ARTICLE pubs.acs.org/jchemeduc
Periodic Table of the Elements in the Perspective of Artificial Neural Networks Maurício R. Lemes*,† and Arnaldo Dal Pino‡ †
Faculdade Anhanguera de Taubate, Engenharia, Av. Charles Schnneider, 585, Parque Senhor Bonfim, Taubate, S~ao Paulo 12062350, Brazil ‡ Instituto Tecnologico de Aeronautica, Prac-a Mal-do-Ar Eduardo Gomes 50 Vila das Acacias, Sao Jose dos Campos, SP 12228-900, Brazil ABSTRACT: Although several chemical elements were not known by end of the 19th century, Mendeleev came up with an astonishing achievement, the periodic table of elements. He was not only able to predict the existence of (then) new elements, but also to provide accurate estimates of their chemical and physical properties. This is a profound example of the human intelligence. Here, we try to shed some light on the following question: Can an artificial intelligence system yield a classification of the elements that resembles, in some sense, the periodic table? To achieve our goal, we have used a selforganized map (SOM) with information available at Mendeleev’s time. Our results show that similar elements tend to form individual clusters. Thus, although SOM generates clusters of halogens, alkaline metals, and transition metals that show a similarity with the periodic table of elements, the SOM did not achieve the sophistication that Mendeleev achieved. KEYWORDS: General Public, Graduate Education/Research, Interdisciplinary/Multidisciplinary, Physical Chemistry, ComputerBased Learning, Atomic Properties/Structure, Chemometrics, Periodicity/Periodic Table, Physical Properties n 1869 Mendeleev1 presented the periodic law of the elements to the scientific community. Mendeleev knew the existence and some properties of about 60 elements. For the vast majority of these elements, his knowledge was restricted to atomic weight, reaction of the element with oxygen, atomic radius, and melting point.2 He had so much confidence in his discovery that he left empty positions in his table. These spaces were dedicated to those elements that, according to him, would still have to be discovered. If one takes into consideration the limited information available, the table developed by Mendeleev deserves the greatest admiration. At that time, scientists knew nothing about the atomic structure and atomic numbers that are used in the organization of the elements of the current table. Over 40 years later, in 1913, Mosely established the concept of atomic number.3 This discovery, however, provoked only minor rearrangements in the classification of the elements created by Mendeleev. Possibly, the biggest triumph of the periodic table of the elements was to foresee the existence and properties of unknown elements at its time. For example, Mendeleev not only claimed the existence of the element eka-silicon, today known as germanium, but also inferred its properties and reactions with chlorine and oxygen with considerable precision. The periodic table identifies similarities between two or more elements and arranges them under the format of periods and groups. The intervals in which these similarities repeated consistently related to the atomic number. In the table, the elements are arranged horizontally, in numerical sequence, according to their atomic numbers, thus, giving rise to the appearance of seven horizontal lines (or periods). Each period, with the exception of the first one, starts with a metal and finishes with a noble gas. The
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Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
length of a period differs, ranging from a minimum of 2 elements to a maximum of 32. The vertical lines are formed by elements whose external electronic structures are similar. These columns are called groups. In some of them, the elements are so closely related that they are called families. For example, group 2 is the family of alkali earth metals (beryllium, magnesium, calcium, strontium, barium, and radium). Such great success of human intelligence yields a fertile field for exploring the capacity of artificial intelligent systems to produce similar results. Kohonen networks,4 self-organized maps, and other techniques have been commonly used in classification efforts, such as in silicon clusters, spectrometry, modeling, optimization, chemical problems511 and others.1215 The goal of this article is to investigate the capacity of an intelligent artificial system to classify chemical elements. To this end, a Kohonen network (KN) is supplied with the information known by the end of the 19th century. The KN is, therefore, fed with similar knowledge that was available to Mendeleev. We show that the 8 8 KN places the elements in such a way that it obeys many properties presented in the original periodic table. Such a fact reinforces the efficiency of the method. We also show that some elements are so similar that they share the same cell.
’ KOHONEN NEURAL NETWORK Neural networks were originally developed16 in the 1940s by the neurophysiologist Warren McCulloch of Massachusetts Institute of Technology and the mathematician Walter Pitts of the University of Illinois. They proposed a simple model of the Published: September 16, 2011 1511
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Figure 1. Schematic of a Kohonen network; input data are represented by the black circles with the solid lines representing possible pathways to the network and the processing is represented by the dotted lines on the 5 4 grid.
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Figure 3. The neuron with the strongest response captures the letter. On the left, the first letter (E) has been previously captured and the letter B is being captured. On the right, the group of letters has been organized; note that the uppercase and lowercase letters are near to each other and vowels and constants are near to each other.
Table 1. The 69 Elements Used in This Worka Elementsa
Figure 2. Uppercase and lowercase letters, vowels and consonants make up the group to be classified. The neuron in the KN that responds more strongly to an object “wins” it (neighbor cells are affected).
neuron that revealed itself as a powerful computing device and proved that a synchronized arrangement of these neurons is capable, in principle, of universal computation. Thus, an artificial neural network can perform any calculation that an ordinary that is based on the human brain. An artificial neural network (ANN) is composed of several processing units whose individual functioning is simple. These units are connected by communication channels that are associated with certain weights. The units operate on their local data, which are entries received by their connections. The intelligent behavior of an ANN is a global effect explained by interactions between the processing units of the network. There are two types of ANN according to the learning scheme: supervised and unsupervised. In this work, a well-known type of unsupervised learning network called Kohonen network (KN)17 is used. The KNs are formed by a set of simple elements organized in more complex structures that work together. Each neuron is a processing unit that receives stimulus (from outside the system or from other neurons) and produces a response (to other neurons or outside the system). Similar to the structure of the brain, the neurons of the neural networks are interconnected by branches through which the stimuli are propagated. The learning process consists of strengthening the links that lead the system to produce more efficient responses. The goal of a KN is to map input patterns of arbitrary dimension N for a discrete geometric arrangement of two dimensions (Figure 1). What distinguishes the Kohonen networks from others is a double-layered structure: one layer for input and another for processing, where the map is formed. The processing layer consists of a geometric arrangement of neurons connected only to their immediate neighbors.
H Li
Ca* Zn*
Y* In*
Mg* Ce*
Ga* N*
Nb* Sb
I Fe
Na*
Sr*
La*
Hf
P*
Ta
Pt
K*
Cd*
Er
Pb
V*
Bi
Ni*
Cu*
Ba
Tl
Th
As*
F*
Cu*
Rb*
Hg
C
O*
Mo*
Cl*
Os
Ag*
Be
Si
S*
Te*
Mn*
Pd*
Cs
B
Ti*
Cr*
W
Br*
Ir
Au Be
Al* Sc*
Zr* Sn*
Se* Tc
U Co
Ru* Rh*
Ag*
a
The asterisk (*) denotes the 41 elements chosen for the training of the KN.
The objects to be grouped for subsequent segmentation (for example, the chemical elements) are presented, one at a time, to the input neurons. At each presentation, the stimuli generated by the object (for example, atomic weight, atomic radius, density, temperature, fusion, etc.) are captured by the input layer and transmitted equally to all the neurons of the layer of the map. In the network, the neuron that responds more strongly to the stimuli of the presented object wins it for itself. Furthermore, it reinforces its links with its neighbors, making them more sensitive to the characteristics of the captured object. The presentation of all input objects to the neural network and the update of the weight for each item is termed the “epoch”. In a new epoch, when an object is presented to the map, the entire sensitized region will react more intensely. However, as the neighboring neurons are different from the winning neuron, each will react more intensely to a slightly different object. With each new presentation of an object to the map, the sensitivity profile of the neurons changes. This is what is termed “training the network” (Figure 2). These changes, however, become smaller each time, so that the configuration of the map converges to a stable arrangement. When this happens, the map has “learned” to classify individuals. The result of processing a trained network is that each neuron becomes the owner of a number of objects (Figure 3) similar to those captured by neighboring neurons. Thus, similar individuals get placed near each other, forming a gradient of characteristics. The KNs may be referred to as self-organized maps. They are an example of unsupervised learning networks. 1512
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The learning process uses a set of known elements and their properties to determine the optimal values for the connections between neurons represented by the weights, w. Mathematically, the learning process of a KN may be described by
because various properties with different orders of magnitude are used.
’ TRAINING AND PREDICTION For the training of the KN, the following properties, known to Mendeleev, were used: atomic weight, radius of connection, atomic radius, melting point, and reaction with oxygen. After the training, an investigation of the behavior of properties different from those that were trained was conducted. These properties were the boiling point, atomic number, ionization potential, electronegativity, and density. The KN was able to map the features that were not part of the training. A list of the 69 elements studied in this work is given in Table 1. Among the elements for training, 41 chemical elements were randomly chosen and, for the training of the networks, the 5 neural properties previously identified were used. For convenience, a KN of square architecture, whose sides were composed of 8 neurons, was used. Training was conducted in 5000 epochs for all tests. Through the systematic variation of the parameters of learning (0.04 e η e 0.2) and of neighborhood (0.7 e σ e 1.5), it was found that the 8 8 network with the highest number of cells filled with a single element was obtained when σ = 1.4 and η = 0.09.
wij ðk þ 1Þ ¼ wij ðkÞ þ Δwij ðkÞ Δwij ðkÞ ¼ ηedðl, jÞσ ½χi wij ðkÞ
ð1Þ
where η is called learning rate, σ is the neighborhood factor (the higher the value of σ, the less the neighborhood will be affected), χi represents the ith training property, wij are the weights to be trained, l and j are indexes that characterize the cells, and d(l,j) is the distance between cells l and j. The weights are initialized from random values and are submitted to training. The process is iterative; that is, the weights obtained in iteration k + 1 are calculated from the values of the iteration k, until the values w(k + 1) and w(k) remain essentially unchanged. Each of these iterations is the epoch. It is important to note that the KN possesses periodic boundary condition. The values of χi are normalized; that is, upon entering the network, they become values between 0 and 1. This is done to ensure uniformity of the input data, Table 2. Map Founda In (4)
La (1)
Sr (2)
Rb (3)
K (3)
Na (3)
—
Mg (2)
Sn (4)
Ce (5)
Y (1)
—
Ca (2)
—
—
—
Te (6)
—
Zr (1)
—
Sc (1)
Al (4)
P (6)
N (6)
Ag (1) Pd (1)
— Ru (1)
Mo (1) —
— V (1)
Ti (1) —
— —
— —
O (6) F (6)
—
—
Cr (1)
—
—
—
S (6)
Cl (6)
Ni (1)
Mn (1)
—
—
—
—
—
Br (6)
Cu (1)
—
—
Ag (1)
Zn (1)
Ga (4)
As (6)
Se (6)
’ RESULTS The KN after the training process is presented in Table 2. By inspecting Table 2, it can be seen that the KN recognized and grouped elements with high electronegativity. The elements fluorine, chlorine, bromine, oxygen, and nitrogen occupy neighboring cells. The transition metals were also grouped: silver and palladium; nickel and copper; manganese (Mn), chromium (Cr), vanadium(V), and titanium (Ti). There were groupings of alkali metals such as rubidium (Rb), potassium (K), and sodium (Na). Another line group that formed was potassium (K), calcium (Ca), and scandium (Sc). There was also a lineup of strontium (Sr), yttrium (Y), and zirconium (Zr). From the 5A group, phosphorus (P) and nitrogen (N) were grouped. Using the trained weights, the cells occupied by the elements erbium (Er), platinum (Pt), gold (Au), and hydrogen (H) were identified and added to Table 2. This result is shown in Table 3. Note the proposed position in the KNs, placing Er and Ce together, hydrogen in the same cell as the fluoride, and platinum together with gold. Compared to the current periodic table, it is noted that the erbium and cerium, which occupy the same cell, are lanthanides. Platinum and gold, which are metals, are close to
a
The numbers refer to transition metals (1), alkaline earth metals (2), alkali metal (3), other metals (4), lanthanides (5), and nonmetals (6).
Table 3. Map with Predictions Using the Trained Weights In (4)
La(1)
Sr (2)
Sn (4) Ce (5) Er Y (1)
Rb (3) K (3) —
Na (3) —
Mg (2)
Ca (2) —
—
—
Te (6) — Ag (1) Pt Au
Zr (1) — Mo (1) —
Sc (1) Al (4) Ti (1) —
P (6) —
N (6) O (6)
Pd (1) Ru (1)
—
V (1)
—
—
—
FH
—
Cr (1)
—
—
—
S (6)
Cl (6)
Ni (1) Mn (1)
—
—
—
—
—
Br (6)
Cu (1) —
—
Ag (1) Zn (1) Ga (4) As (6) Se (6)
—
Table 4. Element Properties, Actual Values, and Normalized Values Used for the Training Atomic Weight/amu
Covalent Radius/Å
Atomic Radius/Å
Melting Point/K
Element
Actual
Normalized
Actual
Normalized
Actual Normalized
Actual Normalized
Nb
92.91
0.45
1.34
0.55
2.08
0.59
2740
Mo
95.94
0.46
1.3
0.53
2.01
0.57
2890
Cd
112.41
0.52
1.48
0.61
1.71
0.47
In Cu
114.82 63.546
0.53 0.34
1.44 1.17
0.60 0.48
2 1.57
Ag
107.868
0.51
1.34
0.55
Rh
102.9
0.49
1.25
Pd
106.4
0.50
1.28
Specific Heat/(J g1 °C1)
Reaction with O2
Actual
Normalized
0.70
0.26
0.11
2.5
0.73
0.25
0.11
3
0.74
594.18
0.23
0.23
0.11
1.2
0.23
0.56 0.42
429.76 1357.6
0.19 0.40
0.23 0.38
0.11 0.12
1.5 0.5 104
0.36 0.1
1.75
0.48
1234
0.37
0.235
0.11
0.5 104
0.1
0.51
1.83
0.51
2236
0.60
0.242
0.11
4
1
0.52
1.79
0.50
1825
0.50
0.24
0.11
4
1
1513
Actual
Normalized 0.61
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’ REFERENCES
Table 5. Element Properties Not Used in Training Atomic Element Number
Ionization
Electronegativity/ Boiling Density/
Potential/V
eV
Point/K (g/cm3)
Cd
48
8.993
1.69
1040
8.65
In
49
5.786
1.78
2346
7.31
Cu
29
7.726
1.9
2836
Ag
47
7.576
1.93
2436
10.5
8.96
Rh Pd
45 46
7.46 8.34
2.28 2.2
3970 3237
12.4 12
Nb
41
6.88
1.6
5017
Mo
42
7.099
2.16
4912
8.55 10.2
silver, ruthenium, and molybdenum and hydrogen was predicted next to fluoride, which is also a nonmetal. The final results starting from Table 2, show 33 cells occupied by one element and 4 cells occupied by 2 elements. (This table is not shown.) Cadmium (Cd) and indium (In), copper (Cu) and silver (Ag), rhodium (Rh) and palladium (Pd), niobium (Nb) and molybdenum (Mo) occupy the same cell. The properties used for training the neuron and the elements that shared the same cell are presented in Table 4. The pair, niobium and molybdenum, presents all the untrained properties with similar values. The pair cadmium and indium has similar atomic weight, connection, as well as atomic radii, and differs in only 20% at the melting point. A similar situation occurs for the pair rhodium and palladium. The pair copper and silver has different atomic weight, but the other untrained properties are similar. The network therefore shows that the atomic weight is not the most important feature for classifying of elements. Some properties not used in training are presented in Table 5. The pair cadmium and indium has similar atomic number and electronegativity. The pair copper and silver features different atomic numbers, but the other untrained properties are similar. The pair rhodium and palladium has different ionization potential, but the other properties are similar. The pair niobium and molybdenum has different densities, but other untrained properties are similar.
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’ CONCLUSIONS Using information known at the time of Mendeleev, an artificial intelligent system was tested to classify chemical elements. The KNs were able to map the chemical elements and to organize them according to various trained as well as untrained properties. The KNs organized alkali metals, transition metals, and even properties that were not present during training, for instance, electronegativity. Using the 8 8 architecture, the system was efficient and managed to map many different aspects of the elements. However, some chemical elements occupied the same cell because they had similar general properties.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. 1514
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