Drawing Lewis Structures without Anticipating Octets J a m e s Allen Carroll University of Nebraska at Omaha, Omaha, NE 68182 T h e Valence Shell Electron Pair Repulsion Theory (VSEPR) rightly deserves a place in the crowded introductory chemistry curriculum. I t is splendidly successful in predicting the geometry about a central atom that is covalently bonded to two or more atoms (I). This predictive facility is i m ~ o r t a n tThoueh . more auantitative theories serve chemist; well as tools Tor discuskon of electronic states, they are less straightforward when applied to structural auestions. and difficult to use for prediction. By contrast; one can legitimately expect students with little chemical sophistication to apply VSEPR to obtain qualitatively correct structures for molecules and ions. For all its usefulness, applying VSEPR alone is analogous to solving a crossword puzzle without any clues. The theorv requires one to start with a reasonable Lewis (electron-dot) structure. Sensible Lewis structures are easily drawn by chemists with experience in reaction mechanisms, for the; recognize the patterns in many structures. However, early attempts to master this skill are likely to he trouhlesome for some students, and attempts to simplify the process generally rely too much on the "octet rule" (2-41, allowing (misnamed) "expanded octets" only when required. Several current college textbooks draw incorrect structures for molecules suchBs SO2 in sections that introduce Lewis structures. After noting the grounds for labelling structures as incorrect, the guidelines for selecting which Lewis structures are most important for a molecule will be introduced. The following discussion includes several examples of appropriate Lewis structures and the fine structural predictions that are possible. Electron Palr Approach What is the best Lewis structure for sulfur dioxide? Though not necessarv. i t is easier t o start with an annroori.. . ate skiletal atom arrangement, withsulfur in the center. The total valence electron count is 18 e-. Usine four electrons in two pairs for the 0 - S bonds leaves 14 These can be arranged with a total of eight electrons ahout each atom (Structure I), or with no formal charge and additional covalent bonding (Structure 11). There are two equivalent ways to generate I, so the best model is a resonance hybrid.
e-.
I
II
The arrangement that is more consistent with reactivity and molecular structure is preferable. Both I and I1 allow explanation of a principal feature of sulfur dioxide, its dual Lewis acid reactivity (5).Each has a lone pair on sulfur for Lewis base character, and each can be shown to accept another pair as a Lewis acid, for example.
Predictions of the molecular structure of sulfur dioxide based on I and I1 would differ, since the increased multiplebond character in I1 indicates shorter bonds. The sum of sulfur and oxygen covalent radii is 168 pm (6).Short sulfuroxygen bonds are found in a cyclic form of SOs (137 and 143 pm) (7),a chain form of SO3 (141 pm) (81,and both OSFz and OSFd (141 pm) (9,10). These are under 85%of the S - 0 single bond length and so equal to or slightly shorter than a S=O 28
Journal of Chemical Education
double hond (11). The two resonance forms of I give a n average hond order of 1.5, for which a bond lengthof ;oughly 165 pm might be expected (12). T h r bond leneth " in SO, is 143 om and the LOSO is 118.5° (13). These values are entirely consistent with two double S=O bonds havine steric reauirements almost as hieh as the sulfur lone pair (12). clearly, the more reasonable structure for SOz is 11. Thus formal charge and total hond order seem to be good predictive tools. T o incorporate these explicitly, the followina - -guidelines for generation of Lewis structures are offered. A) Only valence electrons are to be considered. B) All electrons are assigned as pairs, either to electron pair bonds or lone oairs at an atom. as far as oossible. C, i.rwisstructurea with more bonds tend to be mure important, rxcept that thr elements H.C, N,0.and F can arrommudste a maximum of four rlcctron pairr. and a triple bond must have one of these elements at a terminus to be reasonable. D) Lewis structures with less formal charge are more important. E) Formal charges allow eleetronegativities, with any negative formal charge on a more eleetr&egative atom and positive formal charge on a more electropositive atom, in more important structures. F) When two or more optimum resonance forms are equally likely, the molecular structure can be considered as an average of these. A few comments on these guidelines need to he made. Compounds with one or more atoms having a partially filled d suhshell cannot he expected to follow the guidelines, though they~may in particular cases. Other substances with . . an even number of unpaired electrons, such as dioxygen, would be incorrectly assumed to be diamagnetic, hut to predict magnetism a more sophisticated theory should have been used in the first place. The qualifications to rule C are both emoiricallv hased. The second disallows structures such as t;iplyb&ded dichlorine. In these auidelines the auantitv known as formal charee plays an important role. 1t;s defined as ~
-
~>
~
~
~
~
~
~~~
-
This differs from the calculation of oxidation numbers only in the assignment of bonding electrons: they are evenly divided for formal charge hut assigned t o the more electronegative element for oxidation number. Formal charge has not been widely used, perhaps because it tends to he zero except in ionic lattices, where long-range bonding is important. In fact it appears that molecules with nonzero formal charges and ions with any formal charge beyond the ion charge can he considered unstable. A checklist for writing Lewis structures hased on the above guidelines is: 1) Obtain a working kernel skeleton. 2) Count the total number of valence electrons available and keep track of these as electrons are added to the kernel skeleton. 3) Place a single electron pair hond between adjacent atoms. 4) Startingwith the most electronegative atoms, add electrons in pairs about each atom in turn to give that atom zero formal charge or, until an anion's charge has been accounted for, unit negative formal charge. 5 ) When valence electrons have all been distributed. check for formal chargts and l w k for resonance forms and ways to rearrange rlrctruns to rrnmove any residual formal charges or increased bonding.
6) Consider other atom arrangements which might allow less
residual formal charge or stronger honding. Step 4 produces reasonable electron arrangements in a straightforward manner, one atom at a time. The guidelines given above are meant to be useful rather than exhaustive. Their application frequently produces Lewis structures identical to those based on an octet rule. A significant difference arises in honding to terminal oxygen, as shown in the following paragraphs, which cover the series of oxygen group compounds EOz. Application to EO, Structures Trioxygen or ozone must he drawn (111) with four pairs of electrons at the central oxygen, in accord with the second part of guideline C. Rationalizations given for a limit of four electron pairs a t second row elements (first full period) include: (i) the lack of low-lying d orbitals, (ii) the small size of oxygen and the other 2p-block atoms, and (iii) their high electronegativity (15).
None of these reasons is completely convincing (16). Although 2p-block elements have no low-lying d orbitals, MO calculations for compounds of 3p-block atoms seem little affected by inclusion or exclusion of a 3d or 4s orbital in the atomic orbital basis set (17). The small size of the 2p-block atoms can explain why five "stereochemically active" electron pairs could not fit about these atoms but does not explain why the bonding in ozone does not parallel that in SOn, though the fifth electron pair a t the central oxygen of ozone would bring little increase in steric demand. On the final point, occurrence of more than four lone- and hondairs about a central atom is found onlv when electroneeakvity differences are high between theeentral and ligating atoms. The hieh electroneeativities of second row atoms result in low electronegativity differences between these and surroundine atoms in almost all cases and can he used to rationaliPe'Lhe "octet" rule. Yet even with its high rlectroneentivitv differences. ONFI (Strurture I V ) does nor heha\,e (V). like O P F ~
-
:P:
Rcwnancr hyhrid 111 agrees well with the reactivity and structure of 0,. Omne is appreciuhly unstahle, consistent with residual formal charges. Although suliur dioxide can he used an a nonaqueous solvent, ozone decomposes explosively. The bonds in ozone are indeed longer (see the table) than in dioxygen, as would he predicted from the average hond orders of 1.5 and 2.0. resoectivelv. The best Lewis structure fo;sulfur dioxide is 11. Compared to I it allows less formal charge and an additional hond pair. It is noteworthy that the geometry of molecular SO3 is strikingly similar to that of S02, with virtually equivalent bond lengths (the table) and bond angles (118.5' and 120°,
Comparison of Bond Length for some Oxygen-Contalnlng Substances Gas
Bond
Molecule
Length
Gas Ref.
Molecule
Bond Length
Ref.
respectively) (22). I t is thus quite satisfying that the Lewis structure most appropriate for gaseous SO%,VI, is similar to 11. The asbestos-like, polymeric form of SO3, VII, contains four-coordinate sulfur with terminal, douhle S=O bonds (141 pm) and longer, bridging S-0-S bonds (159 and 163pm) (8).Andes 0 - S - 0 are smaller than LO=S=O ( l O Z O versus 128"), as predicted from the lower steric requirement of single honds compared to double honds (14). For simplicity bond lengths are noted most frequently below; hond angles are virtually always consistent.
SeO2 is not molecular hut is a polymer chain with pyramidal, 3-coordinate selenium. This fourth-row atom is sufficiently larger than sulfur so that the E - 0 hond s t r e n a h decreases,Esperi:~ll~ for double bonds. This is not pnrt d;he minimal set of guidelines nbove but a sensible refinemrnt. useful for e x p l a k n g structural variations in a group. he Lewis structure VIII does not accommodate extended interactions or the Se-0-Se bond angle of 125" except by use of electron arrangements that place positive formal change on oxygen. The hond lengths are only slightly shortened from the single bond distance of 190 pm (Se=O, 173 pm; Se-0, 178 pm) (22).
-
-
The trend toward lone-ranee hondine continues with TeOs, in which T e has a trigonal hipyramidal geometry with the lone air in the trieonal d a n e and all sinele Te-0 honds (23). he tendency to Form E=O double honlds is a diagonal relationship. The single bonds of TeOz are reminiscent of single honding in SiOz. I t should he noted that the structural transition from angular SO2 to pyramidal SeO? to folded-square Te02 does not involve any jump into an "expanded octet3'-simply a smooth replacement of douhle honds hy single, with a consistent total of four bonds in each case. The transition from [rzone to SO? is a jump, one runsistent with thv ditfrrenre in chwnisrry ruund hetween the rompound with the second row element and its lower congeners. Lewls Structures of Ions With the electron pair guidelines above it is common to have several resonance forms for oxyanions. Using hydrogen sulfate for example, the forms Xa-d are all reasonable.
Structures Xa-c are attractive because thev show the formal charge, which must occur somewhere in the ion, on the most electronegative atom. Structure Xd has a maximum number of bonds. A simple average of all these resonance forms suggests hond orders of one for the S-OH hond and about 714 for the terminal S=O honds. The hond lengths, 156 and 147 pm, respectively (24), vary in the predicted way, hut both indicate substantial multiple bonding. The NH30-S bond length in zwitterionic (+)NHsO-SO(-) is 168 pm, and the terminal S=O honds are 145 pm for the same nominal bond Volume 63 Number 1
January 1986
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orders (25). As this comparison suggests, the practice of calculatina averaae, fractional bond orders from a set of resmanw forms is dangerously naive and best avoided. Electron arrangement of' the rrimethyloxosulfonium cation must have a positive formal chargeat some atom. The most reasonable arrangement is that of structure XI. The
LCSO is 112.5' (26). The 145 pm S=O bond length is equal to that in Cl2S0, in a typical S=0, double bond range (27). In contrast the smaller bonds angles, 10l0,and longer hond lengths, 153 pm (28), of dimethylsufoxide (DMSO) indicate a S - 0 bond order near 1.5. Comparing DMSO to both ClzSO and the cation, the charge in the trimethyl cation produces a double bond enhancement similar to that produced bv bunding to mnre highly electroneg~tivegroups;chlorine and oavren in ClSO. The double bond enhancement is consi3tentwith a c&traction in sulfur atomic orbitals, allowing for more effective a-overlap. Elements Other Than S and 0 The great number of structurally characterized compounds make sulfur-oxygen compounds convenient examples, but the electron pair guidelines work for other elements as well. In C1207, XII, the terminal C1=0 bonds are 140.5 pm comnared to 171 nm for the hrideine C1-0-C1 (29).The itreAgth of doublebonding uppare; indichlorine heptaoxide is ereater than in ohosohorus rVI oxides, where terminal P=o&~140 to 150 i m a i d bridging P-0-Pare near 160 pm (30). Replacing oxygen with nitrogen allows for triple honds as well as single and double. Bond order 3, suggested by the Lewis structures for NSF (XIII) and NSFa (XIV) are evidenced by very short (145 and 142 pm) bond lengths (31). The (FSN)4cyclic tetramer XV contains clearly alternating N-S and S=N honds of 165 and 155 pm, respectively (33), while 160.5 pm sulfur-nitrogen honds in XVI, the cyclic trimer (ClSN)> indicate an average hond order of 1.5 (34).
Formal Change The only electron arrangements above with formal charge (in excess of an ion charge for ions) are ozone and ONFa. Formal charges occur rarely for well-characterized species. I t was noted above that residual formal charge could be taken to suggest instability. For instance, metal salts of a i d e (XVII) and fulminate, CNO-, for which Lewis structures
v-I
.. .
-
P xvn 30
Journal of Chemical Education
show residual formal charge in excess of the ion charge, are explosive detonators. Jolly has noted that the pK, values of many hydroxy acids fall into well-differentiated groups when arranged by formal charge, if the electronic structures are derived disallowing any double 0 bonds, even for nitrogen- and carbon-centered acids (35). I t is simpler and less artificial to say that acids in each group have the same number of terminal oxygen atoms ahout the central atom. When Lewis structures are drawn with O=, all except nitric acid have zero formal charge. A comparison of the optimum Lewis structures of alternate molecular skeletons for (1) more bonds, (2) less formal charge, and (3) sensible oxidation numbers can be used indirectly to rationalize the "best" molecular skeleton. For example, if the atom arrangement of SO2 were S - 0 - 0 (XVIII) in SO2, then there would be formal charge, as in ozone, and fewer bonds. Students themselves can be expected to correct the error of placing both hydrogens on the same oxygen of H2SO4, by noting that this places a positive formal charge on the tricovalent oxygen.
Comparison of the six bonds in arrangement XIX to five honds in XX suggests that HS03- might exist as XIX. The existence of both forms in equilibrium is recognized (36) reminiscent of phosphorous acid. (This replacement of E-OH bonds with O=E-H is not general. I t does not produce covalency above four a t the central atom and willnot be seen where the O=E or E-H bonds are weak.) Hybrldlzatlon Lewis structures are the starting point for both VSEPR and hybridization theory. I t is the a-bonding hybrids of central atoms which are noted t o identify its geometry, so it is important for these to he predictable. Thus it is worth noting that the above guidelines lead to Lewis structures which indicate the same a-bonding hybrids as derived from octet structures. For example, sulfur dioxide still uses sulfur sp2 hybrids in the plane of the molecule, as does sulfur trioxide. Hydrogen sulfate is based on an spa set of a-bonding atomic orbitals. Lewis structures drawn according to the guidelines given cannot be used to suggest a-bonding hybrids. The "one valence atomic orbital for each bond" principle, like the octet rule, has lost favor in chemistry but is hard to excise completely. Thus, chemists presented with structures such as If, VI, or VII tend to start interpreting them in terms of five or six hybrids and recognize that such a-bonding hybrids a s p d and pd2 have unreasonable energies and little resemblance to results of MO calculations. These differences do not discredit such Lewis structures, just the hybrid orbital interpretation. Representation of SO2 and SOa with all S=O honds is appropriate by reference to the molecular geometries and gross reactivities. T o reject these structures hecause such simple constructs do not agree with details of fuller bonding theories ignores the different uses of the two.
Lnerature Clted (1) Gillmpie, R.J.. "Molecular Geometw,('Vao NmtrandReinholdCo.,London,1972. 121 Zandler. M. E.. and Talatv. E. R.. J. CHSM. EDUC... 61.124 11984). . . . is cisrk,~. J.. ~.~~eM.~o"c.,61;100(1984). (4) Lpver, A. B. P., J. CHEMEDUC., 49,819 (1972).
G. J., Mmdy. D. C., andEller, P. G.,"Stmeture and Bond'w of Tramition Metal-Sulfur Dioxide Complexes", in '"Stmdure and Bonding, VoL 46? SSpringer-Verlag. Berlin, 1981,pp. 47. (6) Jolly, W . L.."Malern Inorganic Chemistry? McGraw-HiU, New York. 1984, p. 52. (7) McDonald, W. S., and Cruickshank, D. W. J.,Acto C ~ p t .22.48 , (1967). ( 5 ) Ryan, R. R,Kubas,
(8) Westrik,R.,sndMeGillavw,C.H.,Acfo Crysf.,7,764(1954). (9) Fergusm, R.C.. J. Amw. Chem. Soc.. 76.850 (1954).
I101 Gundersan,G.,andHedbcg,K., J.Ckm.Phys..51,2SW(1969). I111 Huheey,J.E.,"lnorgsnicChemist'y,()3rdEdition,Hsrper&Row,Ne.pYork,198J,p. 828. 112) R e t 161, p. 59. (131 Haare, J., and Winnerisse, M.Z. Naturforaeh., A,, 23.61 (1968); Chrm. Abtr., 69, 71360~119681. (141 Hall found that the Psuli forces pmminently increase the steric requirement of bond pain rather thanlane pain, but there has heeninsufficientdcuelopmenftosupport a change in the phrming of VSEPR ideas. Hell, M. B.. J. Amrr Cham. Soc., IW, 6333 (19781. (15) Kwart. H., and King, K., "d-Orbifals in the Chcmiatq of Sillmn, Phospharua and Sulfur,()Springer-Verlag. Berlin, 1917, pp. 2-13. (161 Bri1l.T. B.,J CHEM.E~uc.,56.392(19731. (171 Schmiede*amp,A., Cruickshank, D. W. J., Skkarup, S.. Pulay. P., Hargittai, I., and Bog-, J. E.. J. Amsr. Chem Soe., 101. 2W2 (1979); Zuev, M. B.. Chaukin, 0.P., Chomova. A. V., and Shsgidullin, R. R., Doklady Phyaicol ChemSfry. 234,484 11977). I181 Miller, S. L., and T w o s , C. H.,Phya. Re% 90,537 (19531. (19) Hughe8,R. H., J. Chem.Phya.,24.131 l19561. 120) Aman0.T.. Hirofa, E., Morino, Y., J.Phhs. Sor. Jnpon.22.399 (19671; Cham. Abstr, 66.80645q (19671.
I211 C1arL.A. H.,andBeag1ey.R.. Tmns.Fomdoy Soe.,67,2216 (1971); Chem Abstr, 75, 102360h11971L
Chem. Abatr.. 59.10832b (1963). (27) Palmor, K. J.. JAmer. Chem.Soe.,60,2360(1938). (281 Thomas,R.,Shoemaker, C. B.,endErib, K.,Aclo Crysf.,21,12 i1966):Chem. Abafr.,
(351 Ref. (61.p. 180. I361 Go1ding.R. M., J . Ckm.Soc.,3711 (19601.
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