I
W. F. Luder
Northeastern University Boston, Massachusetts
The Electron Replusion Theory of the Chemical Bond I. New models o f atomic structure
T h e trend toward increasing complexity in t,heories of the chemical bond, which has been dominant for the past generation, may be losing- its momentum. In 1963, R. J. Gillespie, in his electron-pair repulsion theorv of molecular structure (1). ~, demonstrated that the conce~tof hvbrid atomic orbitals is unnecessarv: and H. A: Bent @), in the introduction to his theory of tangent-sphere molecular models, questioned the adequacy of wave mechanics to account for the structure of complicated molecules. Two of Professor Bent's remarks are particularly appropriate: . . . quantum chemistry has so far failed to become a workable,
. ..
everyday theory of chemical structure; massive efforts have been made to solve by approximate methods a philosophically questionable problem whose solution, if it could be obtained, probably could not be used
.. .
An even more critical discussion (too involved to quote here) of the failures of wave mechanics appeared in a book review by Max Black in the Scientific American for August 1965 (3). E. A. Walters (4) has shown that the older model for the C-C double bond has certain advantages over that of the molecular orbital theory. The strongest challenge to the dominant trend is that of J. W. Linnett in his book "The Electronic Structure of Molecules" (5). These papers are based upon Linnett's approach. They will attempt to carry his approach further in two ways: first, by suggesting new models in atomic structure; second, by proposing to abolish resonance hybrids. Before proceeding with these two proposals, a brief review of Linnett's ideas will be combined with suggestions for simplification of his fundamental postulates.
Consistent with the requirement of minimum energy as determined by the positive charge of the nucleus, the valence elec trons in an atom arrange themselves around the kernel of that atom according to the following postulates: (1) All electrons have electrostatic repulsion for one another. (2) Because of their magnetic interaction, a t a. given separation two electrons of opposite spin have less repulsion for each other than two electrons of the same spin have for each other. (3) The electrons in the valence shell tend to minimize their mutual repulsion.
The second postulate is equivalent to one of the many ways of wording the Pauli principle: two electrons of the same spin do not form close-pairs. Occasionally, the Pauli principle is stated in a form that implies belief that the principle causes electrons to behave in a certain way. On the contrary, the Pauli principle, like any scientific law, is a description of observed behavior. Figure 1 illustrates the application of the postulates to Ne, F-, or 02-. The arrangement of the valence electrons a t the corners of a cube as shown minimizes their repulsion a t that distance from the nucleus. This arrangement places electrons of the same spin farther apart (across the diagonals of the cube) compared with the distances between electrons of opposite spin (along the edges of the cube).' No electron is close-paired with another. Thus, although one may continue to use the common electronic symbols he should remember that they do not imply the presence of any close-pairs.
The Electron Repulsion Theory of Electron Configuration
In preliminary form, to which details may be added later, the electron repulsion theory may be stated as follows. Based in part on a paper presented as part of the Alfred Werner Centennial Symposium before the Division of Inorganic Chemistry a t the 152nd meeting of the ACS, New York, N. Y., S e p tember 1966. The figures were drawn by Madeline Weiss. In his book (6) Linnett does not represent atoms ss cubes. However, the cube is equivalent to Linnett's pair of tetrahedra. EDITOR'SNOTE The second paper will appear in the May issue. I t will discuss the models presented in this paper as an alternative to reti onitnee hybrids.
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Figure 1 . (Left) Ne, F-. 02; showing only the eight vdence electrons. Four electrons of one rpin ore reprented by open circler; the four electrons of the opposite spin are represented by Rlled-in circler The arrangement of the eight electrons ot the corners of a cube gives minimum repulsion among them. Two electrons of opposite spin have less repulsion for each other than two electrons of the some spin hove for each other. Therefore, electrons of the some rpin are farther apart, acros the diagonals of the cube facer; and electrons of opposite spin are closer, along the edge. of the cube. No electrons ore in close-pairs. Figure 2. (Center) Ne, F'-, or OP- viewed from a n angle different from the viewpoint of Figure 1 . The four valence electrons of one rpin, reprerented by open circler, ore ot the corners of one tetrohedron. The four volence electrons of the opposite rpin, represented by black circler, ore ot the corners of the other tetrahedron. Within the cube, four electrons of the same rpin occupy the corners of a tetrahedron. Figure 3. (Right) HF. The two tetrahedra of Figure 2 now share one corner, as the two electronr of opposite spin are drown toward the proton by its positive charge. Although the remaining six electrons ore in the same plane they are not close-paired. The kernel d the fluorine atom is not shown.
A slight modification of the common symbols to indicate the two spin-sets by open and filled-in circles result,sin the following electronic symbols
Returning to Figure 1 and viewing it from a different angle (as represented in Fig. 2), one can see that in a fluoride ion the four electrons of each spin-set occupy the corners of a regular tetrahedron. This separation of the two tetrahedra, a consequence of the three fundamental postulates, remains unaltered as long as the fluoride ion is isolated. However, when a proton approaches the cube (Fig. 1) two electrons of opposite spin, having less repulsion than two electrons of the same spin, are attracted by the positive charge of the proton and drawn together to form an electron pair bond (Fig. 3). Thus the two tetrahedra (Fig. 2) now coincide at one corner. But, because of their mutual repulsion, the remaining six electrons in the two tetrahedra are not close-paired. They alternate, each equidistant from its adjacent electrons in the same plane, as shown in Figure 3. This situation may be represented by the electronic formula
in which the six circles a t the right represent the two bases of the two tetrahedra for the two d i e r e n t spinsets.
Figure4. (left) Fe Thesevenvalencaelectron~ofonsrpin,repreronted b y open circler and connected b y lines, are a t the corner. of two tetrohedro having one corner in common on the line joining the two kernels, whish are not shown. The seven valence electrons of the opposite ,pin, represented b y fllled-in circler, ore at the cornen of two other tetrahedro which coEach group of seven electrons forms incide only ot the common corner,. o ~ o i of r tetmhcdra each of whish sharer o comer with the other. The bond canrirb of one dore-pair. Figure 5. (Right) CnH4. Two pair8 of tetrahedra coincide. Each group of six electrons forms o pair of tetrohsdra each of which rharer on edge with the other. The double bond consists of two equivalent close-pairs. The kernels d the corbon atoms ore n d shown.
Because visualization of these d i e r e n t tetrahedra is essential to an understanding of further developments in the electron repulsion theory, one must learn to interpret the six circles in this formula as follows: first, the three open circles are an equilaternal triangle of three electrons of one of the spin-sets in the base of one tetrahedron; second, the three filled-in circles are another equilateral triangle of three electrons of the other spin-set in the base of the other tetrahedron; third, both interpenetrating equilateral triangles are in the same plane with all six electrons equidistant from adjacent electrons. Figure 4 is a similar representation of a fluorine molecule. Again, the only close-pair is the one shared between the two atoms. The corresponding electronic formula may be represented as
Figure 6. (Left) CzH2 The two pairs of tetrahedra coincide only a t the opposite corners a t which the electron pairs m e shared with the protons Each group of flve electrons f o r m o pair of tetrahedra, eoch of which share o face with the other. The bond consists of six electrons in one plane, none in close-pain. Figure 7. (Right) 0%.The magnetic moment of the oxygen molecule indicates that it has two more electrons of one spin than of the other. Thus flva electmns of one spin (open circle4 form two tetrahedra with o face in common; and reven electrons of the other spin (filled-in cirdwl form two tetrahedra with o corner in common. The bond consists of four electrons in the same plane,none in close-pairs.
in which the six electrons a t each end of the molecule are the two bases of the two tetrahedra for the two different spin-sets. For future reference, one should note that, in the Fz molecule as a whole, the seven electrons of each spin-set form two tetrahedra with one corner in common. Furthermore, one should note that six electrons of one spin-set can form two tetrahedra with one edge in common, as illustrated in Figure 5; and that five electrons of one spin-set can form two tetrahedra with one face in common, as illustrated in Figure 6. Ethylene (Fig. 5) has a C-C double bond in which both pairs of electrons are equivalent. Acetylene (Fig. 6) has a C-C bond which has no close-pairs; therefore it can be designated a 6-electron bond, in which all six electrons are in the same plane and each is the same distance from its adjacent neighbors. Thus, ?r electrons have no existence in either structure. The electronic formulas2follow:
H H I I H-C=C-H
and
H-CGC-H
Three of Linnett's most impressive successes are his formulas for oxygen, ozone, and benzene (5). His formula for O2 (Fig. 7) gives a simple explanation of a molecule which has two more electrons of one spin than of the other. Although the hond between the two oxygen atoms is a 4-electron bond, no electrons are in close-pairs. The hond consists of four electrons in the same plane halfway between the two nuclei: three electrons of the same spin and one of the opposite spin. The electronic formula may be written as
9 The electronic formulas in this paper ttre not identical with Linnett's. These represent an attempt at simplification in a way that deviates as slightly as possible from the familiar electronic furmulas, and yet gives a representation of the three-dimensional arrangement of the valence electrons. However, this paper does follow Linnett's convention that a heavy line represents a closepair of electrons and that a light line represents only two electrons of opposite spin.
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Pages 3 7 4 2 of Linnett's book (5) should be consulted for his discussion of the structures of the excited states of the oxygen molecule. Linnett's formula for ozone (Fig. 8) is also a striking success. Its electronic formula might be written as
The experimental value of the bond angle is 116.8'. According to the geometry alone, as shown in Figure 8, the expected bond angle mould be 120'. However, the
Figure 8. Os. The volence electrons of one rpin, represented b y open circler connected b y lines, form three tetrohedro. The valence electrons of the other rpin form three other tetrohedro with the reverse distribution. The central pair of tetrohedro coincide a t the upper comer. Eoch bond con$igtr of three electrons, none in close-pain.
unshared pair of electrons should be closer to the nucleus of the central atom than either of the 3-electron bonds. Therefore, one might expect the unshared pair to exert somewhat more repulsion on the two bonds than the bonds exert on each other. Thus the bond angle should be slightly less than 120°, as observed. Resonance is unnecessary for the structures of the Oz and O3 molecules proposed by Linnett. Furthermore, his structures are in agreement with the bond lengths: 1.21 A in 0%(four electrons), 1.28 A in O8 (three electrons), and 1.48A in HO-OH (two electrons). Impressive as are Linnett's answers to the problems presented by Oz and 08,still more impressive is his solution of the long-standing riddle of the benzene molecule. His structure (Fig. 9) requires neither resonance nor T electrons. Its electronic formula may be represented as H
in which the only close-pairs are those joining the hydrogen atoms to the ring. As with ozone, the bpnd lengths are consistent with ?-electron bonds: 1.34 A in CzHp(four electrons), 1.39 A in CSHS(three electrons), and 1.54 A in CzH6(two electrons). For the effect of the new structure upon the theoretical chemistry of aromatic compounds, Linnett's book should be consulted (5). Atom Models for the Representative Elements
The only atoms that can be described exactly by wave mechanics are those that have one electron such as H, He+, and LL2+ However, atoms, like those of the alkali metals, that have only one valence electron can be represented fairly well. 208
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Thus one might say that any atom having one valence electron can be described adequately by wave mechanics. Such an assumption leaves a large proportion of the elements outside the sphere of exact wave mechanics. This situation is not serious, because much of what is often taken as the result of predictions made by wave mi:chanics is not such at all, but, rather, the result of the study of the experimental facts systematized in periodic tables. On the other hand, the electron repulsion theory cannot he applied to an atom with only one valence electron. At least two electrons are required for interelectron repulsion to be exerted within the valence shell. In this situation a possible solution of the dilemma is to limit the application of wave mechanics primarily to atoms that have one valence electron, and to apply the electron-repulsion theory to all other atoms. This answer to the problem requires one to admit, with only minor reservations, that the model of a molecule like that of SFe, for example, with its definite bond angles and bond lengths has to be essentially a static structure. Apparently, the freedom of motion assnmed for the electron of a "one-electron atom" becomes more limited for additional electrons as their number increases.
H Figure 9. CeHa The six tetrahedra involving electrons of one rpin, rapresented by open circles connected b y liner, alternate with the six tetrahedra involving ele~tronrof the other spin, represented by filled-in circler not connected b y liner. Eoch bond between o pair of carbon atoms conrirtr d three electrons, none in close-pairs.
Assuming that the structure of the hydrogen atom is described by wave mechanics, one may make the first application of the electron-repulsion theory to the helium atom. To minimize their repulsion, the two electrons are of opposite spin. Presumably, most of the time they maintain a position opposite each other, with the positively charged nucleus directly between them. Because these electrons are not valence electrons a picture of a helium atom is unnecessary. The addition of a third electron at the same short distance from the nucleus as the other two apparently involves too much repulsion. Accordingly, in the lithium atom the third electron remains a t a larger distance from the nucleus. Returning to Figure 1, one may regard the Ne atom as the pattern toward which the atoms of the second period are tending. Electrons of the same spin may be removed one at a time from the Ne atom, according to Hund's rule, to obtain the arrangements of the valence
Figure 10. Electronic structures of the valence shells of iond electronic ~ymbolrof) N, 0, and F. In an isolated otom no valence electron is closepaired with another.
electrons in the F, N, and 0 atoms given in Figure 10. The Ke atom of Figure 1 and the three atoms of Figure 10 may he viewed from a different angle, as in the top row of Figure 11. Careful examination of this row reveals the presence, or potential presence, of interpenetrating tetrahedra of two spin-sets. In the bottom row of Figure 11, the bases of these tetrahedra are
period. I n the Be atom the s electrons are of opposlte spin, are the maximum distance apart, and have the positive eharge of the kernel directly between them. In the B atom the third valence electron-the first p electron-encounters considerably more repulsion from the other two electrons: partly because the distances are smaller and partly because the shielding effect of the nucleus is diminished. The marked difference in electron repulsion between Be and B is strikingly reflected in the first ionization energies: Li, 5.4 ev; Be, 9.3 ev; B, 8.3 ev; C, 11.3 ev. In general, the inereasing repulsion of the electrons toward one another, in each atom, as more electrons are added to the atoms of the seeond period, from Li to Ne, is more than compensated for by the increasing kernel eharge. For example, the ionization energies of F and Ne are, respectively, 17.4 ev and 21.6 ev. One might expect that the larger kernel eharge (3+) on the B atom, eompared with that on the Be atom (2+), would mean that the first ionization energy of B should be higher than that of Be. On the contrary, the reverse is true. The lower value for the B atom corresponds with the larger amount of repulsion among the three electrons-making one of them easier to remove-as compared with the Be atom. Thus this method of picturing the B atom agrees, qualitatively, with the values for the ionization energies of Be, B, and
C.
Figure 11. Two other ways of looking a t the atoms of N, 0,F, and No viewed differently in Figure 10. In the upper row the cubes of Figure 1 0 have been tilted up on one corner. In the lower row the atoms are viewed from dnost the same ongle, but with liner drown differently to stress the two interpenetrating trigond pyramids in the Ne atom and incipient in the others. The I electrons ore at the apexes; the p electrons ore in the bares of the pyramids
shown as triangles. From now on, referring to these tetrahedra as trigonal pyramids will prove to be more convenient. Thus one might make the following statement: In the cube of the N e atom the two spin-sets m a y be regarded as two interpenetrating trigmal pyramids. One may designate the eleetrons a t the peaks of the two trigonal pyramids as s eleetrons, and those in the bases of the pyramids as p eleetrons. Although this designation persists back from Ne through N, the identification of s and p electrons is not so obvious in the C and B atom-nor is it necessary. Figure 12 gives tentative atom models for Be, B, and C, with N included for eomparision. The atom of Li is omitted because its structure can be described by means of wave mechanics, and because no eleetron repulsion in the valence shell is involved. For Be the eleetron repulsion theory can be applied again. However, the model for Be shown in Figure 12 is not intended to imply that the atom is two-dimensional. I n an isolated atmn, motion, of some kind, about the nucleus would seem to be inevitable. Upon examination of Figure 12, one can see that the addition of the differentiating eleetron in going from the Be atom to the B atom makes the largest increase in eleetron repulsion to be encountered in the second
In the C atom the seeond p electron, according to Hund's rule, has the same spin as the first p eleetron. Thus three of the four valence eleetrons are of the same spin. Also, following Hund's rule, in the N atom the third p eleetron h a the same spin as the other p eleetrons. Comparison of the models of N, 0 , and F atoms gives an explanation of the apparent reversal in the values of the first ionization energies of N (14.5 ev) and 0 (13.6 ev) similar to the explanation given for the values for Be and B. As can be seen in Figure 10, the sixth valence eleetron in the 0 atom suffers a more marked increase in repulsion eompared with the increase for the fifth electron in the X atom. Consequently, the 0 atom loses one electron more readily. When the electronic symbols of the atoms shon~nin Figures 10, 11, and 12 are being considered one must remember the following eonsequence of the fundamental postulates: I n an isolated atom no valence eleetron is close-paired with another. The remaining rows of representative elements can be pictured in the same way as the seeond row. However, one difference should be noted. Atoms of the other rows, when they form molecules of compounds
Figure 12. Electronic structures of the valence shells of iond electronic symbols ofl Be, 8, C, and N. The plus sign indicates the approximote location of the nucleus.
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like PFs, SFa, and IF7, may have more than eight electrons in their valence shells. Thus the electron repulsion theory should not be called the double-quartet theory. In considering these illustrated models, one must remember that they are not to scale relative to one another. Atom Models for the Related Metals
The importance of the cube and of the two trigonal pyramids in the proposed atom models for the representative elements suggests that perhaps another regular solid, the icosahedron, might serve as the pattern for building up models of the atoms of the related metals. As the Ne atom is the pat,tern for the representative elements, the Zn atom may be taken as the pattern for the related metals. Presumably, the s electrons of the Ca atom are similar in position to those of the Be atom. Assuming that they maintain their position in most of the ten related metals to Zn, one may represent these s electrons at the top and bottom of an icosahedron as shown in Figure 13.
Figure 13. The icorohedron and the corresponding model of the zinc otom, the pottern for t h e reloted metals. In the zinc otom t h e r electrons are a t the apexes of two interpenetrating pentagon01 pyramids; the d electrons are in t h e b a r e r of t h e pyramids.
If the s electrons are a t the apexes of the two interpenetrating pentagonal pyramids contained in the Zn atom, the two groups of d electrons outline the bases of the two pyramids. Apparently, the twelve outer electrons of the Zn atom occupy the twelve vertices of the icosahedron rather than the eight vertices of a cube. As in the Ne atom, application of the three postulates of the electron repulsion theory leads to the conclusion that adjacent electrons are essentially equal distances from one another and that the d electrons occupy positions in the pentagonal bases of the t,wo pyramids of the Zn atom in the same manner that the p electrons occupy the trigonal bases of the two pyramids in the Ne atom. Working back from the Zn to Mn, one can set up the models shown in Figure 14, as was done for the atoms from Ne to N. Then, beginning with Ca as analogous to Be,
The remaining atoms would be analogous but different because of the difference in the numbers of d and p electrons as arranged in an icosahedron instead of a cube. The second and third rows of related metals can he pictured in the same way as the first row. Thus the Zn atom may be regarded as the pattern for all the related metals. Because disagreement exists about the position of La in periodic tables, one should understand that this paper assumes that the third row of related metals begins not with La but with Lu. This assumption will be justified in the next section. As with the representative elements, no valence electrons in an isolated atom are close-paired. Valence electrons in a single atom tend to remain as far apart as possible, consistent with the force of attraction exerted by the kernel of that atom. Only when two or more kernels are involved can electrons be forced into closepairs. Even then, as has already been seen, for example in CIH2 (Fig. 6) and O2 (Fig. 7), many bonds between atoms do not involve close-pairs. More such examples will be considered in the following paper. Consistent with the difficulty of forcing electrons into close-pairs, one should not write electronic symbols as if any of the electrons were close paired. If, because of typographical problems, this apparent pairing is unavoidable, one should remember that the typography misrepresents the nature of an atom. As indicated in Figure 14, the valence electrons of the related metals are assumed to he the s and d electrons. Although evidence for this assumption has been presented elsewhere (6), one example may be mentioned here. The correspondence between the two groups of formulas VOa3-, CrOn2-, 1Lln041-, and P O P , Son"-, C1O4'- indicates that like P, S, and C1 the atoms of V, Cr, and Mn have respectively five, six, and seven valence electrons. One difference between this paper and the preceding reference should be noted. That reference made exceptions of Zn, Cd, and Hg. This paper assumes that the s and d electrons are the valence electrons for all the related metals.
one can postulate that the Sc valence shell is like that of B,
.&=
.&
and that the Ti valence shell is like that of C,
Presumably, V would resemble N as shown in Figure 14.
Figure 14. Electronic structures of t h e valence shells land electronic symbolrl of some related metals.
Atom Models for the Similar Metals
The arrangement of the s and p electrons in the valence shell of the Ne atom as two interpenetrating trigonal pyramids and the arrangement of the s and d elect,rons in the valence shell of the Zn atom as two int,erpenetrating pentagonal pyramids suggests that the valence shell of the last lanthanon, Yb, is composed of s and f electrons arranged as two interpenetrating heptagonal pyramids (Fig. 15).
-
Figure 15. T h e model for the vtterbivm atom, the pattern for the similar metals. In the ytterbium atom the s e k t r o n r are a t the o p e r e r of t w o interpenatroting heptogono1 pyramids; the f electron3 ore in the baser of tho pyramids.
As the Zn atom is the pattern for the related metals, the P b atom may be taken as the pattern for the similar metals. Presumably, the s electrons of the Ba atom are comparable in position with those of the Ca atom. Assuming that they maintain their position in most of the 14 similar metals to Yb, one may represent these s electrons in the Yb atom a t the apexes of two interpenetrating heptagonal pyramids. As shown in Figure 15, the two groups off electrons in the Yb atom outline the bases of the two pyramids. Working backward from Yb, one can set up models like those of Figure 16. However, at Ce the ambiguity
Figure 16. Eiectmnic structures of t h e valence shells land electronic symbols) of soma similar metolr.
referred to in the preceding section is encountered. Although some chemists consider Ce to be the first member of the lanthanons, this paper assumes that La is t,he first lanthanon. It also assumes that Ac is the first actinon, and that No is the last. These assumpt.ions are justified as follows. When the electron configurations of the lanthanons were first investigated, they were thought to be 4f"5d1 Gs2. Gradually, most of these configurations were found to be wrong. Most of the atoms do not contain 5d electrons. I n some of the most recent tables only La and Gd are listed as having a 5d electron. If this trend continues, none of the lanthanons will have one.
Actually, because the energy levels are so close, from a chemical standpoint the two current apparent exceptions could just as well be considered as normal. Such is the assumption of this paper: none of the atoms from La to Yb has a 5d electron. Thus the differentiating electron for each of them is an f electron, and they are all lanthanons. Consequently, the differentiating electron for Lu is the first 5d electron, and Lu is the first member of the third row of related metals. This viewpoint is consistent with the assumption that the valence electrons of the atoms of the similar metals are structured in a manner analogous to the arrangement of the valence electrons of all the other atoms: s and p electrons for the representative elements, s and d electrons for the related metals, s and f electrons for the similar metals. Immediately a question arises. If S (with two s electrons and four p electrons) forms S O P , and Cr (with two s electrons and four d electrons) forms CrO?, why does not Nd (with two s electrons and four f electrons) form a similar oxoion? Furthermore, why do none of the lanthanons form oxoions when ions such as MnOll-, MOO^^-, Ti02+,VOI1+, and Cr02+ are so common among the related metals? The answers to these questions are straightforward. Lanthanons have much less attraction for electrons than have the related metals. According to their reduction potentials and their reactivity with vater, they are better reducing agents than hlg. Thus their atoms have so little attraction for electrons that they cannot form the bonds required to hold oxygen atoms in oxoions. Apparently, thereason for this comparatively weak attraction for electrons is that the lanthanon atoms are so much larger than the atoms of the related metals. Although lanthanon atoms have little tendency to form covalent bonds, some of the actinon atoms do form oxoions. For example, U (with two s electrons and four f electrons) forms U022+,analogous to Cr022+. Apparently, the reason that the U atom forms the oxoion and the Nd atom does not is that the U atom (like the Cr atom) is enough smaller than the E d atom to have sufficient attraction for electrons to form bonds with 0 atoms. The resemblance of UOz2+ to CrOz2+is one confirmation that the number of valence electrons in the U atom (as well as in the Cr atom) is six. Therefore. in the'light of the foregoing emphasis upon the weal; attraction of lanthanon atoms for electrons, one may assume that the valence electrons of the similar metals are the sand f electrons. However, because most of their compounds are ionic, electronic symbols usually are not required. If they are desirable a t times, prohably writing them without using dots is sufficient, for example: La&) Ce(4e)
--
+ 3e+ 3e-
Laa+
Ce(le)'+
r ! d i r v + + cm4+ + I#-
In this list, the third equation is another example of the weak attraction lanthanon atoms have for electrons. The Ce4+ion may be the only exception to the rule that the highest charge on a positive monatomic ion is 3+. Volume 44, Number 4, April 1967
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The obvious explanation for the ionic valence of 3+ for all the similar metals is that they lose electrons so readily. This valence is not unique in correspondence with the third group of the representative elements, as was once thought. Most of the related metals also can have one valence of 3+; and several of the similar metals have a valence of 2+. Conclusion
J. W. Linnett has explained in a beautifully simple manner the structures of molecules. When his ideas are restated in the form of three postulates about the nature of electron repulsion, these postulates lead to a new theory of atomic structure. In this theory, atoms are pictured as built up in a regular way so that the valence shells of outer electrons are analogous for all three types of elements. In atoms of the representative elements the pattern is the arrangement of the eight s and p electrons in two
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spin-sets a t the corners of two interpenetrating trigonal pyramids, as in the Ne atom. In atoms of the related metals the pattern is the arrangement of the twelve s and d electrons in two spinsets a t the corners of two interpenetrating pentagonal pyramids, as in the Zn atom. In atoms of the similar metals the pattern is the arrangement of the sixteens and felectrons in two spin-sets a t the corners of two interpenetrating heptagonal pyramids, as in theYb atom. Literature Cited (1) (2) (3) (4) (5)
GILLESPIE,R. J., J. CHEM.EDUC.,40, 295 (1963). BENT,H. A,, J . CHEM.EDUC.,40, 446 (1963). BLACK. M., Scientific American, August, 1965, p. 100. WALTERS, E. A., J. CHEM.EDUC.,43, 134 (1966). LINNETT,J. W., "The Electronic Structure of 1Iolecules. .4 New Approach," John Wiley and Sons, Inc., Kew York, 1964.
F.,SHEPARD, R. A,, VERNON, A. A., I N D ZUP S., "General Chemistry" (3rd ed.), W. B. Saunders Co., Philadelphia, 1965.
(6) LUDER,W. FINTI,
