Heitler-London, Pauling-Slater

The classic HLSP-PP-VB (Heitler-London-Slater-Pauling perfect-pairing valence-bond) formalism and its chemical applications are described by L. Pauling, The Nature of the Chemical Bond. 3rd edn. (Ithaca, NY, Cornell University Press, 1960 G. W. Wheland, The Theory of Resonance (New York, John Wiley, 1944) and H. Eyring, J. Walter, and G. E. Kimball, Quantum Chemistry (New York, John Wiley, 1944). 

Slater s bond eigenfunctions constitute one choice (out of an infinite number) of a particular sort of basis function to use in the evaluation of the Hamiltonian and overlap matrix elements. They have come to be called the Heitler-London-Slater-Pauling (HLSP) functions. Physically, they treat each chemical bond as a singlet-coupled pair of electrons. This is the natural extension of the original Heitler-London approach. In addition to Slater, Pauling[12] and Eyring and Kimbal[13] have contributed to the method. Our following description does not follow exactly the discussions of the early workers, but the final results are the same. 

Although the aufbau approach of MO theory is adequate in all that follows, it may be useful for the sake of completeness to mention the rather more complicated method developed by Heitler, London, Slater, Pauling and others, and to stress that the two theories do not conflict. Both lead to approximations to the same charge density the difference is superficial and the same Fcynman-Hellman interpretation applies in each case. To appreciate this, it is sufficient to consider the molecule Hg. From the MO standpoint, the full two-electron wave function would be the product... 

Slater had been familiar with both approaches, from the early days of wave mechanics, partly as a result of his friendship with Mulliken. Although his name was associated with the Heitler-London-[Slater]-Pauling method after 1931, he was the first to point to the interrelationship of the two methods. In a short note. Slater came back to this topic and summarized his previous conclusions. He claimed once more that both methods were "complementary" rather than "antagonistic" and that the choice between the two should be made on the "basis of convenience rather than correctness" (Slater 1932, 255). The methods looked very different at first but when properly refined should come into closer agreement. Slater outlined the steps necessary for their refinement in the case of the valence bond method, one should allow for possible ways of... 

Just before returning to Europe in 1929, Slater generalized into an N-electron system the wave function used by Pauling in the treatment of helium in the 1928 Chemical Reviews essay. The title of Slater s paper, "The Self-Consistent Field and the Structure of Atoms," shows his debt to Hartree, although Slater s method turned out to be a great deal more practical than Hartree s, as well as consistent with the methods of Heitler, London, and Pauling.70... 

Historians would later credit Heitler, London, Slater, and Pauling with developing this approach to the chemical bond (in later years it would be called, in their honor, the HLSP theory). But most chemists would remember only Pauling, not only because he applied it to more molecules than the others, but because he alone among them was a chemist, able to communicate his results in a way that chemists understood. 

The problems for quantum chemists in the mid-forties were how to improve the methods of describing the electronic structure of molecules, valence theory, properties of the low excited states of small molecules, particularly aromatic hydrocarbons, and the theory of reactions. It seemed that the physics needed was by then all to hand. Quantum mechanics had been applied by Heitler, London, Slater and Pauling, and by Hund, Mulliken and Hiickei and others to the electronic structure of molecules, and there was a good basis in statistical mechanics. Although quantum electrodynamics had not yet been developed in a form convenient for treating the interaction of radiation with slow moving electrons in molecules, there were semi-classical methods that were adequate in many cases. 

Wheland, G. W. /. Chem. Phys. 1934,2,474 argued that the valence bond method as described by Heitler, London, Slater, and Pauling gives results closer to experimentally observed values than does the molecular orbital method attributed to Hund, Mulliken, and Hiickel. 

The Heitier-London-Slater-Pauling (HLSP) method. This method, which was developed originally by Slater as a generalization of Heitler and London s treatment of the hydrogen molecule, was... 

But it was not really until 1931, when Slater and Pauling independently developed methods to explain directed chemical valence by orbital orientation that it can truly be said that a chemical quantum mechanics, rather than an application of quantum mechanics to chemistry, had been created. In a study of Slater, S. S. Schweber notes the distinction between the Heitler-London-Pauling-Slater theory and the Heitler-London theory. Heitler and London successfully explained the electron-valence pair on the basis of the Goudsmit-Uhlenbeck theory of spin. Slater and Pauling explained the carbon tetrahedron. This second explanation distinguishes quantum chemistry from quantum physics.2... 

Slater developed an approach (the "determinantal method") that offers a way of choosing among linear combinations (essentially sums and differences) of the polar and nonpolar terms in the Hund-Mulliken equations to bring their method into better harmony with the nonpolar emphasis characteristic of the Heitler-London-Pauling approach in which polar terms do not figure in the wave equation. 72... 

E. U. Condon, W. Heitler, F. London, Linus Pauling, and J. C. Slater VB theory and orbital hybridization... 

For atoms having only 5-electrons outside closed shells the Slater-Pauling theory in its results does not go essentially beyond the work of Heitler and London. In the case of p-elec-trons, however, one obtains in a rather simple way an interpretation of the directed nature of the valence bonds. As an illustration take an atom A with two equivalent 23-electrons outside... 

Lewis concept . He reserved his major criticisms for the Heitler-London, Pauling-Slater (HLPS) approach ... 

PROBLEMS of directed valence, like most problems of moiecular structure, can be attacked by either of two methods the method of locaiized electron pairs (Heitler-London) or the method of molecular orbitals (Hund-Mul-liken). While it is now realized that these methods are but different starting approximations to the same final solution, each has its advantages in obtaining qualitative results. Theories of directed valence based on the methods of focalized pairs have been developed by Slater and Pauling and extended by Hult-gren. The method of molecular orbitals has been developed principally by Hund and Mulliken. These methods have been compared extensively by Van Vleck and Sherman. ... 

C). Relative to Lewis s, the Heitler-London-Pauling-Slater (H-L-P-S) theory was more limited in the sense of assuming that in a bond, each electron comes from each atom. To stress this difference, Mulliken suggested calling the H-L-P-S theories electron-pairing theories in contrast to Lewis s theory, which he called electron-pair theory. 

Van Vleck and Sherman did not name whom they considered to be the optimists or the pessimists, and in fact they claimed to have adopted a middle ground between the two opposite points of view, ffowever, one cannot but wonder that there are striking similarities between the praxis of some like Mulliken and Pauling and the optimistic persona and the praxis of some like Heitler, London, or Hund and the pessimistic persona depicted in the review. In between both attitudes, Van Vleck and Sherman, as well as Slater, opted not to enroll in partisan stances, playing the necessary but difficult role of the devil s advocate in a time of stark disciplinary contrasts. Van Vleck s different style was even noticed by the angered Heitler in his correspondence with London. 

The publication of the papers by the Americans and especially those by Slater, Pauling, Van Vleck, and Mulliken prompted a rather desperate exchange of letters between Heitler and London starting in the end of 1935. This correspondence is quite revealing. It shows the attitude of each about the possible development of the approach laid down in their common paper, the tension between them, as well as the search for a means to consolidate their theory at a time when the Americans appeared to be taking over the field of quantum chemistry. The correspondence reflects the different style of their respective environments. Faithful to the Gottingen spirit, Heitler was... 

Pauling (and Slater) envisioned the extension of the Heitler-London Ansatz to each localized gAB electron-pair bond of a Lewis structural representation by replacing hydro-genic orbitals with directed hybrids hA, hs. 

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