THE BUILDING-UP PRINCIPLE AND ATOMIC AND IONIC STRUCTURE D. F. Swinehart University of Oregon, Eugene, Oregon
MODERN valence theory demands that the old octet theory be abandoned and that atomic structure be taught from the point of view of the electronic configurations of the various atoms as found from quantum mechanics and the study of spectra (3). It is convenient to write the configurations of the gaseous atoms or ions as a starting point and to add various groups to construct molecules or ions. This approach will not predict the energies of the completed structures in solution but it will serve to predict coordination numbers and the space structures of complex ions by using Pauling's bond-hybridization method (12). This requires the introduction of spectroscopic notation for the quantum energy levels described by the n and 1 quantum numbers. Tables of the configurations of the ground states of the neutral atoms are readily available elsewhere (3, 4, 6, 9, 10, 11, I d , 13, 14, 16). The labor of memorizing such tables appears so forbidd i g that various rules and principles have been suggested which are easy to remember and which, by systematic application, lead directly to the desired configuration of a particular atom without the necessity of reconstmcting the whole table (15,Ir). In an experimental sense, the assignment of the quantum numbers to the various electrons in the ground state of an atom is made directly from spectroscopic data. In a theoretical sense, this assignment is made according to two well-known principles: (1) The Pauli Exclusion Principle, which states that in any particular atom, no two electrons may have the same four values for the four quantum numbers, these being n, I, m , and m,, m being the magnetic quantum number and m8the spin quantum number. (2) The Building-up Principle, which postulates a purely imaginary process for systematically "constmcting" the atoms of the elements, one by one. This process starts with the simplest, lightest atom, that of hydrogen, and provides for the addition of protons to the nucleus one a t a tinbe (and incidentally one or more neutrons). After each addition of a proton an extranuclear electron is added thus "building" an atom of the element with atomic number one unit more in each case. Thus all the atoms of the periodic table are "constmcted." The principle states that when each electron is added, it assumes that position or level which minimizes the energy of the atom as a whole. The Pauli Principle merely serves to determine the maximum possible numher of electrons in each sublevel, indicated by a particular combination of values of n and 1. It does not indicate the relative energies of the
sublevels. So, in order to apply the Building-up Principle it is necessary to have a mle indicating the order of the sublevels in energy. The rules mentioned above (15,17) serve this purpose. It is the purpose of this paper to point out an error almost always made, so far as the author is aware, in the application of the above principles and rules to the "construction" of the atoms of the transition elements. In textbook discussions of this subject authors seem to concentrate entirely on writing the configurations of the ground states of the neutral atoms. But chemists are much more concerned with atoms in the combined state than they are with free atoms; so valence theory demands that one should be able to write the configurations of the ground states of the ions of the atoms of the elements as well as of the neutral atoms. The usual discussion goes about as follows: starting with one 1s electron in hydrogen we add one proton to the nucleus (and incidentally two neutrons) and the extranuclear electron enters the vacant 1s position, filling the first shell and making a helium atom. A proton and two neutrons are introduced into the nucleus, making a lithium nucleus, and the extra electron enters the 2s orbital, and so on, in succession, the other 8s and six 2 p positions are filled, arriving a t neon. Starting a t sodium the extra electron enters the Ss orbital, and so on until the six Sp positions are filled a t argon. Now a t potassium the extra electron enters the 4s orbital, not the Sd orbital, which is a t a higher energy. At calcium the 4s orbital is filled. At scandium (2 = 21) a new process starts in which the extra electron enters the Sd orhital. Then in succession the other transition elements of the fourth period result from the filling in of the Sd sublevel e n d i g at copper with ten Sd electrons. This discussion is perfectly correct up to the point where scandium is mentioned; that is to say, the electronic configurations of the unit positively charged ions of the atoms of the elements u p to and including atomic number twenty are identical with the configurations of the neutral a l o m of atomic number one unit less in each case. When reading such a discussion for the first time, the thoughtful student will ask, why, in the ionization of the iron atom to produce a ferrous ion, are the two 4s electrons lost from the iron configuration which is completed by Sd64sZif the sixth Sd electron was the last one addedP This is a good question and is unanswerable in terms of the discussion in any textbook which the author has examined, (4-7, 9-14, 16), except one (8) where the extensive use of spectroscopic language is likely to confuse the student who lacks background in spectra.
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chemical viewpoint, however, since none of these elements in these valence states forms a stable series of compounds. LITERATURE CITED (1) "Atomic energy levels," National Bureau of Standards Circular No. 467 (1949). (2) BACHER,R. F., A N D GOUDSMIT, "Atomic Energy States," McGraw-Hill Book Co., h e . , New York, 1932. B., AND A. LEHRMAN, J. CHEM.EDUC.,25, 662 (3) CARROLL, (1948). (4) CHAPIN,W. H., AND L. STEINER,"Second Year College
Chemistry," 5th Edition, John Wiley and Sons, Inc., New York, 1943, p. 270. (5) CR~WTHER, J. A., "Ions, Electrons and Ionizing Radiations," 7th Ed., Longmans, Green and Co., New York, 1938, p. 291. (6) EMELEU~, H. J., .
