A History of Quantum Chemistry

1 Quantum Chemistry qua Physics: The Promises and Deadlocks of Using First Principles In the opening paragraph of his 1929 paper “ Quantum Mechanics of Many-Electron Systems, ” Paul Adrien Maurice Dirac announced that: The general theory of quantum mechanics is now almost complete, the imperfections that still remain being in connection with the exact fi tting in of the theory with relativity ideas. These give rise to diffi culties only when high-speed particles are involved, and are therefore of no importance in the consideration of atomic and molecular structure and ordinary chemical reac- tions, in which it is, indeed, usually suffi ciently accurate if one neglects relativity variation of mass with velocity and assumes only Coulomb forces between the various electrons and atomic nuclei. The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the diffi culty is only that the exact applica- tion of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation. (Dirac 1929, 714, emphasis ours) For most members of the community of physicists, it appeared that the solution of chemical problems amounted to no more than quantum-mechanical calculations. Physicists came under the spell of Dirac ’ s reductionist program, and quantum chemistry came to be usually regarded as a success story of quantum mechanics. Although it took some time for physicists to realize that Dirac ’ s statement was a theoretically correct but practically meaningless dictum, the fi rst attempts to solve chemical problems in the “ proper way ” — that is, in the physicists ’ way — appeared to be rather promising. These attempts started before the publication of Dirac ’ s paper, and they may have provided some kind of justifi cation for such a generalized statement. The Old Quantum Chemistry: Bonds for Physicists and Chemists The prehistory of quantum chemistry has its beginnings in the 1910s with various attempts, both by physicists and chemists, to explain the nature of bonds within two essentially disparate theoretical traditions — physical chemistry and molecular 10 Chapter 1 spectroscopy — and two confl icting views of atomic constitution. For Gilbert Newton Lewis, the emblematic albeit idiosyncratic representative of the fi rst group, the starting point was the static atom of the chemists. For Niels Bohr whose views were closer to those of the second tradition, the starting point was his dynamical atom, soon appro- priated by the physicists and used to explain the complexities of molecular spectra. In the last part of his trilogy “ On the Constitution of Atoms and Molecules, ” Bohr considered systems containing several nuclei and suggested that most of the electrons must be arranged around each nucleus in such a way “ as if the other nucleus were absent. ” Only a small number of the outer electrons would be arranged differently, and they would be rotating in a ring around the line connecting the nuclei. This ring, which “ keeps the system together, represents the chemical ‘ bond ’ ” (Bohr 1913, 862). 1 According to these general guidelines, in the hydrogen molecule the two electrons were rotating in a ring in a plane perpendicular to the line joining the nuclei. Although Bohr tentatively suggested a model for the water molecule, 2 it was in the case of the hydrogen molecule that he ventured to prove quantitatively its mechanical stability, offering a value for the molecular heat of formation twice as large as the experimental one (Langmuir 1912). Thus, the chemical consequences of Bohr ’ s molecular model confl icted with experimental data for the simplest molecule, and the calculations were much too complicated to be carried through in the case of more complex molecules. The exploration of another molecular model — the Lewis model with the shared electron pair, a topic we address in chapter 2 — was, however, to give a satisfactory, albeit qualitative, answer to the problem of chemical bonding. The translatability of Lewis ’ s picture into Bohr ’ s dynamical language was found by “ transforming ” Lewis ’ s static shared electrons into orbital electrons revolving in binuclear trajectories (Kemble et al. 1926). In the simplest case of diatomic molecules, and reasoning by analogy with the hydrogen molecule, the binding orbits of shared electrons were thought to fall into two distinct classes. In the class most directly associated with the Lewis model, shared orbital electrons were thought to move in binuclear orbits around both nuclei, providing the necessary interatomic binding “ glue ” on the assumption that electrons spent most of their time in the region between nuclei. In the second class, following Bohr ’ s suggestion, shared electrons moved either in a plane perpendicular to the line joining the two nuclei or in crossed orbits. Similar models were explored in the case of the hydrogen molecule ion with the difference that only one electron was involved (Pauli 1922). Again, agreement with experimental values for the few cases where quantitative calculations could be carried on could not be achieved. Quite independently from considerations related to atomic spectroscopy, quantization was applied to molecules 2 years before it was applied to atoms (Jammer 1966; Quantum Chemistry qua Physics 11 Kuhn 1978; Hiebert 1983; Barkan 1999). But whereas Bohr ’ s revolutionary assumption related radiation frequencies to energy changes accompanying electronic jumps between allowed orbits, in the case of the molecule, the more conservative Niels Bjerrum (a physical chemist and compatriot and friend of Bohr) accepted the classical electrodynamical identity between the frequency of emitted radiation and the mechanical frequency of motion. His hybrid model assumed simply the quantization of rotational energy, in conjunction with classical electrodynamics and the equipartition theorem. Starting with a simple model of the molecule as a vibrating rotator, Bjerrum provided a model to explain the infrared molecular spectra of some simple diatomic molecules and confi rmed the long-sought interdependence between kinetic theory and spectroscopy within the framework of a very “ restricted ” quantum theory. The close agreement between theory and experiment provided a strong argument in favor of quantization of rotational energies/frequencies. Such was the opinion of Bohr in a letter to Carl W. Oseen: “ I do not know what your point of view of the quantum theory really is; but to me it seems that its experimental reality can hardly be doubted, this is perhaps most evident from Bjerrum ’ s beautiful theory, and Eva von Bahr ’ s papers almost seem to offer direct proof of the quantum laws or at least of the impossibility of treating the rotation of molecules with anything resembling ordinary mechanics. ” 3 The interpretation of infrared molecular spectra proved to be so successful that atomic and molecular spectroscopy developed as quite separate branches until 1919 – 1920. Then, Torsten Heurlinger (a graduate student of Johannes Rydberg who held one of the chairs of experimental physics at the University of Lund) and Adolf Kratzer (Arnold Sommerfeld ’ s former Ph.D. student and assistant), completing the work started by physicist Karl Schwarzschild, showed that Bohr ’ s frequency condition could be extended beyond the motion of electrons and applied to the interpretation of the rotational and vibrational motions of molecules in such a way that Heurlinger and Kratzer managed to unite atomic and molecular spectroscopy under the same theoretical umbrella. The American physicist and expert on molecular spectra Edwin Crawford Kemble noted that the interpretation of band spectra by the Einstein– Bohr hypothesis that spectroscopic frequencies are the measures of energy differences and are not identical to the frequencies of the motion of the emitting system undermined the semiclassical theory of Bjerrum, despite its many successes. “ The abandonment of the initially successful Bjerrum theory has been brought about primarily by the necessity of unifying our interpretation of line and band spectra ” (Kemble et al. 1926, 107). From then on, spectroscopists calculated the frequencies of the emission/absorption in molecular spectra by using the quantization of energy plus the Einstein – Bohr frequency relation, now applied to all frequency regions, whether in the infrared, red, visible, or ultraviolet part of the electromagnetic spectrum. 12 Chapter 1 Walter Heitler and Fritz London: Outlining a Program for Quantum Chemistry The Heitler and London Paper of 1927 The stability of the hydrogen molecule within the newly developed quantum mechanics was fi rst successfully explained by Walter Heitler and Fritz London in their paper of 1927 (Gavroglu and Sim õ es 1994; Gavroglu 1995; Karachalios 2000). 4 In April of that year, Heitler and London, both recipients of a Rockefeller Fellowship, decided to go to the University of Z ü rich where Erwin Schr ö dinger was — they both felt more at ease with his more intuitive approach than with Werner Heisenberg ’ s matrix mechanics. Schr ö dinger agreed to their stay, but there was not much collaboration with him. Fritz London (1900 – 1954) was born in Breslau to a Jewish family. His father was professor of mathematics at the University of Breslau. In 1921, the year he graduated from the University of Munich, he wrote a thesis under the supervision of Alexander Pf ä nder (one of the best known phenomenologists) dealing with deductive systems. It was among the very fi rst attempts to investigate ideas about philosophy of science expressed by the founder of the phenomenological movement in philosophy, Edmund Husserl. It was a remarkable piece of work by a 21-year-old who developed an anti- positivist and antireductionist view. In fact, London ’ s fi rst published paper in a profes- sional journal was in philosophy.

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