The ''Aufbauprinzip" as a Basis for Classi$cation of the Elements H. C. LONGUET-HIGGINS Cambridge University, Cambridge, England
THIS NOTE recommends a presentation of the periodic table designed to show as directly as possible how the place of an element in the table is related to the electronic structure of the atom1 The basis of this presentation is the connection between the energy of an atomic electron and its orbital quantum numbers. I n a coulomb field, for example in the hydrogen atom, the energy of an electron depends only on its principal quantum n ( = I , 2, 3 , . . .) and not on the second or third quantum numbers I, m. In a many-electron atom, however, the effective field on an electron is no longer coulombic, owing to the screening of the outer electrons by the inner shells. This screening effect in' EDITOR'SNOTE: WCt l ~ sthat t our re:tders mpcrt no apology for the appearance of another periodic table. The pages of THIS JOURNAL have described and will continue t o describe msnv. To preface each new exposition with a. critical review of others which have preceded would, we feel, be an unwise and unnecessary use of our space. We feel confident that regular readers of our pages will understand, therefore, why no reference has been made t o previaualy printed discussions which adopt similar but not identical points of view. In this connection the reader may be inter33,69 (1956); 25,658 and 662 ested in referring to TKIS JOURNAL (1948); and 16,394 (1939).
creases with the second quantum number 1, with a result that for a given value of n an s electron ( I = 0) has the lowest energy and p electrons (1 = I), d electrons (I = 2) and f electrons (21 = 3 ) have progressively higher energies. For a given value of 1 there are 221 1 possible values of m, all with the same energy, so an s subshell can house 1 electron pair, a p subshell 3 electron pairs, a d subshell 5 electron pain, and anjsubshell 7 electron pnim. Tn speaking thus of many-electron atoms we arc supposing that in the atom each electron may be assigned a definite set of quantum numbers. This is not strictly true, because the motion of each electron is disturbed by the repulsion of the others. However, the electrons are to a considerable extent independent of one another, and this make9 it possible to regard the atom as built up by the progressive filling of successive subshells. This is the famous "Aufbauprinzip" of Bohr, and is the basic principle of valency theory. The order in which the various subshells are filled as atomic number increases is roughly determined by the following familiar rules: (I) np electrons have a higher energy than ns, but substantially lower than (n l)s,
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(2)nd electrons have about the same energy as (n l)s, but slightly higher in the neutral atom, (3) nf electrons have about the same energy as ( n 1)d. The slight vagueness in these generalizations is necessitated by the fact that the energy of a snbhsell depends on the chemical state of the atom, particularly on the charge. For example Zn++ has 10 3d electrons and no 4s electrons, whereas the Ni atom has 2 4s electrons and 8 3d electrons. With the aid of these rules we can build up the periodic table in a straightforward manner as far as Ba, which has 2 6s electrons outside a Xe core. Up to this point, with one or two trivial exceptions, e.g., the Cr atom in its ground state has one 4s and 5 3d electrons, every atom possesses not morethan one incomplete subshell. The next atom, La, has a 5d electron, hut in the following atoms the 4f shell fills up, and not until we reach Hf does the 5d shell accept any more electrons. This discontinuity is indicated by a step in the 5d block. After Ac the same thing happens again: the 5f shell of the free atom begins to fill up as soon as the 6d shell contains one electron. This is indicated by another step, this time in the 6d block. There is an additional complication in the heaviest elements, namely that the compozands of these elements behave as though the atoms had the following electronic configuration^:^
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Number of 6d electrons Number of 5 j electrons
Ac
Th
Pa
1
2
3
0
0
0
U 4
4 0
Pu Am Cm
Np . 1
i 2
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C N 0 FNe 2P
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1
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Chemically, that is to say, Th, Pa and ti resemble HI, Ta and W rather than Ce, Pr, and Nd; and Np, Pn and Am are more similar to U than to Pm, Sm and Eu. Cm, on the other hand, resembles Gd in its oxidation states, and the later elements probably also have close similarities to the rare earths lying below them in the table. It would be possible to indicate these facts by appropriate tie-lines, but this would complicate the diagram. It seems better to keep the diagram as simple as possible, and to draw special attention to the chemical characteristics of the (6d, 5f) series of elements. Apart from these exceptions, every atom behaves chemically as though it possessed at least as many electrons of a given type as the preceding atom. It is this fact which makes possible the construction of the table, in which atomic numher increases steadily as we read from left to right and upwards. The main advantage of such a table over more compact tables is that the chemical properties of the elements are shown to depend no less upon the nature of the valency electrons than upon their number. The slight resemblances between the so-called "A and B subgroups," which are, in any case, restricted to the highest or lowest valencies, have not been indicated explicitly in the table for fear of masking the much more important differences between A and B type elements such as Cr and S. Attempts to force the d elements into line with the sand p elements have in the past only obscured the true pattern of the periodic table, and it seems undesirable any longer to perpetuate a scheme in which first the rare earths and then the transuranic elements have had to be relegated to,footnotes a t the bottom of the table.
