Heitler-London theory

In 1927, Walter Heitler and Fritz London successfully applied the quantum theory to the problem of the covalent bond between hydrogen atoms using what is known as the variational method. This was one of the great achievements of the quantum theory in that it provided a first principles explanation of this bond which hitherto had been developed phenomenologically by the chemists. Essentially they used a linear combination of the unperturbed wavefimctions for the hydrogen atom as a trial fimction to compute the energy from 

H is the Hamiltonian, which is an operator that includes the potential energy of attraction between the unlike charges as well as the repulsive energy between particles with like charges. 

Putting these wavefunctions into Equation 3.9, the energy becomes 

Now we find the coefficients that minimize the energy in Equation 3.10 by taking the partial derivatives of E with respect to Q and C2 and setting them to zero. 

It may be seen that the only nontrivial solution for Ci and C2 exists when the determinant 

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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... 

The localized-electron model or the ligand-field approach is essentially the same as the Heitler-London theory for the hydrogen molecule. The model assumes that a crystal is composed of an assembly of independent ions fixed at their lattice sites and that overlap of atomic orbitals is small. When interatomic interactions are weak, intraatomic exchange (Hund s rule splitting) and electron-phonon interactions favour the localized behaviour of electrons. This increases the relaxation time of a charge carrier from about 10 s in an ordinary metal to 10 s, which is the order of time required for a lattice vibration in a polar crystal. 

The theory of Born and Mayer has been extended by the work of Landshoff using the methods of quantum mechanics. Taking sodium chloride as an example, Landshoff accepts the assumption that the lattice consists of Na+ and Cl ions and calculates the ionic interaction energy on the basis of the Heitler-London theory using the known distributions of electrons in the Na+ and Cl " ions. In addition to the correction terms of Bom and Mayer, additional interactions related to the superposition of the electron clouds, the attraction between electrons and nuclei and the mutual repulsion of electrons are incorporated. The values obtained by this more exact method, however, differ from the values given in Table CXLVII by only a few kcals, the value for sodium chloride being 183 kcals. 

The fundamental idea of the Heitler-London theory of valency bindiug is as follows. As a model of the hydrogen molecule we imagine two nuclei a and h on the c-axis at a distance It apart, and two electrons 1 and 2 revolving about the nuclei. To the state of two widely-separated neutral atoms there corresponds a large value of It and a motion of the electrons such that each one revolves round one of the two nuclei. Let the two atoms be in the ground state and have the... 

C-atom as in the Heitler-London theory (see section 48), and, moreover, the tetrahedral arrangement of the bonds is explained. 

The third part deals with the theory of the chemical bond. It contains (of course) the seminal paper by Heitler zmd London, as well as a more general paper by London on the chemical bond and the quantum theory of homopolar valence numbers. The Heitler-London theory gave rise to the valence bond (VB) approach in quantum chemistry. There is also a paper with some exact calculations on H2 by Hylleraas, which present a computationally accurate view of the hydrogen bond. 

Heitler-London theory of H2 one has equations for the binding (attractive) and antibinding (repulsive) potentials... 

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