Heitler-London interaction energy

Komasa J and Thakkar A J 1995 Accurate Heitler-London interaction energy for He2 J. Mol. Struct. (Theochem) 343 43... 

A. The Heitler-London Interaction Energy May Contain Basis-set Superposition Errors... 

Comparing the Heitler-London interaction energies corresponding to (25) and (26) one readily finds ... 

The zeroth-order wavefunction yields the first-order perturbation to the energy when combined with the operator V, which describes the interactions between electrons and nuclei on the two different molecules. This first-order correction, known as the Heitler-London interaction energy,may be thought of as consisting of two terms. The first is the classical Coulombic interaction between the charge clouds of the (undistorted) subunits, commonly known as the electrostatic energy, and computed as... 

A Link to the Variational Method—The Heitler-London Interaction Energy... 

Therefore, the Heitler-London interaction energy is equal to the first-oider SAPT energy... 

A LINK TO THE VARIATIONAL METHOD - THE HEITLER-LONDON INTERACTION ENERGY... 

Since the wave function is a good approximation of the exact ground state wave function at high values of R, we may calculate what is called the Heitler-London interaction energy (R ) as the mean value of the total (electronic) Hamiltonian minus the energies of the isolated subsystems... 

Let us assume that if/A,o and b,o, respectively, represent Hartree-Fock solutions for the subsystems/4 and B, Then the corresponding Heitler-London interaction energy equal to may be written as... 

A concise summary of the RVS analysis is schanatically represented in Figure 15.4. In the RVS analysis, the energies of the monomers are first calculated from the respective isolated wavefunction, and the dimer wavefunction is then generated by considering only the occupied orbitals of the monomers. Such an approach hence does not allow any variational flexibility to the dimer wavefunction and results in a combined electrostatic and exchange-repulsion term (ESX), which represents the Heitler-London interaction. Hence,... 

In this way there is obtained an interaction-energy curve (the lower full curve in Figure 1-7) that shows a pronounced minimum, corresponding to the formation of a stable molecule. The energy of formation of the molecule from separated atoms as calculated by Heitler, London, and Sugiura is about 67 percent of the experimental value of 102.6 kcal/mole, and the calculated equilibrium distance between the nuclei is 0.05 A larger than the observed value 0.74 A. 

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

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. 

The valence electron of a promoted atom readily interacts with other activated species in its vicinity to form chemical bonds. The mechanism is the same for all atoms, since the valence state always consists of a monopositive core, loosely associated with a valence electron, free to form new liaisons. Should the resulting bond be of the electron-pair covalent type, its properties, such as bond length and dissociation energy can be calculated directly by standard Heitler-London procedures, using valence-state wave functions (section 5.3.4). 

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. 

According to SAPT formulation of the first-order interaction energy, the Heitler-London term consists of electrostatic and exchange contributions (the former obtained from the perturbation theory formula) ... 

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