ÁREA: Iniciação Científica
TÍTULO: Multivariate Analysis of the Periodic Table Elements
AUTORES: DA SILVA CO (UFRN) ; AMBROSIO RC (UFRN)
RESUMO: This work presents the first results on the application of multivariate techniques to the classification of the elements of periodic table. Principal component analysis was performed on transition metals, lanthanoids and actinoids taking into account twelve properties. The first component takes into account mainly the thermodynamic properties of elements, while the second one is most influenced by the electronic properties, that is electronegativity, first and second ionization energies and effective atomic number. The third component takes into account electronic (electronegativity) and macroscopic (density, electrical resistivity, coefficient on linear thermal expansion) properties of the elements. The plot of two principal components showed that some elements group together.
PALAVRAS CHAVES: principal component analysis, periodic law, multivariate analysis
INTRODUÇÃO: “The properties of the elements are periodic functions of their atomic numbers.” This often cited statement does not sound like a “law” at all, in the sense that it is not a quantitative expression. One must not, however, confuse precision with reliability. The Periodic Law is a broad, imprecise statement that grew out of early efforts, and that still functions as a much-used framework on which comparisons and generalizations of chemical behavior are based.
There are certain general features of chemical behavior shown in periodic table. In moving down a group, there is an increase in metallic character because of the increase of the atom. In going across a period, there is a change from metallic (electropositive) behavior to nonmetallic (electronegative) because of the increasing number of electrons in the outer shell. Consequently, metallic elements tend to be those on the left and towards the bottom of the table; nonmetallic elements are towards the top and the right [1].
Chemists everywhere agree that the Periodic Law expresses deep-seated relationships in chemical properties and in the structures of atoms. On the other hand several physical properties of the elements were measured, although up to now, anyone used this available information to “check” the periodic classification. In this work, several properties of transition metals, lanthanoids and actinoids were collected (12 variables) and analyzed by means of multivariate methods in order to investigate the natural groupings among these elements.
MATERIAL E MÉTODOS: The 47 elements analyzed was (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, La, Ce, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Ac, Th, Pa, U). Among the properties (variables) analyzed are electronegativity (A), first (B) and second (C) ionization energies, effective atomic number (D), density (E), electrical resistivity (F), melting point (G), boiling point (H), thermal conductivity (I), coefficient on linear thermal expansion (J), enthalpy of fusion (K), and enthalpy of atomization (L).
To represent each sample, it is necessary 12 coordinates. On the other hand, with this abundance of data, we can take advantage of redundancy of information. We can simplify our problem by replacing a group of variables with a single new variable. Principal components analysis is a quantitatively rigorous method for achieving this simplification. The method generates a new set of variables, called principal components. Each principal component is a linear combination of the original variables [2]. All the principal components are orthogonal to each other so there is no redundant information. The principal components as a whole form an orthogonal basis for the space of the data reducing its dimensionality [2].
Since the analyzed variables were measured against different scales, its magnitudes are very different. These discrepancies can distort the calculated results. In order to convert all the values in the data set to use the same proportional scale, it was subtracted the mean of all values and normalized by the standard deviation of the variable.
RESULTADOS E DISCUSSÃO: When there are more than three variables, it is difficult to visualize their relationships. Fortunately, in data sets with many variables or groups of variables often move together. One reason for this is that more than one variable may be measuring the same driving principle governing the behavior of the system. In many systems there are only a few such driving forces. Eigenanalysis was performed on the data set in order to choose the correct number of principal components. The first three principal components account for 73 % of the variance:
PC1(36%)= -0.095A + 0.213B + 0.216C - 0.010D + 0.260E - 0.273F + 0.410G + 0.374H + 0.148I - 0.268J + 0.400K + 0.433L
PC2(20 %) = -0.445A + 0.474B + 0.475C - 0.304D - 0.270E - 0.0282F - 0.113G - 0.060H + 0.270I + 0.159J - 0.242K - 0.106L
PC3(17 %) = -0. 403A + 0.117B + 0. 211C - 0.310D - 0. 351E - 0. 362F - 0. 202G - 0.251H + 0. 480I + 0. 273J - 0. 082K - 0. 106L
The first component takes into account mainly the thermodynamic properties of elements, that is, melting point, boiling point, enthalpy of fusion, and enthalpy of atomization. The second one is most influenced by the electronic properties, that is electronegativity, first and second ionization energies and effective atomic number. The third component takes into account electronic (electronegativity) and macroscopic (density, electrical resistivity, coefficient on linear thermal expansion) properties of the elements. Figure 1 shows the plot of the first two components calculated for the data set. As can be seen, some groups are formed indicating a natural clustering of elements.
CONCLUSÕES: In this work, it could be seen that electronic, thermodynamic and macroscopic properties influences on the calculations of the first principal component. In a bidimensional plot of the first two components, I could be seen that some elements tend to group together. In a future, this work will be improved by means of hierarchical clustering analysis to probe the natural grouping of elements based on its properties.
AGRADECIMENTOS: The authors wish to acknowledge CNPq and CAPES.
REFERÊNCIAS BIBLIOGRÁFICA: 1. EBBING, D.D.; wrighton, m.s. General Chemistry, third edition, Houghton, 1990
2. RENCHER, A. C. Methods of Multivarite Analysis, wiley, 1995
