Multiple Bonds and the VSEPR Model Ronald J. Gillespie McMaster University, Hamilton, Ontario Canada L8S 4M1 In many textbooks the applicability of the VSEPR model to molecules containing multiple bonds is often either not discussed or is discussed in only a limited way. The purpose of this paper is to review the application of the VSEPR model to molecules containing multiple bonds and to compare the usefulness and applicability of the model to other models for multiple bonds. The VSEPR Bent-Bond Model The Lewis diagram of the ethene molecule H:C .. : : C.. : H H H
shows that there are four electron pairs in the valence shell of each carbon atom and that two of these pairs are shared between the two carbon atoms. According to the VSEPR model ( 1 3 )the electron pairs in a valence shell adopt that arrangement that keeps them as far apart as possible. In particular, four electron pairs in the valence shell of an atom have a tetrahedral arrangement. The tetrahedral arrangement of the four electron pairs in the valence shell of a carbon atom leads to the prediction that the ethene molecule has a planar geometry as shown in Figure 1.The shared electron pairs are situated one on each side of the C-C axis so that the double bond may be described as consisting of two bent bonds. A similar model for the ethyne molecule describes the triple bond as three bent bonds and shows that the molecule has a linear geometry (Fig. 1).
Figure 2. Balloon models for ethene and ethyne
Figure 1. Bent bond models for ethene and ethyne. (Above) Bond diagrams. (Below)Electron-pair domain models. The bond diagrams in Figure 1give only a very crude representation of the electron distribution in these molecules. Abetter representation can be obtained by assuming that each electron pair effectively occupies a region of space in the molecule that we call a domain and that to a first approximation each domain has a spherical shape (2, 3). This model was fvst proposed by Kimball and by Bent (4,5)and was called the tangenesphere model. We call it the electron-pair domain model. In its simplest form, this model assumes that each electron-pair domain is spherical, has the same size, and does not overlap with other domains. The electron-pair domains in the valence shell are attracted to the central positive core, and they adopt the arrangement that enables them to get as close as possible to the core. For four equivalent spherical domains, this is again the tetrahedral arrange-
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ment. Electron-pair domain models of ethene and ethyne are also shown in Figure 1. Useful demonstration models illustrating these electron distributions can be conveniently constructed from Stynfoam spheres or from balloons as shown in Figure 2 (6). This model implies an H-C-H bond angle of 109.5', compared to the observed angle of 116.2'. However, since the two domains of the double bond are attracted towards the same two carbon cores, we expect them to be drawn together. Thus, the angle between these two domains will be decreased. This allows the two C-H bonding domains to move apart, thereby increasing the H-C-H bond angle to H greater than 109.5'. It is interesting to note the close relationship between Figure 3. Electron-pair domain. this representation of the model for diborane. electronic structure of ethene
Figure 4. Bent bond models for H,CO, HCN and C02. and that of BzHs(Fig. 3).The two electron pairs of the double bond in ethene form three-center bonds in BzHe. The electron-pair domain model can be used to predict the shapes of many other molecules containing double and triple bonds (Fig. 4). The Hybrid-Orbital Bent Bond Model The VSEPR model is not an orbital model. The distribution of the electrons in a molecule is described in terms of electron-pair domains rather than in orbital terms. However, the bent bond model can be expressed in orbital terms if we use sp3hybrid orbitals on each carbon atom to correspond to a n H-C-H bond angle of 109.5~(Fig. 5). Exact agreement with the observed bond angle of 116.2' can be obtained by adjusting 1 / t h e hvbrid orbitals so that tLe two bond orbita l s have 30% rather t h a n 25% s character H a n d so t h a t t h e C-C V I bond orbitals have 80% 1 than 75% p charFigure 5. sp3Hybrid orbital model for acter. This model gives a ethene. description of the bonding in orbital terms, but it does not explain or predict the geometry of the molecule because the form of the orbitals must be chosen to match the prediction of the VSEPR model or the observed geometry.
a,.
electron-pair) domain. Similarly the three electron pairs of a triple bond can be considered to be merged into one still larger triple bond (three electron-pair) domain (Fig. 6). According to this model, each of the two carbon atoms in ethene has three domains in its valence shell-two single bond domains and one double bond domain. These three domains adopt a trigonal planar arrangement. Thus, both carbon atoms have a planar AX3 geometry (Fig. 6). In ethyne, each carbon atom has only two domains in its valence shell-a single bond domain and a triple bond domain. Thus, each carbon has a linear AX2geometry (Fig. 6). Similarly, formaldehyde is expected to have a planar AX? geometry, and COz and HCN are expected to have a linear AX2 ( ~ i g6). . This model is particularly useful for discussing the structures of molecules with multiple bonds in which there are more than four electron pairs in the valence shell. For example, SO2 is an angular AXzE molecule in which the valence shell of sulfur contains two double bond domains and a lone pair domain (Fig. 7). Sulfuric acid is a tetrahedral A& molecule in which the sulfur atom has two double bond domains and two single bond domains in its valence shell. The sulfite ion has a pyramidal A&E geometry because the sulfur atom has a lone pair domain, a double bond domain, and two single bond domains in its valence shell. In fact, the three bonds in the sulfite ion all have the same length and strength. This may be described by the followingthree resonance structure;
1
The VSEPR Multiple-Bond Domain Model The two electron-pair domains of the double bond in ethene are attracted towards the same two carbon atom cores, so we expect them to be drawn closer together than, for example, in the methane molecule. It is often simpler and more convenient to consider that the these two electronpair domains are merged into one larger double bond (two
1
Figure 7. Domain model for SO?.D: Double bond domain. L: Lone pair domain.
I
Figure 6. (a)Double bond domain (sphericalapproximation).(b) Triple bond domain (sphericalapproximation).(c)Multiple bond domain models Volume 69 Number 2 February 1992
117
Table 1. Shapes of Molecules Containing Multiple Bonds
* m e Pair lomains
Linear
O
rriangular
3
Examples
Molecular Shape
I
Linear
Triangular
7 Trigonal Pyramid
0
Trigonal Bipyramid
1
Irregular Tetrahedror
Bipyramid
ktahedron
1
6
0
1
Octahedron
or one structure with partial double bonds -ao = s =04
Table 2. Bond Angles in Some Molecules Containing C=C and C-0 Double Bonds XzC=CYz
In this case we would say that there is a lone pair domain and three partial double bond domains. I n otherwords, There are four domains with a tetrahedral arrangement, so the sulfur atom has a n &E geometry. I n general the predicted ideal geometry of a n ALErn molecule depends only on the number of electron domains in the valence shell of the central atom A and not on the nature of the domains, whether they are lone pair, single, double, or trlple bond domains or pa;tial multiple bonddomains. The shapes uf molecules contaming multiple hunds are summarized in Table 1. 118
Journal of Chemical Education
XCX
HzC=CHz FzC=CHz FzC=CFz CIzC=CClz (CHsrzC=cI 9 6SH2
116.2 110.6 112.4 115.6 115.6
HzCO CLzCO FzCO HFCO
116.5 111.8 107.7 110
XCX
YCY 116.2 119.3 112.4 115.6 116.2
xco 121.7 124.1 126.2 123
XCC 121.9 124.7 123.8 122.2 122.2
YCC 121.9 120.3 123.8 122.2 121.9
Table 3. Bond Angles in AX4 Molecules Containing Multiple Bonds
sb-sb
sMb(tb)
sb-sb
dMb
101.3
117.7
F2S02
96.1
124.0
POCb
103.3
115.7
C12S02
100.3
123.5
POBr3
104.1
115.0
CIFS02
99
123.7
PSF3
99.6
122.7
(NH2)zSOz
112.1
119.4
PSC13
101.8
117.2
(CH3)zSOz
102.6
119.7
PSBr3
101.9
117.1
NSF3
94.0
125.0
POF3
Since a double bond domain is larger than a single bond domain, and a triple bond domain is larger still, there will be deviations from the ideal bond angles. In ethene we expect the angle between the double bond and the single bonds to be larger than the ideal angle of 120'. We also expect the angle between the two C-H bonds to be smaller than 120'. Experimental data for ethene and some other AX3 molecules are given in Table 2. In each case the double-bond-to-single-bond angles are larger than the singlebond-to-single-bond angles. The experimentally determined bond angles for some A& molecules containing multiple bonds are given in Table 3. In each case the bond angles in a given molecule decrease in the following order. db:db > db:sb > sb:sb
In NSF3, the N S - F angle is larger than the 0-SrF angles in SOzF2.This is consistent with the SN triple bond domain having a larger size than the SO double bond domain. Nonspherical Domains A better approximation to the shape obtained by combining two electron-pair domains to give a double bond domain would be a prolate ellipsoidal shape rather than the spherical shape that we have so far assumed. Similarly we exoect a triole bond domain to have an oblate elliosoidal shHpe (Fig. 8). Ab initio calculations of the electron-density distribution of ethene (7) show that the electron densityin the double bond region does indeed have a prolate ellipsoidal shape (Fig. 8). In ethene the ellipsoidal double bond domain will minimize its interactions with the other domains by having its long axis perpendicular to the plane of each CH2
Figure 9. (a)Some AX, molecules with a double bonded iigand. (b) Bent bond and double bond domain models of H2CSF+ group. Thus, the molecule bas an overall planar shape (Fig. 8). Trigonal bipyramidal AX5 molecules The equatorial and axial positions of a trigonal bipyramid are not equivalent. Since an axial position has three close neighbors at 90', while an equatorial position has only two close neighbors, the equatorial positions are less crowded than the axial positions. Consequently, double bond domains preferentially occupy the equatorial positions of a trigonal bipyramid, for example, as in SOF4and the other molecules in Figure 9. The CH2group in CH2=SF4is perpendicular to the equatorial plane through the sulfur. This is most simply accounted for using the bent bond model. According to this model there is an octahedral arrangement of six electron pairs around sulfur. Tho pairs are used to form the double bond to the carbon atom. Thus. due to the tetrahedral arrangement offour pairs aroundcarbon, the CH bonds must lane of the double be ~emendicularto two ~ l a n e s the : boid and the equatorial plane of theLtrigonalbipyramid is in the (Fig. 9).Similarly the C-N bond in CHBNSF~ plane perpendicular to the equatorial plane. Alternatively we may describe the double bond in terms of a double bond domain with an ellipsoidal shape. In a trigonal bipyramidal molecule this domain will be oriented with its long axisin the equatorial plane to minimize interactions with the other domains. Thus, the C-H bonds will be perpendicular to the equatorial plane (Fig. 91.h may be seen from Figure 9, t h e bond angles in trigonal bipyramidal molecules with a double bond in an equatorial position are consistent with the double bond domain having a larger size than the single bond domains.
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Comparison with the o rr Model The most widely used model of the double bondin ethene and related molecules is the o -rr model according to which the carbon atom is described as forming three o bonds by means of sp3 hybrid orbitals and a rr bond by "sideways" overlap of two p orbitals (Fig. 10). However, this model does not predict the planar geometry of the ethene mole-
-
~-~.
Fioure elliosoidal = - - 8. - la) Prolate - , ~ - double ~ wnd doma n ano doma n model of ethene. (b) Oblate el lpso dal triple wnd domaln and domain mode of etnyne. (c) Conto~rplot of tne e ectron oens ty n the perpendicular plane bisecting the C-C &is in ethene. ~
~~
~~~~
~
Figure 10. o - x Model of ethene. Volume 69 Number 2 February 1992
119
cule because the assumption that the o bonds can be described in terms of sp2 hybrid orbitals is based on the observed planarity of the ethene molecule. Moreover, unlike the VSEPR model, the o - n model gives no obvious explanation for the deviations of the observed bond angles in ethene from 120'. In some substituted ethenes even larger deviations from the ideal 120' angles are observed (Table 2). For example, in F2C=CH2 the F-F bond angle is only 110', from which it could be concluded that the bonds formed by carbon are best described in terms of so3 hvbrid orbitals, which is more consistent with the bent'boid model than the o - n model. Another limitation of the o - n model is that, due to the symmetry of the n orbital, it is only applicable to planar molecules, that is toAX2, - AX andAX2Emolecules. It is not applicable to A& molecules, for example, in which the bonds have a tetrahedral arrangement. An objection to the bent bond model for multiple bonds that is sometimes raised is that it appears to imply that there is no electron density along the C-C axis. This is, however, a misinterpretation of the bond diagram. The electron pairs are not as highly localized as the bond diagram appears to suggest, and this is made evident in the domain model (Fig. 1).Moreover, overlap of the two electron-pair domains in the double bond produces a considerable density along the bond axis (Fig. 6). ~
Bond Energies
Another objection to the bent bond model that is sometimes raised is that it imolies that the two electron pairs of the double bond are equkalent, whereas, according to the o - n, model they are not equivalent. Bond energies and ionization energies from photoelectron spectroscopy are sometimes quoted to support the nonequivalence of the two electron pairs in the double bond. The bond energy of a C=C double bond is less than twice the bond energy of a C-C single bond. This observation is consistent with the expectation in terms of the o - n model that a ir bond is weaker than a o bond due to poorer overlap, but it does not prove that a double bond consists of a o bond and a n bond. In a bent single bond, the site of maximum electron density lies off the internuclear axis. Thus, a bent single bond is weaker than a linear single bond. We say that the bond is strained. So we expect two bent bonds to have a bond energy less than twice the bond energy of an unstrained single bond. Ionization Energies
In the photoelectron spectrum of ethene, ionization energies of 10.5 and 14.6 eV are attributed to the removal of an electron from molecular orbitals that may be approximately described as a C-C n orbital and a C-C o orbital, respectively (Fig. 11)(8).This result has sometimes been interpreted to mean that the o - n model is the "correct" model for the double bond because it is thought that the
Ionimtion Emrgier of CzH4
-
-
Use of the Models
For discussing energy changes, as in photoelectron spectroscopy, the o - n model should be used, but for discussing the geometry of molecules with localized electron pair bonds (including double and triple bonds) the VSEPR model should be used. The o - n model is also particularly convenient for discussing the electronic structure and spectroscopic properties of planar molecules such as benzene in which some of the electrons are delocalized. However, it does not predict the planarity of these molecules. I t is only the total electron density of a molecule that is experimentally observable. Any division of this total density into orhital densities is arbitrary. The o - n model and the bent bond model are two approximate but equivalent ways of dividing up the total density corresponding to a double bond. This can easily be seen because taking the sum and difference of a o orbital and a n orhital gives two equivalent. localized orbitals that wrrespond closely to the
Orbital Energies of CzH4
Figure 11. The photoelectron spectrum of ethene. (a)The two lowest ionization energies of ethene. (b) Energies of the o and n orbitals of ethene. 120
model of two equivalent bent bonds implies that only one ionization energy should be observed for the C=C bond. However. such an internretation of the ~hotoelectron spectrum i$ not sound. If b e represent the'two localised orbitals correswndin~to the bent bonds as r, and .(I, then the electron configura%on of the double bond in the bound state can be a~oroximatelvrepresented as - - . HOWever, the elect;bu config&ati& of the double bond in the ion cannot be represented simply as (.r1)'(.rd2, because the is equaliy probable. ?+nelectron may configuration (~;)~(.r~)' be removed from either of the localized orbitals, so that the remaining electron of the same spin as the electron removed may be found in either of these orbitals. In other words, this electron is more delocalised than is implied by r ~ (rJ2(.r2)'. )~ Thus, this either of the configurations ( ~ ~ ) ' ( . or electron is better revresented as occu~vine ." either a o or a n orbital. For the c&+ion, the o - x model is more useful than the bent bond model because the odd electron is more delocalized than the localized electron-pair bent bond model holies. The phou~electronspectrum gives information about the energies needed to reach two different states of the ion from the mound state of the molecule. It dues not directly give anyhformation about the orbital energies of the ground state of the neutral molecule. In order to obtain these orbital energies, it must be assumed that the same set of orbitals can be used to represent both the molecule and the ion. This assum~tionis known as Koo~mans'theorem. If this assumption;s made the negative >the ionization energies then gives the orbital energies. - This assumption is a reasonable approximation if delocalized molecular orbitals are used. But if a set of localized orbitals is used to describe the molecule, they can not also he used to describe the ion. Thus. it is not possible to obtain anv information about the energies of localiz&dorbitals in the neutral molecule from the photoelectron spectrum.
Journal of Chemical Education
Figure 12. Equivalence of the o and n molecular orbitals and the localized "bent bond orbitals 7, and r, for ethene.
bent bond model (Fig. 12). Messmer (9)has discussed the equivalence of the bent bond model and the a - a models in some detail and has shown how the photoelectron spectrum may be interpreted in terms of appropriate combinations of the bent bond orbitals. Conclusions and Recommendations
It is unfortunate that chemists frequently say that the carbon atoms in ethene are sp2 hybridized and that the double bond consists of a a bond and a n bond. Although we realize that we are only talking in terms of a particular model, such statements can be very misleading for students. They are likely to believe that hybridization is a phenomenon and that there is only one correct way to describe a C=C double bond, which is as consisting of a o bond and a n bond. It would be much better to say that the bonds in the ethene molecule may be conveniently, although approximately, described either in terms of sp3 hybrids and bent bonds or in terms of a a orbital, formed from sp2 hybrid orbitals, and a n orbital. When chemists say that a carbon atom is sp2 hybridized or sp3 hybridized, they usually mean only that it is forming three planar bonds or four tetrahedral bonds, respectively. It would be helpful to students if this use of these terms were made quite clear. Students'misconceptions are also reinforced by the very approximate orbital diagrams that chemists habitually draw. Although we understand that these diagrams are drastic approximations and little more than a formalism, this is not always appreciated by students. For students, these diaerams are likelv to reinforce two misconceptions: tbat that byb&ization ofs and p orbitals is a leads to a change in the total elenron-density distribution around a carbon atom, and that the electron density distri-
bution implied by the a - a model is different from that implied by the bent bond model. It is bond formation, not hvhridization. tbat causes the electmn densitv in the val&e shell of the carbon atom to be different the methane molecule from what it is in the isolated carbon atom. Student's difficulties with the concepts that we use to discuss chemical bonds would be lessened if we emphasized more strongly that we are using approximate models and that different models may be more or less useful under different circumstances. The VSEPR model is the most convenient model for discussing the geometry of the ground state of molecules that have localized electron pairs, whereas the molecular orbital model is the most use&l model for discussing spectroscopic properties and excited and ionized states. Since the concept of an orbital is a difficult one for beeinnine students. who have little knowledge or understanding of quantum mechanics, an advantaee of the VSEPR model is that it is not an orbital model. 1i is a model, albeit a very approximate model, of the electron-density distribution in a molecule. The VSEPR model can be formulated in orbital terns, but it is not essential, or even necessarily helpful, to do this.
-
-
Literature Clted 1. Gillespie, R. J.;Nyholm, R. S. Buart Re". C h . Soc. 1967,11,359. 2. Gilleapie, R. J.Mohculor &omfry;~an;V Noatrand Reinhold: landon,1972. 3. Gillespie, R. J.: nargittai, I. T k YSEPR Mo&l dM&,'lor Geomeh.: Albn and B m : Boaton, 199%Prenti-Hall International: Lmdon, 1991. 4. KLnball,G. E. References* unpvblishedwork by Kirnbdl and his atvdenta arrgi" by H. A. Bent lref51. 5. Bent,H.A.L Chem Educ. lW.40,446.523; 1965,42,3M,348: 1%31,44,512, lW,
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