Heitler and London

London (1928) was first to apply this idea to a chemical reaction. London and Heitler developed a simple quantum mechanical treatment of hydrogen molecule, according to which, the allowed energies for H2 molecules are the sum and differences of two integrals as... 

London (1929) suggested an expression for the energy E of a triatomic system that was an extension of the earlier Heitler-London formula for that H2 molecule, given by (London and Heitler, 1927)... 

I suppose that this is what happens, and that neither my treatment nor London s and Heitler s is correct, but that the correct treatment of the secular problem would give London and Heitler s results for large distances, and mine for small, with intermediate ones in between, and with degeneracy at points, so that all the transitions indicated are possible adiabaticaUy (switchings being called adiabatic). Thus both H + H and H + H could go adiabaticaUy to H2. 

Born did not wish to publish anything about the problems of valence, as he had not followed closely the developments. But he thought that it was absolutely necessary that London and Heitler take a position and publish something that would be... 

Lewis s theory and Heitler and London s extension permitted the reasonably certain attribution of specific electronic formulas to a great many compounds. In other cases, however, it was possible to set up a number of alternative electronic formulas for a molecule or crystal, and often no sound argument could be advanced supporting any one of them against the others. For example, Lewis gave the perchlorate ion the... 

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... 

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... 

Figure 5 Areas of validity of Mulliken-Hund (M-H) and Heitler London (H-L) viewpoints, k is the ratio U/4/J, the ratio of one of the two-electron terms to a multiple of one of the one-electron terms.

Fig. 3.6 Binding energy curves for the hydrogen molecule (lower panel). HF and HL are the Hartree-Fock and Heitler-London predictions, whereas LDA and LSDA are those for local density and local spin density approximations respectively. The upper panel gives the local magnetic moment within the LSDA self-consistent calculations. (After Gunnarsson and Lundquist (1976).)...

In this way there is obtained an interaction-energy curve (the lower full curve in Figure 1-7) that shows a pronounced minimum, corresponding to the formation of a stable molecule. The energy of formation of the molecule from separated atoms as calculated by Heitler, London, and Sugiura is about 67 percent of the experimental value of 102.6 kcal/mole, and the calculated equilibrium distance between the nuclei is 0.05 A larger than the observed value 0.74 A. 

Explain the primary difference between the Heitler-London and Hund-Mulliken theories of covalent bonding. 

In our book we present methods of computation of Frenkel exciton states in molecular crystals, which are not based on the molecular two-level model and Heitler-London approximation (Ch. 3). The methods allow us, in particular, to obtain the Frenkel exciton spectra for arbitrary strength of the intermolecular interaction, assuming that the interaction does not violate the charge neutrality. However, in this section we use the simplest form of the Heitler-London method to construct the wavefunctions and to obtain some qualitative results on the properties of the spectra which occur by the aggregation of molecules into a crystal. 

In considering the saturation of valencies it will be convenient to jollpw the method of Heitler and London and consider the interaction of helium and hydrogen. The helium atom possesses two electrons in a completed is orbital. Let these electrons be designated i and 2, in agreement with the Pauli principle the spins of these electrons will be opposite. The electron of the hydrogen atom is represented by the number 3. The system being considered is thus represented by ... 

G. Corongiu, The HEHHE method a combination of Hartree-Eock and Heitler-London approximations. Invited paper, Sanibel Symposium 2005. 

In 1927, Burrau calculated the energy of Hj and Heitler and London treated the hydrogen molecule. In 1928, the Heitler-London or valence bond method was applied to many electron systems, and simultaneously Hund and Mulliken started the development of the molecular orbital theory. In 1931, Slater expressed the v/avefunctions of complex molecules in terms of Slater determinants made up of linear combinations of atomic orbitals. Thus, the Golden Age was born. 

Slater determinants are usually constructed from molecular spinorbitals. If, instead, we use atomic spinorbitals and the Ritz variational method (Slater determinants as the expansion functions), we would get the most general formulation of the valence bond (VB) method. The beginning of VB theory goes back to papers by Heisenbeig, the first application was made by Heitler and London, and later theory was generalized by Hurley, Lennard-Jones, and Pople. The essence of the VB method can be explained by an example. Let us take the hydrogen molecule with atomic spinorbitals of type liaO and Vst (abbreviated as aa and b ) centered at two nuclei. Let us construct from them several (non-normalized) Slater determinants, for instance ... 

None of these assumptions have been rigorously derived from theory, and, as has been emphasised by Coolidge and James, if one assumes for H3, the approximate eigenfunctions used by Heitler and London and Sugiura for H2, the assumptions can all be shown to fail badly. (Eyring 1938, p. 8)... 

In the effective Hamiltonian formalism just reviewed, the diabatic state energies are obtained as the diagonal matrix elements of the effective Hamiltonian, while the resonance interaction between product-like and reactant-like diabatic surfaces is obtained as the off-diagonal matrix elements. The adiabatic states are obtained as the eigenvalues. Thus, the effective Hamiltonian corresponds to the projection of the full Cl Hamiltonian onto the subspace of the (product-like and reactant-like) Heitler-London and no-bond configurations. We now wish to comment briefly on the physical interpretation of the effective Hamiltonian computed via Eq. (17). 

Heitler, W. (1954). The Quantum Theory of Radiation, 3rd ed. Oxford Univ. Press (Clarendon), London and New York. 

London F, Heitler H. 1927. Interaction between neutral atoms and homopolar binding according to quantum mechanics . Z. Phys. 44 455-472. 

Terenziani et al have employed a model Hamiltonian including Heitler-London and non-Heitler-London terms to interpret experimental results on the effects of the environment on the second-order NLO response. In particular, they analyzed i) the self-orientation of the chromophores in... 

---