Heitler-London simulation

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. 

A set of ionization radii with p = 20 was found to correspond fairly well with the characteristic atomic radii [7] that generate chemical bond dissociation energies in either point-charge or Heitler-London simulation. The value of these... 

Heitler-London simulation of general covalence depends on a set of characteristic atomic radii, assumed to describe a single electron in the valence state. Such radii were obtained empirically [17], in the first instance, by point-charge simulation of covalent interaction [1]. A more satisfactory derivation of atomic radii was discovered in the simulated compression of atoms in Hartree-Fock calculations, resulting in ionization at a characteristic compression, closely related to the empirical radii [18]. 

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. 

It is not the purpose of this chapter to produce and present a new force field. We rather want to provide a theoretical basis for MM and therefore also to be able to efficiently produce generic force-field parameters. As it stands, one parameter (ionization radius) is needed to initiate the derivation of all other parameters to model all bond orders of any covalent interaction. It is therefore reassuring to note that the uniform valence density within a characteristic atomic sphere has the same symmetry as the Is hydrogen electron. The first-order covalent interaction between any pair of atoms can therefore be modeled directly by the simple Heitler-London method for hydrogen to predict d, D and kr [44]. The results are in agreement with those of the simpler number-theory simulation [38], which is therefore preferred for general use. 

Interatomic distance is calculated by mathematical modelling of the electron exchange that constitutes a covalent bond. Such a calculation was first performed by Heitler and London using Is atomic wave functions to simulate the bonding in H2. To model the more general case of homonuclear diatomic molecules the interacting atoms in their valence states are described by monopositive atomic cores and two valence electrons with constant wave functions (3.36). 

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