Between accuracy and manageability: Computational imperatives in quantum chemistry

Historical Studies in the Natural Sciences

Volumn 39, Issue 1, 2009, Pages 32-62

  Park, Buhm Soon ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Ab initio; Approximation method; Computation; Computer; Douglas Hartree; Hubert James; John Slater; Practice of theory; Quantum chemistry; Walter Heitler

Indexed keywords

EID: 69849129721     PISSN: 19391811     EISSN: 1939182X     Source Type: Journal    
DOI: 10.1525/hsns.2009.39.1.32     Document Type: Review

References (110)

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 completely 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
5. 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
6. Mary Jo Nye, From Chemical Philosophy to Theoretical Chemistry (Berkeley: University of California Press, 1993)
7. Silvan S. Schweber, "The Young John Clarke Slater and the Development of Quantum Chemistry," HSPS 20, no. 2 (1990): 339-406
8. See also Ana I. Simões, "Chemical Physics and Quantum 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 Press, 2003), 394-412
9. Ana I. Simões, "Dirac's Claim and the Chemists," Physics in Perspective 4 (2002): 253-66
10. Most recently, see Martha L. Harris, "Chemical Reductionism Revisited: Lewis, Pauling, and the Physico-Chemical Nature of the Chemical Bond," Studies in History and Philosophy of Science 39 (2008): 78-90
11. 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 Perspectives, ed. David Kaiser (Cambridge, MA: MIT Press, 2005), 287-319
12. Buhm Soon Park, "Chemical Translators: Pauling, Wheland, and Their Strategies for Teaching the Theory of Resonance," British Journal for the History of Science 32 (1999): 21-46
13. One notable exception is Andrea Woody, "Putting Quantum Mechanics to Work in Chemistry: The Power of Diagrammatic Representation," Philosophy of Science, Proceedings 67 (2000), S612-S627
14. And yet, Woody gives much attention to the emergence of diagrammatic representation 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
15. A growing body of literature examines the practice of theory. Of particular relevance, for their emphasis on calculations and their pedagogical implications, are David Kaiser, Drawing Theories Apart: The Dispersion of Feynman Diagrams in Postwar Physics (Chicago: University of Chicago Press, 2005)
16. and Andrew Warwick, Masters of Theory: Cambridge and the Rise of Mathematical Physics (Chicago: University of Chicago Press, 2003)
17. See also Jed Z. Buchwald, Scientific Practice (Chicago: University of Chicago Press, 1995), for a general discussion of "practice" in science, including experiments
18. For Hylleraas's educational background and Born's influence, see Egil A. Hylleraas, "Reminiscences from Early Quantum Mechanics of Two-Electron Atoms," RMP 35 (1963): 421-31
19. Albrecht Unsöld, "Beiträge zur Quantenmechanik der Atome," Annalen der Physik 82 (1927): 355-93
20. Georg W. Kellner, "Die Ionisierungsspannung des Heliums nach der Schrödingerschen Theorie," ZP 44 (1927): 91-112
21. Egil A. Hylleraas, "Über den Grundzustand des Heliumatoms," ZP 48 (1928): 469-94
22. Hylleraas, "Reminiscences" (ref. 8), 427
23. Egil A. Hylleraas, "Neue Berechnung der Energie des Heliums in Grundzustande, sowie des tiesfsten Terms von Orthohelium," ZP 54 (1929): 347-66
24. ++ usw.," ZP 65 (1930): 209-25
25. Linus Pauling and E. Bright Wilson, Introduction to Quantum Mechanics with Applications to Chemistry (New York: McGraw-Hill, 1935), 224
26. Pauling and Wilson, Introduction (ref. 13), 222-24
27. John C. Slater, "The Electronic Structure of Atoms - The Hartree-Fock Method and Correlation," RMP 35 (1963): 484-87
28. Hylleraas, "Heliumatoms" (ref. 11)
29. Victor Guillemin, Jr. and Clarence Zener, "Über eine einfache Eigenfunktion für den Grundzustand des Li-atoms und der Ionen mit drei Elektronen," ZP 61 (1930): 199-205
30. Clarence Zener, "Analytic Atomic Wave Functions," PR 36 (1930): 51-56
31. John C. Slater, "Atomic Shielding Constants," PR 36 (1930): 57-64, on 57
32. Nevill F. Mott, "Walter Heinrich Heitler," Biographical Memoirs of the Fellows of the Royal Society 28 (1982): 141-51
33. and Kostas Gavroglu, Fritz London: A Scientific Biography (Cambridge: Cambridge University Press, 1995)
34. For reactions to Heitler and London's paper, see Gavroglu, Fritz London (ref. 19), 51-53
35. Gavroglu and Simões, "The Americans, the Germans" (ref. 4), 70-75
36. Heitler and London, "Wechselwirkung neutraler Atome" (ref. 1), 461
37. Werner Heisenberg, "Mehrkörperproblem und Resonanz in der Quantenmechanik," ZP 38 (1926): 411-26
38. On the origins of the resonance concept in physics and its use in chemistry, see Cathryn Carson, "The Peculiar Notion of Exchange Forces - I: Origins in Quantum Mechanics, 1926-1928," SHPMP 27 (1996): 23-45
39. Park, "Chemical Translators" (ref. 5)
40. On Heisenberg's study of helium, see Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory, Vol. 3: The Formulation of Matrix Mechanics and Its Modifications, 1925-1926 (New York: Springer-Verlag, 1982), 282-301
41. Heitler and London, "Wechselwirkung neutraler Atome" (ref. 1), 465-681
42. Fritz London, "Zur Quantentheorie der homöopolaren Valenzzahlen," ZP 46 (1928): 455-77
43. Fritz London, "Zur Quantenmechanik der homöopolaren Valenzchemie," ZP 50 (1928): 25-51
44. Buhm Soon Park, "The Contexts of Simultaneous Discovery: Slater, Pauling, and the Origins of Hybridisation," SHPMP 31 (2000): 451-74
45. Yoshikatsu Sugiura, "Über die Eigenschaften des Wasserstoffmoleküls im Grundzustande," ZP 45 (1927): 484-92, on 492 for Born's guidance
46. Katherine R. Sopka, Quantum Physics in America, 1920-1935 (New York: Aron Press, 1980), 3.48-3.50, and 3.102
47. Shou C. Wang, "The Problem of the Normal Hydrogen Molecule in the New Quantum Mechanics," PR 31 (1928): 579-86
48. Shou C. Wang, "PR Ibid., 579
49. After his research trip in Europe, Sugiura returned to Tokyo to join the Institute of Physical and Chemical Research (Riken) established in 1917. Along with Bunsaku Arakatsu and Yoshio Nishina, Sugiura also lectured on quantum mechanics at Kyoto from 1929 to 1931. See Dong-Won Kim, Yoshio Nishina: Father of Modern Physics in Japan (New York: Taylor & Francis, 2007)
50. Hideki Yukawa, Tabibito, trans. Laurie M. Brown and R. Yoshida (Singapore: World Scientific Publishing, 1982), 176-77. In comparison, Wang continued to study the new quantum mechanics and atomic theory at Wisconsin and Chicago on a National Research Fellowship in 1928-29
51. Like Sugiura, however, he finally went back to his home country, China, to teach modern physics at the University of Chekiang and later at Beijing University. For Wang's professional career, see National Research Fellowships, 1929-1944 (Washington, DC: National Research Council, 1944), 37
52. Nathan Rosen, "The Normal State of the Hydrogen Molecule," PR 38 (1931): 2099-114, on 2099
53. Sydney Weinbaum, "The Normal State of the Hydrogen Molecule," JCP 1 (1933): 593-96
54. Hubert M. James and Albert S. Coolidge, "The Ground State of the Hydrogen Molecule," JCP 1 (1933): 825-35
55. In fact, James started his graduate study in the chemistry department in 1928. But after finding that his interests were in mathematics and physics, he switched over to the physics department. For James's switch and Kemble's role in the James-Coolidge collaboration, see Hubert M. James, Response to Early 1930s PhDs Survey, 1980, American Institute of Physics, College Park, MD, MB31142
56. Hubert M. James to Katherine R. Sopka, 9 May 1972, quoted in Sopka, Quantum Physics (ref. 29), 4.87-4.88
57. The molecular orbital method was based on a different way of describing the wave function (ψ1 + φ1)(ψ2 + φ2). The calculation of hydrogen's binding energy based on this method, however, gave a poorer result (2.68 eV) than Sugiura's. Charles A. Coulson, "The Energy and Screening Constants of the Hydrogen Molecule," Transactions of the Faraday Society 33 (1937): 1479-92
58. Charles A. Coulson, Valence (Oxford: Oxford University Press, 1952), 118
59. See also Henry F. Schaefer III, Quantum Chemistry: The Development of Ab Initio Methods in Molecular Electronic Structure Theory (Oxford: Oxford University Press, 1984), 1-2
60. Henry Eyring, John Walter, and George E. Kimball, Quantum Chemistry (New York: John Wiley & Sons, 1944), 217
61. Hubert M. James, "Wave-Mechanical Treatment of the Li2 Molecule," JCP 2 (1934): 794-810
62. +," JCP 3 (1935): 9-14
63. See also John H. Van Vleck and Albert Sherman, "The Quantum Theory of Valence," RMP 7 (1935): 167-228
64. Van Vleck and Sherman, "Quantum Theory" (ref. 42), 185-86
65. James, Response, 1980, AIP (ref. 36). In 1940, James became an assistant professor at Purdue University, where his interests were diverted to polymer and solid-state physics
66. Buhm Soon Park, "The 'Hyperbola of Quantum Chemistry': The Changing Identity and Practice of a Scientific Discipline in the Early Years of Electronic Digital Computers, 1945-65," Annals of Science 60 (2003): 219-47
67. Schaefer, Quantum Chemistry (ref. 40), 4
68. Indeed the quantitative investigation of molecules, being limited to relatively simple ones, languished in the late 1930s and 1940s. Only a small number of studies on the hydrogen molecule (seven) were reported in this period, and all of them, using various trial functions, fell short of the accuracy of James and Coolidge's. See A. D. McLean, A. Weiss, and M. Yoshimine, "Configuration Interaction in the Hydrogen Molecule - The Ground State," RMP 32 (1960): 211-18
69. Andrea I. Woody, "Early Twentieth-Century Theories of Chemical Bonding: Explanation, Representation, and Theory Development (Quantum Chemistry)" (PhD dissertation, University of Pittsburgh, 1997)
70. Charlotte F. Fischer, Douglas Rayner Hartree: His Life in Science and Computing (London: World Scientific Publishing, 2004)
71. C. G. Darwin, "Douglas Rayner Hartree," Biographical Memoirs of the Fellows of the Royal Society 4 (1958): 103-16
72. R. B. Lindsay, "Douglas Rayner Hartree," in Dictionary of Scientific Biography, vol. 6, ed. Charles C. Gillispie (New York: Charles Scribner's Sons, 1970), 147-48
73. See also Ana Simões and Kostas Gavroglu, "Quantum Chemistry in Great Britain: Developing a Mathematical Framework for Quantum Chemistry," SHPMP 31 (2000): 511-48, esp. 515-20
74. For the tradition of mathematical physics at Cambridge University see Warwick, Masters of Theory (ref. 7)
75. Douglas R. Hartree, "On Some Approximate Numerical Applications of Bohr's Theory of Spectra," PCPS 21 (1923): 625-41
76. Simões and Gavroglu, "Quantum Chemistry" (ref. 48), also note the importance of Hartree's 1923 paper in the development of the idea of the selfconsistent field
77. Hartree, "Bohr's Theory of Spectra" (ref. 49), 625
78. Hartree acknowledged that Erwin Fues did similar calculations independently, but argued that his own method was more general than Fues's. In 1924, R. B. Lindsay sought to derive a charge density straightforwardly from a spherical average of Bohr orbits, which Slater saw as a step closer to the self-consistent-field method. See John C. Slater, Solid-State and Molecular Theory: A Scientific Biography (New York: John Wiley & Sons, 1975), 53
79. See also Slater, "Electronic Structure" (ref. 15), 485
80. Douglas R. Hartree, "The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I: Theory and Methods," PCPS 24 (1928): 89-110
81. Douglas R. Hartree, "The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part IV: Further Results Relating to the Optical Spectrum," PCPS 25 (1929): 310-15
82. Hartree, "Part II" (ref. 53), 111-14, on 113
83. J. A. Gaunt, "A Theory of Hartree's Atomic Fields," PCPS 24 (1928): 328-42
84. Schweber, "Young John Clarke Slater" (ref. 4), also notes critical comments on the Hartree method by Gaunt and Slater
85. John C. Slater, "The Self Consistent Field and the Structure of Atoms," PR 32 (1928): 339-48
86. Slater, "Self Consistent Field" (ref. 59), 346-48
87. Douglas R. Hartree to John C. Slater, 6 Jul 1928, JSP, D. R. Hartree, #1
88. John C. Slater, "The Theory of Complex Spectra," PR 34 (1929): 1293-322
89. John C. Slater, PR Ibid., 1299
90. Slater, "Theory" (ref. 65), 1294
91. Slater mentioned Dirac's earlier papers and the recent paper by Iva Waller and Douglas R. Hartree's "The Intensity of Total Scattering of X-rays," PRS A124 (1929): 119-42
92. Slater, Solid-State and Molecular Theory (ref. 51), 62-63
93. John C. Slater, "Note on Hartree's Method," PR 35 (1930): 210-11, on 210
94. Vladmir Fock, "Näherungsmethode zur Lösung des Quantenmechanischen Mehrkörperproblems," ZP 61 (1930): 126-48. The paper was received on 21 Feb 1930. In it, Fock made no mention of Slater's work, although he cited Gaunt's paper on Hartree's method
95. Douglas R. Hartree and William Hartree, "Self-Consistent Field, with Exchange, for Beryllium," PRS A150 (1935): 9-33
96. See also Douglas R. Hartree, "Theory of Complex Atoms," Nature 138 (1936): 1080-82
97. For the source of the errors in the SCF method, see Frederick Seitz, The Modern Theory of Solids (New York: McGraw-Hill, 1940), 237
98. Eyring, Walter, and Kimball, Quantum Chemistry (ref. 42), 166
99. Hartree to Slater, 6 Jul 1928, JSP (ref. 63)
100. Douglas R. Hartree to John C. Slater, 1 Nov 1939, JSP, D. R. Hartree, #1
101. Perhaps it was Slater who provoked Hartree to pay a visit to MIT. In one letter to Hartree, Slater gave a description of Bush's differential analyzer, saying he planned to use this machine in the SCF calculations. John C. Slater to Douglas R. Hartree, 25 Nov 1931, JSP, D. R. Hartree, #1
102. Douglas R. Hartree, Calculating Machines, Recent and Prospective Developments (Cambridge: Cambridge University Press, 1947)
103. Thirteen out of Hartree's forty publications after 1946 were intended to inform readers of various journals and government officials about calculating machines. For Hartree's role in the introduction of computers in England, see Mary G. Croarken, "The Emergence of Computing Science Research and Teaching at Cambridge, 1936-1949," AHC 14 (1992): 10-15
104. Paul A. Medwick, "Douglas Hartree and Early Computations in Quantum Mechanics," AHC 10 (1988): 105-11
105. See Slater, Solid-State and Molecular Theory (ibid., 42
106. Clemens C. J. Roothaan, "New Developments in Molecular Orbital Theory," RMP 23 (1951): 61-89
107. See also Park, "Hyperbola" (ref. 46)
108. Werner Heisenberg to Pascual Jordan, 28 Jul 1926, quoted in Mehra and Rechenberg, Historical Development (ref. 24), 301
109. James to Sopka, Quantum Physics (ref. 37)
110. Per-Olov Löwdin, "Recent Simplifications in the Molecular Orbital Theory of Calculating Energy Levels," Proceedings of the International Conference of Theoretical Physics (Tokyo: Nippon Bunka Insatsusha Company, 1953), 599-609, on 599