The Molecular Structure Conundrum R. G. Woolley Trent Polytechnic, Clifton Lane, Noningham NG11 ENS, U.K.
Stephen Weininger's challenging account of what he calls "The Molecular Structure Conundrum" has recently ap(I). The importance and usefulpeared in THIS JOURNAL ness of the molecular structure hypothesis is not an issue here; no one is suggesting that it he abandoned. What is of concern is our understanding of the structure concept in the light of current knowledge of physics. It is banal to recall that molecular structure first emerged in a very different scientific context. Hence this discussion. At the end of his paper Weininger asks, "What should we tell our students?" This is obviously something individuals must decide for themselves; however, as one of the main advocates of this radical critique of ideas in chemistry I should like to draw attention to two of the key points that arise out of his summary. What Can We Say About Molecular Structure? One of the most important ideas to be clear about is that there is R deiinite phi&,sophical content commonly assoriatrd with classical chemistrv. Van't Hoffs stereochemistry ( 2 ) is clearl\, fuunded on his nrofound belief in the realits of molecules as material objects in ordinary 3-dimensional ("nhvsical") " . svace: . , molecules could not he verceived directly simply because of the limitations inher'nt in our senses. For van't Hoff, stereochemistrv was vart of an areument to give a "proof" bf the physical reality bf m o l e c u l e ~ t h eargument, however, is no more than a statement of an a priori philosophical position (classical realism). And if it is said (3, 4). that the "vhvsical realitv" of atoms and molecules is no longer disputkd; this really bnly means that there is a more or less universal acceptance (conscious or unconscious) by physical scientists of the metaphysics of classical realism. None of the usual arguments for the "reality" of atoms as concrete, material entities ("building blocks") are conclusive; all so-called "experimental proofs" (X-ray diffraction, Brownian motion, radioactivity, etc.) can he described perfectly well with or without this materialist conception, which is metanhvsical me. . in character. For examvle, . quantum . chanics can account for the X-ray diffraction experiment abstractly using wavefunctions (or the density matrix) and the operator describing the interaction of radiation with matter (5, 6). According to Heisenberg's formulation of the quantum theory such a description is complete; even though this seems repellent to minds that thrive on "physical pictures of reality," there is nothing else as far as quantum theory is concerned (7). The pictures are metaphysics; of course they are very useful when they enable minds to engage creatively with science, but equally they can he harmful to science if they become more than tools for thought. Our beliefs help to define the unthinkable-those thoughts that ordinarily are put out of mind-and hence limit what we regard as possible. Progress in science may well require the acceptance of what hitherto has seemed "unthinkable"; thus, for example, and central to the discussion in Weininger's article (I), is the relatively recent recognition that there is no necessity for us to interpret euery chemical experiment in terms of classical molecular structure. The quickening transformation of much of "physical chemistry" into chemical physics is witness to this fact.
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Every chemist has some philosophical position whether or not helshe acknowledees it.. and i t is therefore important that students gain some facility a t distinguishingscience from metaphysics. Let me give an example of how metaphysics insinuates itself into our beliefs about the practice of science. In mv view it is absurd to suppose that metaphysics can be eliminated from the practice of science, and concerns about "reality" and "Truth" are best avoided! Still, the contrary view i s widely held, and many chemists will assent without difficulty to some such statement as the following which denies any role for metaphysics in "proper" science: Proposition "A": Truth is that which can be verified experimentally or according to the laws of formal logic. The first nart of this "scientific view" of certain knowledge (away with mere metaphysical speculation!) is captured sucrinctlv in a famous anhorism attrihuted to Max Planck: " ~ x ~ e r i m e n are t s the only means of knowledge a t our disposal. The rest is poetry, imagination." And we will hardly quibble with the addition of formal logic to Planck's statement. Nevertheless, caueat emptor! What we are being offered here is no more than a metaphysical regulatioeprinciple, an exhortation to the disciples of the philosophical position called positivism. As such, we can take it or leave i t according to personal taste without thereby sullying our credentials as nracticine scientists. The crucial k e p thatlustifies this claim, and the one that is so difficult to "see" without the benefit of hindsight, is this; Proposition "A" offers an explicit characterization of "truth." so we can ask whether it satisfies its own test (turn "A" on itself). When looked at in this way it becomes apparent a t once that "A" fails the test it proclaims, i.e., in its own terms it is not a true statement! It is quite evident that this formula for the "truth" is beyond the limits of hoth experimental investigation (what conceivable experiment could he invoked to verify it?) and formal logic. More explicitly "A" 1) has the character of a universal statement, something valid
independently of our experience, 2) is not a truism-I see no reasonable reading of it such that by means of definitions only it can be transformed into a truth af logic. Although we have here a damaging criticism of positivism, and therefore cannot simply dismiss metaphysics out of hand on the basis of such anargument, there is a certain kind of skeptical attitude that is wholly appropriate. Experiments and logical thought are of course the tools that give science its cutting edge; where Proposition " A errs is in what i t denies, and it is as well t o be vigilant with respect to the overstated claims of illusory principles such as that enunciated hv Planck. In mv experience students will be lucky to learnihis kind of anaiysisj'rom their coursebooks, so they will hare to rely on either their instructors or their own effirts to develop acritical attitude. Weininger quotes Gilbert Newton Lewis approvingly; "No generalization of science, even if we include those capable of exact mathematical statement has ever achieved a greater success in assembling in a simple way a multitude of heterogeneous observations than this group of ideas which we call structural theory" (8). One can only agree, and for most
chemists this is the bottom line. Still, it is an elementary point of logic that seems easily overlooked that the success of this model in accounting for chemical observations does not imply that the molecular structure hypothesis is a true acco&i of the nature of chemical suhsiawes as they "really" are (of "reality"); to go down that road is to become entangled in the mirages of metaphysics (9). The metaphysics of classical realism is optional. Molecular structure is a concept for solving chemical problems, not an object of belief (10). Arguments of this kind persuade me that molecular strucas a nowerful metaohor. If we leave ture is best regarded " aside all the connotations of classical realism associated with the structure hypothesis, we may still conclude that what is really important about the molecular structure hypothesis is that it gives a representation of chemical phenomena that has enabled chemists to grasp fresh and significant relationships in the experimental data obtained in their lahoratories. Since this representation is achieved through symbols (structural formulas) there is an ohvious connection with metaphor. What has to he decided then is how the symhols of chemistry function as signs; what rules of convention or habitual association are there between.. savs. - . the chemical symhol CsH6 and its ohject, the substance we call benzene? Classical chemistrv. chemistrv and quantum the".auantum . ory all give answers to this sort of question. The gist of Weinineer's article is that students can (should?) now he told th& there are real doubts as to whether these answers are the same. Readers are urged to consult the original literature before making up their own minds as to what they might or might not do, hut should find Weininger's article to be a useful guide. The second point I wish to raise is this: What are the Foundations ot "Theoretical Chemistry"?
For more than half a century we have taken it for granted that the anulicationof auantum theow to chemistrv must he developed i s an extension of the co&eptual framework of classical chemistry; classical stereochemistry is hased on an idea of molecules as atoms joined by bonds in ordinary physical soace. Such an exvlicit mechanical model can he quantized'in well-known ways that need not he described-here (11). But if one starts again and aims to confront the empirical evidence of chemistry with qnantum theory, where should one begin? One possible starting point is hased on the acceptance a t the outset of the classical metaphor of molecules as the microsconic "huildine blocks" of suhstances: it then seems that a mdlecule shouid be regarded, in the fir& instance, as a closed (i.e.. . . comnletelv isolated) collection of a specified numher of electrons and nuclei interacting through elertrostatic furces. Thts leads to what 1 have called the "lsolnted Molecule Model" (5, 6, 10). I am very well aware that its direct relevance to chemistrv is strictly limited because chemists do not ordinarily deal with iiolated molecules; however, in views of misconceptions in the literature (1215), I reiterate here that the aimof my discussion has been to make clear that the implications of this model do not coincide with the results of quantum chemistry. Even so, the failures of the "Isolated Molecule Model" are instructive for they invite us to ask how the success of quantum chemistry comes about. This is one of the main points made in Weinineer's discussion (I). T h e significanck o f the "Isolated Molecule Model" to theoretical chemistrv can usefullv he compared with the role of the principle of inertia in mechanics: When Galileo founded his new science of dynamics he had to begin with the conception of an entirely isolated body, a body which moves without the influenceof any external forces. Such a body had never been observed and could never be observed. It was not an actual body but a possible body-and in a sense it was not even possihle, for the condition upon which Galilea hased his conclusion, the absence of all external forces, is never realized in nature . .. . Nevertheless without the aid of these quite unreal
conceptions Galileo could not have proposed his theory of motion; nor could he have developed a new science dealing with a very ancient subject (16). These words, with ohvious modifications, apply to molecular theory every bit as much as to the science of motion. But there is a difference. The putative assimilation of chemistry by physics (reductionism) may lead us to expect a priori that this model will easily give us a quantum science of molecules. Stephen Weininger's article ( I ) warns us against any such facile conclusion. A succinct statement of the difficulties has been given by Aronowitz (17); the full spin-free, nonrelativistic molecular Hamiltonian describes the interactions of an assemblage of electrons and nuclei. I t does not describe a oarticular molecular soecies. T h e Hamiltonian shared hv, 'for example, cnhane and cyclooctatetraene is also shared by vinvlhenzene or anv other system where eight carbon nuclei, eight protons and 56 electrons are interacting. Its stationary state wavefunctions describe the correlations between the electrons and nuclei due to their Coulomhic interactions, but they do not lead to anything that can he called classical molecular structure (5,18). This leads to two conclusions: 1) As far as we know, molecular structure has to be put into
"quantum chemistry." 2) Theredoes not appear to be roominquantum theory to assign o fundamental significance to molecular shape (5,6,1O, 17).
These conclusions seem to me to he of sufficient importance to warrant their inclusion in anv course that claims t o deal with "theoretical chemistry." I t is, of course, appropriate to show students how molecular structure is vut into a quantum theory of molecules, and to develop the program of conventional quantum chemistry, hut this must surely be done after the fundamentals have been faced squarely. Attention ought to he directed toward the differences in the concepts employed in classical chemistry and qnantum theory-the discussion must not get hogged down in heavy mathematics! Finally, there is an even more radical view of the foundations of theoretical chemistry; this starts from the observation that if we want a fundamental account of the properties of chemical substances using quantum theory, a meaning has to be found for the classical concepts "atom," "bond," "molecule," and "shape" if they are to he retained. Now quantum field theory (QFT) is used routinely in the theory of condensed matter (19), and physicists claim that condensed matter physics is the part of physics most closely allied to chemistry (20), so one can try to use QFT for chemical substances (21). Three conclusions seem to he of interest: 1) There are heuristic arguments to support the view that atoms and molecules con he interpreted in terms of a QFT descrip-
tion of matter in hulk (21).
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2). Prieoeine and coworkers have shown that the foundations of
the Second Law of Thermodynamics (irreversibility) involve the same sort of field theory formalism (22).
(1) and (2) taken together suggest to me the conjecture that chemical structures and chemical kinetics flow ultimately from the same theoretical structure, which is certainly as it should he. 3) There is a striking generalization (21) of the discussion
Aronowitz gave for the molecular Hamiltonian (17), namely: all substances that contain the same chemical elements, in whatever proportions by weight, share thesame quantum field theory Hamiltonian constructed from the Heisenherg field operators (the quantities that replace the coordinate and momentum ooerators of wave mechanics) for electrons and the nu& uf the ipec~fiedelements. Fur example, instead of there being a fundamental Hamiltonran fctr ray. benzene, regarded as a substance, there isone Hamiltonianoperator carrying the burden of describing the dynamics and interrelationshipof all hydrocarbon substances. Volume 62
Number 12 December 1985
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Such a formalism may seem to he amonster, and much needs to he done before we can really see what benefits may come from its use; nevertheless, as far as we know, this is the formalism that provides the most fundamental physical description of chemical substances. As far as chemistry education is concerned, the upshot of this discussion is that students can he encouraged to think critically about the primitive concepts of their subject (bonds, molecules, shape, etc.) rather than passively accept them as received "Truth." Once these questions begin to be asked, the ideas sketched above and reviewed in Weininger's article ( I ) are hound to become involved. Literature Clted (11 Weininger,S., J . C H E M E D U C . , G I , ~119841. ~~ 121 uan't Hoff, 3. H.,"Ls ehimie d a m I'espace: P. M. Bazendijk, Rotterdam, 1875. (3) Dewsr, M. J. s.,"lntrduction foMadernChemistry,"UniversityofLondonAthlone press. 1965, pp. 1 4 . ( I ) Atkinn, P. W.. "Phyaicsl Chemistry," 2nd ed., Oxford University Pres, 1982, Ch.1.
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I51 Wwlley, R. G., Adu. Phys., 25,27 (19761. (61 Woolley, R. G., Israel J. Chrm., 19.30 119801. (71 Heisenberg. W.,Zeils. lur Phyrik, 43,172 (19271. (8) Lewis, G.N.,"Veleneesnd rheSVuctureofAtomsandMoleculea,"ChemicalCatalag Company, New York, 1923. (9) ~ ~ h P.,"To m , Save the Phenomena. An Essay on the Ideaof PhysicalTheory from Plafoto Galileo: (English franslstion. Do1and.E. andMaschler, C.l,Univemity of Chicago Prear, Chicago, 1969. (101 Wmlley. R. G., J. Amer Cham. Soc.. LOO, 1073 l197Sl. (111 Pauling, L., and Wilson, E. B.. Jr.. "Introduction toQusnfum Mechanics." MeGrawHill, New York, 1935. (121 Wilson, E. B., h . , I n l . J Quonf. Chem., S13.5, 119791. 1131 Bader. R. F.W. et al..lsraol J. Chom.. 19.8 11980). iiii ~ ~ tG . . A~~ u .c~h m ~k h y ~a .58.55 , , (19851. (15) Garcia-Sucre, M., and Bunge, M . , lnf. J. Qunnt. Chem., 19, 83 (1980), (16) Cassirer. E., "An Easav on Man," YdeUniversitvPress, 1944, p. 59. 1171 Aionowitz.S., Inf. J Quonl. Chom.. 14.253 (19781. i,~.. l R l Clavcrie. P.. and Diner. S..lsroel J. Chem.. 19.54. (19Ml. - ~ (19) Edwards, s.'F.,Phy& '%A, 212 (19791. 1201 Andernon.P. W..Scirnee. 177.393 (19721. izii w ~ o a ~k. y G., , stmcr. ond ding, 52, I (1982). (221 Prigogine, I., Tanner Lecture, delivered at Jawaharlsl Nehru Universify, New Ddhi. Tndia na~emhpr198%: Mavne. F..Georee.C.. and ds Hean. M..Pror. ~ Priewine. ~ "- , I.. ~ Not. Arod. Sci. USA. 74,4152 (1977): Prigogine, I., and Geowe, C., LC. Not. Acad. Sci. USA, 80,4590 (19831
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