding electron, λ = h/p, where p is its momentum and h is the Planck constant.

Here is the first bead VSM (BVSM) of ethane (C₂H₆) made by Qing Pang (龐晴) of the Taipei First-Girls High School (北一女). She used the so-called Windsor-knot technique (雙活結) to bind beads that are not parts of loops in a molecular graph. For simplicity, she used beads of the same size to build the BVSM of ethane. This is equivalent to making the assumption that all valence electrons have the same momentum. The paper below the bead model is from the manuscript entitled "Approximate Molecular Electron Density Profiles. I. Construction" that I got from Prof. Bent last month.

BTW, Prof. Bent has just published a new book entitled "Molecules and the chemical bond" which is the first book-length sequel of his early articles on tangent sphere model last year. If you want to know more about the tangent sphere model, you should read the book or the original articles published in J. Chem. Edu.
You can read parts of this book at the google book.

1. Bent, H. A. J. Chem. Edu. 1965, 40, 446.
2. Bent, H. A. J. Chem. Edu. 1965, 40, 523.
3. Bent, H. A. J. Chem. Edu. 1967, 42, 308.
4. Bent, H. A. J. Chem. Edu. 1967, 42, 348.
5. Bent, H. A. J. Chem. Edu. 1968, 44, 512.
6. Bent, H. A. J. Chem. Edu. 1967, 45, 768.

Advantages of beaded models

Compared with other methods for building physical models of fullerenes, the beaded molecules have many advantages:
1. The hard-sphere interactions among beads correctly mimic the microscopic valence-shell repulsion.

2. The only information needed to build a particular fullerene with a spiral is completely encoded in its spiral code.

3. The resulting shape of a beaded fullerene is in good agreement with the real geometry of the corresponding fullerene.

4. The mechanical response of a beaded molecule is related to that of a true fullerene molecule under pressure.

5. The beaded molecule can be made quite compact by using beads with small diameters. The sizes of the beaded molecules for fullerenes with even several hundreds of carbon atoms are less than 10 cm, which can be held in hand easily; while using the commercial models for the same fullerene, the sizes are typically much larger.

6. The resulting beaded molecules are aesthetically pleasing.

7. The structures of beaded molecules are stable, robust, and durable.