Research: Science and Education
A New Method for Studying the Periodic System Based on a Kohonen Neural Network David Zhekai Chen Merrill F. West High School, 1775 W. Lowell Avenue, Tracy, California 95376
[email protected] The periodic table is one of the important foundations of chemistry. However, several phenomena cannot be explained by simply looking at the positions of elements on the periodic table, such as similarities between beryllium and aluminum. Chemists have recently employed clustering techniques to classify elements using physicochemical properties (1). A main drawback common to the methods reported in the literature is that they are essentially one-dimensional. No information about the relationships between clusters is available. In this article, the Kohonen neural network is used to classify 54 elements and produce a twodimensional map, offering much richer information about the relationships among the elements. It will also show that the trained neural network can also be used to make predictions. Methodology The basic purpose of a Kohonen network is to construct a nonlinear projection of a high-dimensional pattern to a lowerdimensional space, generating maps of the studied information (2). In this contribution, the combination of a Kohonen network with the configuration of 12 8 and 10 physicochemical properties (atomic mass, minimum oxidation state, maximum oxidation state, atomic radius, electronegativity, state of matter, melting point, boiling point, heat of atomization, and ionization
potential) is used to cluster the first 54 elements on the periodic table. Results and Discussion Classification of 54 Elements The 54 elements were grouped into three major clusters (Figure 1): cluster 1 consists of all metallic elements shown in the upper portion of the map; cluster 2 (underlined) consists of nonmetallic elements shown in the lower part of the map; cluster 3 (in black background) consists of semimetallic elements, which are located between metals and nonmetals. The Kohonen map contains rich information. In cluster 1, highly reactive metals are separated from less reactive metals and the metalloid, germanium. Placing Li and Mg in neuron (11, 0) and Be and Al in neuron (5, 0) is consistent with the prediction from the diagonal relationship (3). Three iron-group elements, Fe, Co, and Ni, were mapped onto the same neuron (3, 2). In cluster 2, five noble-gas elements (He, Ne, Ar, Kr, and Xe) are well separated from other nonmetals. The second-period elements (Be, B, N, O, and F) were separated from other members of their respective groups, which is consistent with the prediction by the singularity principle (3). Hydrogen's placement on the periodic table is the most arguable one.
Figure 1. Classification of 54 elements into 3 clusters using a 12 8 Kohonen map: cluster 1 consists of all metallic elements shown in the upper portion of the map, cluster 2 (underlined) consists of nonmetallic elements, and cluster 3 (in black background) consists of semimetallic elements.
_
_
r 2010 American Chemical Society and Division of Chemical Education, Inc. pubs.acs.org/jchemeduc Vol. 87 No. 4 April 2010 10.1021/ed800125v Published on Web 03/09/2010
_
Journal of Chemical Education
433
Research: Science and Education
Mapping H onto neuron (10, 6) between neuron (10, 7) (F) and neuron (11, 5) (He) is reasonable. This arrangement also allows all gas elements to gather together.
Five elements (Cs, Au, Hg, Pb, and Rn) excluded from the training data set were chosen to test the trained Kohonen network. It placed them in excellent locations on the map. For example, radon is placed in the same neuron mapped by another heavy noble gas, Xe, which is a reasonable prediction.
cluster. Furthermore, this study confirmed the existence of the singularity principle and the diagonal relationships. Finally, the trained Kohonen neural network was successfully applied to predicting the properties of 5 test elements, a capability that may be employed to studying new chemical elements. This twodimensional map based method can be used as a complementary tool to the standard periodic table for both teaching and research. Readers are referred to the supporting information for detailed discussion on the Kohonen network and classification results with additional figures and a full list of references.
Conclusion
Literature Cited
A new method for studying the periodic system is described based on the combination of a Kohonen network and a set of physicochemical properties. The classification results are directly shown in a two-dimensional map and easy to interpret. The generated Kohonen map contains rich information on the relationships of chemical elements. This approach was not only able to group 54 elements into three clusters, metal cluster, semimetal cluster, and nonmetal cluster, but also offered detailed information on the (dis)similarity of the elements within each
1. Restrepo, G.; Mesa, H.; Llanos, E. J.; Villaveces, J. L. J. Chem. Inf. Comput. Sci. 2004, 44, 68–75. 2. Kohonen, T. Self-Organizing Maps; Springer-Verlag: Heidelberg, Germany, 1995. 3. Rayner-Canham, G. J. Chem. Educ. 2000, 77, 1053.
Prediction of 5 Elements
434
Journal of Chemical Education
_
Vol. 87 No. 4 April 2010
_
Supporting Information Available A detailed discussion on the Kohonen network. This material is available via the Internet at http://pubs.acs.org.
pubs.acs.org/jchemeduc
_
r 2010 American Chemical Society and Division of Chemical Education, Inc.
