( Henry A. Bent University of Minnesota Minneovolis
II
Tangent-sphere models o f molecules, 111
Chemical Implkations of Inner-Shell Electrons
In Parts I and I1 of this series (I), it was proposed that the Pauli Principle may play a more important role in chemistw than has previously been supposed. The Pauli Principle in its mathematical form (here x, represents the spatial and spin coordinates of electron i) implies (Part I ) that electrons of parallel spin cannot be a t the same place a t the same time. This statement does not necessarily exhaust the physical implications of the Pauli Principle, however. Indeed, an examination of the shapes of molecules has suggested (1) that the behavior of electrons in combined atoms may usefully be described-at least to a first approximation in many c a s e e b y this stronger statement: The elecfron clouds of electrons with parallel spin do not overlap. In effect an electron appean to interact with other electrons of the same spin as if it had a hard-sphere radius equal approximately to onehalf its de Broglie wavelength. This radius may be called the electron's de Broglie radius. If, on this supposition, an electron's density distribution function is taken to be finite and uniform over its de Broglie radius, and beyond this zero, one obtains the computation~lly useful charge-cloud models introduced by Kimball and his co-workers in the early 1950's (2). Interesting in this context is a statement made 25 years ago by Weisskopf in a paper on the self-energy of an electron (3). The presence of an electron in a vacuum (considered from the viewpoint of Dirac's theory of the positron) causes a considerable change in the distribution of the vacuum electroas because of a peculiar effect of the Pauli exclusion principle. According to this principle it is impossible to find two or more electrons in a single cell of a volume ha in phase space. If two electrons of equal spin are brought together to a small diatance d, their momentum difference must be a t leaat h/d. This effect ia similar to a repulsive force which causes two particles with equal spin not to he found closer together than approximately one de Broglie wavelength. As a consequence of this we find a t the position of the electron a "hole" in the distribution of the vacuum electrons which completely compensates ita charge. But we also find around the electron a cloud of higher charge density coming from the displaced electrons, which must be found one wavelength from the original electron. The total effect is a broadening of the charge of the electmn.
The notion of "hard" electrons-whose modern quantum-mechanical counterpart is expressed in such Thk study was supported by a grant fmm the National Science Foundation. 302 / Journal o f Chemical Education
phrases as "localized orbitals," "zero squared-overlap," and "the strong orthogonality condition" (4)leads to models of covalent compounds in which the electrons, or the electron pairs, or, less specifically, the Fermi holes associated with these electrons are repre sented by tangent-spheres (1). Specifically, the spheres are tangent to each other for first-row elements to the right of beryllium in the periodic table. If we consider the construction of combined atoms of these elements from their valenceshell electrons and atomic cores (nuclei plus innershell electrons), we may say in these cases that as the valence-shell electrons approach their atomic cores they touch each other before they touch strongly the inner-shell electrons. For second- (and later) row elements just the opposite happens. In tetrahedral coordination the shared valence-shell electrons touch their neon-like cores before they touch each other. This simple fact has a number of interesting chemical implications. Linnett has suggested (6) that the configuration of maximum probability of the eight electrons in the valenceshell of neon, four of one spin and four of the other, is one in which, owing to the Pauli Principle, the electrons of each spin-set are disposed a t the corners of a regular tetrahedron a t whose center lies the atomic core, with the two separate tetrahedra, one for each spin-set, anticoincident (51, as shown in Figure 1. An arrangement of L-shell electrons like that in Figure 1, without the distinction regarding electron spin, was given by Lewis in 1916 We shall refer to this electron configuration, therefore, as the LewisLinnett octet configuration, or the Lewis-Linnett cube. Regarding this configuration for neon and related ions, Linnett has recently written (5a), "It must, in all honesty, be stressed a t this stage that there is no proof that this is the correct way to regard the electron octet in the second quantum shell. However, the general considerstiona about spin. . together with simple ideas regarding the effect of charge, suggest that such an attitude or hypothesis might he successful."
.
This hypothesis, called by Linnett the "Double Quartet Hypothesis" (5), has been used by its author to describe an elegant and heuristically interesting solution to a perennial classroom problem; namely, that of describing in correct and simple physical terms the electronic structures of such well-known anomalies in classical valence theory as molecular oxygen, nitric oxide, and nitrogen dioxide. The suggestion that the Pauli Principle may hold in a strong form--so that it is meaningful to say, for example,
nonbonding electrons in the L-shell of a second-row atom strive toward and, in the presence (see later) of expansible lone pairs in the valenceshell, may some times attain the Lewis-Linnett anticoincident configuration illustrated schematically in Figure 1.' For now consider the attachment to this core of a bonding pair; e.g., an H- ion, which contains electrons of each spin type. The best location for the bonding pair-best in the sense of permitting close penetration of the bonding electrons to the heavyatom nucleus while avoiding as much as possible overlap of the bonding electrons with core electrons of identical spin-is for the spin-paired and the space paired electrons of the bonding pair to settle down on one face of the L-shell Lewis-Linnett cube. Placement of another pair on an adjacent face (see arrows, Fig. 1) would produce a bond angle of 90°, close to that obsemed for the hydrides of phosphorus, arsenic, antimony, sulfur, and selenium. That the bond angle in hydrogen sulfide is near 90" rather than the 180" that would be expected if the bonding pairs settled down on opposite faces of a LewisLinnett cube-as presumably they would (Part IV) if there were no other electrons present in the heavy atom's valence shell-stems from the fact that there are additional electrons in the valence shell, the lone pairs. These lone pairs, unlike the bonding pairs, are relatively free to spread out over the exposed faces of the heavy-atom core (discussed later). Their delocalieation presumably occurs more effectively, i.e., with a greater decrease in electronic kinetic energy, when the bond angle is 90" than when it is 180". This admittedly is an important conjecture, one that merits further consideration; however, as its quantitative investigation would require methods very dierent from those of the present study, we shall not pursue at this time the interesting problem of the self-energy of lone pairs attached to large atomic cores. I n the present explanation of the bond angles in heavy-atom hydrides, s-p promotion energies and d Figure 1 . The LewirUnnett onticoincident octet conflgvration for neon. orbitals have not been mentioned explicitly. From the T h e r m d l block circles a t t h o s v b e corners lie o t t h e centers of a set of tetrapoint of view of the present treatment, which deals the 1-shellelectronrof one hsdrolly a r r a n g e d tongentspheresthatrepre~~nt spin-typs. Thermallopencircle~repre~ent,~~~re~p~ndingly,thefourL-shelldirectly with the electron density distribution in electrons of the other spin-type. Envelopes of these 1-shell electrons are molecules without going through the intermediary of indicated b y the outer liner. The inner, stippled sphere represents t h e one-electron orbitals, these terms are not particularly K-shell electron poir of neon a t whore center lies the neon nucleus I r m d circle). Arrows indicote directions of best approach for coincident useful in describing the physical factors that are electron pairs. It m a y b e noted t h a t in the L e w i d i n n e t t "anticoincident" believed to govern the geometries of the hydrides of configuration t h e t w o spin-sets ore not completely antisoincident. The groups V and VI.= mutually tangent spheres represented b y t h e m o l l black circler p o r t i d l y overlop the mutvoily tangent spheres represented b y r m d l open circler. Evidently a Lewis-Linnett cube carrying a net positive charge acts as an acceptor of localized electron Structural Implications of the Lewis-Linnetl Odel pairs at its cube faces. Occupancy of all six faces by Configuration bonding pairs would produce an octahedral arrange ment of ligands. This is a not uncommon ligand Bond Angles geometry about the cores PS+and So+. It is also the Explanation of bond angles in the hydrides of groups ligand geometry about the isoelectronic cores Mg2+ V and VI has been a troublesome problem in valence and Na'+ in ionic, sodium chloride-like lattices. theory (8). Why do the nearly tetrahedral bond Interestingly, many such lattices (40% of the alkali angles for the first-row hydrides (NH3 = 107.3'; halides, for example) occur well outside the range of H 2 0 = 104.45") drop suddenly to nearly 90' in the stability predicted for them by the classical radius second row (pHa = 93.3'; H2S = 93.3") and remain ratio rules (9). near this value the rest of the way down (AsHa = 91.S0, SbHa = 91.3"; H2Se = 91°)? This question receives a simple answer if, following 'The degree to which this inner-shell oon6guration is attained Linnett, it is assumed that--because of electrostatic by second-row atoms in chemical oompoundw may depend in repulsions between electrons of opposite spin-the part upon the nature of the attached atoms. See Part IV to be eight spin-paired (but not necessarily space-paired) published in the July issue of THIS JOURNAL, 42, 348 (1965). that an atom's valence-shell electrons press harder against their atomic core than against each othersuggests a further test, of application, of Linnett's point of view. Combined with the large-core model, the hypothesis of the Pauli Principle in a strong form suggests the possibility of using the locations of valence-shell electrons in chemical compounds--as reflected, for example, by bond angles and bond lengths-as probes of the shapes and sizes of atomic cores. It might in this way be possible to study departures of the neonlike cores of second-row elements from the spherical symmetry often predicted for them by applications of Unsold's theorem (7)-a theorem that ought to be regarded, however, more as a mathematical statement about spherical harmonics than as a physical statement about the shapes in chemical compounds of closed shells in many-electron atoms. The purpose of the present paper is to discuss some experimental facts that appear to bear upon these points. While a study of atomic core sizes might seem to hold little promise of offering interesting insights into the main body of chemical theory, it will be found that from such a study emerges a picture of chenical bonding that encompasses as particular cases covalent, ionic, and metallic bonds.
Volume 42, Number 6, June 1965
/ 303
Table 1. Trends in Bond Length (Bond lengths in angstroms. Bond length differences in parentheses.)
CHI-CHa 1.534- .
. . (-0.060)
CH8-NH2
1.8668~. CHaSiHs
. . (-0.OU9) . . . 1 . 8 5 ~. ~. . (-0.040) . . . 1.8177 . . . (-0.034)
.
CHAH
. . 1.474 . . . (-0,047) . . . 1.427
CHa-pH1
. . . (-0.042)
CHISH
"ALLEN,H. C., JR., AND PLYLER,E. K., J. C h m . Phys., 31, 1062 (1959). WKB,R. W., (1957). BARTELL, L. S., J. Chem. Phys. 32,832 (1960).
Conversely, a Lewis-Linnett cube that carries a net negative charge should act as an electron donorpresumably most effectively off its eight cube corners. This is the cation geometry about the C4- ions in beryllium carbide and about the 0%ions in isoelectronic lithium oxide--and, indeed, about the anions in any binary compound that, like Be& and LizO, adopts the anti-fluorite structure. I n summary, a selection of bond angles suggests that it may be profitable to consider that inner-shells in combined atoms have less than spherical symmetry. This fact cannot he disputed rigorously-if for no other reason than that an electron cloud with a finite polarizahiiity in a nonspherically symmetrical environment must suffer some di~tortion.~The moot question is, are departures of inner-shells from spherical symmetry chemically significant? If they are, this fact ought to he reflected in the shapes of chemical compounds, and also in their sizes. Bond Lengths
The changes in hond lengths tabulated in parentheses in Table 1 show an interesting discontinuity a t the silicon-phosphorus position (10). The decrease in bond length at this position is not as great as would be expected from subsequent hond length decreases in the second row, or as would be expected from bondlength decreases in the first row. All hond lengths considered, the expected difference a t the siliconphosphorus position is about 0.053 A [0.040 (0.0600.047)], not 0.009 A. The discrepancy is 0.044 A. Alternatively, one may note that the increase in bond length to carhon in going from a first-row to the corresponding second-row element is rather less for group I V than for groups V, VI, and VII. Compared to the lengths of the bonds to carbon from carhon,
+
'Textbook discussions of one-electron orbital theories often stop short of a full description of the eleetmn density distribution in molecules. Generally they stop with a listing of occupied (and unoccupied) orbitals. This treatment may produce misleading impressions of the distribution of electrons in molecules when the basis orbitals that are used overlap geometrieelly in s p a c e a s they do, for example, in the molecular orbital description of a. double bond. Properly the formalism of a product function formed from (probably fictitious) one-electron orbitals should he carried two stages further; the wave function should be rendered antisymmetric [otherwise the full force of the Pauli Principle is not represented and equation (1) ia not satisfied]; and, following this, there should be performed upon the square of the wave function n multiple integration [THIS JOURNAL 40. 446 (1963). . .. footnote 11. As a substitute for the lest stenwlhh i n prwrw would bc' very diftieult t u prfmm all k w l { . s ~ i mny bc mud,. o i rile configurn~iunof ~ r ~ w i ~ npmlz,ldtly. uw ' A fnvt r~nplmsi,crlfor mlny y c ? h) ~ l h l t s r ir K . Faims.
AND
CHI-F
. . . 1.385
.
. . Lf84
CHa-C1
PIERCE,L., J. C h m . Phys., 27, 108
nitrogen, oxygen, fluorine, and silicon, the lengths of the bonds to carbon from phosphorus, sulfur, and chlorine are abnormally long, or the bond from silicon to carbon is abnormally short. This may be explained by supposing that in the tetrahedral silicon atom of methyl silane the two spinsets in the silicon atom's Lshell are (suitable to the observed geometry of the molecule) in angular coincidence with each other, forming thereby an inner tetrahedron of electron pairs, with the atom's four valence-shell pairs nesting on the four faces of this tetrahedron, as shown diagrammatically in Figure 2 ;and by supposing also that, by contrast, the spin-sets in t h e L shells of the phosphorus, sulfur, and chlorine atoms of the other molecules have developed-perhaps owing (indirectly) to the presence in their valence-shells of unshared electrons-a degree of mutual anticoincidence, in the sense illustrated in Figure 1. Bond angles in the molecules lend support to these suppositions. Thus, as previously postulated for phosphorus and sulfur and as now postulated also for chlorine, the bonding pairs about these atoms are presumed to nest on the faces of atomic cores that in the present instances may be (at least approximately) in Lewis-Linnett octet configurations. For either Lshell spin-set taken separately, this configuration corresponds to tangency between the bonding pairs and the L-shell electrons along an edge, not a face, of the inner tetrahedral spinset (Fig. 1). The result is a bond longer than it would otherwise he. A similar change in packing between valence- and inner-shell electrons presumably occurs in going from tetrahedral PCla+ to octahedral Pel6-; as expected the hond length increases, by approximately 0.09 A. Even larger changes are observed in corresponding instances for the larger germanium and tin atoms. On the other hand, the increase in bond length from PC13 (bond angle 100.lo) to PC1,- is much less, about 0.03 A. And in going from SbFn (hond angle 88") to SbFsZ- (bond angles near 90°), there is essentially no change in bond length, despite the antimony atom's increase in electron-pair-coordination-number from 4 to 6; if anything, the bonds to the equatorial fluorine atoms in S b F S 2may he slightly shorter than the bonds in ShF3. These changes are the changes anticipated if near-90' valence angles in unstrained systems reflect the presence of underlying Lewis-Linnett anticoincident cores. The angle between unstrained covalent bonds to atoms whose valence-shell electronpair-coordination-number is 4 frequently is found to he closer to 90' than to 109' (the tetrahedral angle) for second-row elements, but never for first-row elements.
Table 2. SiSi 2.35
eke 2.450
Sn-Sn 2.81
. . . (-0.17
. .
. . . (+0.055) .
Further Trends in Single Bond Lengths
P-P .
2.18 .
. . . (+0.09) . .
.
+
Sh-Sh
. 2.90 . .
- 0.171
=
S S
. 2.04
Cl-CI
. . . (-0.05)
. . . 1.99
Br-Br
. . - 0 . 1 . . . 2.321 . . . ( - 0 . 3 ) . . . 2.283 . (-0.04) . .
Significantly, the atomic cores of second-row elemeuts may adopt the Lewis-Linnett octet configuration. Another illustration of the effect of a presumed change in inner-shell configuration on bond lengths for bonds involving second-row, third-row, and fourthrow elements of the periodic table is given in Table 2. The tabulated bond lengths in Table 2 are for structures of the elements in which each atom is bound to its neighbors by 8 - N bonds, where N is the group number of the element. Bond-length changes are tabulated in parentheses. Again, these changes show an interesting discontinuity at the group IV-group V position. As in Table 1, the decrease in bond length a t this position is not as great as would be expected from subsequent bond-length contractions in the same row; indeed, for the third and fourth rows, the group Vgroup V bonds are longer than the group IV-group IV bonds. While these bond lengths are probably not as accurate as those tabulated in Table 1, it may be estimated t,hat. the bond-lengthening effect in passing from a coincident core configuration in group IV to (probably at least partially) an anticoincident core configuration in group V is, for the second row, per atom, about '/2[0.14 (0.14 - 0.05 ) X (13/5) [(13/5) from top row, Table I]
. .
Se-Se
As-As
. . 2.49s
. . (-0.14
0.10 A
I n summary, the change from a coincident to an anticoincident core appears to make bonds to secondrow elements l o n ~ e rthan they would otherwise be by about 0.04-0.10 A.
Te-Te
. 2.864
1-1
. . . (-0.203) . . . 2.661
A theoretical estimate of this effect can be made with the aid of Figures 2 and 3. I n these figures T and T' represent the centers of the tetrahedral holes occupied by the cores C4+ and Si12+ (or PIS+), r e spectively. 0 represents the center of the siliconcarbon (or phosphorus-carbon) bonding pair, 0' that of one of the L-shell pairs about Si12+ (or PI3+). Point A in Figure 2 represents the center of the equilateral triangle whose vertices are the centers of the uppermost %shell pairs about SiIz+. If we let the radius of the Si"+ (or P'a+) L-shell pa115 R = the radins of the Si-C (or P-C) bonding pair
r
=
then in Figure 2 00' = R
O'A
+r
(2/d3)r
=
TrA = (l/v%)r
and OA
=
d ( 0 0 ' ) ~- (O'A)>
=
g R Z 2rR - (1/3)rs
+
Hence, for a coincident L-shell T'O
=
(I/%%)?
+ d R 2 + 27R - (1/37?
Similarly, in Figure 3 T'B = ( l / d ~ ) r
+
OB = ~ R Z 2rR
and hence for an anticoincident L-shell T'O
=
+~
(l/d?)r
+
R Z21R
With appropriate values for r and R, T'O for a coincident L-shell (Fig. 2) corresponds to one half the silicon-silicon distance- in elemental silicon. Using for R the value 0.77 A given by an equation to be discussed later (R's precise value is not critical to the present discussion), one calculates from equation (6) and the Si-Si distance in silicon (Table 2) that rsiw+
=
0.32 d
(10)
From this it is calculated in the Appendix that rpl.+ =
Figure 2 (1eftl.Tangent-sphere model of methylsilane. The methyl g r o v p i r shown a t the t o p , the rilyl group o t the bottom of t h e flgure. The tetrahedral cluster of rmoll spheres represents the silicon atom's coincident 1-shell. Stippled sphere, represent silicon's valence-shell electrons, t h e bottom three Si-H bonds, t h e upper one the Si-C bond. The three l a r g e spheres a t the t o p represent the C-H bonds of the methyl group. Figure 3lrightl. Valence-hell-inner-rhell inner-shell.
geometry for an anticoincident
0.2Ss d
(11)
An estimate can now be made of the PC14+--PC16bond-length difference. The R valye for a P-C1 bond (see later, Part IV) is 0.70 A, a value valid for both PClr+ and P C k . That is to say, in the present model the entire increase in bond length,
-
~ P C I ~- ~PCIA+
A(T'T)
(12)
is attributed to the effect of changing from a coincident to an anticoincident L-shell; i.e., to the change Volume 42, Number 6, June 7 965
/
305
b
0
Figure 4. Possible electronic rtrvctvres for HFa; ond the tangent-sphere model of F*. lo1 Tangent-sphere model of Fz. Small open circler represent the centers of the valence-shell elestranr of one molecular spin-set. The other valence-shell seven-electron spin-set (not shown) would be coincident with the flrst set in the bonding region, but not In tho nonbonding region. Black dots represent the fluorine corer ib) Proposed model of the electronic rtruslure of HFn; Shown ore two partially merging Lewis-Linnett mticoincldent 1-rhellr. Block dots ot the cube centers represent the fluorine corer; the smaller dot between represents the proton [or the He2+ nvclevr of coniectured Heh; PIMENTEL, G. C., AND SPRATLEY, R. D., I . Am. C h m . Sor., 85, 8 2 6 (196311. (4Tangent-sphere model of H h - for the core of wo coincident 1-rhells. The F.. .F distance predicted for this structure is olmort half on angstrom too large.
in T'O in going from Figure 2 to Figure 3, R and r constant. Using equations (6) and (9), one finds that for r = 0.2% and R = 0.70 ( T ' O ) - (T'O) = 0.097 A. Anticoincidrnt Coincident L-shell L-shell ew. (9) esn. (6)
(13)
This is to be compared with the experimental value 0.09 A,' Similarly, for the bond-length difference ~ H , P - c ~H ~~ H , s ~ - c(Table H~ I), one finds that for R = 0.66 A (see later), (.T ' O..L ,-: - (.T ' O h - c- = 0.060 r = 0.28. r = 0.32 Anticoincident Coincident L-shell L-shell
(141
Thus, with the present model one calculates that the P-C bond in methyl phosphine should he 0.06 A longev than the Si-C bond in methyl silane. In fact, the two bonds are approximately the same length (Table 1). Now the bond-shortening effect of a simple L-shell contraction in going from the silicon core to the phosphorus core is by the present model (T'O) r = 0.32 Coincident Lshell
-
(T'O) = r = 0.28. Coincident L-shell
0.031 A.
(15)
(This may be compared with the change in bond length in going from methyl phosphine to methyl sulfide of 0.040 A.) Summat,ionof equations (14) and (15) shows that the development of anticoincidence in the L-shell of This good agreement between the cslculated and observed values is partially fortuitous. It has been asaumed in the caleulcttion that the radii of the Lshell electrons do not change as the spin-sets go from a coincident to an anticoincident configuration. Owing, however, to diminished electron-electron repulsions in the anticoincident configuration, the electrons probably contract as they pass to the latter configuration. The present caloulation suggests that this contraction ia not large.
306
/
Journal of Chemical Education
the phosphorus atom of methyl phosehine-for vhich the appropriate value of r is 0.28~-4-increases the length of the phosphorus-carbon bond over what its length would he for a coincident L-shell by approximately 0.06 0.03, = 0.09, A. This estimate of the bond-lengthening effect of L-shell anticoincidence agrees well with the previous estimates based upon the experimental data in Table 2 and upon the bond lengths in PCllf and PCI6-. That the full effect of L-shell anticoincidence is not observed experimentally in the case of methyl phosphine may be laid to two effects (probably related): the bond angle HPC in methyl phosphine is probably greater than 90' (in the electron diffraction studies on this molecule the HPC angle was assunled to be 96.5"; in dimethyl phosphine, the CPC angle is 99.2 0.6"); and the methyl group in methyl phosphine probably tilts toward the lone pair on the phosphorus atom (11). Both effects would tend to decrease the length of the phosphoruscarbon bond. In the examples discussed above, L-shell anticoincidence was invoked to explain diminished bond angles and enhanced bond lengths. For bonds to second-row elements of groups I V and V the bondlengthening effect has been estimated by calculation and direct comparison of experimental data to be approximately one tenth of an angstrom. In some instances, by permitting electron clouds to overlap in a manner that would not otherwise be possible, owing to Pauli repulsions between electrons of parallel spin, L-shell anticoincidence may have a pronounced bond-shortening effect. Such a case, perhaps, is the hydrogen-bond in the bifluoride ion. This hydrogen bond is several tenths of an angstrom shorter than other known hydrogen-bonds (18) and it has the largest bond energy, 37 kcal/mole, of any hydrogen bond reported to date (13). %. schematic representation of its electronic structure is proposed in Figure 4, which sbows also an electronic fornlulation for a hydrogen-bond between coincident L-shells, such as in ice.
+
+
In the hydrogen-bond of HF2- one L-shell electron in each fluoride ion is oriented toward the face or "pocket" of the corresponding spin-set in the adjacent fluoride ion. Following the terminology introduced previously ( 1 ) to describe short intermolecular contacts between electron-pair donors and acceptors, the bydrogen-bond of H R - may be described as two partially coincident protonated one-electron-pocket bonds. Other implications of the Large Core Model
The hypothesis that for second-row elements the valence-shell electrons as they approach their atomic cores touch their atomic cores before they touch each other carries with it a number of qualitative implications that are largely independent of assumptions regarding the precise configuration of the inner-shell electrons. These implications of the large-core model fall into two categories, depending on whether they stem from gross size effects or from the presence in the valence shell of dispersed lone pairs. Gross Size Effects
The model pictured in Figure 2 illustrates: Why bonds to second-row elements are longer, and why ionization potentials and electronegativities of second-row elements are smaller, than those of the corresponding first-mw elements. Why the accessibility of second-row elementa to additional electrons (beyond an octet) is generally greater than that of firsbrow elements, as reflected by
(1) Increased reactivity toward nucleophilic reagents, (2) Increased ability to form intermolecular complexes with electron donors (id), (3) Increased ability to expand valence-shell eleetron-pair quartets to quintets and sextets, and (4) Increased back-bonding ability, as evidenced by (a) The stabilization of low oxidation states (16), (b) The anomslously low cohesive forces of siloxanes (16) and low dipole moments of the chlorides and fluorides of silicon (17), (c) . . The trans-orienting effect in inorganic substitution reactions of heavy-atom ligands (18), (d) The formation of relatively short bonds to first-mw elements with lone pairs; this makes such bonds as Si-0 and P-O unusnally stmng-thereby diminishing the thermodynamic probability of catenation--and such bond angles as SiOSi [in silicatea and (HSi)zO] and SiNSi [in (HIB)~NIunusually large (19).
In short, the model in Figure 2 illustrates why second-row elements are better adonors and better Tacceptom-but poorer s-donors (20)-than first-row elements. The model provides also a rationale for the existence of "diagonal relationsbips" in the periodic table (21). And it accounts for the difficulty of multiple-bond formation between second-row elements. For if the inner-shell electrons of second-row elements touch strongly the valence-shell electrons before the valenceshell electrons touch each other, it follows as illustrated in Figure 5 that in the formation of a multiple bond between second-row elements the inner-shell electrons of adjacent atoms come close to and may touch each other before the bonding pairs touch simultaneously both sets of inner-shell electrons (22). Inner-shell-inner-shell repulsions in multiple-bond formation should diminish in importance as the atomic
cores shrink in size. While no compounds containing silicon-silicon double bonds are known, structures with sulfur-sulfur double bonds have been proposed; e.g., S 4 F i (83). Conventional triple bonds between second-row elements appear quite impossible to make. Finally, it may be noted that the trigonal bipyramidal arrangement of five valence-shell electron-pairs about an atomic core does not fit nicely about either a coincident or an anticoincident L-shell. Indeed, it appears that whereas electron-pair-coordination-numbers 4 and 6 occur fairly commonly, electron-paircoordination number 5 (EPCN 5) occurs much less commonly. And when it does occur, the compound is often relatively unstable, as illustrated, for example, by the gas-phase dissociation of PCl5 to chlorine and PCla (EPCN 4), and by the solid-phase disporportionation of PC15 to PCLf (EPCN 4) and PCla- (EPCN 6). This instability is illustrated, also, by the relatively high reactivities of SF1 (a versatile fluorinating agent) and CIFa [the analogous iodine compound disproportionate~to IF1+ (EPCN 4) and IF,- (EPCN 6) (84)], and by the well-known acceptor properties of arsenic and antimony pentafluoride. Dispersed lone Pair Effects
Dispersal of a lone pair over a large atomic coreover several faces of a Lewis-Linnett cube, for example -should lower the basicity of the lone pair and reduce its contribution to the molecular dipole moment. Thus, phosphine is a weaker base than ammonia, by perhaps 23 pK units, although phosphorus is less electronegative than nitirogen. Also, the dipole moment of phosphine is only one third that of ammonia. Further, while the substitution of a methyl group for hydrogen in ammonia increases the basicity 1.4 pK units and decreases the molecular dipole moment, the same substitution in phosphine increases the basicity approximately 14 pK units (26) and increases the dipole moment (86). It has been said that this change in basicity is probably the largest effect of a modest structural change known to organic chemistry (27). Its explanation may lie in the fact that replacement of a hydrogen atom in phosphine by a methyl group probably increases the bond angles about the phosphorus
Figure 5. Tangant-sphere model of the hypothetical HnSi=SIHa structure. Large spheres represent volsnco-shell electron pairs; smdl spherss represent silicon atom Lshell electron p d n .
atom6 leading thus to a compression of the lone pair on the phosphorus atom and hence to an increase in basicity-and perhaps also to an increase in the molecular dipole moment. That the basicity of a localized lone pair on phosphorus may indeed be very See Table 1, footnote c. Volume 42, Number 6, June 1965
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307
great, reflecting directly the electro~~egativity of this atom, is shown by the proton location in, and the low acidity of, the anion HPO? in which the OPO bond angles are 110". These brief remarlcs on the qualitative implications of the large-core model suggest that a more quantitative confrontation between the model and experiment might prove interesting. Appendix The effect of nuclear charge on the size of the I,-shell electrons of an atom may be estimated ss follows. The energy of the L-shell electron6 when the spin-sets are coincident is E = 4V.. 6V,, 4V, ST, (A-1) where V,, = electrostatic energy of mutual repulsion of the two electrons of a coincident &hell pair. Vp, = electrostatic energy of mutual repulsion of two L-shell eleotron pairs. V , = electrostatir energy of attraction between an L-shell pair and the atomic core (nucleus). T. = kinetic energy of an L-shell eleotron.
+
+
+
If, following Kimball and co-workers (8), each electron is represented by a uniformly charged sphere of charge -e and radius 1, these spheres being tangent to each other, V.. = (6/5)e2/r (A4 V , = 4e9/2r (A4 V,. = -2ZeP/(3/2)L'2r (A-4) where Ze is the charge on the atomic core (the nucleus plua innershell electrons). By dimensional arguments the electronic kinetic energy must to the inverse second power of r: be proportional . . T. = a/+. (A4 The parameter a may be determined in several ways. It may be selected to give the correct energy for the hydrogen atom when used with the expression En = a/+ - b/r (A-6) with b = (3/2)ea (A-7) or it may be selected to give the correct energy for the helium atom when used with the expression Eae = 2a/rP - 4b/r c/r (A-8) with c = (6/5)eP (-4-9) In the former ease one obtains for the quantity a/aael, aa = B o b radius, the value 0/8; in the letter case the value obtained is 1.01. We shall w e the former value: a/& = 0/8. (A-10) Substituting these resnlts into (A-1), one finds that E has a minimum value when (A-11) r/a, = (2.25)/[(0.817)2 - 2.11
+
(In deriving this equation the effect of the Lahell electron6 on the inner- and outer-shell electrons has been ignored.) For Z = 12, r = 0.16 A. This is smaller than our previous estimate, eqn. (lo), by a factor of 2. The discrepancy arises chiefly from the choice of a in the expression for the kinetic energy. In the eelculstion of r w + from rs,t*+,however, this term drops out. I t has been included here to show that the equations that yield
308 / Journal of Chemical Educafion
the result rpIir
= (0.802)rw%+ =
0.286 A
(from eqn: A-11) = 0.32 1)
(~gi"+
yield also reasonable values for r,
Literature Cited (1) BENT,H. A,, J. CHEM.EDUC.,40, 446 (Part I), 5'23 (Part 11) (1963). (2) KLEISS,L. M., Dissertation Absb., 14, 1562 (1954); WESTERMAN, H. R., DiSsertation Ab~tr., 15, 350 (1955); J. D., Disse~tationAbsb., 16, 2040 (1956). HERNITER, (3) WEISSKOPF, V. F., Phgs. Rev.,56, 72 (1930). W., J. Chem. (4) For a. leading reference, see KUTZELNIGG, Phys., 40, 3640 (1064). J. W., "The Eleetronio Structure of Molecules. (5) (a) LINNETT, A Nepi Approach," John Wiley and Sons, Inc., New York, 1964: see also (h) LINNETP,J. W., J . Am. Chem. Soe., 83, 2643 (1961). (6) LEWIS, G. N., J. Am. Chem. Soe., 38, 762 (1916). (7) PAWLING,L., AND WILSON,E. B., JR., "Intmduetion to Quantum Mechanics," McGrsw-Hill Book Co., Inc., New York, 1935, p. 150. T., Ann. Rev. Phys. (8) hlrzuse~ma,S., AND SHIMANOUCHI, Chem., 7, 440 (1056). (0) WELLS,A. F., "Structural Inorganic Chemistry," 3rd ed., Oxford University Press, London, England, 1962, p. 76. (10) Bond length and bond angles, unless otherwise indicated, are taken from the compilation edited by SUTTON, L. E., Soeoial Publicstion No. 11. The Chemical Society, ~ u r l m g t a nHouse, W. 1, London, 1958. PIERCE,L., AND HAYASAI,M., J. Chem. Phys., 35, 479 (1961). HAMILTON, W. C., Ann. Rev. Phys. C h m . , 13,19 (1962). HARRELL,S. A., AND MCDANIEL,D. H., J. -4m. Chem. Sac., 86, 4497 (1964). C., Quart. Rev. (Lads), 16, HASSEL,O., AND R~MMING, 1 (1962); LINDQVIST, I., ''Inorganic Adduct Molecules of Oxo-comoounds." Academic Press. Inc.. New York, 1963. (15) AHRLAND, S., C H A ~J., , AND DAVIES,N. R., Q1~al.1.Rev. (Lnda),12, 265 (1058). M. J., ET AL., J. Am. Chem. Sac., 68, 2284 (1046); (16) HUNTER, ROTE, W. L., AND HARKER,D., Acta Cwst., 1,34 (1048). (17) . . CURRAN.C., WITUCKI,R. M., AND MCCUSKER,P. A., J. A&. c&. Soe., 72, 4471 (1050). (18) B m m . F.. AND PEARSON.R. G... Prw. . Inow. Chem., 4 , 381 (i96i). (19) GILLESPIE,R. J., J. Am. Chem. Soe., 82,5078 (1960). C. K., "Structure and Mechanism in Orgrtnio Chem(20) INGOLD. istry," Cornell University Press, Ithaca, New York, 1953, p. 77. F. A., AND WILKINSON, G., "Advanced Inorganic (21) COTTON, Chemistry," Interscience Publishers, New York, 1962, J., A B G E ~ N G EW. R , J., JR., AND p. 150; KLEINBERG, GRISWOLD, E., "Inorganic Chemistry," D. C. Heath and Co., Boston, 1960, p. 65. (2'2) C o m p a r e P ~ ~ zK. ~ nS., , J . Am. Chem. Soc., 70, 2140 (1948). (23) KUCZKOWSKI, R. L., J. Am. Chem. Soe., 86, 3617 (1964). (24) See STEIN,L., Science, 143, 1058 (1964). (25) HENDERSON, W. A,, JR., AND STREULI,C. A,, J. Am. Chen;. Soc., 82, 5701 (1060). (26) MCCLELLAN, A. L., "Tables of Experimental Dipole Moments." W. H. Freeman and Co., San Francisco, 1963. (27) ARNETT,E. M., in "Progress in Phys. Org. Chem.," Vol. I edited by C ~ H E NS., G., ~TREITWIESER, A., JR., AND T m , R. W., Interscience Publishers, New York, 1963, p. 304.
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