Periodicity and Some Graphical Insights on the Tendency toward Empty, Half-full, and Full Subshells Ronald L. Rich and Robert W. Suter Blumon College, Bluffton. OH 45817 The kevs to understandine ohvsical ~rooertiesand thermodynamic and kinetic aspeck df reac;iviiy clearly include (11 knowledge of the energy levels availahle to electrons in a species and 72) the extentto which these levels are populated. Virtually every introductory text, whether at the secondary or college level, therefore describes the quantization of atomic energy levels; many, if not most, also a t least refer to molecular orbitals. In fact, inadvisable as i t is, even some seventh and eighth graders are being required to memorize eround-state electron confieurations for common elements. Two recent articles in t&s Journal have contributed to readers' knowledee of certain seeminelv anomalous oxidation states of thetransitional (1) a n d h t h a n o i d (1-3) elements. "The calculation of formation enthalpies", however, cannot serve as "the key to understanding the relative stabilities of lanthanide oxidation states." Thermodynamics always yields predictions, albeit precise ones, of one kind of thermodynamic data from related thermodynamic data, never from the fundamental keys to understanding in atomic and molecular structure. Certainly we need both the precise thermodynamics and these other really basic considerations. However, the promise of the usefulness of electronic structures for a deeoer anoroach to chemistrv is still severelv limited by thecompleni;i& of evaluatingen& levels to thk rewired r recision. Thus. at the introductorv level. we show what canbe done with cl'assical thermodynakics and kinetics; then we try to give students a "feeling" for the underlying reasons by qualitative reference to the character of the fundamental particles. The broadest concept for relating the nature of those particles and their behavior is chemical periodicity. The success of the correlation is so apparent that it serves as the framework for discussing the descriptive chemistry of the elements, and hence is familiar to practically every beginning student. There are "problems", however, with the simplest efforts a t correlation using the periodic chart alone, for example, Why do Cr and Nb have s1 ground states? Why is 3+ chemistry so much less prominent with Mn than with Cr and Fe? Or why are Sm2+,Eu2+,and Yb2+the only stable 2+ lanthanoid ions found in water? The "explanation" for these ohservations is often given as, for example, "the tendency for one electron to be present in each of the five 3d orbitals" and as "the relative stahility of systems in which each of the f orbitals is 'half filled"' (1). The following more extreme example from a contemporary freshman chemistry textbook (4) is not really unique: "This anomalous behavior is partly due to the special stability associated with precisely half-filled sets of degenerate orbitals" (our italics). Related statements would in fact be quite legitimate and useful if presented only as summaries of ohservations, with the real reasons possibly to be examined later. There is a correlation between filled or half-filled subshells and stable oxidation states, but an emphasis on these configurations alone may convey to the student the impression, whether intended or not, that there is a tendency toward such structures per se.
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Before discussing this further let us review the relative energies of s and p electrons for several second- and thirdperiod elements. Figure 1 is a plot of differences between successive ionization energies (5)for atoms of Ne through P. (Other elements for which ionization energies are availahle can be used without any substantial difference in the interpretation.) Figure 2 is a plot of differences between first ionization energies for successive second- and third-period elements. The striking thing illustrated in these is that the difference between the energy required to remove an electron from a filled p subshell and that needed for the fifth electron is part of a regular series of such differences for the
+
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1.5 (2d-2$)
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Configurations
(zp2-2;)
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Figwe 1. Differences between lonlznilon energies far successive elecmrns within the same atom.
Configurations compared Figure 2. Differencesbetween first ionizationenergies for successive serondand third-period elements.
Figure 3. Energies (schematic) and occupancies (entries in Ib figure) of the outer orbitals of isolatedatoms of the 3dand 4d elements in their groundstates VS. atomic number. The two big d m in each graph show the intersectionsthat are not adjustable.
other n electrons. Successive electrons do reauire additional energ;, but this increase is remarkably reguiar for a given p subshell, and reflects essentially the increased effective nuclear charge. T o the precision shown on this plot there is no extra stability for a filled p subsbell, compared with the pS configuration, that cannot be accounted for by factors influencing the energies of the other p electrons. Likewise, when one c&npares the energy required to remove an electron from the half-filled p subshell with that needed for a p2 structure, nothing sperial is found. There is something special about the difference between the ionization enerw for o4and that for n'. but this is clearlv due to the ~oulomcinteiactionof two eieitrons in the sank orbital in a n4 confieuration. Similarlv. the large energv difference between el&trons in 3s' and i p 6 config&ations% readily explained by the difference in principal quantum number; this again indicates no more "extra" stability of a filled n subshell than i t does for ap5or any other structure in whichthe electron being removed is at the lower principal quantum level. We turn next to the d orbitals, using a slightly different approach toward similar goals. Figure 3 shows, with minor modifications, two of six related graphs presented earlier (6) hut perhaps not known to many readers. Here we plot the enereies schematicallv versus atomic number in such a way as tolead to the correct configuration within each neutrai, isolated atom. while remainine aware that most chemistrv does not startaith such atom: The extra Coulomb energy for electrons that are paired in orbitals has already been mentioned. Partly for clarity in the figure we assign all of the extra energy of pairing to the "second" of the two electrons. This gives us two approximately parallel curves for the energies in each subsbell, the lower one for unpaired electrons and the higher for the paired ones. I t also reflects the fact that when one electron leaves, i t does carry with i t essentially all of the pairing energy. (We note, incidentally, that only two intersection eranh noints in each . in Fieure 3 must be set without anv leeway in order to interpret the electronic configurations for 10 elements in each case.) We consider, then, that the pairing energy effectively divides each subshell into a low-energy half and a hieh-enerev half. This seuaration, though illustrated differently here, is of the same-sort as brought out for p electrons in Figure 2. What does this mean for electron configurations? Electrons will occupy the lowest available energy levels. Because ~~~
~
~
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Figure 4. Energies (schematic) and occupancies (entries in the figure) of the outer orbitals of MZt and M3+of the 41 elements in their ground states, but not isoiated, VS. atomic number. The dashed lines sloping gently down to the right represent the negative energy that can be overcome by an oxidant-iigand combination in the medium: this is more negative for the smaller ions to the right. The upper dashed line represents water as the oxidant: the lower one. any aqueous oxidant with a standard potential of at least 1.7 V.
there are five such vacancies before the energy rises sharply, five electrons, or a tendency toward five in a d subshell, should occur frequently, buttbere is clearly nothing magical about the group of five. Figure 4 deals with the ions of the 4 t elements, and again has a somewhat different basis, partly in order again to bring out some additional points. (Boldface symbols here designate regions of the periodic chart (6), as opposed to regular roman type for types of orbitals.) The spectra of these elements are complex, and not all the relevant energies are well known. Therefore, and because the ions are here assumed to be surrounded by other species, for example, in an aqueous solution. the eneraies are given onlv schematically. The sioping dashed lines represent the energies above which an electron is lost to the strongest oxidant(s) in the medium. These lines reflect lower energies toward the right as the smaller 4 f ions with greater effective nuclear charge, and hence smaller radii (7,8), interact more strongly with the ligands after oxidation. The upper dashed line corresponds to water itself as an oxidant, the lower one to any of several strong oxidants in water, or to a standard electrode potential (IUPAC) of a t leastC+1.7 V. We see that SmZC,EuZf, and Yb2+ are the only stable M2+ ions in water, and we note that E u ~ and + Yh2+have exactly half-full or full subshells, while Sm2+is sometimes said to show a tendency toward the former configuration. The figure shows all values of occupancy of each half subshell from 1 to 7 on a straight line, analogously to Figure 3. At the same time we see again that starting a new half subshell would indeed lead to (suddenly) higher energies for the "highest" electron of the next several elements. hence to that electron's easy removal by aqueous oxidants. Readers will notice the chanee of slooe at the point of half filling a subshell. After this point we have Ghat can be considered the normal slope for a constant configuration. Before this we have the effect of increased lowering of energies due to the rising number of electrons of the same spin, yielding greater (negative) quantum-mechanical "exchange Volume 65 Number 8 August 1986
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energies". This is less significant in the p and d suhshells, which have fewer electrons. (Still, additional exchange even between singly occupied s and d orbitals, together with the other factors, helps stabilize 4s13d5in Cr and 5s14d4in Nb, for example.) T o rationalize the important results even for f electrons, however, does not require us to consider this phenomenon further. On related aspects of periodicity, the periodic chart recently recommended by the IUPAC has provoked much discussion. The present authors originally shared the frequent impression that the new form was being adopted as the only official one. Actually, however, the purpose is simply to eliminate the amhiguity-costly for all of us directly or indirectly-especially for abstracting and indexing purposes, of the A and B suhgroups, and to have a way of doing this consistent with the widely used tables that have gaps in the middle and have the inner-transition elements a t the bottom (9). Also in connection with the problem of placing some elements into periodic charts it is stated ( I ) that "The one characteristic Zn possesses in common with Co2+, Ni2+, Cu2+,etc., is approximate size." We note, however, various chemical similarities of Zn2+ (not shared with ions from other regions of the periodic chart), including the tendency to form stable complexes with ammonia, cyanide ion, and so forth. These justify, hut of course do not by themselves necessitate, classifying the zinc group as transitional.
configurations is not the result of a special driving force toward precisely these configurations per se. The d5 structures occur more frequently than the d6 (or higher intermediate) ones because the sixth or subsequent electrons in such configurations have additional energies as a result of the Coulomb repulsion. These higher energies cause such electrons to be readily lost to another subshell or to even mild external oxidants. The d5 configurations also occur more often than the d' (or lower intermediate) ones mainly because the absence of the Coulomb repulsion in any empty orbitals helm such orbitals accept an electron, perhaps from an s2pair or a surrounding reductant. The exchangeenergy is a smaller contributor. Analogous arguments can he made for f electrons. We thus need to explain the observed tendencies in electron structures by stressing the energy differences due to one or more of the following: 1. occupancy of differing shells,
2. occupancy of differing suhshells within a given shell, 3. double occupancy vs. single occupancy of an orbital, 4. quantum-mechanicalexchange.
Literature Cited 1. Fcmeiius, W . C. J. Chem Edue. 198463,263;on the periodic table. 2. Smith. 0. W. J. Chem. Educ. 1986.63, 228: on ".. . the Enthaipi~sof Formation of LsnthenideHalides and Oxides': 3. Chriatianaen,J.A. J. Am. Chem. Sot. 1960,62,5526.Hare theAm.Chem. Soe. r m m mended the term "lsnthanoid", avoiding the "ide"e"ding for this vasge. 4. Bmvn,T. L.: Lemqv, H.E., Jr. Chrmlalry:The CentrolScionea,3rdod.;Prcatiee-Hall: Englewaod Cliffs. NJ. 1965; p 5. Mwre, C. E. "Ionizstion Potentials and Ionization LimitsDerivedfmm the Analyaisof
162.
Summary On the one hand there is no magic in empty, half-full, or full suhshells, or in empty or filled shells, for that matter. On the other hand there are certainly far more such structures than would he expected randomly. The abundance of such
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OpticslS~tra:'NSRDS-NBS,34.NationaiBumauofStandsds:U.S.Governmenl p;intin6omee:waahingtan, IWO. 6. Rich, R. Periodic Correlonions; Benjamin: New York. 1965; 0 9 (some unex~iained
9.
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simn,~. E., Chemical Ahstrads Service. personal communication, 1986
