Intra-atomic exchange integral

The interatomic exchange integrals would be zero in any approximation where diatomic differential overlap is neglected, while the intra-atomic exchange is included in the approximation called Intermediate Neglect of Differential Overlap (INDO). The form of hamiltonian in Eq. (10.72) is more restricted than the one which applies for the NDDO approximation. These restrictions are imposed by Eq. (10.34) as soon as the dipole moment operator cannot be expressed in terms of the Na s only. 

Here, denotes the energy of the orbital a (a = s, p, d) at atomic site i and hiao are the corresponding occupation-number operators. The are the hopping integrals describing electronic transitions between atoms i and j. The third term in Eq. (1) approximates the electron-electron interactions [30, 31]. The prime in the sum indicates that the terms with a = P and a = a are to be excluded. is the effective on-site interaction between electrons with spin a and a in the orbitals a and P of atom i. In Eq. (1) only the Coulomb and exchange intra-atomic integrals Uafi = otP /r 2 otP) and J fi = otP lr 2 Pot) are... 

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