Simple models which explain the shapes of molecules have In the valence state of A (denoted by A*), each of n hybrid played an important part in the practice and teaching of orbitals, directed along the hond axes, is singly-occupied; any chemistry. The popular VSEPR (Valence Shell Electron Pair remaining valence electrnns of A will be in doubly-occupied Repulsion) model ( I ) , is easy to handle and is usually reliable h e pair orbitals. The standard euthalpy change for the in its uredictions. However. there are a number of well-known Process (2)

Derek W. Smith School of Science

University of Waikato Hamilton. New Zealand

exceitions to the VSEPR rules. For example, some alkaline earth dihalide molecules are bent (2). although the VSEPR

The Valence Bond Interpretation of Molecular Geometry

m d r l suggests that they should be linwr. N'hilr most AH.. species withour lone pairz on the central ntont are trigmal hilpramidal, ns predicted hy the \'SEPR model, some arr square pyramidal. I'crhapa the mcgst seri(ms ohj~ction to thr \'3EPR model rat least in thr form in whirh it is usunll\. Dre. " . sented to students) lies in its concentration on repulsive forces as dominant in determining molecular geometrv, ignoring complctrly the hmding forces (which must I>(. yriuter in n stable molrrulel. A theorv whirh describes the honding in H

molecule, while a t the same time explaining its geometry, would be preferable.

Simplified molecular orbital (MO) approaches to molecular geometry have been advocated (3-6), but these are more dif- ficult to apply than the VSEPR model.

The purpose of this paper is to show that the valence bond (VB) theory not only provides an attractive means of de- scribing the bonding in a molecule but can also explain its geometry. The ideas behind the following discussion are not new; they follow directly from the principles laid down by Pauling and others (7) in the 1930's.

The Energetics of Molecule Formation The standard enthalpy change for the process (1)

AR,,(g) - A(g) + nR(g) (1)

is the total th~rmochemical bo'nd energ.y of the molecule AB,. When divided by n , this gives the mean th~rmochemical bond energy in AB,. Since the standard entropy of AB,(g) is not strongly dependent on its geometry, the most stable config- uration of AB, will he that which maximizes the total ther- mochemical hond energv.

AB,(g) - A * k ) t nB*(g) (2) is the total intrinsic bond energy of AB,, and exceeds the total thermochemical hond energy by the amount of promotion energy required by the atoms to attain their valence states. The promotion energies for the B atoms are usually disre- garded; atoms such as hydrogen, halogen and oxygen can he considered to he in suitable condition for bonding in their ground states. Thus the promotion energy involved in the formation of AB, can he taken to be that of A alone.

I t then follows that the most stable configuration of A& is that which affords the best compromise between the total intrinsic bond energy and the promotion energy. These two factors must now he considered in more detail.

Promotion Energies Consider an atom in a valence state, for which we have

constructed ase t of n hybrid orhitals 91, $ 2 , . . . &, using the s, p, and d orbitals in the valence shell of the atom. The orbital 9j can he described as sniphido, where the superscripts indi- cate the relative amounts of s, p, and d character in the hybrid. The valence state arises from the configuration srp:prd", where

x n;a;l(ai + bi + c;)

y = n,b;l(a; + bi + c ; )

z = 13 n;c;l(ai + b; + c;)

and ni is the occupation number ( O , l , or 2) of $; in the valence state. If the ground state of the atom arises from the config- uration s2pm, the promotion energy P is given by (3),

P = ( 2 -xIP"d + ( r n - >)P,d (3)

where P,d and P,,d are respectively the energies required to

Valence States (VS's), Valence State Conliguratlons (V.S.C.'s) Promotion Energies (P.E.'s) and 29 for Various Values

o f O ( = ~ - A - B )

Molecule 0 (deal V.S. V.S.C. P.E. 2 SZ

where P,, is the energy required to promote an electron from s to p . Thus for any valence state, we can write down the promotion energy in terms of P,,, PSd and Pdp. However, the numerical evaluation of these auantities is not easv. Promo- tion energies are usually obtained from atomic spectra (8), hut ~recise calculations are not straightforward (9). and values quoted in the literature are best regarded as rough estimates (10).

Intrinsic Bond Energies We need to determine the relative magnitudes of the total

intrinsic bond energies for the possible configurations of a molecule. This can he done by invoking the concept of orbital "strength," introduced by Pauling (71, The strength S of an orbital is the magnitude of the wave function along a specified axis, relative to that of an s orbital having the same principal quantum number. The intrinsic hond strength obtainable from an orbital is proportional to S2. Thus S for an s orbilnl is, by definition, equal to unity. For a p orbital directed along the bond axis, S is 3'12. For a d z 2 orbital, S is 5'12 along the

106 1 Journal of Chemical Education

z-axis and 51/2/2 in the xy plane. For a d,z-,z orbital, S is 1 5 ~ / ~ / 2 along the x - and y-axes. These values are strictly ap- plicable only to hydrogen-like orbitals.

A hybrid orbital of the typesp" takes the form (1 + n)-'l' (S + n1/2p). The strength S for such a hybrid is given by (5).

S = (1 + n)-'12[1 + ( 3 r 1 ) ' ~ I (5)

Similar formulae can be derived for hvbrids involving d or- bitals, depending on which d orbital(;) is or are beingwed, and on the orientation of the honds with resoect to the d or- b i t a l \~ ) . The tut:d ~ntrinsic bond energy tor a-givm gromrrry w~ll he oroourtion to 2.5". the s~lmmat im being perlmned over alith' hybrid bond orbitals.

We can now determine how the promotion energy and the total intrinsic hond energy for any molecule depend on its geometry, and hence deduce the geometry which will maxi- mize the total thermochemical bond enerev. We shall first ""

consider AB.E, molecules, where A is a main group atom with the around state electronic confiauration s2p"+ 2m-2. B is a univaient atom or radical, and E represents a lone pair. For n + rn < 4, only the s and p valence orbitals of A are consid- ered. For n + rn > 4, d orbital participation is invoked. We then discuss briefly the extension of the model to molecules containing multiple bonds. Arguments relating to molecules are deemed to he also valid for isoelectronic ions.

AB2 Molecules The valence state for an AB2 molecule is ( ~ p " ) ~ ( s p " ) l ,

where n = -sec 0 , 0 being the B-A-B angle. Promotion ener- gies and ZS2 for various values of 0 are given in the table. The minimum orornotion enerw is obtained with fl = 180' and n = 1. As O iH lowered from 1800, the intrinsic bond energy in- creases sliahtlv. reachina a maximum at 109.5", while the - .. promotion energy increases steadily. If the total intrinsic bond energy is sufficiently large compared with the promotion en- ergy, such bending might be energetically favorable. This would explain the observed geometries of the alkaline earth dihalide molecules. The value of P, falls down the alkaline earth group atoms from about 300 kJ mol-I for Be to about 170 kJ mol-I for Ba, while the total thermochemical hond energies range from 1200 kJ mol-I for MF2 to about 700 kJ mol-1 for MI? (11). All the barium dihalide molecules are Iwnt. nc >ire SrF?, SrCI,, CaF2, ;and MgF,, ahile the rest are h e m . Parricioation bv (n - l ld ort1i1.d~ as well as nz and np orbitals would also f a k r bending; the best sd hyhrids are at rieht angles, while the best spd hybrids make an angle of 133" (3. ow ever, the observed geometries can be kxplained qualitatively with d orbitals. For Zn, Cd and Hg, P, is higher than for the alkaline earths, about 400-500 kJ mol-l; these atoms form linear dihalide molecules.

AB. and AB,E Molecules The dependrncc of the prnmotim energy and total intrinsic

bond energit,; in A H , molc~c~~ls. on the H-A-B angle a is shown in the tahlv. A deviation from plnnarity to\riird a n\.ramidal configuration with 0 = 109.5' w31 result in a negligil& increase in the total intrinsic bond energy, a t the expense of a consid- erable increase in promotion energy. Clearly, AB:, molecules should he planar, as found experimentally. For AB2E mole- cules (in their sinelet states). the valence state is (sor ' )- ' ( ~ p " ) ' ( s p ~ ) ~ , with rn = 2/(n - 1). The promotion energy falls and the total intrinsic bond energy increases as the molecule is bent toward the tetrahedral angle of 109.5°. If the molecule is further bent toward a bond angle of 90°, the promotion energy continues to fall while the intrinsic hond energy hegins to decrease. The best balance between these two will be struck somewhere hetween 90 and 109.5"; the exact value may de- pend on other factors, such as nonhunded atom interactions. According to the VSEPR model, the interbond angle s h d d he somewhat less than 120°; experimentally, molecules such as CH:, CF2 and SiF2 have hond angles in the range 100- 105".

AB.,, AB3E and AB,E, Molecules - .

For an ;\H, mnleculi~, the tt.tr;lhedml sp. . h~hr ids cmsrirute the hrsr p~swhlc set; ncmrq~~i\,alent .<on hsl~rids lead to louw . . intrinsic-hond energies, without any relief of promotion en- ergy. Thus AB, molecules are expected to be tetrahedral.

The valence state of an ABnE molecules is (spn)l- (sp")'(sp")'(spm)', with m = 3/(n - 2). As seen from the table, the promotion energy falls as 0 is reduced from 120° to 90°, while the maximum intrinsic hond energy is a t 109.5'. Thus the most likely angle will he between 90° and 109.5", in agreement with experiment. Similarly, for an AB2E2 molecule, the minimum promotion energy is a t O = 90' and the maxi- mum intrinsic hond energy is obtained a t 0 = 109.5'. Thus molecules such as Hz0 should be bent, with 8 between 90° and 109.5'.

A&, AB,E, AB3E2 and AB,E, Molecules The most svmmetrical confieurations for an ABs molecule

:lrc t hr tripmnl hipyramid ant1 rhe square pyramid.'l'o I'orm fiw Ilcmds n d d ~ t t ; t l is recluired in tht hshridimtlm sc heme: d,r isused tinr thc,triytmal hipyram~d,an(l dl .- , . ior thesquarr pyram~d. In the trigmal bipyrnmid, the ax~al and rqunrurial hyl)rid;are nor equi\.alent; rhev ran he deicrihed asq 'd- 'p a t ~ d - ' - 'd .p ' , respecti\,ely. Thr promotion energy is equal r r , I'., rcgnrdle\~ i r l x . Thus th? c~~~rinium value <I: x is that n h ~ c h mnxi~n~zei 2s-; this turns our to he U.2Y.I. The axial hst~rids then have S = 2.9:I: and the eouat<lrial hvbrids S = . ~~

2.249; ZS' is 32.43. For a square pyramihal AB, molecule, the simplest hybridization scheme using only one d orbital leads to a set of four sp'd equatorial hyhrids, with the axial hond using a pure p orbital. This gives ZS2 = 32.01. The square pyramidal configuration can be improved slightly by trans- ferring some s character into the axial orbital, while increasing the p character of the equatorial hybrids. The maximum in- trinsic hond strength is obtained with an axial sp" hybrid and equatorial no.7fl p - ' 5 . d hybrids; the axial-equatorial bond angle

is 95.4" and ZS' is 32.55, which is now sliahtlv better than for the trigonal hipyramid. However, there isvery little to choose between the two (the promotion energy is P.d in both cases). Exnerimentallv. most kBs molecules are trieonal biovramidal. . . . . hui Sh(CsHs)s and lnclii- are square pyramidal. Even in the trieonal biovramidal snecies. the sauare ovramidal confieu- . . . . ration is nut very far away in energy; the PF:,, for example, the enerav harrier to axial-eauatorial fluorine exchanee (which procekds uia a square pyramidal intermediate) is oily about 12 k.1 mol-I (12).

In most trigonal bipyramidal molecules, the axial bonds are apparently weaker than the equatorial bonds, as shown by bond lengths, force constants etc. This appears to he incon- sistent with the greater S values for the axial bonds. I t should be remembered. however. that ex~erimental measures of hond strength reflect therrnuchernicai bond energies, whereas S' is a measure of the intrinsic hond enerav. If in AB5 we oarti- tiun the total intrinsic bond energy between theaxial and equatorial bonds, the former are certainly intrinsically stronger. But if we partition the promotion energy, the axial hyhrids (which are about 36% d) must he allocated much more than the equatorial hyhrids (which are only about 10% d). It turns out that in rnr,lecules iohere d orbitals are used, the strongest bonds th~rrnuchernically are those hauinp the least d character.

A common objection to the use of a d orbital in ABs is the large promotion energy entailed; P,qd for phosphorus .is prohahly around 1500 kd mol-I. But the intrinsic bond energies pn~duced by sp:'d hybrids are much larger than those which can be obtained by use of only s and p orbitals. The nonexistence of PHs and PIs could he attributed to the lower intrinsic hand energies expected in these molecules, which would be insufficient to render them stable with respect to PX:, and XZ. Promt)tion energy is a particularly important factor in determining the equilibrium geometry of a molecule where d orbitals are invoked. In SiF4, fur example, the total

Volume 57. Number 2. February 1980 1 107

intrinsic bond energv is prohably ahout six times preater than the uromotion enerrv I'.,,: but in PF;, the total intrinsic hond -. .-. e n e k is probably only about twice great as the promotion enerev. In molecules where d orbitals are to be used, thege- ome;iy in which thepromotion energy is minimized is likely to be more stable than that which maximizes the intrinsic bond energy.

Promotion energies (such as can be estimated from atomic spectra) may not be the only factor which determines the ac- cessibility of d orbitals for bonding. I t is generally agreed that d orbital involvement is facilitated in a molecule such as PX5 if X is of high electronegativity, i.e. the bonds are appreciably polar. This is likely to be relevant to the nonexistence of PHs and PIS.

We now consider trieonal bi~vramidal ABAC. where C mav be axial or equatorial.u~o maximize the total intrinsic bond energy, the best hybrids should be reserved for the atoms which can make best use of them, i.e. the ligand atoms which are likelv to form the intrinsicallv stronger bonds should use hybrids bn the central atom withihe greater S value. Bearing in mind the importance of electronegativity difference, i t would seem likely that the most electronegative ligands should use hybrids having the most d character. Tbusin PF4C1, it can be uredicted that the C1 atom should be eauatorial. while in P&F the F atom should hrawal rcf. Ben;'s Rule (13)).

In .4BnE. we m~eht rxnect a structure based on a tr~eonal bipyramid kith th; lonebair occupying one of the fiveposi- tions. thoueh a sauare planar structure must be considered also. If the structure is bawd on the trigonal bij).vramid. the lone oair r ( d d he axial or eauatorial. To maximi7e the in- trinsic bond energy, the lonebair should be accommodated in a hvbrid orbital of lowest S , while to minimize the promo- tion energy, the lone pair should be placed in a hibrid of minimum dcharacter. Clearly, the lone pair in an equatorial position is favored. The optimum hybridization for an AB4E molecule with this configuration is obtained with axial hybrids ~0.26d0.7~~ eivine ZS2 = 27.39 and reauirine a ~romotion en- . - " - . ergy of 0.75P.d + 0.33Ppd. The square planar form requires four sp2d hybrids for binding, with the lone pair in a pure p orbital. This has a higher total intrinsic bond energy than its rival (XS2 = 29.01) but requires a promotion energy of Pad. Since Pad is probahly about twice as great as Ppd, the pro- motion energy for the square coplanar configuration is greater; in accordance with the rule that the minimization of promo- tion energy is more important than the maximization of in- trinsic bond strength where d orbitals are involved, the tri- zonal bipyramidal arrangement of hybrids is preferred. 'However; the square planar configurati& may noi he murh higher in energy; in SVI , the enrrgy barrier to axial-equatorial fluorine exchange (which presumably proceeds via a square planar or square pyramidal intermediate) is only about 20 kJ mol-' (14).

The promotion energy for the trigonal bipyramidal ar- raneement of hvbrids can be further reduced (thoush with ~. som'e lussolintr"insic hond energy) hy the transferofp and d character from the lone pair orbital to the others. In the limit where the lontb pair is in a pure s orbital, we could have two axial d~ hvhrids tS = 2.8061 with the eauatorial bonds usine purep br6itals (at right an&: S = 1.73i), giving ZS2 = 21.75: The promotion euerw becomes Pnd. representing a saving of - several hundred kJ&ol-I compared with the optimum hy- bridization with three equivalent equatorial hvbrids. However, the equator~ill hondstrengthsran be enhanced by the injec. tion of ,I little d character into the equatorial hyl~rids, while transferrine some additional D character to the axial hvbrids: the promotion energy is uniffected. The effect of this is to increase the anele between the eauatorial bonds from 90' and to reduce the &lr Iwtween the'axial honds from 180'. l 'he maxinlum vsl~lc a ~ f Z'S' (22.521 is obtained with a cunfiguru- tion similar UI that found experimentally for AB,K muleculrs, with ewi~torial and axial inrerbond aneles of abuut 96" and 170°, rkspective~~. The interbond angGs observed in AB4E

108 1 Journal of Chemical Education

molecules reflect a compromise between the regular structure (with axial and equatorial angles of 180° and 120°, respec- tively) which has greater intrinsic bond strength, and the distorted structure which reauires less ~romotion enerw.

By similar arguments, it can be predicted that an A B ~ E ~ molecule should adopt a T-shape, i.e. a trigonal bipvramidal . . arrilngement of hgl& with the lone occupying equa- torial positions. If the s charac1t.r of the lone pair orhitals is increased, the promotion energy is reduced and the molecule distorts to give an axial-equatorial bond angle somewhat less than 90°, as found experimentally for molecules like CIF3.

We expect ABzEz to be linear, with the three lone pairs occupying equatorial positions in the trigonal bipyramid. The intrinsic bond energy can be increased slightly by bending the molecule, but onlv if more than one d orbital is used. at a pnjh~hitive rust in promotion energy The linear configuration mas be furth4.r stabilized bv the transfer of r, and d orhital rh&'ter f n m the lunr pair.s to the bmd ort~~tals.'l'he mini- mum pnmorion energy is i,btained I)). ~~sinf!.,p' hyhrids tor the lone uniri and linear od hvhrids ti,r the bunrls. \\'herher . . we minimize the promotion energy or maximize the intrinsic bond streneth (while still usine iust one d orbital) the linear configuratibn is favored.

AB., AB& and AB& Molecules For an AB6 molecule, the best set of hybrid orbitals are the

familiar s p V 2 octahedral hybrids (S = 2.923). A trigonal prismatic arrangement produces intrinsicallv stronger honds (S = 2.983) hut requires more promot inn energy; thc valenre state corresoonds t u the ronfiruration s " " ~ ~ D ~ ' "'d2 '21. Thus molecules like SF6 are expected to be octahedral. The pro- motion energy required to attain the octahedral su3d2 valence state is probablyabout 3000 kJ mol-1 for an i tom such as sulfur, i.e. about 500 kJ mol-' per bond; but the intrinsic strengths of these bonds are 2.85 times greater than those obtained using pure p orbitals.

An ABsE molecule mav be expected to adopt a sauare DV- ramidal c&figuratioo, wGb the [one pair direcied toward &e apex of an octahedron. The total intrinsic bond enerev is maximized withs0.59p2d'.41 equatorial hybrids (S = 2.935Yand s 0 4 1 ~ d o 5 9 axial hvbrids (S = 2.892). The nromotion enerw reqiired is 0 . 7 9 ~ ~ ; + l.50Ppdr which is slightly less than GI six equivalent sp3d2 hybrids. Thus the axial and equatorial bond orbitals have similar S values, but the latter has much more d character. Hence the axial bond should be thermo- chemically stronger than the equatorial bonds, as is found experimentally for molecules like BrFs. The fact that the axial-equatorial hond angle is slightly less than 90° may be explained by considering the effect of the transfer of p and d ~

character from the lonepair to the bonding pairs. 1n-the ex- treme case where the lone pair is a pure s orbital, the promo- tion energy is lowered to 2Ppd, a saving of a t least 1000 kJ mol-'. We could then describe the equatorial bonds in terms of square p2d2 hybrids, with the axial bond using a pure p orbital; the S values are 2.752 and 1.732, respectively. How- ever, the axial bond can be improved greatly by the injection of some d,2 character into the axial bond, while introducing some D, into the eauatorial bonds. The coefficient of d,2 in an eq;?torial hybri'd must be of opposite sign to that in the axial hvhrid. To preserve the orthogonalitv of the hvbrids, the coefficients of must of the same sign in all thk hybrids. Thus, as the s character of the lone pair orbital is increased, the axial-equatorial bond angle will decrease from 90".

An AB4E2 molecule may be expected to adopt a configu- ration in which six hybrid orbitals are directed toward the apexes of an octahedron. The question then arises as to whether the lone pairs will be cis or trans. In the latter case. the best set of hibrid orbitals directed to the corners of a sauare have the com~osition s0.44~2d1.56(S = 2.943): the lone pair orbitals have the composit~on s 0 5 6 ~ d ~ ~ 4 , so'that the valence state configuration is s1.56p4d2.44. The promotion energy is equal to 0.44& + 2Ppd. In the alternative configu-

ration, with the lone pair orhitals cis to one another, the best set of hyhrid orbitals is found to comprise two axial s027pd073 hybrids (S = 2.943) and two honding equatorial hybrids s04Spo.s9d0-83 (S = 2.9471, with the lone pairs in s025p1.81d044 hybrids. Thus the total intrinsic bond strength is slightly greater than for the trans arrangement, hut the promotion energy is 0.75PSd + 1.69Ppd, which will he considerably greater than 0.44PSd + 2Ppd. For both configurations, the promotion energy can be reduced by the transfer of d character out of the lone nair orhitals. The minimum nromotion enerev for the cis ". arrangement is obtained with the lone pairs in pure p orhitals; the axial hvbrids are so 2 8 ~ d o (S = 2,940) while the eaua- torial hyhAds are so72dI is (S = 2.388), giving ZS2 = 28.70 with a promotion energy of P,d + Ppd. For the trans (square planar) arrangement, the minimum promotion energy is oh- tained with the lone pairs in s p hybrids, usingp2d2 hybrids for honding (S = 2.752). This yields ZS2 = 30.29, for a pro- motion energy of 2Ppd. Thus the square planar configuration is more stable for molecules like XeF4.

AB,, and ABBE Species At least three d orhitals are required to form an AB7 mol-

ecule, 2nd the I w t set of hvhridi ulhich require nc, mom thnn three d orhttitls is the set ot pentagonal hip\.nltnidnI hyhrias IS = 2.976 ior the tmllatorinl hvbrids. and 2.520 fur the axial ones). Less symmetrical configurations leading to greater intrinsic bond strengths can he devised, hut these require more promotion energy since a t least four d orhitals are used. Thus molecules such as IF7 are expected to be pentagonal hipyra- midal.

In ABeE, we would expect the lone pair to occupy an axial . . position i n the pentagonal hipymmid, sinw thc itpprupriute h\,hrid urhitnl hns the I#ww value of s and less d character, leading to less promotion energy. Other less symmetrical structures might he more favorahle. The geometry of the XeFs molecule is complex (15), hut it is certainly not a regular oc- tahedron. However, some MXs2- ions (M = Se, Te, Po) are octahedral in the solid state. This is difficult to explain bV any . . model of molecular geometry. A possible description within the VB anproach might involve the formation of octahedral s p q 2 hyi);ids using the (n + l)s, np, and nd orbitals, with the lone pair in the ns orbital. In the Se atom, the 4p - 5s pro- motion energy is about 700 kJ mol-l; the 4s - 4p promotion energy cannot he determined from the available spectroscopic data. hut nrohablv exceeds 1000 kJ mol-'. ~ ~ ~,~ . Systems Involving Multiple Bonds

Here we are mainly concerned with oxides, oxoanions, and oxohalides. The arguments developed already can he extended easily to such species; in the valence state of the central atom A in AO,B,, the electrons to he used for s-bondingare placed in pure p or d orhitals. The most favorahle geometry will he that which optimizes the a-bonding. Thus in AO,B,, the best arrangement of 0 and B atoms about A will he the same as for AB,+, if A had m fewer valence electrons. For.example, SO3 should have the same shape as AIB? (where B is a univalent atom or radical), i.e. planar. XeOF4 should have the same geometry as IFs (square pyramidal), and SOz(0H)z should have the same shape as Si(OHh (tetrahedral). In cases where the 0 atom (or atoms) may occupy either of two nonequivalent positions, it is helpful to regard the bonding of an 0 atom to A as involving resonance between the structures:

A = O - A - 0 I I1

In the valence state corresponding to structure 11, the donor orbital on A is doubly occupied, and the promotion energy will be minimized if the electrons to be donated are placed in hy- hrid orhitals of the least nossihle d character and the greatest possible s character. TGS explains the fact that in ~ o , B , molecules, the AB, fragment has the same geometry as in AB,Em; for example, in SF40, the 0 atom occupies an equa- torial position in the trigonal bipyramid.

Conclusions I t has long been accepted that the VB theory provides

reasonably satisfying descriptions of honding in molecules and polyatomic ions. The neglect of VB theory in the last 20 years or so has arisen from the fact that the theory is ill-adapted to the interpretation of phenomena such as electronic spectra and is less suitable than MO theory for more elaborate quantum mechanical calculations (although there are sieus I161 that theoretir;d chemist.; are heginning to questiun the wlue o1'detailed oh initio m d semi-ernp~ricnl\lO cnkl~lations i n t h t , undtr.;tnnding ot the chemicalbond and ma" turn to \'H theory again, I t has not heen ai~preciated gcnen~lls that VB theory also offers a useful methdd for the interpretation of molecular geometry. The approach outlined in this paper is a t least the equal of the VSEPR model in explaining the shapes of simple molecules and ions. If the VB approach in- volves rather more calculation than the VSEPR model. it provides as a bonus a satisfying description of the honding, which the VSEPR model fails to do, and gives some insight into the energetics of molecule formation. The VB approach is certainly simpler than the MO approach, especially for more . . complex molecules.

The most serious objection to the VB approach outlined here is Pauling's concept of hyhrid orbital strength. The rel- ative values of S for pure s , p and d orbitals are valid only if an electron experiences the same effective nuclear charge in all three. This may he approximately true for ns and n p or- bitals. but it certainlv is not for nd orhitals which are much more diffuse, although they can he appreciably contracted in some circumstances (17). Thus Pauline's values of S for d orhitals may he too large. However, it t i n s out that the VB predictions concerning molecular geometry are not critically dependent on the valuis of S allotted to d brhitals in spd h i - hrids; although the absolute values of S for spd hybrids are strongly dependent on the chosen values of S for pure d or- bitals, their relative values are much less sensitive.

Cogent arguments can he put forward against the idea of full d orbital participation in molecules such as ABS and ABs; the honding in such species can he described adequately without d orbitals. For example, the bonding in CIF3 could he depicted thus:

F * P F-a+-F

This is essentially equivalent to the three-center bond model in MO theory. If, however, we allow that a structure with lo- calized two-center, electron-pair bonds using a d orbital makes a significant contribution, the considerations in this paper are relevant to a discussion of the molecular eeometrv.

The VB theory of molecular geometry may not bffer many overwhelming advantages over its rivals and is open to several objections, but it c1ea;ly deserves closer consideration than it has been given in recent years.

Literature Cited Ill Gillespie, R. J.,"Muteeular Geometry." Van Norfrand Reinhold. London, 1977. (2) Rurh1er.A.. Stauffer,d. I.. and Klempeier. W. J. Amrr. Chsm Soe.. 86,4544 (19441. (:I) Gavin.R. M.. J. CHEM. EDUC.48.418 119691. 14) Cimarc.B.1. J. Amen C h e m S o r . 92.286 ~1970):93,593.815 11871). (5) l3urdett.I. K..Slructureand Rondsnn, 31, 67 11976). 16) Baird. N.C.,d. C H E M EDUC..EL,412 11978). 17) Paulinr. L.."The Na tu r ed the Chemical Rond."Cornell University Pmsr. Ithacs. N.Y..

I9RO. IS) Cntbn.F.A.and Wilkinsn,C.,"AdvaneedInorganicChemi&ri,)'~rdEd.,lntemcienrr,

NewVnrk. N.Y., 1972.pp.86-87. 19) Mefliff, W.. Pmr. R,,y. Slit iLondon). A202.53" 648 (1960).

(10) Pmmotion enersies given in this paperare calculeted by tho mothod described in ref. 9, u r i n ~ the specf?orcopic data <of Mnnre. C. E.. "Tshier of Atomic Enerpy Leueln." National Bureau of Standard3 Circular 467. Washingtan. ,967-56.

I l l ) Haheey.i.R., "lnorganieChemistry."Harper and Row, New VorL. 1972, pp.696-6. 112) Bernrtein. l..S.,Ahramc,witz, $.,and Levin 1. W . d Chem. Phys.. 64,3228 119761. I191 Rent. H. A..d.CHRM. EDllC..37.616 i1960). (141 Schmidt, M. nnd Siehait, W.. in 'Comprehensive lno r~an ic Chemistry."Pergamun

Prers.Oxford. 1973,Vol. 2, p. 845. (15) Pitrer,K. %and Rernrtein.1.. S.. J . Chrm Phys. 6%.3S49 (L97Sl. (16) Cook. D. R.SLi~rLur~ondHnndin*l . 35. :37 11978). I171 Kwart. H.A. md King, K. G.."dOrhitalr in theChemistryofSilicon.Ph~xphorusand

Sullur."Sprinwr-Varlng, H e h . 1917.

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