Coulombic Models in Chemical Bonding Description and Some Applications of a Coulombic Model
I.
Lawrence J. Sacks' Christopher Newport Wlege, Newport News, VA 23606 Few other subjects have received the attention given in THIS JOURNAL and elsewhere to chemical bonding. It is the
framework on which are hung explanations for a w a e variety of chemical phenomena, but i t is more than t h a e i t pervades our thinking about \.irtually all aspects of chemistry, from naming com~~ounds to visualizing reaction pathways. A minor modl;ficatibn of bonding theory may affect only a limited area, but a substantial change could have far-reaching effects, well beyond those initially envisioned. I t is suhmitted that current bonding theory is in need of major revision. that an attractive alternative is available. and that somk significant effects can already be described.' A bondine theorv is offered whicb provides a framework for the de~&~tion"ofa wide range oi substances and provides quantitative information of remarkable accuracy with far less computational effort than is required of other approaches. In this paper the model is described and some Hpp~icationsare presented, including the calculation of bond energies of two important binary hydrides, methane and diborane. Results in all cases suooort the alternate theorv to a degree of accuracy unavailable from other models except with extraordinary effort, if at all.
..
The Coulombic Model The "new" model, which is really a very old model refurbished in more auantitative terms. is based on coulombic interactions of pdint charges. I t is easily visualized and may be used at varvina levels of so~histication.The explanations and predictions appear to he generally applicabie, but are particularly significant for compounds of hydrogen. The model is not intended to he a substitute for an aceurate quantum mechanical description; rather, i t offers a different ~ o i nof t de~arture.In some cases it amears .. to brine us directly to significant information not previously described. Some of this information is aualitative (such as the criteria for molecule formation), some quantitative; much is inconsistent with certain provisions of valence bond (VB) theory (I). The proposed model is more compatible with the models of Linnett (2), Gillespie (3), and, particularly, the some Tangent-Sphere model descrihed in THIS JOURNAL two decades ago by Henry Bent (4). It also appears to he closely related to an approach described by Kimhall (5)and apparently developed with success by his students for certain cases (6);unfortunately, only brief descriptions of this work are readily available. I t is, in some respects, an initial simplification of some aspects of each of these, but it includes quantitative aspects that support the qualitative concepts and extend the use to areas not ~reviouslvaccessible thiough just a qualitative approach. The sphe;ical charge cloud of most of the other models has been reduced to point charges a t the center of the charge cloud. Interactions among atoms are considered to he primarily coulombic, involving, as a first approximation, only cationic cores, anions, and airs of electrons. A more adequate description of some systems requires anions also t o b e considered as cationic cores surrounded by four pairs of electrons. Four tenets provide the basis for the Coulombic model. These lead to four corollaries and to operating rules, based on the tenets and corollaries, for predicting structures and related properties.
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Journal of Chemical Education
Postulates 1) All compounds and complex ions may be considered as assemblages of ions with electron pairs sometimes acting as anions. 2) The formula of the assemhlage is determined by the charge ratio of the ions and, for complex ions, the net charge. 3) The structure of the assemhlage is primarily determined by the size ratio of the ions. 4) A molecule is a neutral assemblage in which the cati o n ( ~is ) (are) completely surrounded by anions andlor electron pairs: i t has a negatively charged surface.
1) Oppositely charged ions continue to assemble into extended arrays until a neutral species is obtained in whicb each cation is completely surrounded by anions or by anions and electron pairs. If such an aggregate is accessible with a finite number of ions, a molecular compound results; if not, the compound formed is a one-, two-, or three-dimensional array, giving, respectively,linear polymers, sheet polymers, or salts. Included as salts are such crystalline eompounds as potassium chloride, lithium hydride, sodium hydroxide, and calcium oxide; materials such as hydrous iron(II1) oxide (hydroxide) are better considered as multibranched linear -polymers. 2) The packing properties of ions can be predicted from the ratio of the radii of the o~positelvchamed ions. In most cases, a set of rules d&ed on geomet& considerations allows unambiguous determination of structure type. Where indeterminate results are obtained, estimates of the relative energies of the alternate possibilities are needed to predict the more probable structure. Where two or more structures of comparable energy are predicted, they may correspond to different structuresfavored st differentconditions or to one or more unknown substances of potential interest. Two hypothetical eompounds are PHs and NHs; the former is predicted to have properties similar to those of PFs, but to dissociate into PHs, Hz,and probably higher P,H, polymers; the latter would probably exist only at Hs pressures. Conversely, the molecular structure predicted from molecular orbital calculations (7) for the hypothetical CH2Li2would be an exception-it is predicted not to exist as such a molecule at ordinary temperatures. 3) An electron pair can behave as an anion of zero atomic number; thecenter of the sphere can be considered as a point charge (-2) for calculations involving ground states. An electron pair bridging two cationic cores constitutes a traditionally descrihed covalent bond. ~
Taken in part, from papers presented at the 184th ACS National Meeting, Kansas City, MO (1982); the 177th Meeting, Honolulu, HI (19791: and the Sixth Biennial Chemical Education Conference.Roch-
I o n leave 1985-86, Laboratory of Chemical Evolution, Department of Chemistry, University of Maryland, College Park, MD 20742.
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41 -H"v d r o ~ e nexists in combination with other elements
exclusively as hydride ion, H-, aproton a t the center of a n electron air. For most calculations the hvdride ion is considered as a -1 point charge. Hydrogen is never involved in "covalent" honding.
Rules for Predlctlng Structures of Blnary Compounds A) Determine the charges on the ions. 1) Decide which ion will be the anion:
The atom which requires the fewest electrons to fill its valence shell is the anion. If two atoms are in the same family, select the smaller atom for the anion. 2) The other ion(s) will be the eation(s). Remove all valence electrons to form the cation. 3) Establish a tentative empirical formula for the compound. B) Determine the structure of the compound. The radius ratio (anionlcation) determines the number of anions that can pack around the cation. The structure of the c o m ~ o u n dis ~ r e d i c t e dhv comoarine this coordination number of the cation with thk ten'tative em~iricalformula. Three ~ossihilitiesexist, d e ~ e n d i u e on how well the anions fill the space around the cation.1) The eoordination number for the cation is the same as the
number ratio in the empirical formula: in the neutral assemblage the anions fill the space around the cation. This initial assemblage meets both requirements for a molecule. 2) The coordination number for the cation exceeds the number ratio of anions to cation according to the empirical formula: the space around the cation would not be completely filled, so additional anions are added to fill the space around the cation; this produces a complex anion. More cations are now sdded to balance the charge; but, then, more anions are needed to fill the space around the added cations, and so forth, giving an extended structure: a) If only one more anion is required to fill the space around the original (empirical formula) unit, a dimer or a onedimensional polymer will result, the polymer terminating when extra bridging to the chain occurs through two bridging anions or cyelization. h) If more than one extra anion is needed, s multidirectional polymer results. When several extra anions are needed, a three-dimensionallattice results: a salt is formed. 3) The coordination number for the cation is Less than the number ratio according to the empirical formula: there is not enough room around the cation properly to pack the number of anions required. (This will occur mainly when halide ions surround highly charged cations.) In this ease, two options are available: a) The molecule is formed by "crowding" the anions. This will more likely occur if a regular polyhedron (coordination numher 3,4,6, or 8) is thus attained. b) The coordination numher of the cation is reduced by adding a pair of electrons (e22-) as one of the ligands, thus reducing the positive charge of the assemblage by two units. Anions are added to fill the remaining coordination positions. This situation is frequently encountered with cations from groups V-VII, which add electron pairs to form pseudotetrahedral molecules. If the crowdine is not suffieientlv relieved. or if an unsvmmetrical arrangement results (coordinationnumbers 5 or I ) , one or two additional pairs of electrons can be added to the cation ~~
~
for predicting or descrihing structure type. Possible prohlems in current hondine theorv. first sueeested hv discreDancies with quantitative results based oniKe coulokbic model, t now anaear to he inherent in current theorv. .. i n d e ~ e n d e nof the acceptance of an alternate model. I t is frequently implied, if not explicitly stated, that apparent problems with current honding theories disappear with achievement of the mathematical sophistication required to master the quantum mechanical explanations. That is undouhtedly true in many cases; however, as shown hy the calculations of dipole moments in the following paper of this series, there are some references to quantum mechanical equations that only reflect inherently specious arguments. Such situations are of particular concern a t the introductory level, where much of the presentation is far beyond the comprehension of the student and some of what is "clear" is inaccurate and illogical. I t is relevant to consider the justifiability of a presentation at any level that demands acceptance of concepts that none of the students can understand and few instructors can evaluate.
Period N nydrdes
The hydrides of Period I1 illustrate several of these concepts (Table 1). Since hydrogen is involved, each Period I1 element is, successively, considered as the cation of the hydride compound. The radius for H-, 1.5 A, and other values are from ref. 8; see, however, the discussion of ionic radii below. Lithium hvdride. The radius of Li+ is 0.65 A: the radius ratio of 2.3 rdquires six H- to fill the space around each Li+ ion. There is no wav to achieve a neutral snecies for anv small assemblage; therefore, a molecular compound is excluded. Since the numher ratio of Li+ to H- is 1:1, the H- is also 6coordinate, giving rise to a sodium chloride structure. A higher energy 4-coordinate structure would also he a salt and might exist a t a higher temperature. Beryllium hydride. The minimum coordination number of Be2+for H- is 4. If four hydride ions are arranged around the BeZ+(tetrahedrally), they will fill the space but leave a net 2- charge; an additional Be2+ is needed. The numher ration requires each H- to he 2-coordinate for asymmetrical arrangement; hence. hridgingof the hydride ionsisrequired. A single bridging hydride will give rise to still higher negative charge, since three more hydride ions will he needed to Table 1.
Perlod ll Hydrldes
Formula from
r
Charge Cation Ratio
Sire Ratio4
K
C.N. for P- a
~~
An important consequence of these considerations is that the usual "ionic" uersus "coualent" dichotomy is not operatiue for describing structure type; instead the occurance of molecules uersus ionic crystals is attributed primarily to the packing properties of the ions making u p the assemblage and is predictable withgreat confidence just from the relatiue sizes of the ions. This approach requires a reexamination of the concepts of electr&egativity and the associated "polar bonds". Representative examples of structure type described above verify the expendability of these concepts
Redined Structure NaCl structure: salt: (both Ions are octahedrally coordinated) Linear polymer of (BHn),; each Hbridges to 2 Be. Olmeric &He, with two bridging H- ions: favored over m o m e r i c BHJ. CH, (Td) (molecular) NH5 or (molecular) (ti)20H, (molecular) it l\.FH lmolecularl (t h),Ne (moiecular)
/INH~
- . to Nee+
. . ., NeH.
-
>20
(est)
2
.
values horn re1 s:the radius of H- is given as 1.54 i. on spaoelilling model. See, for example, ref. 1, p 545: note mat size ratios given inref. lareme morecmmon @/Ar ratios. mdarerecipmcally relatedtornose used here.
Volume 63 Number 4
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fill the space around the added Be2+ion. While both BeH42and Be2H& ions appear possible (packed with suitable cations into salts), the binary Be-H compound is possible witha double hydride bridge, since it allows a repeating, neutral, BeH2 unit: the Be2H62- unit adds another Be2+, then two more H- ions and so forth, giving a linear polymer. Cyclization or cross-linking to other chains terminates the polymer. Boron hydride. The 3:l charge ratio provides the horon with a sufficient number of hvdride ions to fill the soace around the boron ion and prod;ce a molecule. Analogy k i t h methane (and our knowledee of this svstem). reouires . that we consider also a 4-coordinate (tetrahehral) structure.2The BH4- ion is expected, analogous to the isoelectronic BeH42and CH4. Bridging of BH3 through two hydride ions (analogous to the BeHz structure) provides each boron a coordination number of four. The addition of the second BH3 unit leaves the aggregate uncharged. Each horon cation is now completely surrounded by negatively charged hydride ions, providing a negatively charged surface; B2H6is thus directly described. This molecule is considered further in the following section on bond energies. Carbon hydride. Packing four hydride ions around a C4+ cation gives the tetrahedral, nonpolar CHI directly. Because good data are available for this system, i t provides a unique test of the model. As shown in the followine section (Bond , Energies), the point-charge calculation for ;he bond energy of methane eives aresult within the ranee of reoorted values. The procedLre for describing higher lhydrocmhons is described in the section on hvdrocarbons below. Note the formal similarity to other carbon tetra halide^, partirularly fluoride: this s~ructuralsimilaritv is reflected in similaritv of properties. Nitrogen hydride. No structure with five equivalent anions around a central cation is eeometricallv possible: there.. fore, the postulated NH5 wouid necessarily have two subsets-three equivalent eauatorial hvdrides and a pair of axial hydrides,~prohatdyn i a differen; distance (to minimize the potential energy of rhe compound). This "overcrowded" stmcture is not hut must be considered in conjuntion with an alternate structure in which a pair of electrons is added to the nitrogen cation (N5+)to act as an anion, giving ammonia molecule as a distorted tetrahedral (C3J structure. Since the pair of electrons constitutes a unioue e t ~ dof the molecule, we predict that ammonia will be poiat. The structure can he predicted. walitatirelv. as follows: the molecule can be considered a s ' a - ~ cation ~ + k r o u n d e d by four electron pairs, three of which have embedded protons and, hence, will be smaller spheres than the remaining lone pair. The repulsion of the proton for the nitrogen core requires that the equilibrium N-H distances be greater than for N-electron pair. The lower repulsion between two hydride ions than between a hydride ion and an electron pair gives an H-N-H angle less than tetrahedral. The results are consistent with observation. In this case., onantitative information is available concerning angles and distances for the three hydride ions, hence the center of charge of the electron pair can be located unequivocally along the C3 axis. The electron distribution in ammonia is treated further in the section on electron distributions below; dipole moments are considered in more detail in the second . oaper . of this series, to follow. Oxygen hydride. While six hydride ions around the 0 6 + cation would provide a svmmetrical arrav. the hvdride ions would exhibitkxtreme "ciowding"; that is, they would not be able to approach the 06+ core as closely as they could with a ~
~~
.
This assumes the (constant)ionic radius of hydride ion (154 pm). See the section on Ionic Radii (vide infra)for a furtherdiscussion on this point; it makes the assiunment of tetrahedral coordination less arbibary.
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Journal of Chemical Education
lower coordination number for the oxygen. This suggests consideration of an alternate structure with one or more pairs of electrons returned to the oxygen core. One electron pair would give a 5-coordinate structure, with problems more severe, for the 6+ oxveen cation. than for the lareer 5+ nitrogen, hence this stru&re is highly unlikely. ~ e p l a c e ment of four hvdride ions with two electrons pairs aives the 4-coordinate dihydride as a reasonable str&ture, a "finding" supported by calculations of the relative energies of the structures. The qualitative treatment of the angles and distances follows that for ammonia. Since there are only two hydride ions, the H-O-H angle is expected t o be smaller than the H-N-H angle in ammonia. Fluorine hydride. Three pairs of electrons are returned to the fluorine to give FH. The single hydride requires a dipole moment with the hydride end positive and the resultant of the three electron oairs contributine the neeative end of the dipole, consistent with qualitative predictions based on sizes and aneles for the electron oairs (the are made in . nredictions . the manner described for ammonia and water). Neon hydride. I t is tempting to state that the ionization energy of neon is too high to allow i t to lose eight valence electrons, but the results with methane suggest that further exolanation mav be reouired. As with nitroeen. - . oxveen. . - , and fluorine, the s m h l corecannot provide space for the hydride ions to a u ~ r o a c hcloselv enoueh to release enoueh coulombic energy &remove eight elect;ons. Returning eikctron pairs, rather than hvdride ions, allows a lower coordination number, but the successive additions give either unfavorable geometries (7-coordinate Ne(ez)H6 and 5-coordinate Ne(ez)sH2)) or overcrowding (Ne(e2)2H4). Neon molecule can thus be considered in the usual (s2p" manner or as a core surrounded tetrahedrally by four electron pairs. I t is noted that, while the hydride or other halide of neon is not expected, structures with anions of higher charge, particularly oxides, are not excluded.
-
-
Bond Energies
The coulombic model allows a convenient format for information about known structures and reliable oredictions concerning unfamilar substances; however, the fkature that distinguishes it from other models is the ease with which reliable quantitative or semi-quantitative informati2n can he obtained. Two calculations of bond energies are described here-the average bond energy of methane and the dissociation energy for diborane. These two are selected because they pertain to discrete molecules which contain no lone pairs of electrons; no satisfactory quantitative treatment for electron-electron interactions within lone pairs has been found. The geometric relationships among the angles and distances for the three symmetrical cases of 4-coordinate cations (tetrahedral and pseudotetrahedral bonding) are shown in Appendix A. Bond Energy of Methane. The average C-H bond energy of methane can be calculated by using an energy cycle similar to Dart of the familiar Born-Haber thermochemical cvcle for ionic crystals. Since a molecule is formed, the calculation cornoarable to that for the crvstal lattice enerev -.involves onl;10 terms-four C4+-H- attractions and six H--H- repulsions. The general equation for these interactions is
where e is the electron charge, 1is the bond length, zlis the charae on the cation. and z? is the charge on the anion ( ~ p i e n d i Bl). x For the process, CHl(g) C(g) + 4H(g), the average bond energy is defined as one fourth the enthalpy of atomization. The cycle used consists of the first four ionization enereies of carbon, ionizing C(g) to C4+(g) 4,; electrenic affinity of
-
,+
Table 2.
1X
E.A. of H
=
-288 rw. prna
-
Net Coulornbic Energy
= -15,698
Enhlpy diagram lor calculation of bond ensrgy in memm, (not to scale). Values are in W md-'. Heavier lines enclose valuss used to calculate oond energy: values are from Appendix 82. Lighter lines show data used to describe cycle: values are horn ref. 8: H2 bond energy, p F-22% entbipy 01 f~rmallm sublimation enlhalpy for graphite, p F-230; A@, p D-78.
hydrogen; and assembling the ions a t the equilibrium C-H distance (Annendix B2). The cvcle is shown in the figure. Also included are data relating the enthalpy of formation of methane. The average bond energy calculated by the "ionic methane" model, 427 kJmol-I (102 kcal mol-9, is consistent with accepted values for the C-H bond energy (9-11). The value from the heat-of-formation cycle is somewhat less certain, reflecting less certainty in the energy terms added for this part of the cycle, especially the beat of sublimation of carbon. Borane u e r s u Diborane. Quantitative estimates have been made of the relative stability of B2H6versus 2 BH3, using the D3h configuration for BH3, first with doubly bridged tetrahedra (sharing an edge) and then using the experimental bond angles and distances of BzHs (see Table 2). For the former case, the dissociation energy of B2H6 t o 2 J mlr mol, giving positive BH3 is predicted to be 2.3 X values for all B-H distances, r, and a typical value of about 150 kJ mol-I a t r = 150 pm, in reasonable agreement with a (questionable) reference value of 23.9 kcallmol (100 kJ mol-I) (12). For the latter case, using experimentally determined distances and angles for diborane (13,14), the calculated dissociation energy is (16.65 - 2.019 X 10-smlr) MJ mol-I, which is negative for r < 120 pm, increasing rapidly
. .
Calculated Enthalples of Dlssoclatlon of B2H.
A* Dlssoclatlon. kJ rnol-' Tetrahedral Model Experimental Structure
thereafter. This model eives acce~tabledi'ssociation enereies at distancess~i~htly greater than.120 pm, consistent withthe radius calculated from H-H internuclear distances (see the section on ionic radii below) and the reported radius of B3+ (8). Other Blnary Structures (Examples) Calcium-fluorine. The radius ratio of fluoride ion to calcium ion req&es at least eight F- to fill the space around each Ca2',so earh Ca2+is fixed at the cenrer of a cubeof eight F-. Since the charee ratio reouirea two F- ner Ca2'. each F- will have, on aveige, four 'Ca2+ ions te'trahedraily arranged around it. The structure that accommodates these reauirements is the lattice named for this compound, the fluorite structure. Note that while the freauentlv cited Lewis structure for the compound will give the c o r r k t formula, i t does not provide guidance t o structure type, allowing the prediction of a molecular structure, analogous to SiF4. Nitrate ion. The small N5+cation is reasonably well surrounded by three oxide ions, whether they are considered as point 2- charges or as assemblages of 6+ cores with four pairs of electrons. The latter model allows bonding through either one or two pairs of electrons, but either model gives the planar (D3d arrangement if anionic repulsions are to be minimized. Sulfur-oxygen. The S" cation is adequately surrounded bv three oxide ions onlv if one or more acts as a chelatine anion (using two electron pairs); therefore, molecular SO3 6 expected to be susceptible to attack on the sulfur. The available space around sulfur permits strong interaction of SOs molecules: since there is snace for onlv one more 0 2 - around the S6+,the structure ( ~ 0is ~expecied ) ~ to be a linear polymer. Cyclization and random length chains are expected, hence SO3 would be expected to have a rather high temperature softening point rather than a sharp melting point. Sulfate ion is analternate aggregate that fills the space around the S6+ and would be predicted to be the favored arrangement whenever cationsare available to balance the char&. Sulfur-fluorine. The minimum coordination number for S6+ with F- is four. The charge ratio calls for SF6, which would b e - a tightly packed octahedral molecular species. Since the molecule has no unique end, it is nonpolar; since the central ion is inaccessible to the negative surface of another molecule, the intermolecular forces are weak, and this compound is expected to have a very low boiling point, similar to that of a noble gas of comparable molecular weight. Because of significant repulsions among the anions, consideration must also be given molecules in which one or more pairs of electrons occupy coordination position(s) on the sulfur. These give, in turn, tlSF4, either C2, or C4", and (tl)2SF2. Given the formula S2F10 for another molecule, the structure is predicted as follows: two S6+ ions and 10 F- ions require one extra pair of electrons for electroneutrality. The electron pair is located adjacent to the highest charged Volume 83 Number 4
April 1986
291
ion(s), in this case between the two S6+cations. The 10 Fions then occupy the remaining octahedral positions around the two S6+cores, giving a nonpolar molecule of Dqh or Dgd symmetry. Like SF6, i t should have a relatively low boiling point. Hydrocarbons. The methane structure has been described. Higher alkanes are constructed by the same procedure described for S2Fla-the electron pairs needed for neutrality are placed between adjacent carbon atoms, with hyd r i d e ions filling t h e r e m a i n i n g s p a c e s t o give a pseudotetrahedral, negatively charged surface around each carbon core. Olefins are constructed with two bridging electron pairs, retaining a pseudotetrahedral configuration for the carhon cores with respect to the electron pairs but a triangular configuration if only the nuclei are considered. Alkynes are similarly constructed with three bridging pairs of electrons, linear with respect to the nuclei. The frequently cited description of hydrocarbons sharing a corner, edge or face of the tetrahedron is applicable to this model. Models of aromatic systems are similarly constructed, with the odd electron from each carbon shown formally on that core but enjoying mobility not found in bonding electrons due to the availability of bonding sites on adjacent carhon atoms as well as on its own. Silicon-halogen. Because silicon is larger than carhon, the silicon core in the tetrahedral silicon-halogen compounds is less effectively shielded than is the smaller carbon core of analogous compounds. This is reflected to a minor degree in higher boiling points; but the major consideration is in the much greater rates of reaction for the Six4 molecular compounds than the corresponding carbon compounds toward S Nsubstitution. ~ Titanium-halogen. The sliehtlv laraer size of Ti4+ compared to Si4+ (68bm versus & PA) (8i explains why TiC14, like SFa. is a molecular compound. hut the corresponding fluorides are vastly dit't'eren-there is room for six tluoridr ionsnruund theTi4'cwe. ioTiF,, unlike SiC',, is not mdecular. Multi-dement Compounds
The coulombic point-charge model for structures with three or more elements usually involves deducing the structure of an anionic complex of high symmetry to pack with the lareer of the cations present. For examde. . . .potassium sulfateuis considered by first packing oxide anions around the sulfur cation (S6+)to provide the tetrahedral sulfate ion, and then treating that ion as a large anion to be packed with potassium ions. Ammonium ion is structured from four hydride ions tetrahedrally arranged around the N5+core; this ion can be packed with anions into salts. The multicharged oxyanions are special in that they can he prqtonated to give the less symmetrical protonated anions (e.g., phosphate and mono- or dihvdroeen nhosnhate anions): while it is a oroton that is addedto t c e okyanion, the result is a hydride ion-a proton embedded in an electron pair on one of the anion cores (usually oxygen). A special case of the polyatomic anion is that of groups of complex anions consisting of a single kind of atom. Oxygen molecules, for example, can gain one or two electrons, forming the superoxide a n d peroxide ions; "carbide ion" may be either monoatomic or polyatomic, as can the sulfides and polysulfides. Group Trends
Higher memhers of any group are expected to exhibit higher coordination numbers than the elements of lower atomic number due t t ~ increased core sbe, thus, while neither has vet been ~revared.it would be predicted that PH5 could be s;nthesiz;d a t more moderate conditions than those likely to be needed for NH5. Similarly, higher hydrides of sulfur should he easier to prepare than those of oxygen. The larger 292
Journal of Chemical Education
core size in the higher memhers of a group leaves them more accessible to nucleophilic attack than lower memhers with the same number of ligands, accounting for the greater rate of nucleophilic substitution, for example, for compounds of silicon, germanium, and tin than for the corresponding carbon compound. The larger cores also cause greater interionic distances to the anions, accounting for theweaker bonds. Protonic Acids and Bases
The hydridic hydrogen of the coulombic model is not only compatible with the proton-transfer concept of Bransted acid-base reactions hut is also properly a part thereof. This is more evident if a minor modification is made to the usual Bransted-Lowry definitions of acid and hase: a base is a proton extractor;
an mid is a proton source.
The emphasis is shifted from the strength of the acid to that of the hase. "Proton donor" leaves the impression, fortified by the usual structural diagrams, that the protons are hanging out on the periphery of the acid, like ripe plums on the tree. By either this or the usual Bransted definition, the proton itself is not an acid, but hydride ion is clearly an acid, since it contains an extractable nroton. The ease of extraction of the proton (acid strengtd) and proton affinity (base strength) are d e ~ e n d e norimarilv t on the size of the electron pair and on thecharge of nearh; atomic cores. In general, repulsions of highly charged cores adjacent to or near the electron pair enhance acidity and, therefore, decrease the hase strength. The trend is seen, e.g., in isoelectronic series such as Si4-, P3-, S2-, and C1-, in which the hasicity decreases significantly with increase in core ionic charge. A similar trend is found in the series of isoelectronic oxyanions of elements of the Third Period, SiOq4-, Pops-, and C104-. For cores of the same charge, the more diffuse electron pair on the larger core is less basic than the more compact electron pair on a smaller core. This effect is predominant within families, with the larger ions being less basic, as in Group VIA, Te2- < Se2- < S2- < 0 2 - or the halogens, I- < Br- < C1- < F- < H- (although H- is unique in structure type). These "inherent hasicity" factors must be considered in connection with other factors-primarily solution effects-which affect the proton transfer process if accurate predictions of hasicity are to be obtained. Hydrogen in the Periw'c Table
The position of hydrogen in the Periodic Table has evidently been a cause for concern for some time; current variations of the Periodic Table show i t in Grouo IA. VIIA (or VllR depending on the con\.ention followed): IVA (or IVR) or all of the above. Since the oroton is extracted in acid-base reactions, a relationship to other atoms forming unipositive ions is suggested and hydrogen is assigned to Group IA. Its existence as an undisputed anion in saline hydrides has given it a position at the head of the halogens, and its halffilled shell evidently allows it t o share a position, in some tables, with the carhon family. Each of these assignments can be iustified on the basis of usual structural diaerams showing hydrogen a t the end of the line representing pair of bonding electrons, implying, by analogy to all other cases, the location of an electron pair between a proton and the next atomic core. The historical basis for such interoolation involves some of the most prominent names in development of bonding theory (15). Hydrogen, however, is not analogous to any element except, perhaps, the halogens, and then only if i t is considered to react exclusively as hydride ion. Lacking underlying valence electrons, a positive hydrogen ion would have no radius of chemical dimensions, the proton being effectively a point charge among atoms and electron pairs. In the coulombic model, combined hydrogen always has a pair of electrons in
a
the spherical ls2valence shell to provide a physically significant radius for the anion. Unlike any other anion (or cation, for that matter), hydride ion can transfer its nucleus; thus, mobility of the proton from electron pair t o electron pair is a feature unique to this element and, therefore, not a valid basis for grouping it with the alkali metals. On the other hand, the physical and chemical properties of the element agree quite well with those of the (other) halogens, especially the next higher member, fluorine. Such evidence suggests the exclusive assignment of hydrogen to Group VII as the first halogen. Ionic Radii The prediction of structure type based on the relative sizesof ions presumes that aphysically significant radius can he assigned to each ion. Such predictions have proved quite successful in distinguishing molecules from extended arrays of ions. Part of the success is attributable to the rather forgiving nature of the structure criterion-most questions arising from small differences in the ratios affect only the details of each tvne of structure. In many cases the uncertainites are relatkd to questionable valueifor the ionic radii; this. in turn, reflects, at least in part, a problem of defining any ionic radius. Most ionic radius values are based on internuclear distances in ionic crystals, this crystal radius being obtained by partitioning the distance between adjacent oppositely ihareed ions accordine" to theoretical arguments or to an u empirical assignment that provides greatest consistency for those crystal structures considered (16, 17). An alternate definition is the distance from the nucleus of the ion to the center of charge of the valence electron pair. This effectiue radius, usually calculated by quantum mechanical methods, will necessarilv be less than the crystal radius because of the electron-election repulsions of outer electrons of adjacent ions. However they are determined, and whichever type of radius is used, variations are found in reference values, particularly for the crystal radii, which are found to depend not only o n ionic charge hut also on coordination number and crystal structure. Reference values for the radius of hydride ion cover a much wider range than for any other ion, regardless of which radius is cited. While crystal radius values of all ions are susceptible to the influences of surrounding ions, such influences have a much more substantial effect on hydride ion. Primary among such influences is the charge on the adjacent coreis). In this and other respects the hydride ion more closely resembles a lone pair of (valence) electrons than other anions: both consist of a pair of electrons without underlying core electrons. I t is not surprising, therefore, that the effective size of the hvdride ion. like that of a nair of valence electrons, decreases sharply kith increasing charge on adjacent core(s). On the same core, hydride ion is expected to occupy a smaller region than an electron pair, because the proton greatly restricts its pair of electrons, while lone pairs can spread out over the available spaces. These effects are illustrated by the binary hydrides (Table 3). Consider, for example, the Period I1 hydrides. In B2H6 there are both bridging and terminal hyride ions; yet, even though the B-H distance for bridging hyrides is sign~ficantlygreater than for the terminal hydrides, the three H-H distances vary by only one or two oercent. The monotonic decrease in the effective radius, &en as half the internuclear distance, is much ereater for different core charees than within the B2H6 molecule: 89 pm in methane, 81
