Reduction to quantum mechanics

Paradoxically, the issue of the reduction to quantum mechanics no longer appears to be such a pressing concern. The project of the unification of the sciences by reducing one body of disciplinary theory to another has run up against iimumerable obstacles, and has been attacked by at least a generation of philosophers. Those who want to discuss the relationship between quantum mechanics and chemistry do so in much more subtle... 

The historical development of the electronic configuration model is traced and the status of the model with respect to quantum mechanics is examined. The successes and problems raised by the model are explored, particularly in chemical ah initio calculations. The relevance of these issues to whether chemistry has been reduced to quantum mechanics is discussed, as are some general notions on reduction. 

Similarly the apparent success shown by orbital model as a zero order basis for the classification of spectral lines should not be taken to suggest a reduction of the chemical phenomena to quantum mechanics. 

Eric Scerri studied chemistry at the Universities of London, Cambridge and Southampton, and obtained a Ph.D. in the history and philosophy of science from King s College, London on the question of "The Reduction of Chemistry to Quantum Mechanics," He has been a research felloiu in the history and philosophy of science at the London School of Economics and at the California Institute of Technology. He is currently an assistant professor of chemistry at Bradley University, where he also teaches histoiy and philosophy of chemistry, which are also his main research interests. He is editor of the new journal Foundations of Chemistry. Address Department of Chemistry, Bradley University, Peoria, IL 61625. Internet scerri bradley.edu. 

It is indeed a great honor to be invited to contribute to this memorial volume. I should say from the outset that I never met Lowdin but nevertheless feel rather familiar with at least part of his wide-ranging writing. In 1986 I undertook what I believe may have been the first PhD thesis in the new field of philosophy of chemistry. My topic was the question of the reduction of chemistry to quantum mechanics. Not surprisingly this interest very soon brought me to the work of Lowdin and in particular his analysis of rigorous error bounds in ab initio calculations (Lowdin, 1965). 

When we come to apply the results we have so far discovered to quantum mechanical situations, we will find that the application usually revolves around the reduction of some reducible representation for the point group concerned. We have already seen how to find out which irreducible representations appear in the reduction of a reducible representation, namely if we write... 

In the thought experiment two systems I and II are assumed to interact during the period 0 < t < T, after which there is no further interaction. Suppose that the states of both systems are known at t < 0. The state of the combined system at any t > 0 can be calculated, in particular at t > T. However, the state of any one of the systems can no longer be calculated after the interaction. According to quantum mechanics such information can only be obtained by further measurement, that amounts to reduction of the wave packet. 

In the area of electron affinities of organic molecules, other electrochemical measurements were made and compared with half-wave reduction potentials. Quantum mechanical calculations for aromatic hydrocarbons were carried out using self-consistent field calculations. Many advances were made in the determination of the acidity of organic molecules. The effect of substitution and replacement on electron affinities and bond dissociation energies was recognized. This work is summarized in Chapters 10 and 12. A. S. Streitweiser provides an excellent review of the role of anions in organic chemistry up to 1960 [12]. 

In other words, Sklar s position parallels Woolley s with respect to quantum mechanical reduction. In both cases, the reducing theory can, in principle, provide satisfactory accounts of the phenomena deduced from the reduced theory, but only if certain constraints are invoked that themselves lack rationalization from within the reducing theory. In each case, the theoretical connections between the two frameworks, while clearly fruitful and most likely consistent, are insufficient to allow one theory actually to replace the other. Such a result should not be surprising, although it does stands at odds with much of the philosophical discourse on reduction. 

In contemporary chemistry, concepts such as orbitals, configurations, and hybridization are frequently used as though they were "real," contrary to the pronouncements of modern physics and philosophers of science who deny the reduction of such typically chemical concepts to quantum mechanics. In this case, the realism I am identifying takes the form of an unwarranted belief in microscopic entities that the theory tells us do not, in fact, exist. My claim is that modern chemistry correctly continues to adopt an intermediate position between realism and reduction in the tradition of Mendeleev and Paneth. 

If reduction of chemistry as a whole is considered from a naturalistic viewpoint as I have advocated previously (Scerri, 1998a), the question of whether or not chemistry has been reduced to quantum mechanics is more subtle and depends on the present state of computational quantum chemistry and in particular ab initio calculations of chemical properties. In this sense, one might want to concede that chemistry has been approximately reduced to... 

Eric Scerri studied chemistry at the Universities of London, Cambridge, and Southampton. He holds a Ph.D. in history and philosophy of science from King s College, London, where he wrote a thesis on the question of the reduction of chemistry to quantum mechanics. He has held several appointments in the United States, including a postdoctoral fellowship at Caltech, and is currently visiting professor in the chemistry department at Purdue University in Indiana. Scerri is the founder of the journal Foundations of Chemistry (http //www.wkap.nl/journals/foch), and has published extensively on the philosophy of chemistry in Synthese, the PSA proceedings. International Studies in Philosophy of Science, British Journal for the Philosophy of Science, and Erken-ntnis, as well as in American Scientist, Scientific American, the Journal of Chemical Education, and other chemistry journals. His research interests include philosophical and historical aspects of quantum chemistry and the periodic system, as well as general issues in philosophy of chemistry. 

Eric Scerri is currently a lecturer in the Department of Chemistry and Biochemistry at UCLA. After obtaining his bachelor s and master s degrees in chemistry he wrote his PhD dissertation in History and Philosophy of Science at King s College in London. This was on the question of the reduction of chemistry to quantum mechanics. For the past ten years Scerri has been a leading pioneer in the efforts to establish the philosophy of chemistry as a new academic discipKne. His contributions have included the foundation and editorship of the journal Foundations of Chemistry as well as the publication of about 90 articles in journals and edited collections. Throughout this work he has maintained a focus on the application of philosophy of chemistry to the field of chemical education and many of his articles have appeared in the Journal of Chemical Education. 

By cOTitrast the new volume does not repeat any of these topics with the possible exception of the perennial topic of reduction of chemistry to quantum mechanics, but this time by Hinne Hettema, one of the newcomers to the field who did not appear in the earlier volume. Olimpia Lombardi writes about a related topic, that of the ontological autonomy of the chemical world as mentioned above. Another newcomer, Alexandru Manafu, proposes a novel approach to another related issue, that of emergence in chemistry. 

The reduction of chemistry to quantum mechanics has neither failed completely, as some philosophers of science have claimed, nor has it been a complete success, as some contemporary historians have claimed. The reductive enterprise has been highly successful but not to the extent of deposing the chemical facts or the quintessential discovery of chemical periodicity made by De Chancour-tois, Newlands, Odling, Hinrichs, Lothar Meyer, and most significantly, Mendeleev. Rather than undermining chemical periodicity, modern quantum physics has ht-erally re-presented the periodic system and has provided it with a theoretical justification. More important, quantum physics has achieved this feat without assuming the imperialistic role that it is sometimes attributed. 

The question of the reduction of chemistry to quantum mechanics has been a central issue in the renewed interest in philosophical aspects of chemistry. L. McIntyre, The Emergence of the Philosophy of Chemistry, Foundations of Chemistry, 1, 57-63,1999 J. van Brakel, On the Ne ect of the Philosophy of Chemistry Foundations of Chemistry, 1, 111— 174, 1999 E.R. Scerri, L. McIntyre, The Case for the Philosophy of Chemistry, Synthese, 111,305-324,1997. 

Coming back to chemistry, the sentence of Dirac neglects a basic difference between quantum mechanics and chemistry. Quantum mechanics in its traditional form decribes reversible evolutions in short, the rotation of a state vector in the Hilbert space. But chemistry in concerned with irreversible processes. A chemical reaction is a typically irreversible process, driving a system towards equilibrium there is no possible reduction of chemistry to quantum mechanics. 

The opening section is on the question of philosophy of chemistry as a whole, and on the question of reduction. I should mention that the collection does not cover the entire field of philosophy of chemistry. However it does cover what I think is the most fundamental question, namely the alleged reduction of chemistry to quantum mechanics. 

One of us (Eric Scerri) has previously referred to this form of reduction as pragmatic reduction . Scerri, E. R., Has Chemistry Been At Least Approximately Reduced to Quantum Mechanics , PSA 1994, Vol. 1 (East Lansing, Mich. Philosophy of Science Association), 160-170. 

I believe that the findings of this paper are relevant to the question of the epistemological reduction of chemistry, that is reduction in practice rather than in principle. A considerable amount of work has been carried out on the question of reduction of chemistry, both in principle and in practice, to quantum mechanics. Very little has been done however with regards to chemistry and the earlier quantum theory. I suggest that the hafnium episode represents one of the few specific instances of an attempted reduction of a chemical fact to quantum theory. As I have argued in this article, I believe that this is a failed reduction in that it does not constitute an ab initio approach. Of course this episode has no bearing on the question of whether chemistry can be reduced in principle (ontological reduction) to quantum theory or quantum mechanics. 

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