Heitler-London method

Herring, C. Critique of the Heitler-London method of calculating spin couplings at large distances,... 

Like Hund, Mulliken developed the basic Schrodinger equation in the direction of establishing the electron charge density resulting from a combination of the attractions of two or more nuclei and the averaged repulsions of other electrons in the system. This is a method that favors some particular region of space and disfavors others. In contrast to the Heitler-London method, it over-emphasizes, rather than underemphasizes, the ionic character of a molecule. For example, for the H2 molecule, Hund s wave function equation assumes that it is just as probable to have two electrons around the same nucleus as to have one electron around each nucleus. For a molecule made up of identical nuclei, this treatment is a considerable exaggeration of the ionic character of the molecule. 

Many of the transition states examined according to the Heitler-London method, should be of continuing interest for years to come (Glasstone et al., 1941). The stereochemical legacy of the period may be summarized explicitly as follows ... 

Figure 5.8 Potential-energy curve of first-order C-C interaction, in dimensionless units, calculated by the Heitler-London method.

Figure 5.9 Potential-energy curves of integral-order dicarbon bonds, calculated by the Heitler-London method for screened nuclei, superimposed on the point-charge covalency curve.

Bond length The Heitler-London method allows the calculation of all first-order diatomic interactions using valence-state wave functions as defined in terms of characteristic ionization radii. 

The Heitler-London method, although approximate, has the advantage that a physical picture of the nature of the chemical bond may easily be obtained. The bond is formed by two electrons, one from each atom with opposite spin and owing to the transfer of the electrons, two states arise, which on superposition yield a transitional cloud, which serves to bond the atoms together. Such a bond is termed the homopolar or covalent bond. This physical picture of the bond is clearly the basis of the electron pair bond of Lewis. 

The first two terms represent the two electrons as being one at nucleus a and the other at nucleus b the third term describes the ionic state where both electrons are at nucleus a, viz Ha and the fourth term represents the alternative and equally probable ionic state where both electrons are at nucleus by viz Ho+ H . Let us compare this expression, with that obtained for Hg by the Heitler-London method. This is... 

The Heitler-London method, which is obviously a suitable method of approximation when we assume strong repulsion of the electrons, was first applied to the crystal by Heisenberg in his theory of ferro-magnetism. 

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 order to calculate the transfer cross sections of the processes by the PSS method, it is necessary to obtain the interaction potential curves of the system of He + He. The curves are calculated by the usual Heitler-London method. Considering the fact that the cross section will mainly be determined by the interaction at distant nuclear separation, we adopt the single term atomic base wave function of He and He. ... 

Heitler-London method will more nearly approximate the truth for larger distances and smaller nuclear charge. The intermediate cases, which after all are the ones most frequently met in chemistry, can be approximated by including both types of terms with independent coefficients which are to be determined by one of the previously... 

The difference between this approach and the Heitler-London method is that here we are considering the molecule as a whole, rather than just the bond. We are constructing for the molecule the orbital... 

The simplest form of the VB model follows the Heitler London method for the structure of the H2 molecule an approximate wavefunction is written as a (antisymmetrised) product of electron-pair functions. Each electron-pair function is a product of a (symmetric) spatial function and a (emtisymmetric) singlet spin function. The spatial function is chosen to model the chemist s intuition about the structure of the electron pair usually a simple symmetrised product of (hybrid) atomic orbitals. The resulting total approximate wavefunction will not be a determinant but, since it is a function which is antisymmetric with respect to exchange of electrons coordinates, it must be capable of being expanded as a linear combination of determinants. If polar structures are added to the VB model the same general result must obtain any antisymmetric function may be expressed as a linear combination of determinants of the space/spin functions ... 

The reason why the Heitler-London method gives such a bad Hellmann-Feynman force-constant is thus that R is "attached to the nuclei so that 9 / R is not zero the same applies to the Weinbaum function 94), to the Wang function (95), and to the Coulson function 96) for Hg. To yield better force results, the variable parameters ) must be "detached from the nuclei and their values determined at each internuclear configuration. A wave function in which the parameters are determined by the variational procedure is called a floating function by Hurley 93, 97, 30, 31, 32) (this is eqtuvalent to Hall s stable wave functions 88)). This procedure can be extended to the scale factors, as discussed by McLean 81) and Lowdin 83). The vibrational frequency of H2 determined by Ross and Phillipson using the differentiation of the virial theorem (which assumed that all the variable parameters are variationally... 

Corongiu, G. (2007). The Hartree-Fock-Heitler-London Method, III Correlated diatomic hydrides. J. Phys. Chem. A 111, 5333-5342. 

Slater, J. C. 1965. Molecular orbital and Heitler-London methods. Journal of Chemical Physics 43 S11-S17. 

The two states have been discussed by Kemble and Zeener (Loc. Cit) with the help of the Heitler-London method, but the result is not satisfactory from a quantitative point of view. 

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