Heitler-London calculation

The two methods of calculation are complementary in the sense that the point-charge method does not distinguish between bonds of different order, but fails to predict interatomic distance. The Heitler-London calculation, without further modification, only applies to homonuclear single bonds. 

The observation that point-charge simulation reproduces the exact same result as a Heitler-London calculation, but only for first-order bonds, confirms the previous conclusion that covalent interactions are mediated by the sharing of a maximum two electrons per bond, allowed by the exclusion principle. In view of this stipulation the conventional assumption, that several pairs of electrons contribute to the formation of high-order bonds, should therefore... 

In point-charge simulation this electronic rearrangement is of no immediate consequence except for the assumption of a reduced interatomic distance, which is the parameter needed to calculate increased dissociation energies. However, in Heitler-London calculation it is necessary to compensate for the modified valence density, as was done for heteronuclear interactions. The closer approach between the nuclei, and the consequent increase in calculated dissociation energy, is assumed to result from screening of the nuclear repulsion by the excess valence density. Computationally this assumption is convenient and effective. 

Almost all of the ideas were laid down before WWII, but difficulties in carrying out calculations precluded firm conclusions in any but the simplest cases. The H2 molecule does allow some fairly easy calculations, and, in the next section, we give a detailed description of the Heitler-London calculations on that molecule. This is followed by descriptions of early... 

The original Heitler-London calculation, being for two electrons, did not require any complicated spin and antisymmetrization considerations. It merely used the familiar rules that the spatial part of two-electron wave functions are symmetric in their coordinates for singlet states and antisymmetric for triplet states. Within a short time, however, Slater[10] had invented his determinantal method, and two approaches arose to deal with the twin problems of antisymmetrization and spin state generation. When one is constructing trial wave functions for variational calculations the question arises as to which of the two requirements is to be applied first, antisymmetrization or spin eigenfunction. 

Fairly soon after the Heitler-London calculation, Slater, using his determi-nantal functions, gave a generalization to the n-electron VB problem[10]. This was a popular approach and several studies followed exploiting it. It was soon called the method of bond eigenfunctions. A little later Rumer[ll] showed how the use of these could be made more efficient by eliminating linear dependencies before matrix elements were calculated. 

We may demonstrate this difficulty by giving a result due to Slater. [39] Applying a symmetric orthonormalization to the basis normally used in the Heitler-London calculation we have a His function on each of two centers,... 

A continuation of London s theory of adiabatic chemical reactions, especially for atomic reactions. The total binding energy of single atom pairs is obtained as a function of atomic distance from optical data euid using the Heitler-London calculations corrected for the Coulomb energy. Linear reactions of the systems... 

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