Hydrogen molecule, Heitler-London

In contrast, if we look at the simple VB function for the hydrogen molecule (Heitler-London plus the two equivalent polar structures), these three functions... 

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 ... 

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 ... 

In the late 1920s, it was shown that the chemical bond existing between two identical hydrogen atoms in H2 can be described mathematically by taking a linear combination of the Is orbitals [Pg.176]

Even though the problem of the hydrogen molecule H2 is mathematically more difficult than, it was the first molecular orbital calculation to appear in the literature (Heitler and London, 1927). In contrast to Hj, we no longer have an exact result to refer to, nor shall we have an exact energy for any problem to be encountered from this point on. We do, however, have many reliable results from experimental thermochemistry and spectroscopy. 

In the case of the hydrogen molecule-ion H2" ", we defined certain integrals Saa, Taa, Tab, Labra- The electronic part of the energy appropriate to the Heitler-London (singlet) ground-state wavefunction, after doing the integrations... 

The original VB wave function was introduced in the treatment of the hydrogen molecule by Heitler and London in 1932. This treatment considered only the one Is orbital on each hydrogen atom and assumed that the best wave function for a system of two electrons on two different atoms is a product of the two atomic Is orbitals i/ — XisXis- This wave function needs to be modified, however, to accommodate the antisymmetry of the wave function and to take into account the spin of the two electrons. 

The most satisfactory treatment which has been given the structure of the hydrogen molecule is that of Heitler and London... 

The Interaction of Simple Atoms.—The discussion of the wave equation for the hydrogen molecule by Heitler and London,2 Sugiura,3 and Wang4 showed that two normal hydrogen atoms can interact in either of two ways, one of which gives rise to repulsion with no molecule formation, the other... 

Quantum mechanics was the dominant theory in chemistry even before the advent of electronic computers. The conventional date for the beginning of this period may be fixed at 1927 with the publications of the Heitler and London paper on hydrogen molecule [3]. The growth of theoretical chemistry (or better, theoretical quantum chemistry) between 1930 and 1960 (thirty years, again, as for the last period) has followed a research programme different from that accepted in the most recent period. 

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... 

Heitler and London s 1927 paper on the hydrogen molecule gained attention among both physicists and chemists. 

Two sets of papers in 1927 now provided successful treatments of the hydrogen molecule. One was written by Heitler and London, in residence at Schrodinger s institute in Zurich. The other was by Hund, Bom s assistant in... 

Coulson described the first ten years of quantum chemists work on the electron valence bond (roughly 19281938) as work spent "escaping from the thought-forms of the physicist [my emphasis], so that the chemical notions of directional bonding and localization could be developed."45 Heisenberg earlier claimed that the Heitler-London treatment of the hydrogen molecule was not a characteristically physical approach, in contrast to Hund s more "general"... 

Heitler-London covalence theory phys chem A calculation of the binding energy and the distance between the atoms of a diatomic hydrogen molecule, which assumes... 

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. 

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).)...

The second method of discussing the electronic structure of molecules, usually called the valence-bond method, involves the use of a wave function of such a nature that the two electrons of the electron-pair bond between, two atoms tend to remain on the two different atoms. The prototype of this method is the Heitler-London treatment of the hydrogen a olecule, which we shall now discuss. 

The Heitler-London Treatment of the Hydrogen Molecule.—The hydrogen molecule consists of two nuclei, which may be designated A... 

The formal results of the quantum-mechanical treatment of valence, developed by Heitler, London, Born, Weyl, Slater, and other investigators, can be given the following simple statement an atom can form an electron-pair bond for each stabh orbital, the bond being of the type described for the hydrogen molecule and owing its stability to the same resonance phenomenon. In other words, for the formation of an eleo-tron-pair bond two electrons with opposed spins and a stable orbital of oach of the two bonded atoms are needed. 

When the ionization spheres of two neighbouring atoms interpenetrate, their valence electrons become delocalized over a common volume, from where they interact equally with both atomic cores. The covalent interaction in the hydrogen molecule was modelled on the same assumption in the pioneering Heitler-London simulation, with the use of free-atom wave functions. By the use of valence-state functions this H-L procedure can be extended to model the covalent bond between any pair of atoms. The calculated values of interatomic distance and dissociation energy agree with experimentally measured values. 

The origin of the VB model the Heitler-London treatment of the hydrogen molecule... 

According to Heitler and London [1], the electronic states of the hydrogen molecule can be formed by distributing the two electrons between the atomic orbitals (AOs), Ls and 1 sb (abbreviated by a and b), on the two hydrogen atoms. The singlet wave function characterized by quantum numbers S=0 and M=0 (M denotes the z-component of total spin S) can be described using the form... 

It was Pauling and his collaborators who generalized the Heitler-London treatment of the hydrogen molecule to general polyelectronic systems and gave the rules for evaluating the Hamiltonian matrix elements [3,4], which could also... 

The calculation of Heitler and London (1927) of the energy of the hydrogen molecule must indeed be considered, together with the conception of the spatial model of the carbon atom by Van t Hoff and Le Bel, as the most important contribution to theoretical chemistry, since the advent of Dalton s atomic hypothesis. We shall, however, let the treatment of the hydrogen molecule itself be preceded by the discussion of the hydrogen molecule ion H2+, since this problem with only one electron is still simpler than that of the H2 molecule itself. 

To introduce the concepts, we must of course start from the classic 1927 paper of Heitler and London [1], referred to by Pauling himself [2] as the greatest single contribution to the clarification of the chemist s conception of valence. .. since G.N.Lewis s suggestion that the chemical bond between two atoms consists of a pair of electrons held jointly by the two . The electron-pair bond in the hydrogen molecule was described using a wavefunction of the form... 

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