Heitler-London Valence Bond theory

Figure 3.4. (a) The overlap of two one-electron atomic wave functions, each centered on a different atom, constitutes the Heitler-London (valence-bond) theory, (b) A one-electron molecular wave function, or molecular orbital, in the molecular orbital theory of Hund and Mulliken. 

One widely used valence bond theory is the generalised valence bond (GVB) method of Goddard and co-workers [Bobrowicz and Goddard 1977]. In the simple Heitler-London treatment of the hydrogen molecule the two orbitals are the non-orthogonal atomic orbitals on the two hydrogen atoms. In the GVB theory the analogous wavefunction is written ... 

Historically, molecular orbital theory was preceded by an alternative and successful description of the bonding in H2. In 1927, W. Heitler and F. London proposed the valence bond theory, in which each electron resides in an atomic orbital. In other words, in this model, the identity of the atomic orbital is preserved. There are two ways in which the two electrons in H2 can be accommodated in the pair of Is atomic orbitals ... 

In 1927, Heitler and London carried out a calculation for the hydrogen molecule using what has become known as valence bond theory.12 Each electron of the pair could be assigned to nuclei corresponding to wavefunctions of the type... 

The first electronic function to be defined in direct association with a formal chemical bond was, as expected, for the H2 molecule. It marked the beginning of the so called valence-bond theory, in 1927, and was suggested by the Austrian physicist Walter H. Heitler (1904—1981) and by the German physicist Fritz W. London (1900-1964). 

In 1927, Heitler and London used valence bond theory to treat the H2 molecule but to treat larger molecules, further simplifications were needed. In 1931, Erich Hiickel introduced an extremely simple approximation which could be used to treat the 7i-electrons in flat organic molecules such as benzene, napthaline, and so on. This approximation yielded matrices to be diagonalized, and it is a measure of the state of computers at that time to remember that during World War II, Alberte Pullman sat in a basement room in Paris diagonalizing Hiickel matrices with a mechanical desk calculator, while her husband-to-be Bernard drove a tank with the Free French Forces in North Africa. Alberte s hand-work led to the publication of the Pullmans early book Quantum Biochemistry. ... 

The application of Walter Heitler and Fritz London s valence bond theory was the first description of the binding forces in the H2 molecule, the simplest neutral molecule. Linus Pauling and John Slater later extended the principles to larger molecules.The key element in their proposal was the synthesis of a bonding wavefunction resulting from a combination of atomic orbitals that link the two atoms in a bond. It was hugely important that this localized approach concurred with the Lewis dot model. For the simplest neutral molecule, H2, the Hamiltonian operator may be written... 

Valence bond theory is usually introduced using the famous Heitler-London model of the hydrogen molecule [Heitler and London 1927] This model considers two non-interacting hydrogen atoms (a and b) in their ground states that are separated by a long distance. The wavefunction for this system is ... 

The first quantitative theory of chemical bonding was developed for the hydrogen molecule by Heitler and London in 1927, and was based on the Lewis theory of valence in which two atoms shared electrons in such a way that each achieved a noble gas structure. The theory was later extended to other, more complex molecules, and became known as valence bond theory. In this approach, the overlap of atomic orbitals on neighbouring atoms is considered to lead to the formation of localized bonds, each of which can accommodate two electrons with paired spins. The theory has been responsible for introducing such important concepts as hybridization and resonance into the theory of the chemical bond, but applications of the theory have been limited by difficulties in generating computer programs that can deal efficiently with anything other than the simplest of molecules. 

This paper attracted Pauling s attention, who recognized that the Heitler-London procedure could not only be extended to larger molecules but also serve as a bridge between Lewis classical idea of chemical bond and the new quantum theory. In a series of papers ", where he introduced the concepts of hybridization, resonance, electronegativity, etc., and also in a famous book that influenced many generations of chemists, Pauling developed his ideas which formed the basis of the classical Valence-Bond theory. 

The valence bond theory is a quantum mechanical model of the chemical bond that was proposed by Heitler and London in 1927. It uses Lewis s concept of a covalent bond as a shared pair of electrons and the idea that a molecule is described by a series of resonance structures. 

The main features of the chemical bonding formed by electron pairs were captured in the early days of quantum mechanics by Heitler and London. Their model, which came to be known, as the valence bond (VB) model in its later versions, will serve as our basic tool for developing potential surfaces for molecules undergoing chemical reactions. Here we will review the basic concepts of VB theory and give examples of potential surfaces for bond-breaking processes. 

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). 

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