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Química Nova

Print version ISSN 0100-4042

Quím. Nova vol.36 no.6 São Paulo  2013 



The use of Rich and Suter diagrams to explain the electron configurations of transition elements



Hugo Orofino; Sergio P. Machado; Roberto B. Faria*

Instituto de Química, Universidade Federal do Rio de Janeiro, 21941-611 Rio de Janeiro - RJ, Brasil




Rich and Suter diagrams are a very useful tool to explain the electron configurations of all transition elements, and in particular, the s1 and s0 configurations of the elements Cr, Cu, Nb, Mo, Ru, Rh, Pd, Ag, and Pt. The application of these diagrams to the inner transition elements also explains the electron configurations of lanthanoids and actinoids, except for Ce, Pa, U, Np, and Cm, whose electron configurations are indeed very special because they are a mixture of several configurations.

Keywords: periodic table; electronic configuration; Rich and Suter diagrams.



The electronic configuration of chemical elements is a very important and initial topic in all introductory chemistry courses. To obtain them, the Aufbau principle is used in connection with the orbitals energies. However, the explanation of the s1 ground-state electron configurations of Cr and Cu is generally based on the special stability attributed to a half-filled and filled subshell, respectively.1-3 Otherwise, these configurations can be explained by the very elegant Rich and Suter diagrams.4 These and some other authors clearly state that there is no extra stability for a filled or half-filled subshell compared with a subshell containing one electron less.4 - 7 The s1 and s0 electron configurations of neutral isolated atoms of some transition elements can be explained by considering that each subshell energy level is split into two levels, a and b, related to the spin of the electrons, as can be seen in Figure 1. The Coulomb energy on account of the pairing of two electrons in the same orbital is assigned to the b level, because of which this level appears to be at a higher energy than the a level. In Figure 1a, the number 6 at the crossing point between the 3da and 4sa lines has the meaning 3da5 and 4sa1, and the same meaning applies to Figure 1c.



This type of diagram is very easily grasped by students and makes the explanation of the "anomalous" s1 and s0 electron configurations of transition elements much more reasonable. As can be seen in Figure 1a, the 4s2 3d3 vanadium electron configuration comes from the fact that both levels, 4sa and 4sb, have a lower energy than 3da. As we move to the right on the periodic table, the atomic number increases and all the levels go down. Because the 3d levels are closer to the core, they decrease faster than the 4s level, and the 3da level crosses the 4sb level when passing from V to Cr. It causes that for Cr, the 3da level must be completely filled with five electrons before we can put any electrons in the 4sb level. Because Cr only has six electrons in the valence shell, there is no electron to occupy the 4sb level, which results in the 4s1 3d5 electron configuration of Cr. The same situation occurs upon going from Ni to Cu. For Ni, the 4sb level is below 3db, whereas for Cu these levels cross and 3db becomes lower than 4sb. This means that the levels must be filled in the sequence: 3da5 4sa1 3db5, and because there are no more electrons, the Cu electron configuration is 4s1 3d10. Using the Rich and Suter diagram for the second transition period (Figure 1b), it is also easy to explain why Pd has a 5s0 4d10 electron configuration. Because the two levels 4da and 4db are lower than the 5s level, the ten electrons of the Pd valence shell fill the 4d levels, namely 4da5 4db5, giving the 4d10 electron configuration. The same diagram also explains the electron configurations of Nb (5s1 4d4), Ru (5s1 4d7), and Rh (5s1 4d8), which cannot be explained by using the half-filled or filled subshell argument.

As far as we know, these diagrams are not presented in general chemistry textbooks, and there is no reason for this because they are simple and contribute to a much more logical reasoning in the explanation of the electronic configurations of transition elements. The diagrams are, however, presented in an inorganic chemistry textbook by Miessler and Tarr.8

Rich and Suter diagrams also explain why the first transition elements apparently lose their 4s2 electrons when they go to a higher oxidation state. For example, vanadium has a 4s2 3d3 electron configuration, which turns into 4s0 3d3 for vanadium(II). As can be seen in Figure 1a, the electrons to be removed must be those with a higher energy, which are the 3d3 electrons. After two of them have been removed, the atom's positive charge causes a decrease in all the orbital energy levels, the levels with lower principal quantum number being more sensible (Figure 2). This makes the 3d levels go below the 4s level so that the electrons can now occupy the lower 3da level, which eventually results in a 4s0 3d3 electron configuration and gives the impression that the 4s electrons have been removed during the oxidation process. This same reasoning can be applied to all the first-period transition elements (as can be seen in Figure 2), justifying the fact that the coordination chemistry of these transition elements in oxidation states higher than zero does not involve any electrons in the 4s orbitals.



Similar diagrams can be constructed for lanthanoids and actinoids, as can be seen in Figure 3 for the first case.



Despite its success in explaining the electron configurations of transition elements, we would also like to mention in this article that the Rich and Suter diagram cannot explain the electron configurations of the lanthanoid element Ce or the actinoids Pa, U, Np, and Cm.

In Figure 3, the electron configuration of Ce is predicted to be 6s2 5d2, in contradiction with the experimental configuration of 6s2 5d1 4f1.9-13 In this figure, the crossing point involving the levels 4fa and 5da has been positioned between Ce and Pr; however, if it is moved to the left (i.e., between La and Ce), the predicted Ce electron configuration will be 6s2 4f2, which is again in disagreement with the accepted electron configuration for this element. Using Rich and Suter diagrams, there is no way to obtain an electron configuration containing one electron on each of the levels 4fa and 5da. The reason for this is that these two levels can accommodate seven and five electrons, respectively, and that all electrons must go to the lower energy level until it is complete.

The elements Pa (7s2 6d1 5f2), U (7s2 6d1 5f3), Np (7s2 6d1 5f4), and Cm (7s2 6d1 5f7) present the same difficulty.14 For these actinoids, a Rich and Suter diagram can be constructed for the 6d (a and b) and 5f (a and b) subshells, similar to that shown in Figure 3. Again, it is not possible to let a small number of electrons go into levels 6da and 5fa because these levels must be completely filled with five or seven electrons, respectively, before the next one can start to be occupied.

Because Rich and Suter diagrams are a better-but still simplified-way to explain electron configurations, we must be aware that the correct electron configurations of these elements are indeed special. Students usually do not know that it is not a simple task to determine the electron configuration of an element, and that it requires the correlation of experimental line spectra and theoretical work, such as the assignment of the split of lines by the presence of a magnetic field (Zeeman effect) and the determination of associated g values. To give an idea of these difficulties, the Ce spectra has approximately 25000 lines, and approximately 15000 lines were mainly assigned to transitions from high levels to terms belonging to the lowest configurations 6s2 5d1 4f1 and 6s1 5d2 4f1. The lowest energy term 1G4o is not a pure term, accounting for only 55% of the composition of the neutral Ce ground level.11 In addition, the application of Hund's rule predicts a 3H term as the most stable one for a 6s2 5d1 4f1 configuration, contrary to the accepted 1G4o term, which does not follow this rule.12 Nevertheless, the elements Pa, U, Np, and Cm have the low-energy terms 4K11/2, 5L6o, 6L11/2, and 9D2o, in agreement with Hund's rule. This means that Ce has a very special electron configuration of the kind ns2 (n-1)d1 (n-2)fx, which has been the subject of specific studies to explain its occurrence.15

In conclusion, Rich and Suter diagrams are a very useful tool to explain the electron configurations of all the transition elements. These diagrams are easy to draw and are based on the orbitals' relative energies, considering the energy separation of different spin levels and their crossing as we move along a transition-element period. The use of such diagrams eliminates the traditional half-filled and filled subshell argument, which does not have any physical support. The discussion of the electron configurations of Ce, Pa, U, Np, and Cm is an additional subject that leads to a richer and deeper understanding of electron configurations. It helps students to substitute the "electron configurations dogma" by the correct view that the electron configuration of an element is the description of the atomic electronic structure based on a theoretical model, which is intended to explain the experimental line spectra. Because these spectra become more complex for heavier elements, the model needs to consider that for these atoms, the fundamental energy level is a mixture of several electron configurations.



The authors thank CNPq, CAPES and FAPERJ for financial support.



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Recebido em 25/9/12
Aceito em 2/2/13
Publicado na web em 24/5/13



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A pedido do autor, segue abaixo a Figura 1c, corrigida, do artigo publicado no vol. 36, n. 6, p. 894-896, 2013:


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