Resource Papers IV Prepared under the sponsorship of The Advisory Council on College Chemistry
Henry A. Bent
University of Minnesota Minneapolis
lsoelectronic Systems
chemical combmation frequently disguises essential resemblances. The molecules CaH, and NzO, for example, have very different chemical formulas. Yet, to judge by their shapes and by their color (in the infrared, both molecules are transparent in the visible part of the spectrum), these molecules have very similar electronic structures, sufficiently similar to be called 'Lisoelectronic." As a general rule, or principle, molecules are isoelectronic with each other when they have the same number of electrons and the same number of heavy-atoms.' Usually, then, they have similar heavy-atom geometries -and, by inference, similar electronic structures. The molecules H2CCCHz (allene), HzCCO (ketene), HNCO (isocyanic acid), OCO (carbon dioxide), NNO (nitrous oxide), HNNN (hydrazoic acid), and H&NN (diazomethane), for example, all have 22 electrons and three heavy atoms; and all have linear, heavy-atom skeletons. Similarly, the molecules (CH&CCHz (isobutylene), (CH&CO (acetone), (H2N)zC0(urea), (HO),CO (carbonic acid), (CH3)(HO)C0 (acetic acid), F2CO (carbony1 fluoride), FNOa (nitryl fluoride), HONOI (nitric
acid), H2NN02 (nitramide), and CHaN02 (nitromethane), all have 32 electrons and four heavy atoms; and all have planar, Y-shaped, heavy-atom skeletons. (Frequently molecules have similar heavy-atom geometries if they have the same number of heavy atoms and the same number of valace electrons. Examples are and 0% (bent), and XeFz NF3 and PF3 (pyramidal), 80% and IC1,- (linefir).) Even the general locations of bound protons are similar in molecules that have the same number of electrons and the same number of heavy atoms. The bound protons of ketene (H,CCO), for example, lie with respect to each other and the heavy-atom skeleton as do two of the bound prot,ons in allene (HzCCCHz). Similarly, the bound proton of isocyanic acid (HNCO) lies approximately at one of the proton positions of allene, or ketene. Even more striking, perhaps, is the prediction, based on the statement above and the geometry of methane, that ammonia should be pyramidal and water bent. Figure 1 shows how much alike are the shapes of these three molecule^.^ These facts may be related to each other by imagining that removal of a proton from a hydrogen-heavy-atom bond leaves behind an electron pair-an unshared pair, which possibly occupies about as much space in the heavy-atom's valence shell as did the original bonding pair-and that the remainder of the electron cloud is essentially u~changed.~ Ketene's structure, for example, may he obtained from that of alleue by replacing two of the C H bonds This study was supported by a grant from the National Science Foundation and by the grant from the University of Minnesota of a Faculty Single Quarter Leave. 1 "Heavy atom" means here any atom other than hydrogen or helium, or lithium. G. N. Lewis wrote in 1938 (J. Franklin Inst., 226, 295) "It wm an essential element in the original theory of the octet, not only that an atom bonded to four others would have the electmnpairs in tetrahedral positions, but that this would still be true even if one or two of the electron-pairs were not used in bonds. From this it wn.. deduced that water would not have a linear strurtort. MI mmonia x plansr struclure, and that t h position ~ oi 3 nun-bondiuy pair wwlrl he so situnted at s rorner r,f x terrxhednm as to pnaluce o~nirnlimrnrrism, snch ac has I w w avlt~nlly found in sulfonium compounds." a G. N. Lewis wrote in 1923 (Trans. Faraday Soc., 19, 454) "Important as the bonding pair is to the whole theory of valence. it must be observed that such aoair is not fundamentally differ& from other pain which do notact as bonds." ~~
~~~
~
.. .
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a t one end of the allene molccule by lone pairs on an oxygen atom; the protons of the original C-H bonds may be thought of as placed, by some alchemy, in the nucleus of the terminal heavy-atom, changing the atomic number of that atom from 6 (carbon) to 8 (oxygen). By a similar alchemy, indicated by the dashed arrows below, one obtains from ketcne the structure of isocyanic acid.
Allene
Ketene
lsocyanic Acid
From the latter one obtains the structure of carbon dioxide, and from carbon dioxide, by a proton-shift from one heavy-atom nucleus to another, the structure of nitrous oxide, and so forth.
..
Nitrous Oxide
Hydraaaic Acid
Again, it should be emphasized, if for no other reason than to remind ourselves of the manner in which chemical theory develops, that constructions, such as these, although in general use among chemists for approximately a century, still represent unique chemical conjectures. I n atomic theory the existence of atoms was postulated-and generally accepted by chemists, hecause atoms were useful-almost a century before direct physical evidence for them existed. Now in valence theories, and their companion, the isoelectronic principle, the existence of electronic structures is postulated although direct proof or disproof of them lies beyond the present capabilities of physical theory and measurement. I n summary, the group -CHp in a molecule (acetone, for example) may be replaced, without producing major structural changes in the remainder of the molecule, by the isoelectronic groups -NH2 (to give urea), -OH (to give carbonic acid), or -F (to give carbonyl fluoride). Similarly, the structural group =CHI may be replaced by the isoelectronic groups =NH or =O; and so forth, as illustrated more completely (though not exhaustively) in Figure 2.
..
= C.N,or 0 nucleus
Diaeamothxne
Bond diagrams such as these suggest the following conjecture, hereafter to be referred to as the isoelectronic principle:
= H nuclei: I CH4. 2 NH3, 3 H 2 0 Figure 1. A comparison of the rhoper of a CH1 group in CHI (C-H: = 1.014 A. 1.093 A, HCH = 109.5'1. an NHs group in NHs (N-H HNH = 107'). and an H10 molecvle (0-H = 0.957 A, HOH = 104.5'1.
Molecules that have the same numbev of electrons and the same number of heavy atoms have similar eleo tronic structures and similar heavy-atom geometries.
This statement is a still-to-be-proved conjecture; neither theoretical nor experimental methods have revealed with precision, for a system more complex than the hydrogen molecule, the contribution made to the system's over-all charge distribution by its valenceshell electrons. What the chemist calls "the electronic structure of a molecule" has not in any case (except Hi) been rigorously calculated by theory or determined by experiment." Molecules will be called isoelectronic if they have similar electronic structures. For the series of isoelectronic molecules allene-ketene- . . . -dimomethane and isobutylene-acetone- . . . -nitromethane, classical valence theory gives the following electronic structures:
AlleneDiaaomethane Series
IsobutyleneNitrometIlsne Series
-
Here X = a heavy atom (C, N, 0, or F), = an electron pair that is involved in a bond between two heavy atoms, and : = a protonated ov unshared electron pair.
Figure 2.
Structural interchonger.
Read ho~irontdly.
Contrasts and Comparisons
The term "isoelectronic" may he compared withIthe terms "isomorphous" and "isomeric." Crystalline compounds that have similar chemical formulas and similar external symmetries are said to heisomorphous. Isomorphous compounds may or may not be
With very careful work absolute structure factors can he determined with X-rays to an accuracy of about 1%. This accuracy has been achieved, however, in only a very limited number of cases (the noble gases and a few solids such as aluminum, copper, diamond, silicon, and germanium) and the problems encountered in converting the measured structure factors to charge density distributions have not yet been adequately solved. Volume 43, Number 4, April 1966
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mutually soluble, may or may not have the same internal symmetry, and may or may not be isoelectronic with each other. Cubic BN, BeO, and NaCI, for example, could, under appropriate conditions of growth, have the same external symmetry. The first two have the same internal symmetry and are isoelectronic with each other. The internal symmetry of NaCl is different from that of the other two and it is not isoelectronic with them. Molecules that have the same chemical formulas (and. therefore. the same heavv atoms) but different ~, nuclear arrangements (and, therefore, usually different electronic structures) are called isomeric molecules. Isoelectronic molecules, by contrast, have essentially the same electronic structures hut usually different heavy atoms (and, therefore, usually different chemical formulas). I n some cases, isoelectronic molecules have the same heavy atoms differently arranged. Dimethyl ether, CH30CH3, and ethyl alcohol, CHaCHsOH, are an example; another such pair is cyanate ion, NCO-, and fulminate ion, CNO-. I n some respects the isoelectronic principle is like the octet rule. Both have played an important role in the development of valence theory, particularly in the work of Gilbert N. Lewis, Irving Langmuir, and Linus Pauling. Both are easily used and require for their application not even an approximate solution of the Schrodinger equation. Both apply equally well to the compounds of organic and inorganic rhemistry, and help, thereby, to unite these two sometimes diverging disciplines. And both deal with aspects of a system's electron cloud that, broadly speaking, are topologically invariant. The octet rule deals with an aspect of a combined atom's local electronic environment-the number of shared plus unshared valence-shell electrons-that survives essentially unchanged through the distortions and stretchings produced in the system's electron cloud by ordinary chemical reactions. The isoelectronic principle deals with an aspect of a system's entire electron cloud-its over-all articulation-that survives essentially unchanged through the distortions and stretchings produced by chemical and alchemical proton shifts. It is, in a sense, "an octet rule in the largc." Conversely, the stereochemical expression of the octet rule-the tetrahedral atom-and the stereochemical rules of inorganic chemistry for atoms with expanded octets-the trigonal bipyramidal atom and the octahedral atom (and, more loosely, the transition-metal atom of a compound that satisfies Sidgwick's inert gas rule5)-may be viewed as expressions of the isoelectronic principle applied on a "local" scale to the
valence-shell electrons of combined atoms: Atoms that have the same number of valence-shell electrons ( i n chemical compounds often eight, but sometimes more) have similar electronic structures. A corresponding statement holds for free atoms: Atoms that have the same number of valence-shell electrons (in the free state, often less than eight) have similar electronic structures and consequently similar chemical properties. Also, those aggregates of identical atoms, the elements, that are composed of atoms that have the same number of valence-shell electrons, have like their constituent atoms similar chemical properties. As such, they are grouped together in the Periodic Table. The groups of this table are to atoms (or their aggregates, the elements) what families of isoelectronic structures are to molecules. The broad view of structure embodied in the isoelectronic principle gives to certain inferences based upon it a unique flavor. These inferences are distinguished from, and complementary to, the usual inferences about electronic structure based on structural data-the estimation of a bond order from an internuclear distance, for example, or the calculation of the state of hybridization of an atom from bond angles. In an application of the isoelectronic principle, the over-all topology of an entire chemical structure forms the basis for drawing an inference about the essential articulation of the system's entire electron cloud. The earliest, and perhaps still most important, example of such an inference was Gilbert N. Lewis's suggestion that methane, ammonia, and water-three molecules with the same number of electrons (lo), the same numher of heavy atoms (I), and similar shapes (Fig. 1)-have similar electronic structure^.^ Unlike some structural principles, the isoelectronic principle may be effectively used whatever one's persuasion regarding the best way to describe the electronic structure of matter-by molecular orbital theory, by valence bond theory, or by some other theory. The principle is subsumed by classical valence theory, where it has been worked out. Where classical theory has not been worked out, the isoelectronic principle may help to extend its limits. Like classical theory, the isoelectronic principle deals directly with the electron density distribution in molecules rather than with an abstract, orbital description of that distribution; for like classical theory, the isoelectronic principle grew out of a study of chemistry, not mathematics. Thus, like classical theory, it may not be wholly right (i.e., quantitative); but it probably is not wholly wrong. The general applicability of the isoelectronic principle, although not a topic of further discussion in this
6 This rule states that the number of inner-shell and valence shell electrons about a transition metal nucleus in a complex is
.
.
all'of which are isoelect&o
with'each other. For'fart'her disi
Inc., New York, 1965, Section 1-4; DOUGLAS,B. E., AND McD-~NIEL,D. H., "Concepts and Models in Inorganic Chemistry," Blaisdell Publishing Co., New York, 1965, p. 340; and PEILLIPS,C. S. G.,AND WILLIAMS,K. J. P., "Inorganic Chemistry," Oxford University Press, Inc., New York, in press, Val. 11.
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(Chemical inferences such as this msy help quantum chemistry help chemistry. The history of quantum chemistry has been marked by a.search for orbitals for localized electron groups in molecules that could be transferred with reasonable accwacy from one molecule t,o the next [for leading references, see KLESR., J . Chem. P h ~ s .42,3343 , (1065), SINGER,M., A N D MCWEENY, and ADAMS,W. H., op. cit., p. 40301. The isoelectronie principle
cul&should have the sitme number of heavy atoms and the same number of electrons.
paper, presents two requirements that should be met by any more detailed description of the electronic strueture of matter. Both requirements stem directly from the manner in whieh the principle is stated. They are to explain the importance in molecular architecture of (I) pure numher and (2) the Pauli Principle. The importance of the latter arises from the fact that, aecording to the isoelectronic principle, molecular shapes are determined by the number of heavy atoms and not by the number of hydrogen atoms, which alone have no inner-shell electrons and hence may move freely about, in and out of individual electron pairs, without modifying through effects of the Pauli Exclusion Principle the basic shapes of electron clouds.
Toble 2. Vibrotional Frequenciesa for Nitrous Oxide, Carbon Dioxide, and Reloted Molecules with Lineor, Triotomic Heavy-Atom Skeletons
Molecule
Toble 1. Similorities in the Physical Proverties of Nitrous Oxide ond Carbon Dioxide ~ d t e db y Longmuir. [ I . Am. Chem. Soc.. 41. 1 5 4 3 ( 1 9 1 9 ) l
-MoleculNzO
Property Critical pressure (atm.) Critical temperature Viscosity at 20' Heat conductivity at lOOD Density of liquid at -20' Density of liquid at + l o D Refractive index of liauid.. D line. 16' ' Dielectric constant of liquid at 0' Magnetic susceptibility of gas at 40 tltm. Solubility in water at 0' Solubility in deohol at 15'
.
Asymmetric bond stretching vibration
+.-.-.+ +.-.+-+.
t
;---+ 589 667 588 564
NxO CO. H2CC0 HzCNz HNa HNCO NBNCOROzNO1+
Eorly Uses
The isoelectronie principle provides a simple recipe for generating analogies. If molecule A is demonstrably like molecule B in certain respects (same number of electrons and same number of heavy atoms), it may be like B in other respects, especially in its shape but perhaps also, in an extension of the original statement of the principle, in its other properties as well. Thus, as Irving Langmuir noted in 1919, carbon dioxide and nitrous oxide have remarkably similar physiea! properties (Table 1).
Symmetric bond stretching vibration
Bond bending vibration
a
1285 1388 1120 1170 1269 1327 1348 1205 1070 1400
...
572 630 629
610 538
2223 2349 2152 2102 2140 2274 2080 2170 1970 2375
Frequenciu are for heavy-atom skeletal modes only, in em-'.
fered for this unexpected behavior is that during the out-of-plane vihration the electron cloud of ketene accommodates itself to the changing molecular geometry in a manner suggested by the curved arrows in the diagram below. These electron shifts tend to produce about the methylene carbon atom of the vibrationally excited ketene molecule an electronic configuration similar to the electronic configuration about the hydrogen-carrying nitrogen atom in cyanamide, whieh is known to be a non-planar molecule in its ground state.
COs
Ketene
1.193 1.598
1190 1.582
0.12 x 101.305 3.25
0.12 x 10-6 1.780 3.13
Cyanamide
I n water, ketene produces acetic acid. This reaction may he compared with the hydration reactions of carbon dioxide and the nitronium ion.
To Table 1 Langrnuir adds these comments: "Both gases form hydrates, N10.6H%0and e 2 . 6 H * 0 . The vapor pressure of the hydrate of nitrous oxlde is 5 atm. at -6". wherees the hydrate bf carbon dioxide has this vaDor pressure at -9". The
dioxide has this same surface tinsion at 9.0'. ' ~ h u s .nitrous oxide at any given temperature has properties prscticilly identical with those of carbon dioxide at a temperature of 3' lower."
Today we may add to the data of Table 1 the v i b r a tional frequencies of these two molecules, as given in Table 2. These frequencies are sensitive functions of the distribution of charge and mass in a molecule. Also listed in Table 2 are the corresponding frequencies for several molecules and ions that are isoeleetronie with carbon dioxide and nitrous oxide. Recently it was found that two of the molecules listed in Table 2, ketene (H,CCO) and diazomethane (H,CNd, have unusually low force constants for the CHP out-of-plane vibration (1). The explanation of-
I n a similar spirit, the relatively small quadrupole couplimg constants of the nitrogen atoms in hydrazoic acid (HNa) have been compared with the correspondingly small coupling constants for the related nitrogen atoms in nitrousoxide (3). When irradiated with ultraviolet light, ketene breaks up into two fragments, carbon monoxide and methylene (CH,). Diazomethane, hydrazoie8acid, isoeyanic acid, and carbon dioxide exhibit similar behavior.
hu
HNNN
+ N2 HN4 + CO hv -0 + CO HN
hu
HNCO OCO
Volume 43, Number 4, April 1 9 6 6
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173
The fragments H,C, HN, and 0 from these reactions are highly reactive, owing to the open sextet of electrons about their heavy atoms. They are strikingly similar to each other in their dierization reactions,
--
2 H2C
HpC=CH2
2 HN
HN=NH
2 0
- 0 4 ,
in their single-bond insertion reactions, H,C-H H2N-H
+ H,C + HN
--
HaC-CHa HIN-NHs,
and in their double-bond insertion reactions? H2C=CH2
+ H2C
-
HnC-CH? 'C/ Hz
The other products of the decomposition reactions, carbon monoxide and nitrogen, also are strikingly similar to each other in a number of respects, a fact emphasized by Langmuir in 1919 (Table 3). Table 3. Similarities in the Physical Properties of Carbon Monoxide and Nitrogen Noted b y Langmuir [ I . Am. Chem. SOC., 4 1 , 868 (191911
Freezing paint (OK) Boiling point (OK) Critical temperature ( O K Critical pressure (atm.) Critical volume Solubility in H1O. O°C
In addition to the early uses of the isoelectronic principle by Lewis and by Langmuir, who presented numerous revisions of chemical formulas, the principle has long been used in spectroscopy and quantum chemistry under the heading "united atoms" (5). Pauling has used the principle successfully in discussions of crystals structures (vide infra); and in 1933 he suggested that the formula of antimonic acid should be written HSb(0H)s (cf. Te(OH), and HsI06)and that "Xenic acid, H Z e 0 6 , should form salts surh as AgZeOs and AgH,XeOa (4)." Noble Gas Compounds
The recent synthesis of compounds of the noble gases provides interesting illustrations of the isoelectronicprinciple. In addition to the now well-known fluorides XeF2, analogous to IC12-, and XeF,, analogous to
The analogies between BH8 and 0--e.g., BnHa snd OX, HsBCO and Cog, HaBCO1-- and CO.--, FaPBH3 and F8PO, (HaB)(NHx)CO- and (NHdCO-have been developed by R. W. PARRY AND CO-WORKERS; see Adv. in Shem. Series, 4 2 , 302 (1964) and J. I n o ~ g Nuel. . Chem., 17, 125 (1961).
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Journal of Chemical Education
IC1,-, XeF6 has been synthesized and may he analogous to TeCla2- (5),and possibly XeF5+has been synthesized (from XeFs BF,) (6). XeFs+ would be isoelectronic with known XeOFl and IF5, whose infrared spectra are remarkably alike (7). Also reported are XeOIFz (isoelectronic with TeF4) and XeOa (isoelectronic with SnF,). Two better characterized oxides are xenon trioxide, Xe03, and the perxenate ion, xeO~'--, in Na,XeOmH20 (n = 6 or 8). The crystal and molecular structures of XeOa are very similar to those of HIOa (and, probably also, H2Se03). And the ion XeOe4- is so much l i e IOa5- that, as one set of investigators said (a),
+
...
The geometry of the perxenate ion offers no surprises and adds further weight to the accumulating body of evidence that the rare gas compounds have molecular structures which are readily understood in t e r n of conventional ideas of structural chemistry. In particular, there are marked similarities to the compounds of the neighboring halogens.
Prior to the discovery of these fluorides, oxides, and oxy-fluorides of xenon, there had been reported from studies with mass spectrometers such species as ArH+ (isoelectronic with HCl) and XeCH3+ (isoelectronic with CHJ) (9). Since the addition of a proton to a heavy-atom nucleus is chemically equivalent to the loss from that nucleus of a negative electron, it is possible to produce compounds of xenon, XeC14 and XeCH3+, for example, from the beta decay of the isoelectronic compounds of radioactive iodine, 1C4- and CHJ. Similarly, the radioactive decay of H T produces HeH+. Recently the production of the bifluoride of helium, HeF2, from the radioactive decay of TF2- has been proposed (10). Further Alchemy
The sequence of alchemical steps beginning with neon and ending with methane may be continued by removing a proton from the carbon nucleus of CH4 and placing it in one of the valence-shell electron pairs of the heavy atom (formerly carbon, now boron). In this way one obtains BHa(Hz)or BH3(He) from CH,; i.e., a boron atom with three singly protonated valence-shell pairs and one doubly protonated pair. The latter entity (HPor He) has little residual nucleophilic activity and splits out as a neutral particle, leaving behind the planar fragment BHa, whose heavy-atom electron-pair-coordination-number (EPCN) is 3 and whose structure is very different from that of tetrahedral CHI (heavy atom EPCN 4). Continuing in this way, one obtains linear BeH2 (heavy-atom EPCN 2) from BH,, LiH (heavyatom EPCN 1) from BeH2, and He from LiH. As the nuclear charge of the heavy atom decreases in the sequence of non-isoelectronic molecules CHI, BH3, BeH2, and LiH, the radius of the heavy-atom's helium-like core increases from 0.15 A for C4+ to 0.60 A for Li+. Correspondingly, the character of the heavy-atom-tohydrogen bond changes from the essentially covalent bonds of CH4 to the more nearly ionic bond of LiH. Similarly, one obtains from ethane the electronic structure for the lithium alkyl LiCHa, and from the l a b ter the electronic structure of Lip (11). Propane yields linear (and as yet unreported) LizBe, a molecule that should have a large octopole moment; and so forth. A variation on this theme may he illustrated with SFs. The elect,ron-pair-coordination-number of the
sulfur atom, the central atom in this molecule, is 6. Withdrawal of a proton from the sulfur nucleus and its placement in one of the molecule's valence-shell electron pairs produces (after splitting out HF) the molecule PFK,whose central-atom electron-pair-coordination-number is 5. Continuing, one obtains SiF, from PFs, AIFa from SiF,, and so forth. One may equally well use this procedure in the opposite direction, as illustrated by the following alchemical transformations :
+ HF = IFdEPCN 5) IF8(EPCN 5) + HF = XeF4(EPCN 6) TeF?(EPCN 4)
I n the same way one obtains from SnFz in succession SbFa, TeF4, IF& and XeFs. The alchemical changes described in this section are reminiscent of the Fajans-Soddy Radioactive Displacement Law. This law states that loss of an alpha particle by a nucleus produces a daughter nucleus displaced two positions in the Periodic Table. Analogously, the loss or gain of an electron-pair in the valenceshell of a combined atom produces a daughter atom whose local electronic environment is displaced one position in the following tabulation of valence-shell electron-pair arrangements: EPCN 6: octahedral EPCN 5: trigoml bipipyramidal EPCN 4: tetrahedral
EPCN 3: planar EPCN 2: linear
Applications to Crystal Structures
The isoelectronic principle has uses beyond its applications to ordmary polyatomic molecules. It may be applied, often witb comparable success, to those large, multiatomic molecules called crystals. Calcium oxide, scandium nitride, and titanium carbide, for example, are isoelectronic. These compounds have the same number of electrons per heavy atom and the same nuclear geometry-the rock salt structure. They may be thought of as related to each other by the following alchemical transformations (an arrow witb the symbol np over it indicates the transfer of n nuclear protons in the direction indicated): P
P
r\
Y-\
CaO = ScN
SON= T i c
Lithium oxide is related to beryllium carbide in a similar manner.
Both compounds adopt the antifluorite structure, so called because (taking an ionic view of the bonding) the Li+ and BeZ+cations occupy the F- positions and the 02-and C4- anions the CaZ+positions of the CaF2 structure. The latter structure is isoelectronic with sodium sulfide and magnesium silicide. 4P
n
F2Ca = NalS
2P
n
Naps = Mg,Si
Similarly, diamond, written CC, is isoelectronic with cubic boron nitride, BN (a hexagonal form of BN isoelectronic with graphite exists also), and with beryllium oxide, BeO. The next member of the series, LiF, is not isoelectronic with the previous members: it has the rock
salt rather than the diamond structure; it is, however, isoelectronic with the series' next member, sodium hydride, which in turn is isoelectronic with the series' last member, magnesium electride (6). A related, more extended isoelectronic series is Ge-GaAsZnSe CuBr. L i e the last pair (ZnSe-CuBr), the other zinc chalcogenides and corresponding copper halides are isoelectronic with each other: ZnTe with CuI, ZnS with CuCl, and ZnO with CuF. All exhibit the zinc-hlende or wurtzite structure, or both. The last comparison may be generalized. Just as copper fluoride may be used as a model of zinc oxide, so may fluorides generally be used as weakened models of oxide systems (I$), particularly if the corresponding cations are similar in size and polarizability. An example is BeF2 and Si02 (IS). These compounds have the same valence-electron-to-hepy-atom ratio and similar cation radii (0.31 and 0.41 A. respectively). I n the solid state they exhibit similar polymorphic crystalline forms, well-known for silica, connected by sluggish reconstructive transformations. I n the molten state they show similar low electrical conductivities, high viscosities, and marked tendencies t o form glasses. Grimm-Sommerfeld Compounds
Compounds witb four valence electrons per atom that adopt the diamond, zinc-blende, or wurtzite structure are quite common; they are called Grimm-Sommerfeld compounds (14). Examples of some bmary GrimmSommerfeld compounds, several of which have already been cited, are listed below. (IV-IV)
111-V
11-VI
I-VII
C Si Ge Sn
BN Alp GaAs InSb
Be0
...
ZnSe CdTe
C;B~ .%I
.. .
L i e water, Grimm-Sommerfeld compounds have melting points that decrease with increasing pressure (15). L i e silicon, many Grirnm-Sommerfeld compounds are semiconductors (16). The compound indium antimonide (InSb) bas received considerable attention. This compound is isoelectronic with tin. It was conjectured, therefore, that under pressure InSb might adopt the metallic white tin structure. This conjecture was verified by quenching a sample t o 77OK and releasing a previously applied pressure of 30 kbar. Following this result, it was conjectured that, because white tin becomes superconducting below 3.7'K, InSb might become superconducting a t low temperatures. This conjecture, too, wasverified: "white tin" InSb becomes superconducting below approximately 2OK. Grimm-Sommerfeld compounds may h a v e i n addition to the formulas A"'Bv, A"BV', and ATBVIT--such formulas as A'B111X2V', an example of which is CuInTea and A"B1"X2", an example of which is ZnGeAsz. The latter compound is isoelectronic with germanium. Another Grimm-Sommerfeld isoelectronic pair is CuAISr ZnGeP,. Pauling has given a description of the discovery of a more complex Grimm-Sommerfeld isoelectronic pair, in the days when the successful application of X-ray methods to structural problems was generally limited to structures that could be characterized by two or three parameters. He writes (17) : Volume 43, Number 4, April 1966
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175
"The mineral enargite, CusksSc was found (in 1934) on X-ray investigation to have an orthorhombicynit of structure with a = 6.46 A, b = 7.43 1,and e = 6.18 A. This unit contains six copper n t u n ~ s ,trr-t, ~ r w n i rxtnnls, and eichi s>dfuratoms. Thr dimensions an: 1.1mrly5inliLr to those of the hrmgonnl mirwml I I , S : thr tlicw,~rior..;~ , fx douhlc orrh~~lexanonnl unit of wofiz'ite, containing eight zinc atoms and eight s u l h r atoms, are d 3 a = 6.65 1,2a = 7.68 A, and e = 6.28 A. This comparison suggests that the atomic arrangement of ensrgite is that which results from replacing one-fourth of the einc atoms in wurtzite by arsenic atoms and the remaining three-fourths by copper atoms in such a way as to give discrete As& groups. I t was found that the calculated X-ray intemitiesfor thepost~dated Although the structure agree well with the observed ones . structure depends upon thirteen parameters, there is little doubt it is correct." 8
. ..
Infinite Anion Ldtices
Sodium peroxide is written Na?Oz,not NaO, because it is known from X-ray data (and, less directly, from chemical data) that the oxygen atoms in the crystal occur, understandably enough, in pairs; for 0- ions are isoelectronic with fluorine atoms, which are known to .- dimprize --..-. .-. This simple observation may be generalied. The anion lattice lsroduced bv the chemical union of a metal with a non-metal can iften be understood in terms of the crystal structure of a neighboring pure element by considering that the electrons received by the non-metal atoms from the metal atoms increase by unity for each received electron the effective group number of the non-metal atoms. Put another way, if metal atoms in their chemical union with non-metal atoms provide electrons insufficient in number to promote separately each non-metal atom to its neighboring noble gas configuration, the non-metal atoms may share electrons with each other, after the fashion of the elements of Groups IV, V, VI, and VII. Below are illustrative examples of the promotion of a non-metal atom from Group 111to Group IV, IV to V, and V to VI. 111-to-IV
MgB2 LiGa CaGar
IV-to-V
CaSb
V-to-VI
LiAs
The boron stoms form planar sheets isoelectronic with graphite. The gallium atoms form a three-dimensional network isoelectronic with that of el?mental germanium. The silicon atoms form puckered layers analogous to those in elemental arsenic. The arsenic atoms form spiral chains isoelectronic with those in elemental denium.
I n CaSi the silicon atoms form planar, zig-zag chains isoelectronic with the trans extended form of SinHlnc2. The following examples extend the above tabulation. VI-to-VII
NaOl
VII-to-VIII
NaF
The oxygen atoms form dimers isoelectronie with elemental fluorine. The fluorine a t o m form a lattice isoelectranic with that of crystalline neon.
This solution of the structure of enargite is cited as an example of the "stochastic method." I t has been applied with striking success by Pauling in the elucidation of the structure of proteins. The term "stochastic" was introduced in the present sense by Alexander Smith in 1907 from the Greek ("to divine the tmth by conjecture") to describe an hypothesis that, like the isoelectronic principle, "predicts the probable existence of certain facts or connections of facts'' and "professes to be composed of entirely verifiable facts and is subjected to verification as quickly as possible" (18).
176
/
Journal of Chemical Education
The structure of GeAsz is interesting: I t presents simultaneously an example of a three-electron Group V-to-VIII promotion and a one-electron Group V-to-VI promotion. Half the arsenic atoms in this structure are promoted by germanium to the noble-gas Group VIII configuration; these arsenic atoms have no arsenic neighbors. The other half of the arsenic atoms are promoted by germanium to the Group VI configuration of elemental selenium; these arsenic atoms have two arsenic neighbors, forming zig-zag chains that run throughout the strueture. It is interesting to consider the possibility of infinite cation lattices. The zirconium atoms in zirconium trihalides and the transition metal atoms in nickel arsenide structures (19) may be examples of infinite cation chains. Infinite threedimensional cation structures presumably occur in the pure transition metals, in which metal-metal bonds are believed to exist between atoms that are partially ionized, owing to the loss of electrons to conduction bands. Metals
Application of the isoeleetronic principle to sodium hydride yields, in one direction, the fluoride of lithium 2~ N
Na+H-
=
F-Li+
and, in the other, the "electride of magnesium."
The symbol ES2-stands for an unprotonated electron pair-the "electride ion" (5). If the latter application is legitimate, the magnesium nuclei in metallic magnesium should lie on the same space lattice as do the sodium nuclei in sodium hydride. Now sodium hydride has the sodium chloride structure. I n this structure the cation lattice may be pictured as generated by the centers of cubic closepacked spheres, the ABCA . . . stacking arrangement of close-packed layers-designated, usually, simply "ccp" (without intending to imply thereby that the corresponding atoms or ions are actually in contact with each other, which often they are not). This is nearly the right structure for magnesium. The space lattice of the magnesium nuclei in metallic magnesium is that generated by the centers of hexagonally close-packed spheres, the ABA . . . stacking arrangement of closepacked layers. Interestingly, magnesium's cogener calcium does adopt, among othcr structures, the "ecp" structure. Continuing in this way, one obtains from magnesium hydride, MgH2, which has the rutile structure, a bodycentered tetragonal structure for silicon. While this is not the structure of silieon a t atmospheric pressure, it is one of the structures adopted a t high pressures by silicon's cogener tin. It has been noted, also, that metallic silver may be isoelectronic with palladium hydride (20). Both substances have "ccp" heavy-atom lattices; and they have nearly identical molar volumes. Similarly, zinc may be isoelectronie with copper(1) hydride: the two substances have hexagonal close-packed heavy-atom lattices, and similar molar volumes (20).
These examples suggest that in an extension of a chemical theory of valence to metals the isoelectronic principle may play a useful role. At least two precautions should be noted, however. First, in passing from a hydride to a metal that has the same electron-to-heavy-atom ratio, there may occur in the less firmly bound electron cloud of the metal subtle, though structurally significant, changes in the system's electron cloud, such as have been postulated to occur in passing from the electron cloud of methane to that of neon ( $ I ) , for example, or as are known to occur in passing from the diamagnetic electron cloud of ethylene to the paramagnetic electron cloud of molecular oxygen. And, secondly, the phenomena responsible for radius ratio rules, though not unimportant for polyatomic molecules, are especially important for solids. For this reason magnesium hydride and lithium oxide, though they have the same electron-to-heavy-atom ratio, have distinctly different structures. Similarly, among the alkali nitrates it is sodium nitrate, not potassium nitrate, that adopts the calcium carbonate structure. Despite these qualifications, one general, relatively novel conclusion emerges from the present application of the isoelectronic principle to metals. It is this: The electron clouds of metals probably are more subtle and varied structures that are probably related more closely to the electron clouds of other substances, especially those of salts, than one would expect from the common, spherical-atom-in-contact-with-spherical-atom model of metals. I n metallic magnesium, for example, that portion of the structure's total electron cloud that is centered spherically about a single magnesium nucleus is probably no more (indeed, probably less) in contact with similar, spherical clouds about adjacent magnesium nuclei than is a sodium ion in sodium hydride in contact with other sodium ions. Hume-Rofhery's Rules
The role of theory in making manageable and interesting a large body of experimental information is well illustrated by the intermetallic compounds. As Pauling has observed, nearly three-quarters of the elements in the Periodic Table-all those except a small fringe across the top of the table and down the right-hand side-are metals. Consequently somewhat over half of all possible binary combinations are alloys or iutermetallic compounds. Yet most textbooks scarcely mention these substances, and not because they are lacking in intrinsic interest, but, rather, because there exists a t this time no satisfactory theory to account for their existence. The usual valence rules fail to provide a basis for understanding such formulas as KCd13and Mg32A149. Some regularities regarding similar compounds are known, however. Hume-Rothery has noted that intermetallic compounds with unrelated stoichiometry but closely related structures often have the same number of valence electrons per atom; see Table 4. If one symbolizes by I, 11,111,and IV elements from these groups of the periodic table, it may be seen that Hume-Rothery's rules are an illustration of the isoelectronic principle applied to the valence-shell electrons of intermetallic compounds.
For Hume-Rothery's 3/2 compounds, for example, one may write CuBe
-
P Doubling
I I1
N
I2 I1 I1
=
2~ Tripling
N
11 11. I1
=
- 11111
- IJV
CuAl Cu&
Similarly, for the 21/13 compounds one may write
-
Cu6Zn8
8~ Doubling
IjIIg
=
N
-
-
1 6 ~ Triplin~
=
-
II~IISII. IlsIIIB 4.111aIIa- I d V a
CurA14
NaalPb8.
The structure of FesZnll suggests (Table 4) that in this compound iron should be assigned to group 0 (or VII1)-its usual location in the periodic table. This interference may be viewed as a use of the isoelectronic principle in reverse: From the nuclear geometry of a compound inferences are drawn about the compound's electronic structure-in this instance, about the oxidation states of its constituent atoms. Table 4. Relation Between Electron-to-Atom Ratio and Crystal Structure for Some Intermetallic Compounds
Compound
Valence-electron-twatom ratio
Bodv-centered-cubic structures
"7
Brass" structures
The use of the isoelectronic principle in determining the states of ionization of combined atoms will probably become increasingly common as the structures and properties of complex substances become better known. Indicative of this, for example, is the inference from structural data that the metal atoms in metal-rich scandium sulfide phases (formally Sc& Sc) are all equivalent, and that these phases should therefore be formulated as "electron compounds" (Sca+)z+x(E-)3x(S2-)3, where E - represents a valence-shell (or conduction-band) electron ($9). Analogous in some respects is the conclusion that lanthanum diiodide, which has a high electrical conductivity and a low molar susceptibility, contains tripositive metal ions and 'Lmetallic"lattice electrons, and should probably therefore be formulated as La3+(E-)(I-)% Vanadium-oxygen compounds comprise another system with interesting, unsolved problems for valence theory. The monoxide, for example, is such a good conductor that Berzelius mistook it for the pure metal. A satisfactory chemical description of these substances has not been given.
+
Bonding
Thinking in terms of the isoelectronic principle is an Volume 43, Number 4, April 1966
/
177
interesting and sometimes useful habit. While there is no guarantee (except experience) that it will not send its practitioner off on a line of unfruitful conjectures, there always is the chance that it will lead to a search for facts that lend themselves to the formulation of empirical rules and structural principles that may further our understanding of chemical bonding. Sketched below are several illustrative examples that show how the isoelectronic principle may be used to organize chemical and structural information in a manner that may suggest interesting, perhaps novel hypotheses. Unusuolly Long Bonds
I n the molecule OzN-NOz (the stable form of the dimer of NO2) the nitrogen-nitrogen bond is veryyeak and unusually long-1.75 A, compared to 1.47 A, for example, for the nitrogen-nitrogen bond length in hydrazine. A similarly weak and presumably long nitrogen-nitrogen bond occurs in ON-NO, the dimer of NO. Likewise, the sulfur-sulfur bond in the dithionite ion, 02S-SOZ2-, the dimer of the relatively stable radical SOz-, is unusually long. Longer and weaker than normal bonds are found also in the dimers of the comparatively stable radicals CIOz, HCO, and COz-, which are isoelectronic, respectively, with the radicals S02-, NO, and NO1. The dimer of C1OZ,in fact, has not been reported. The dimer of HCO, glyoxal, is well known. Its carboncarbon bond is approx~mately0.1 A longer than would be expected for a single bond flanked by two double bonds to electronegative atoms. The dimer of the GOz- radical (whose ultraviolet spectrum is comparable to that of NOz) is the oxalate ion, CZO~~-.Its carbon-carbon bond, like the nitrogennitrogen bond of N204,is longer than normal. Also, as is the case for the dimer of NOS, there is evidence that the dimer of C02- can exist in three forms: A planar and non-planar form of 0 2 C C 0 2 2 -isoelectronic with the corresponding forms of 02N-NOz, and a less stable, unsymmetrical form OCOCOZ~-isoelectronic with nitrosyl nitrate, ONON02 (BS), an isomer of 02N-NO2. And, further, there is evidence that in a polar medium a t high temperatures the unsymmetrical, "carbonyl carbonate" form of the dimer, formed by isomerization of the more stable form OzC-C022-, dissociates heterolytically
=
NO+
+ NO1-
I n many respects the nitrogen system serves as a weakened model for the corresponding carbon system, and the chlorine system, similarly, for the corresponding sulfur system, analogous to the fact, mentioned earlier, that fluorides may serve as weakened models for oxide systems. Conversely, the hifluoride ion FHF- probably serves as a strengthened model for postulated FHeF (1O), as do the compounds of chlorine and bromine for the isoelectronic fluorides and oxides of argon and krypton, which have so far generally resisted synthesis, possibly for reasons discussed elsewhere in THIS JOURNAL (5). 178
/
Unusually Short Bonds
The end-to-end distance in nitrous oxide is 0.06 less than the distance expected for the structure N=N=O, and 0.16 A less than the distance expected for the structure N--N-0. As the data in Figure 3 illustrate and as was first noted by Pauling in 1932 on the basis of less evidence, the situation described by him as "resonance between two or more structures.. .leads to interatomic distances nearly as small as the smallest of those for the individual molecules" (26). The nitrogen-nitrogen distance in N 2 0 is almost as short as that expected for the structure N s N - 0 and the nitrogen-oxygen distance is almost as short as that expected for the structure N=N=O. Similar short interatomic distances occur in hydrazoic acid (HNJ and diazomethane (HzCN,), molecules isoelectronic with nitrous oxide.g
-
Figure 3. Bond length comparisons for nitrous oxide. Allowanser have been made in this figure for the bond-shortening effect of adjacent multiple bonds.
I n formamide, also, there occur adjacent bonds, each of which seems unusually short.
As suggested by the arrow above, the carbon-nitrogen bond in formamide is shorter than t&e normal C-N single bond distance (by about 0.1 A). The carbonoxygen bond (length 1.19(3) A) is not correspondingly longer, however; in fact, it is slightly shorter than the corresponding bo2ds in formaldehyde (1.206 propynal (1.215 A), and acetaldehyde (1.2155 A). Similarly paired, short bonds occur in the molecules 08, NO2-, and HC02-, which are isoelectronic with formamide. I n each of the above instances a build-up of electron density beyond that suggested by the octet rule appears to occur about an atom that is bound by a multiple bond and that has, attached by another bond, an atom to which is assigned a strongly basic electron pair. This hypothecated build-up of electron density may he indicated, with customary imprecision, by a curved arrow and described (more precisely and with more chance of being wrong) as an intramolecular pair-pocket
A),
yielding products isoelectronic with those produced in the heterolytic dissociation of nitrosyl nitrate (24) : ONONOl
Similarly, XeF2 probably serves as a strengthened model for conjectured CsF2+.
Journol of Chemical Education
'These conclusions are based on the use of conventional covalent radii.
hond (26) ; or, equivalently, as an incipient intramolecular nucleophilic attack upon an activated atom by a basic lone pair on an adjacent atom; or, following Werner, as the first step in the build-up of a secondary coordination shell of electron pairs about the activated atom. Charge distributions of this sort correspond in molecules that have nitrogen-atom acceptors (N20, HNa, HtCN2, NO2-) to an approach toward the formerly fashionable notion of "pentavalent nitrogen." More significantly, such charge distributions may help to explain the relatively small dipole moments of the molecules N20, HN3, H2CN2,and Oa, all of which have highly polar Lewis octet structures. While it might he argued that this explanation is not required for the first three molecules, whose classical resonating octet structures have oppositely directed dipole mo+ ments (N=N=O and N=N-0, for example), it would seem that some such charge distribution is required in the case of ozone, whose dipole moment (0.52 Debyes) is much less than that expected for the vector sum of the dipole moments of the Lewis octet structures
. .
The Nofure of the Double Bond
I n a water molecule the locations of two of the valence-shell electron pairs about the oxygen nucleus may be inferred from the locations of the protons of the hydrogen atoms. The locations of the other two valence-shell pairs-the unprotonated, lone pairs-may he inferred, following G. N. Lewis, from a comparison of the electronic structure of the water molecule with that of the more fully protonated isoelectronic molecule methane. The spatial distribution of protons in the fully protonated methane molecule provides a clue (by the isoelectronic principle) to the spatial distrihution of electron pairs in the partially protonated water molecule. The clue is well supported in this instance by experimental data: the diamond-like structure of ice, for example, and the pyramidal structure of the hydronium ion. A similar strategy may he used to determine the probable locations of electrons in metals (vide supra), or in a double bond. In ethylene, for example, as in water, there are two unprotonated valenceshell electron pairs-those of the douhle bond. Their more precisely given positions between the carhon nuclei could perhaps be determined if it were possible to compare the electronic structure of ethylene with that of a more fully protonated isoelectronic molecule. Such a molecule exists: dihorane, B2Hs which may he viewed as two edge-sharing BH4 tetrahedra. The electron pairs of the bridging B-HB bonds in this structure correspond in the isoelectronic molecule C2H4to the electron pairs of the carboncarhon double bond. From the comparison of ethylene with dihorane, one infers, following van't Hoff's suggestion of 1874, that a carbon-carbon douhle hond is composed of two equivalent bent-bonds. I n many respects this description of a douhle hond fits modern experimental facts concerning the ground states of olefins and related small-ring compounds better than does the currently popular a-a description.
Thus, while hond angles, for example, have often been cited in support of the u-a description of double honds, i t is now known that the HCH angle in ethylene is not, as was once supposed, 120". More recent values are 117.37" and 117.57'. I n substituted ethylene the angle opposite the double hond is often much less than 120'; in F2C=CH2, for example, the FCF angle is 109"15'. The average angle opposite the douhle hond of a trigonally hybridized carbon atom for molecules whose structures are known is ahout 113'. In carbonyl fluoride the FCF angle is 108.0°, significantly less than the tetrahedral angle. Such facts as these have prompted a re-examination of the a-a formalism (37). It is found that the a-a description of douhle bonds does not require the use of sp2 hybrid orhitals. The u-a formalism may he used with an infinite set of a hybrid orbitals. Orbitals for the honds opposite a double bond may he hybridized sp (afrequent choice for the lone pair orbitals of the oxygen atoms of carbonyl compounds), sp2 (the familiar choice for the single bond orhitals of doubly bonded carhon atoms), spa (Pauliig's choice), or pure p (and more complex fractions thereof), with the hybridization of the a component of the associated double hond being, correspondingly, pure p, sp2,sp, or pure s (28). The previous remarks do not by themselves constitute an argument against an informed use of the a-a terminology. What they constitute is an argument against the argument that a bond angle of 120' (or something close to it) is evidence in support of the a-a description--or that an angle greatly different from 120' is an argument against it. More questionable is the use of the a-a description together with the concept of conjugation to explain why single honds adjacent to multiple honds are often shorter than normal. The lengths of the carboncarbon single bonds in methyl acetylene, HaC-kCH, and diacetylene, HC=C-C=CH, for example, are 1.46 and 1.38 A, respectively. The value for ethane is 1.53 A. If the shortening of these honds arises from a borrowing of electron density from adjacent multiple honds, the multiple honds should he longer than normal. I n fact, for the examples cited the triple bonds are nearly the same length as, perhaps even a bit shorter than, the triple bond in acetylene. It also is not easy to rationalize in the a-a description of hond lengths the fact that the carbon--earban single bondsoinnowplanar 1,3,5,7-cyclooctatetraeneare 0.010.02 A shorter than the corresponding bond in planar l,3-butadiene. Also curious from this point of view is the equilibrium orientation of methyl groups adjacent to double bonds. I n propylene and acetone, for example, one methyl group proton, viewed from a position along the carbon-carbon single hond to the methyl group, is in an eclipsed position with respect to the hypothecated a-component of the double hond. It has been suggested that the facts cited above are compatible with and lend support to the classical henthond formulation of a double hond (26). On the other hand, it has been said that by the use of a-bonds one avoids the introduction of hent honds "which chemists do not like." It should he noted, however, that if bond curvature is reasonably defined in terms of an electron density distrihution, conventional d o n d s arevery hent. Volume 43, Number 4, April 1966
/
179
Actually, there is no logical conflict between the n-71 description of a double bond and the classical, bent-bond picture given by van't Hoff, by the isoelectronic principle, and by the strong form of the Pauli Exclusion Principle (26). The two descriptions are in a sense orthogonal and (perhaps) complementary. The classical description purports to specify the relative positions in space of the bonding electrons, but not their excitation energies. The r-71 description purports to describe electron energies, but, for this very reason, dealing as it does with energy eigenfunctions, it does not yield, without further analysis, the relative locations in space of the bonding electrons. What is perhaps illogical about the prevailing descriptions of the electronic structure of ethylene is the use of bond-like functions for one part of the molecule and energy eigenfunctions for another. I t is sometimes interesting to consider what chemistry would have been like if history had been different. How would double bonds have been described today if the structure of diborane had been illucidated threequarters of a century before that of ethylene? Energetics
The isoelectronic principle postulates that the electron cloud that holds together the atoms in a molecule is invariant (approximately) to certain chemical and alchemical proton transfers. It would seem that it should be possible somehow to use this hypothecated invariance to acquire information regarding the influence that various factors, perhaps particularly nonelectronic factors, have on the strengths of chemical bonds. Sketched below are several suggestions as to how this might be done. Molecular Vibrations
Of course, the assumption of a rigid charge cloud cannot be rigorously true. For one thing, each peripheral proton carries with it a cusp of electron density, which presumably moves about with the proton as the proton moves about in the electron cloud. For another, the center of gravity of a truly rigid charge cloud would not be affected by a molecular vibration. This would mean, however, that a molecule such as carbon dioxide would not absorb infrared radiation. For during a molecular vibration, the center of mass of a molecule does not move. Therefore, if the magnitudes of the positive charges on the nuclei bear a nearly constant proportion to the magnitudes of the nuclear masses, as they do in carbon dioxide, there would be, in any distortion that leaves unchanged the molecule's center of mass, essentially no change in the center of gravity of positive charge. But with no change in the center of gravity of positive charge and no change in the center of gravity of negative charge, there would be no change in molecular dipole moment and, hence, no absorption of radiation. There is some truth to this. Compared to the electron-cloud-distorting transitions in the visible and the ultraviolet, the intensities of infrared absorptions are relatively low. Interestingly, vibrations that absorb well in the infrared frequently involve nuclear motions that should alternately strengthen and weaken the intramolecular pair-pocket interactions described in the previous section, thereby producing within the molecules oscillating electric dipoles whose frequencies would be related directly to the frequencies of the nuclear oscillations. Heats o f Reaction
+
Many reactions of the type A-A B-B A-B are exothermic. LW for the reaction
Inward migration of a peripheral proton in ammonia produces a water molecule.
+ HnN-NHz
HsC-CHs 4
3
5 5 5 d m
dcc
Outward migration produces an amide ion.
/
Journal o f Chemical Education
2HsC-NH?
2
2 ) dcr*
Some Exothermic Reactions of the Type A-A
B-B
180
2
for example, is -18 kcal/mole. (For the significance of the expressions immediately following the chemical formulas, see below.) Other examples are given in Table 5. The exothermicities of the first four reactions in Table 5 have been cited by Pauling (SO). The exothermicities of the last three reactions, in particular, the one mentioned ahove, may be understood as follows. Table 5.
If such large proton movements as these do not alter the essential shape of the electron cloud, and to judge from the hydrogen-heavy-atom-hydrogen bond angles (107', 104.5", and l M O in NHb H20, and NH2-, respectively), they do not, the much smaller nuclear motions that occur in normal molecular vibrations should have, correspondingly, little effect on the main features of the molecular charge distribution. Indeed, Platt has found that for diatomic hydrides surprisingly good estimates of internuclear distances and vibrational force constants can be made by supposing that the protons move in a rigid charge cloud whose charge distribution is the same as that of the corresponding united atom (89).
=
=
=
2A-B
+
Ethane, hydrazine, and methyl amine are isoelectronic with each other; they have nearly the same bond angles, for example, and nearly the same bond lengths. If these molecules had identical charge clouds, bond lengths and bond angles, it would follow that of the four terms that contribute to the heat of reaction, three of the terms, the kinetic energy of the electrons,
the potential energy of electron-electron repulsions, and the potential energy of electron-nuclear attractions, would be the same for the reactants and the products. Only the potential energy arising from nuclear-nuclear repulsions would be different. The major part of the nuclear-nuclear repulsion term, and that part which changes the most in going from reactants to products, is the part that arises from the mutual repulsions of the heavy-atom cores (charges +4 and +5 for carbon and nitrogen, respectively). This would be so especially if the C-C, N-N, and C-N internuclear distances, dm, dNN,and d c ~were , small compared to the other internuclear distances in these molecules. I n this "short-bond approximation," the potential energy arising from the core-core repulsions in ethane, hydrazine, and methyl amine would be simply, in units of 330 kcal/mole when internuclear distances are in Angstroms, 4 X 4/dcc, 5 X 5/dNN, and 4 X 5/dcN, as indicated beneath theformulasabove, and the calculated difference between the enthalpies (or energies) of the products and reactants, H,,,dUct, -H t,.t,, would be, taking dcc = ~ N N= ~ C = N d = 1.5&
,,.,
The sign of the calculated diierence is correct. But in absolute magnitude the value calculated is too large by approximately a factor of ten. The importance of nuclear-nuclear repulsions in determining molecular properties has been emphasized by several authors: by Lewis in 1916in connection with the Strain Theory of Baeyer and the instability of multiple bonds; by Pauling and Hendricks in 1926 in a discussion of the relative stabilities of isoelectronic ions and molecules; by Latimer in 1929 in a discussion of organic rearrangements; and by the author in a discussion of the effects of multiple bonds, electronegative groups, and lone pairs on molecular properties.1° The statement that in chemical systems, formal charges tend to he as small as possible corresponds to the view (following Lewis, Pauling and Hendricks, and Latimer) that, owing to core-core repulsions, atoms with large core charges tend to reside on the periphery of molecules. Thus NCO- (cyanate ion) is more stable than its isomer CNO- (fulminate ion), NNO (nitrous oxide) is more stable than NON (not known), and FNO (nitrosyl fluoride) is more stable than NOF (not known). For such systems as these, the calculated differences in core-core repulsion energies, though usually of the same sign as the observed energy differences, are in magnitude generally, again, approximately ten times or so larger than the obscrved values. This discrepancy arises because the preferred location of atomic cores within an electron cloud is influenced, in fact, by two opposing factors: by the mutual repulsions of atomic cores, as already mentioned; and by the mutual attractions between atomic cores and valence-shell electrons. From the viewpoint of core-core repulsions, a central location for a highly charged core is undesirable; from the viewpoint of core-electron attractions, however, such a location is desirable. It is a striking fact that, in their effect on the total lo
For references, see the Annotated Bibliography,
molecular energy, these two factors nearly cancel each other. The differences between the energies of systems chemically equivalent to each other are relatively small. Systems with the same number of electrons and the same number of protons and the very same heavy atoms have nearly the same energies. Heats of reaction, to a first approximation, are almost zero. A small, in fact zero, enthalpy change for the reaction H3C-CHa H,N-NH2 = 2H3C-NH2 would be predicted if, as before, it were assumed that the molecules C2He,N2H4,and CHsNH2were isoelectronic with each other and if, contrary to the previous assumption, the central bonds were assumed to he relatively long. I n this "long bond approximation," the molecules could be written, for purposes of electrostatic calculations, in the form R+(EZ2-)R+, where E z 2represents the electron pair of the central bond and R + represents, as viewed from the other end of the molecule, a +1 (not +4) point charge for the CHa group (C4+ core plus 3 protons and 3 electron pairs) and a +1 (not 5) point charge for the NH2group (N" core plus 2 protons and 3 electron pairs). For the R+(Ez2;)R+ model the difference in the nuclear-nuclear repulsion energies of the reactant and product molecules, which by present assumptions is the difference in their enthalpies, is zero. Actually, of course, the heavy-atom-heavy-atom distances in these molecules are neither very small nor very large compared to the other internuclear distances in the molecules. To estimate the change in nuclearnuclear repulsion energies, and, hence, within the approximation of the isoelectronic principle, the heat of reaction, the actual bond lengths should he used. This may be done in the following simplified manner. To estimate the heat of the reaction HC-CHI H2N-NH2 = 2HaC-NHz, we note that this reaction may be viewed as the sum of the following two alchemical transformations. (In thermodynamics it is the ends not the means that are important.) : : 2~
+
+
+
I n the first the active proton moves toward a CHI group; in the second it moves away from an NH2group. Both transformations produce changes in the interaction of the active proton with the following molecular components. (i) (ii) (iii) (iv) (v) (vi)
The adjacent heavy-atom core The valence-shell electrons The geminal protons The gauche protons The trans protons The non-adjacent heavy-atom core
-
Volume 43, Number 4, April 1966
/
181
If ethane and hydrazine had identical charge clouds, bond lengths and bond angles, the changes produced in interactions (i) through (iv) in the first transformation would be cancelled exactly in the second. Deleting from the structural formulas these common items (the valence-shell electrons and the primed nuclei in the structural formulas for ethane and hydrazine), one obtains for transformations (1) and (2) the following condensed representations.
This is of the same form as the expression
given by Pauling (80). X A and X B in Paulimg's expression stand for the electronegativities of the heavy atoms in A and B. The two expressions for -AH will be equivalent if Pauling's electronegativities for the heavy atoms of groups A and B increase linearly with the core charges of these atoms. This they do. The relation is x* = '/% z* '/, Pauling's electronegativities for carbon, nitrogen, oxygen, and fluorine are equal to one-half the core charges of these atoms plus one-half (Table 6).
+
I n (1') a +1 point charge moves toward +4 and +1 point charges; in (2') i t moves away from a +5 point charge. Deleting a t the site of the non-adjacent heavy-atom core the 4 positive charges common t o both diagrams, one obtains the following further simplification of transformations (1) and (2).
These diagrams show clearly why the reaction CzHs N2Hl = 2CH3NH2 is exothermic. More energy is released in step (2") (the diierence in the reciprocals of the lengths of the light lines) than is absorbed in step (1"). The calculated changes in potential energy for the charge movements (2") and (I"), in units of 330 kcal/ mole, are, respectively, 0.20 and 0.10~. The calculated A H for the reaction is, therefore, - (0.20 - O.lOE) X 330 = -31 kcal/mole. (This calculated value would be slightly smaller if the equilibrium configuration of hydrazine were taken as gauche instead of trans.) If it is legitimate to apply the virial theorem, which states that the energy of a molecular system is one-half its potential energy, the magnitude of the calculated value is reduced still further to -15 kcal/mole, not far from the experimental value of - 18 kcal/mole.
+
Pauling's ElectronegafivityScale
By the "short-bond approximation" described in the previous section, or by its refinement given at the end of that section, the energy liberated to the surroundings by the reaction A- A
for A, B pression
=
+ B-
B
=
2A-B
CH3, NH,, OH, or F, is given by the ex-AH
+
= ZA~ Z2 - 2 2 ~ 2 ~
where ZA and Ze are the core charges of the heavyatoms in A and B. The previous expression for -AH is algebraically equivalent to the expression 182
/
Journal of Chemical Education
Table 6.
Core Charges and Pauling's Electronegativities for First-Row Elements
Pauling has described electronegativity as "the power of an atom in a molecule to attract electrons to itself" (SO). The present discussion suggests this alternative description: The 'electronegativity' of an atom is its power in a molecule to repel adjacent atomic cores. The two descriptions are qualitatively equivalent. Both imply that electronegativity should increase with increasing core charge and decreasing core size. The latter description also explains why the electronegativity of an atomic valency varies with the nature of the attached atomsconsider, for example, the inductive effecGand why it varies with the presence of adjacent multiple bonds (86). Classroom Questions
The isoelectronic principle offersteachers of chemistry many interesting opportunities to codify for classroom use diverse facts from the current literature of organic, inorganic, and physical chemistry and, simultaneously, to reveal t o students some of the characteristic patterns of thought of modern research chemists and, also, to promote in students the acquisition of a working knowledge of the nuclear atom, molecular structure, and the Periodic Table. Some illustrative examples of these uses of the isoelectronic principle culled from the recent literature are given below, in the form of short questions. A set of possible answers is appended to each series of questions.
I. With what might one compare (a)the physiological activity of CN-; (b) the splitting out of HCN in the mass spectra of organic compounds; (c) the dissociation energies of Beof, BO+, CO+, NO+, OzC, FO+; (d) the bond dissociation energy of F2; (e) the complexes of T13+; Cf) the low barrier to the methylgroup rotation in cis CHCH=CHF; (g) the hydrogenbonded network formed by the anion in NaHC08; (h) the ligand-bridging properties of ONOz-; (i) the bond angle a t oxygen in (SiH&O; ( j ) the bond lengths
8.
in SiO14-; (k) the basicity of H,O in H F ; (1) the solubilities of HC1, HBr, HI, and NiF2 in HF; (m) the increase in the Bronsted acidity of H F when BF3 is added; (n) the properties of carbanions derived from saturated carbon atoms; ( 0 ) the stereochemical sta(p) the retention bility of alkenyl anions, (>c--=Si--OSiT in quarts, (p) SO2, (p) cyclic trimer of SOs (r) (s) TeC$ ( t j I02F2-,(u) TeF4, ( 8 ) IF,, (u)SiOa (all three modificat~ons, quartz, tridymite, and cristobalite, are known for AlPOd, (2) Pho4-, (y) NHdC104( a ) ( 2 ) H904+,(aa) ice.
SO^:
111. With what might one compare (a)the infrared spectrum of (i) H30+ (the hydronium ion), (ii) H C O c +
(the bicarbonate ion), (iii) CHsC=N-CH3 (the dimethylnitrilium ion), (iv) C(NH&+ (the guanidiuiurn ion) ; (b) the raman spectrum of F e ( C 0 ) P ; (c) the microwave spectrum of fluoroprene (H,C=CH-CF=CH,) ; (d) the ultraviolet spectrum of (i) the trimethyl carbonium ion, (ii) COz+; ( e ) the nmr spectrum ypyran; (0the esr spectrum of (i) (CsH&N+, (ii) adamantane in ethereal solutions over sodium-potassium alloy?
Asymmetric Symmetric stretch stretch
&$&
In-plane bond bend
Amers: (a) (i) NH8, (ii) HNOs (iii) Table 8, (iv) Table 9; (b) CO(CO)~-and Ni(COIr; (c) isoprene (H&=CH-C(CHd= CHI); (d) (i) trimethyl boron, (ii) NCO; (e) 1,4dihydrapyridine; (f) (i) triphenyl methyl radical, (ii) hexsmethyltetraemine in ethereal solutions over sodium-potassium alloy. Exceptions
Exceptions to a theory are exceedingly valuable: They are the raw material from which may he fashioned new and better theories. For the purpose of science is not to verify theories: That is a logical impossibility, and would not lead to essentially new knowledge. The purpose of science is to test theories and, if possible, to falsify them--or, equivalently, to discover their natural limits-and in this way to improve them and make them more useful (54). Each exception to the isoelectronic principle reppresents, therefore, a challenge and a potential opportunity: A challenge to find in existing theory reasons for the exception, and, that failing, an opportunity to formulate and to test new ideas, which might prove useful in a broader context. Some representative exceptions to the isoelectronic principle, with accompanying comments, are mentioned below. Although they have the same electron-to-heavyatom ratio, the compounds of the pairs LiF-BeO, MgFrSiOz, CaFrTiOz and KNOrCaC03 do not have the same structures. Present theory offers a ready explanation for these exceptions in the familiar radiusratio rules for ionic crystals. Similarly, the non-existence of NON, isoelectronic with NNO, and of NOF, isoelectronic with FNO, can he accounted for, as mentioned above, in terms of unfavorable core-core repulsions. It has been suggested that the non-existence of Ar04, isoelectronic with P O P and S O P , and the instability of C10,- may be accounted for by applying the radius-ratio rules for ionic compounds to individual valence-shell electron pairs and atomic cores (5). Volume 43, Number 4, April 1 9 6 6 /
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Similar considerations-and/or steric interactions between valence-shell electrons on adjacent ligands-may explain the non-existence of the molecules S(CH& and SCh, isoelectronic, respectively, with SFe and PCk. The fact that O2 is not isoelectronic with C2H1and the suggestions that C02 (in its configuration of maximum probability) may not be isoelectronic in the usual sense with C3Hl, or Ne with CH4, or SiH, with pH3, have been discussed in terms of electron-electron repulsions in the context of the recently proposed doublequartet hypothesis (5,21). Also, it may be noted that in the ground state C (3P) is not isoelectronic with CH+ ('2) and isoelectronic BH ('2); N (") is not isoelectronic with NH+ (TI)and isoelectronic CH (ZII); but 0 (3P) is approximately isoelectronic with OH+ (%) and isoelectronic NH (32). These examples suggest that protonation of an electron cloud tends to decrease anticoincidence and decreases, or leaves the same, but never increases, the multiplicity. The suggestion that gaseous B203 has a trigonal hipyramidal structure rather than the planar V OBOBO structure suggested by analogy with CH2(CN)2,or an open V structure approaching the linear structure of C302 (owing to the relatively large size of the boron cores, perhaps), if correct, would introduce into valence theory, evidently for reasons different from any previously mentioned, a molecule with a unique valencebond structure. None of the above considerations seems to rule out the possible existence of a carbide of xenon, XeC2, isoelectronic, essentially, with crystallme ICN. It may be argued that the non-existence of compounds isoelectronic with known compounds need not be construed as constituting exceptions to the isoelectronic principle. If the principle is to he used in a predictive sense, however, its limitations in that direction need to be known. The isoelectronic principle is sometimes applied to compounds that have the same number of valence-shell electrons but different numbers of inner-shell electrons-as in the discussion of Hume-Rothery's Rules, for example. Used this way, numerous exceptions to the principle may be noted, both qualitative and quantitative: Qualitative in the sense that the bond angle in H2S, for example, is significantly smaller than the bond angle in HzO; and quantitative in the sense that compounds of second- and later-row elements that contain atoms with expanded octets have no stable counterparts among compounds of first-row elements, which, in turn, when they contain multiple bonds, have generally no stable counterparts among compounds of the laterrow elements. I n the following sense, however, the principle admits of few exceptions: Covalent compounds that have the same number of electrons and the same number of heavy-atoms can have essentially the same heavy-atom geometry. Since the class of stable compounds that has a given number of electrons and a given number of heavy atoms usually contains several members, or else is empty, it follows that covalent compounds that have unique structures (no isoelectronic analogues) are exceedingly rare. 184
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Epilogue
Science, it is said, begins with definition; though probably, more often, that is where it ends. This paper began with the definition that molecules are isoelectronic if they have similar electronic structures. But how similar? Are the electronic structures of H 2 0and NH3 '8 similar"? Certainly they are not identical. Even D 2 0 and HzO have small (and for some purposes important) differences in their electronic structures, owing to differences in zero-point vibrations. How finely, then, should the line be drawn? Personal preference in this matter will depend in part on whether attention is focused on family resemblances or on individual differences. It would appear that generally, though not always, '
Molecules are called isoelectronic if they have equivalent bond-diagrams.
by "equivalent bond-diagrams" is meant identical bond-diagrams when one disregards two things: Differences between the symbols for the elements (provided, usually, that the number of inner-shell electrons is the same), and differences between protonated and nnprotonated electron-pairs. This definition does not cover systems whose classical bond diagrams require modification, to allow for "resonance," for example, or for "pair-pocket interactions"; nor does it cover systems whose bond diagrams have not yet been worked out. Acknowledgments
The author is indebted to his colleague Dr. Doyle Britton and to the editor of THIS JOURNAL and the members of the AC8 Resource Papers Committee, particularly Dr. Milton Tamres, to whom numerous improvements in the paper are due, for many helpful suggestions and comments. The point of view adopted in this paper is the author's and not necessarily that of his colleagues, who, while they have given freely of their time, are not responsible for any errors and ambiguities that may remain. Litemlure Cited (1) MOORE,C. B., AND PIMENTEL, G. C., J . Chem. Phys., 40, 1529 (1964). (2) FORMAN, R. A., AND LIDE,D. R., JR., J . Chem. Phys., 39, 1133 (1963). (3) See, for example, MULLIKEN, R. S., P h w Rev., 41, 52 (1932); SATURNO, A. F., AND PARR,R. G., J . Chem. K. E.,AND HAKE,R. B., Phys., 33,22 (1960); BANYARD, J . Chem. Phys., 41, 3221 (1964). (4) PAULING, L., J. Am. Chem. Soc., 55, 1895 (1933). (5) BENT,H. A., J. CHEM.EDUC.,42, 348 (1965). (6) SELIG,II., Sciaee, 144, 537 (1964). (7) SMITH,D. F., Sciace, 140, 899 (1963): BEGUN,G. M., FLETCHER, W. H., A N D SMITH, D. F., J. Chem. Phys., 42: 2236 (1965). (8) IBERS,J. A., HAMILTON, W. C., AND MACKENZIE, D. R.. Inorg. Chem., 3, 1412 (1964). (9) FRANKLIN, J. L., J. CHEM.EDUC.,40,284 (1963); CARLSON, T.A., AND WHITE,R. M., J. Chem. Phys., 36,2883 (1962). (10) PIMENTEL, G. C., SPRATLEY, R. D., AND MILLER,A. R., S c i a e e ,. 143. 674 (1964). But see also ALLEN.L. C.. , ,
.
ERDAHL, R. M., AND WHITTEX, J. L., J. Am. Chem. Soc., 87, 3769 (1965). (11) KIMBALL, G. E., AND LOEBL, E. M., J. CHEM.EDUC.,36,233 (1464)
(12) GOLDSCHMIDT, V. M., "Geochemistry," Oxford University Press, London, 1954; BARRON, T. TI. K., BERG,W. T.,
AND
MORRISON, J. A., PTOC. Roy. Soe. (London), 250, 70
,.""",.
11050\
(13) EVEREST,D. A,, "The Chemistry of Beryllium," Elsevier Puhl. Co., New York, 1964. (14) BOLLER,H., A N D PARTH*,E., Acta Cryst., 16,830 (1963). (15) BABB,S. E., JR., Rev. Mod. Phys., 35, 400 (1963). (16) MOOSER,E., AND PEARSON, W. B., J . Chem. Phys., 26, 893 (1957); MOOSER, E., Seiaee, 132, 1285 (1960). L., Am. Sei., 43,285 (1955). (17) PAULING, (18) SMITE, ALEXANDER, "Introduction to General Inorganic Chemistry," The Century Co., New York, 1907, pp. l dl R Ls.
(19) KJEKSHUS,A., AND PEARSON, W. B., Prog. in Solid Slate C h a . , 1, 83 (1964). (20) GIBB, T. R. P., JR., Pmg. Ino~g.C k m . , 3, 315 (1962). (21) LINNETT,J. W., "The Electronic Structure of Molecules. A New Approach," John Wiley & Sons, Inc., New York, 1964; J. Am. Ckem. Soc., 83, 2643 (1961); Am. Sn'., 52, 459 (1964). (22) DISMUKES, J. P., A N D WHITE,J. G., Inorg. Chem., 3, 1220
