Study of Interionic Potentails and Polarization Models | Original Article

ABSTRACT:

Formula for the energy of an ionic crystal with ions having complete electron shells have been derived in the Heitler –London approximation by Hylleraas and others [102].Hylleraas formulated the physics of the problem and derived the energy expression for the LiH crystal. Landshoff [160 ] introduced a convenient calculating device of using approximately orthonormalised one electron wave function, obtained as linear combination of the one electron wave functions of free ions .Later Lowdin derived a mathematically exactly energy expression in the Heitler-London approximation by using a mathematically exact method of orthonormalisation. In his calculation, however he used a series expansion in the overlap integrals defined below and considered the so called S2 approximation better than that of Landshoff’s analysis. The calculation of the cohesive energy is based on the realization that the free ion one electron wave functions of Hartree and Hartree Fock do not form an orthonormal set of wave functions when the ions come as close as they are in the solid.The correct value of the cohesive energy can be obtained as the lowest eigen value of the complete Hamiltonian of the solid.The evaluation of this value demands a knowledge of the true wave functions for the solids as a whole. These wave functions can be expressed as a linear combination of the free ion wave functions by imposing the condition of orthonormality of the linear combinations we can obtain the true wave functions corresponding to the solid.