It is an essential characteristic of the compounds with which Kossel's theory deals that the two combining atoms should be of opposite character : that they should stand in the series on oppo site sides of an inert gas, so that one has an excess and the other a defect of electrons. But, as we have seen, there are many com pounds in which we do not find this opposition, and cannot say which of the atoms is positive and which negative ; as in the com pounds of carbon with hydrogen and oxygen, or more striking still, in the compounds of the elements with themselves which occur in the polyatomic molecules of the free elements, as H2, N2, 02, P4, etc. Such compounds are further distinguished by the fact that they do not ionize in solution. It is evident that the linkage in such molecules must be due to some different physical mechan ism from that established by Kossel in ionized molecules. Theory of Lewis.—The solution of this problem was given by Lewis in the same year in which Kossel's paper appeared. He suggested that it was possible for electrons to be shared between two atoms in such a way that they formed part of the constitution of both. As he accepted the static atom, he did not discuss how the sharing took place. Even now, though we know that the electrons are in motion, and have some knowledge of how they move round the nucleus of an isolated atom, very little has been discovered about the dynamics of the shared electron; we may, however, assume that as in the isolated atom the electron moves round one nucleus, so an electron which is shared between two atoms revolves round the nuclei of both. But for our present pur pose it is enough to assume that the sharing is in some way pos sible, without inquiring more closely into its mechanism. This assumption makes possible a kind of link which is not broken in solution by ionization, and does not involve any opposition of character between the linked atoms; it further explains why this form of link is peculiarly common amongst atoms a few places before an inert gas, since they can remedy their defect of elec trons by using some of them twice over. We can also explain by its means the remarkable fact that the valency of an atom has normally the same value in its non-ionized compounds as in its salts. For example, chlorine forms a univalent negative ion, be cause it is one electron short of the stable number of argon. This defect also enables it to form a single covalency (non-ionized link) as in methyl chloride, because by sharing a single electron belonging to the carbon it can complete its stable num ber. Both the covalency and the electrovalency of such a negative atom are equal to the number of electrons needed to make up the inert-gas number, and hence equal to the number of places in the periodic table by which the element is removed from the next following inert gas. On the other hand, a metal like aluminium, as it has three loosely attached electrons, can lose these by ioniza tion and form a trivalent positive ion Alf++. . . . For the same reason it can share three electrons with other atoms or groups, as in but it cannot share more without disturbing the ar rangements of its inner electrons (the core of the atom). The covalency of such a metal is, like its electrovalency, the number of electrons which it has in excess of an inert gas.
One other point is to be noticed about the covalency. A funda mental principle in all theories of valency other than that of co ordination is that when two atoms form a link, whether covalent or electrovalent, each of the two uses up a unit of combining power. Thus sodium has one such unit, and so has chlorine. When they combine, neither has any power of further combination. So too, hydrogen has one unit, and carbon four: when four atoms of hydrogen combine with one of carbon to form methane, the hydro gen loses its power of further combination as well as the carbon, and a saturated molecule is produced. When the linkage is ion ized the explanation is simple. Every such link involves the migration of an electron from one atom to the other, so that the metal loses one loosely attached electron, and at the same time the other atom fills up one of its gaps. If the same is to hold for the covalent link, we must suppose that when atom A combines with atom B, nbt only does A share one of B's electrons, but at the same time B shares one of A's : the covalent link must consist of two shared electrons. so that its formation involves the addition of one
electron to each of the atoms concerned. This was pointed out by Lewis in 1916, as a necessary result of the simple laws of valency. Later work has shown that an unstable linking of hydrogen to an other atom by means of a single shared electron is possible in a few compounds ; but it is clear that the two-electron link is the almost invariable form of the covalency.
Co-ordinate Valency.—Thus the physical theory of atomic structure has provided an explanation of the mechanism both of electrovalencies and of covalencies. The explanation of the third form of attachment, the co-ordinate link, is almost equally simple : it was suggested by Lewis in 1916, although he did not develop the idea in detail. It is clear from the behaviour of Werner's corn pounds that the co-ordinate link is of the nature of a covalency.
As we have seen, the units of the co-ordination complex do not ionize, while other groups in the molecule outside the complex do so. The occurrence of optical activity (see STEREOCHEMISTRY) dependent on the position of the groups composing the complex, and independent of the ionized groups outside it, is further evi dence of the same thing. We may therefore conclude that the co-ordinated atoms or radicals are attached to the central atom by covalencies, that is, by pairs of shared electrons. Where these groups have a valency of one in the ordinary sense (univalent radicals or groups such as chlorine or this needs no further explanation : the difficulty is to explain the replacement of such radicals by complete molecules like water or ammonia. In am monia the nitrogen has increased its valency electrons from the original five to eight by combining with three hydrogen atoms. It thus has a complete valency group of eight electrons ("octet"), of which six are shared with the three hydrogen atoms, while the other two are not shared, and form what is called (in America) a "lone pair." All that is necessary to explain the co-ordination is to suppose that the nitrogen shares this lone pair with the plati num, thus forming a covalency differing from that previously dis cussed only in this, that the two shared electrons both come from the same atom. This explanation of the co-ordinate link of Werner satisfies all requirements. It explains why the link is not ionized, since it is in fact a covalency. It explains why it is of ten more easily broken than an ordinary covalency, since the nitrogen or other atom forming it can recall the two electrons which it has lent. It explains why the co-ordination number of an element can remain constant through a whole series of compounds, in spite of variations in the electrovalency, that is, in the electrical charge of the complex, for the co-ordination number is the num ber of pairs of shared electrons required to make up a stable valency group for the central atom. It accounts for the fact that while the valency in the ordinary sense changes by one unit as we go from one atom to the next, the co-ordination number is usually six or four independently of the periodic group to which the ele ment belongs : the ordinary valency depends on the number of electrons which the atom originally had (the atomic number), whilst the co-ordination number depends only on the stable size of the valency group, which for most atoms is 12 or 8. We can also account on this theory for the remarkable change in the elec trovalency which, as we have seen, accompanies the replacement of, say, an ammonia molecule in the complex by a chlorine atom, the electrovalency increasing by one if it is negative, and dimin ishing by one if it is positive, as is shown in the change from [Pt to [Pt For when the ammonia mole cule is removed, it takes with it the pair of electrons which formed its co-ordinate link to the central atom ; when a neutral chlorine atom takes its place, it only offers one electron for the link, and so another electron must be introduced from outside, which gives the complex a negative charge ; or, to put it in another way, if the chlorine is to take the place of the nitrogen and provide both electrons for the link, it must already have a complete octet, and so must be not a neutral chlorine atom (which has only seven valency electrons), but a negatively charged chlorine ion.