provocative opinion Should Orbitals Be X-Rated in Beginning Chemistry Courses? Henry A. Bent North Carolina State University, Raleigh, NC 27650
"I see no reason whatever to mention molecular orbitals in a beginning course in chemistry," writes Linus Pauling in a recent issue of The Science Teacher (September 1983, pp. 25-29). "Molecular orhitals have special value in the discussion of excited states of molecules," continues the father of the mathematical theory of orhitals for molecules, "but they are quite out of place in an elementary chemistry texthook." True, rote learning and regurgitation of the geometrical properties of hybrid o orbitals has attractive features. It gives students the security of participating in an activity that has definite, easily memorized rules. It gives teachers the security of writing questions that have definite, easily graded answers. And hoth students and teachers may. in fact, enioy that game of telling and retdling. ~ u ~ e r f i r i a l lit; has t he nppearance of heing a soohsticated artivitv. Also, it keeps students out of mis&ief in the ~ a b o r a t o r ~ i a nteachers d but of difficulty in lecture experiments. Definitely, it cuts course costs. But a t what cost? At the cost of knowing what science is. Education. it is said, is what is remembered after all that has heen learned is iorgotten. So, how well are students of chemistry edurated? What do they remrmher after all that they haw: hecn told ahuut orhitals is forgutten? That rhemistry is a mystery, to be memorized? The trouble with memorizing properties of orbitals is a subtle one, yet obvious once one sees it. For the memorized rules are right. T h e trouble is not there. Orbitals are the current paradigm. The trouble is in how one gets to them. The orbital game, to paraphrase Pauli, isn't even wrong. It's a game all right. But it's not the game of science. The paramount rule, the overarching, game-making rule, is absent.
Lavoisier's Rule "In commencing the study [or presentation] of a physical science," wrote Lavoisier [slightly augmented], "we ought to form [or advance] no idea but what is a necessary consequence, and immediate effect, of a n experiment or observation"
Lavoisier's Rule of Restraint is the sovereign rule of science. It's the common sense rule of not jumping to conclusions before you have the facts. It's the restraining, thought-provoking, theory-creating rule of thermodynamic's phenomenology, of Einstein's relativity, of Heisenberg's quantum mechanics, of Bridgman's operationalism. Lavoisier's Rule is a difficult rule to play by. Science (and science teaching) is not easy. Casting aside Lavoisier's Game Rule, however, is, in Robert Front's words, like playing tennis with the net down. It may he easy to score points that way, but what's the point? A high score on an AP exam? Well, in fact, whv not? ff education is not useful, asks Whitehead, what is it? Scoring fours and fives on AP exams certainly is a use of orbital rules. In the minds of many students it may be their chief l use. For then thev " mav " be able to wlaceout of ~ " e n e r achemistry in college and perhaps never take cbemistry-or any science-again. Perhaps counter-intuitively, the orbital game is counterproductive. It helps students beat the game of credits in science without knowing what science is. Worse, it leaves students not knowing that they don't know what science is. And worse yet, what they think they know about science we may wish they didn't think. The problem is one of thought:
Toward Molecular Orbitals Carbon is tetravalent. KCkulC cited in support of the tetrahedral hypothesis eight molecules: C h ,CH2CI,CHCL, CC4, COClz, COz, CSs HCN. Behind K6kul6's list is, of course, an entire course in chemistry chemistry's central concepts of pure substance and elementary composition, Dalton's hypothesis, Gay Lussac's law, Avogadro's hypothesis, Cannizzaro's procedure, relative molar masses with the concepts of single, douhle, and triple bonds, even merely the concept of "substitution," emphasized Mendeleev, one can cover an enormous amount of chemistry. Carbon is tetrahedral. h n ' t Hoff riled numerous supportive inrts. Perhaps m e fact suffirrs: there exi,w only one whzunce with the formula C'H?CI?. The tetrahedral rnwJ~Iacrout~ts:mmed~ntelyfor the rtercuchcmi.;try nhout single, doohle, and triple lwndi. I'crhaps n e w in the h1~10ry of ~ c ~ ~ ~ c c - C O ~Newtm, F ~ ~ ~and C UDarwin J. included-hassos~ml~lro rhwght exylaiurd vu murh so rnsll!..
AN octet-rule atoms are tetrahedral. Lewis cited especially the facts of organic chemistry and much of beginning atomic physics: R6nntgen's X-rays, J. J. Thomson's electron,Moseley's atomic numbers. Lewis' emphasis on the stereochemical importance of lone pairs, generalized to electron pair coordination numbers other than four, accounts for the stereochemistry of atoms with expanded and diminished octets, as pictured, e.g., in the Valence Shell Electron Pair Repulsion Theory and Tangent Sphere Models of Matter.
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too much deductive thought from memorized rules, too little inductive thought from ohserved facts. Rigorous adherence to Lavoisier's Rule requires that facts he used aggressively, inductively, to capture ideas and hynotheses. not merelv nassivelv. deductivelv. ". to illustrate ihoughts'and theories. ~ecause;for example, there's only one compound with the molecular formula CHzC12, chemists inferred that methane must he tetrahedral. Much later it was noted. hv Pauline and Slater. that the simnlest description of tet&edrally iirected affinities from acarbon atdm in terms of spherical harmonics centered a t the carbon atom makes use of "sp3 hybrid orbitals." Hybridization followed from the facts, not the facts from hybridization. Adherence to Lavoisier's Rule is a creative activity. It's how students did qual under Hildehrand at Berkeley. It wasn't the fastest way to do unknowns: But it was a sure way to learn what science is: observe chemistry and create your own qual scheme. Playing by the Rule in the Big Game requires concrete knowledge, a lively imagination, good judgment, and patience-in short, it generally requires a t the outset a scientist. But once creative scientists have invented a Rule-abidinz game, it is possible for teachers to help students to understad the game and to appreciate what science is. How? By rewriting history, Ruskie style, and putting chemistry in orbit about physics? We've tried that. So, what else is there to do? Well, when in doubt, said Mark Twain, tell the tmth-the scientific truth. Tell i t as it happened. Advance no idea hut what is a necessary consequence of observation. The truth regarding necessary ideas concerning molecular orbitals is sirnay told; see box.' Lewis' Orbltals In summary, out of the test tube and cathode ray tubes h t the valence stroke of classical organic came the t h o ~ ; ~ that chemistry corresponds to two electrons. The tetrahedrally directedvalence-strokes of classical chemistry's structural theory correspond in the language of modem quantum chemistry to localized molecular orbitals. They might he called "Lewis orbitals." Included would he the orbitals of Lewis lone pairs and the inner orbitals of Lewis' atomic cores. Chemists have had molecular orbitals all alone. from the time of Crum Brownii graphic formulas. Only theididn't call them that. They didn't call them orhitals. They called them valence-strokes (later, after Lewis, shared electron pairs) and the svmhols for the elements (later. again after Lewis-and ~ o s s & electrons of atomie cores or kernels). Chemists formed those concepts as necessary consequences of chemical experiments, exactly as one may do today in the classroom. And that makes all the difference. For when all is said and forgotten, even the shape of methane, what remains from a chemistry course, one hopes, is the essence of the science: a process more than a product. The process of concept formation in chemistry often foreshadowed later developments in physics. As Pauling noted some year ago, "[Ilf quantum theory had been developed by the chemists rather than the spectroscopists [as, indeed, i t was; for chemistry with its stationary states that can he named-its elements and comoounds-is nothine if not a quantum theory of matter], it is prohahle that the tetrahedral orbitals would olav the fundamental role in the theorv. .. in place of s and p drbsals." Hvhridization works both wavs. One can ao from s and D orhitals to tetrahedral orhitah. 0; one can go From tetrahedr& orhitals to s and D orbirnls-and, thence, from the architecture of molecules to the electron shell structure of atoms.
Chemistry to an Exclusion Principle (as a disciple of Lavoisier might wish to do). For i t is an unstated rule of structural theory that valence strokes neuer cross. Combined with Lewis's identification in 1916 of the valence stroke as two electrons, Chemistry's Non-Crossing Rule leads to the rule that two but no more than two electrons can share the same region of space. In 1926 Heisenberg found a mathematical expression for that fundamental property of electrons: waue functions for electrons must be antisymmetrical. Heisenherg's statement implies that the probability of finding three electrons at the same place at the same time is zero, in agreement with chemistry's Rule of Two. Chemistry's Physics The van't HofflCrum BrownlG. N. Lewis model of methane astutelv" exoresses for chemical .DurDose . . the insights of modern electron p h y s k regarding the behauior of close confederations of electrons. The valence-strokes of classical t if crudely, in one dichemical t h e ~ r y ' r e ~ r e s e nshrewdly, mension, the wave-like character of electrons. (Better would be three-dimensional valence-spheres.) The symbols for the elements (C and H in methane) represent Rutherford's atomic nuclei and the localized orbitals of inner-shell electrons. Termination of valence-strokes a t the symbols for elements represents operation of Coulomb's Law. Tetrahedral disposition of valence-strokes (for Octet-Rule-obeying atoms) represents operation of Pauli's Exclusion Principle. Three cheers for classical chemistry! What should be Xrated in beeinnine chemistrv courses are not. as now. chemical arguments& chemical mAels hut, rather, quantum physical areuments for chemical models. Let's teach chemistrv in heginning chemistry courses, not Johnny-come-lately pronouncements from quantum physics regarding orbital approximations to eigenfunctions of partial differential equations. The modern tendency in chemistry to slight chemical facts and to go first to physics for chemical concepts is, of course, understandable. With the discovery of quantum physics, said Dirac. all of chemistry is in principle solved. But in practice efforts to achieve what ~ i r a prociaimed e as possibleln princinle have created ~rohlemsfor education in chemistry a t all
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CPT's Problem Students are coming to colleges with little knowledge of descriptive chemistry. Silver chloride is a pale green gas, the symbol for lead Ld, the formula for potassium carbonate PCOo. Reluctantlv. ,. after several vears of deliberation. the American Chemical Society's ~ ~ m m i t t eone ~rofessknal l'rainine ICPTI has decided that it must sacriiicesome tlrxibility in appru"ed programs and mandate tiw the core curriculum additional work in fundamental descri~tiverhemistry, a t the expense of an optional advanced cokse. Pushed aside. for examole. mav be a hiehlv .. . desirable course in biochem'istry. 11 u.(;uld be>xceedingly hdpful /or education in chrmistrv of all levels if d e s r r i ~ t r rhrntisfrv ~r were hiyhl, rated in iigh school chemistry cburses. Fewer students &ght be orbited right out of chemistry, and it would be possible to go further in college. There would be less repetition. For, in fact, all of the work in high school chemistry with modern "molecular orbitals"-and with formal thermodynamics, too-is generally repeated in college. ~
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Bibliography K6k,,l6,August, in '"ClsssiaintheTheoryof Chemical Combination." (Edilac&nfey.o. T.), Dwer Publications, Inc., Ne* York. 1963, p. 127. Lavoiaier. Antoine. "Elements of Chemistry." Dover Publications. Ine., New Yark, 1965, p. xw.
Leais,G.N,J Amer Chem. Soc,38,762 (1916):"Valanee,"DoverPublicstianr, Ine., New
Pauli's Principle Similarly, one can go from Pauli's Exclusion Principle to Chemistry (as modern textbooks do). Or one can go from 422
Journal of Chemical Education
York. 2nd d.. 1945. p. 82.
van% H&, J. H., in '"Classics in the Theory 01 Chemical Combination," ( E d i l o ~Benfey. : 0. T.), Dover Publications, Inc., 1963. whitehead, Alfred North;~TheAimsofEducatlon,"TheFree Press. MaemillanPuhlhhiw Co. New York p. 2. gent,~.A., chemist& 39,[12],9 (1966).40,[1~,8(1967);J.C~~~E~~~..40,446,5Z(1963), 42,302,348 (1965). 45,768 (19681. See. also, Chem Reu.,61.275 (19611. Thelast referonces (thme bythisauthor1 descrihesnon-mathematicalroutethroughchemistry
t o a unified modelof bonding in covalent, ionic, and metallicsuhstancos. Not needed is hybridization or o and r orbitals. Even that route, however, is notone the author
trsvelr very far on in his beginning course in chemistry, which attemp* to put into practice what Levoisier preached and which remains, thereby, largely in Whiteheads '"stag ofromanco" with the often surprising and always interesting transformatiom of descriptive chemistry The very lsst reference istoarev%wof the emfeetsoforbital hybridization on moleculsr properties.
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