HSNS3901_02 1/12/09 3:33 PM Page 32 BUHM SOON PARK∗ Between Accuracy and Manageability: Computational Imperatives in Quantum Chemistry ABSTRACT This article explores the place of computation in the history of quantum theory by ex- amining the development of several approximation methods to solve the Schrödinger equation without using empirical information, as these were worked out in the years from 1927 to 1933. These ab initio methods, as they became known, produced the results that helped validate the use of quantum mechanics in many-body atomic and molecular systems, but carrying out the computations became increasingly laborious and difficult as better agreement between theory and experiment was pursued and more complex systems were tackled. I argue that computational work in the early years of quantum chemistry shows an emerging practice of theory that required human labor, technological improvement (computers), and mathematical ingenuity. KEY WORDS: computation, computer, quantum chemistry, practice of theory, approximation method, ab initio, Douglas Hartree, John Slater, Walter Heitler, Hubert James INTRODUCTION In the traditional narrative of the history of quantum physics, the problem of chemical binding appears only briefly at the end of the long march toward quantum mechanics. It is usually introduced as one of the exemplary problems *School of Humanities and Social Sciences, Korea Advanced Institute of Science and Tech- nology (KAIST), 335 Gwahangno, Yuseong-gu, Daejeon, Korea; [email protected]. The following abbreviations are used: AHC, Annals of the History of Computing; HSPS, His- torical Studies in the Physical and Biological Sciences; JCP, Journal of Chemical Physics; JSP, John C. Slater Papers, American Philosophical Society, Philadelphia; PCPS, Proceedings of the Cam- bridge Philosophical Society; PR, Physical Review; PRS, Proceedings of the Royal Society; RMP, Reviews of Modern Physics; SCF, self-consistent field; SHPMP, Studies in History and Philosophy of Modern Physics; ZP, Zeitschrift für Physik. Historical Studies in the Natural Sciences, Vol. 39, Number 1, pps. 32–62. ISSN 1939-1811, electronic ISSN 1939-182X. © 2009 by the Regents of the University of California. All rights reserved. Please direct all requests for permission to photocopy or reproduce article content through the University of California Press’s Rights and Permissions website, http://www.ucpressjournals.com/reprintinfo.asp. DOI: 10.1525/hsns.2009.39.1.32. 32 | HSNS3901_02 1/12/09 3:33 PM Page 33 BETWEEN ACCURACY AND MANAGEABILITY | 33 that quantum mechanics solved, thereby validating its general applicability. Singularly recognized as groundbreaking is Walter Heitler and Fritz London’s famous paper of 1927, which provided a theoretical explanation of why two hy- drogen atoms combine to form a molecule.1 The possibility of understanding the whole territory of chemistry with quantum mechanics—a reductionist ideal shared by other physicists—seemed within Heitler and London’s reach.2 In- deed, excitement about the new theoretical framework abounded in the late 1920s. As the historian Max Jammer put it: “Satisfied that the theory ‘works,’ since it provided unambiguous answers whenever invoked, physicists engaged themselves rather in solving problems which so far had defied all previous at- tempts or which promised to open up new avenues of research.”3 However, historians of quantum physics, including Jammer, have paid lit- tle attention to whether the reductionist program worked well or faced diffi- culties in chemistry after 1927. It seems that they have largely believed that quantum chemistry, a new field which came into being after Heitler and Lon- don’s paper, successfully carried out the mission of reducing chemistry to physics. Historians of quantum chemistry have been rather critical of this picture. They have shown that early optimism about reductionism quickly devolved into pes- simism in the 1930s in the face of the complexity of chemical systems, and that quantum chemistry developed into a discipline with diverse methodologies, indigenous languages, and separate institutional bases. To them, the acceptance of quantum mechanics in chemistry has not necessarily meant the reduction of one discipline to another.4 1. Walter Heitler and Fritz London, “Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik,” ZP 44 (1927): 455–72. 2. For instance, Paul Dirac made an oft-quoted statement that “the underlying physical laws for the mathematical theory of a large part of physics and the whole of chemistry are thus com- pletely known.” P. A. M. Dirac, “Quantum Mechanics of Many-Electron Systems,” PRS A123 (1929): 714–33, on 714. 3. Max Jammer, The Conceptual Development of Quantum Mechanics, 2nd ed. (College Park, MD: American Institute of Physics, 1989), 359–60, 384–86. 4. Kostas Gavroglu and Ana I. Simões, “The Americans, the Germans, and the Beginnings of Quantum Chemistry: The Confluence of Diverging Traditions,” HSPS 25, no. 1 (1994): 47–110; Eric R. Scerri, “Has Chemistry at Least Been Approximately Reduced to Quantum Mechanics?” Proceedings of the Biennial Meeting of the Philosophy of Science Association 1 (1994): 160–70; Mary Jo Nye, From Chemical Philosophy to Theoretical Chemistry (Berkeley: University of California Press, 1993); Silvan S. Schweber, “The Young John Clarke Slater and the Development of Quantum Chemistry,” HSPS 20, no. 2 (1990): 339–406. See also Ana I. Simões, “Chemical Physics and Quan- tum Chemistry in the Twentieth Century,” in The Cambridge History of Science, Vol. 5: The Modern Physical and Mathematical Sciences, ed. Mary Jo Nye (Cambridge: University of Cambridge HSNS3901_02 1/12/09 3:33 PM Page 34 34 |PARK While agreeing in general with the latter point of view,5 I would point out that most historians of quantum chemistry have not fully examined the efforts made following Heitler and London to solve the Schrödinger equation for multi-electron atomic or molecular systems without using empirical data.6 This paper thus aims to reassess the place of the pioneers of ab initio methods in the history of quantum theory. I suggest that we broaden our attention from the conceptual development of quantum mechanics to the practice of theory in order to appreciate the significance of computation-oriented work in the spread of quantum mechanics into various problems in physics and chemistry. By the “practice of theory” I mean, in this case, a set of activities required to solve the Schrödinger equation, such as devising approximate Hamiltonians and trial functions, calculating complicated integrals, and formulating schemes to nar- row the gap between theory and experiment. There was no dearth of problems to solve. And yet, the more complex the atomic or molecular system, the more difficult the problem, especially because of the increasing amount of labor that computations involved. A compromise had to be reached between defining a manageable problem and solving it accurately. What, then, would be this ac- ceptable compromise? By shifting our focus to the practice of theory, we can see who sought to solve the wave equation using ab initio approaches and how they tested the level of compromise between manageability and accuracy. It is worth noting that graduate students, postdoctoral scholars, and junior faculty members created this domain of study, not the inventors of quantum mechanics. That is, the multi-electron atomic or molecular system presented itself as an Press, 2003), 394–412; Ana I. Simões, “Dirac’s Claim and the Chemists,” Physics in Perspective 4 (2002): 253–66. Most recently, see Martha L. Harris, “Chemical Reductionism Revisited: Lewis, Pauling, and the Physico-Chemical Nature of the Chemical Bond,” Studies in History and Phi- losophy of Science 39 (2008): 78–90. 5. Buhm Soon Park, “In the ‘Context of Pedagogy’: Teaching Strategy and Theory Change in Quantum Chemistry,” in Pedagogy and the Practice of Science: Historical and Contemporary Per- spectives, ed. David Kaiser (Cambridge, MA: MIT Press, 2005), 287–319; Buhm Soon Park, “Chem- ical Translators: Pauling, Wheland, and Their Strategies for Teaching the Theory of Resonance,” British Journal for the History of Science 32 (1999): 21–46. 6. One notable exception is Andrea Woody, “Putting Quantum Mechanics to Work in Chem- istry: The Power of Diagrammatic Representation,” Philosophy of Science, Proceedings 67 (2000), S612–S627. And yet, Woody gives much attention to the emergence of diagrammatic represen- tation of molecular orbitals as a way of getting around computational difficulties. I focus more on the nature of computational constraints and some developments in approximation methods during this period. The term ab initio, which means “from the beginning,” was first used around 1950. Peter W. Atkins, Quanta: A Handbook of Concepts, 2nd ed. (Oxford: Oxford University Press, 1991), 1. HSNS3901_02 1/12/09 3:33 PM Page 35 BETWEEN ACCURACY AND MANAGEABILITY | 35 entry-level problem for those who aspired to learn and master quantum theory, although they were located at various universities around the world.7 MAKING APPROXIMATIONS The point of departure for the problem of many-electron atoms was the nor- mal helium atom—the two-electron system. Various approximation methods were first developed and tested for the helium atom before being applied to larger atoms, and that experience would prove important for quantum chem- istry in its wake. Outstanding agreement between theory and experiment for the helium problem was achieved by the Norwegian