Crystal extended charge contribution

D. Garda and M. Faucher, Crystal-field parameters in rare-earth compounds Extended charge contribution. Physical Review, 30,1703-1707 (1984). 

I, j indicate the cells (a prime means that there is no contribution from the charge interaction with itself). Since the summations over I and j extend over the whole crystal,... 

In terms of BOLS perturbation to the Hamiltonian of an extended solid, one is able to reconcile the change of Eq, pl, pa, bandwidth, core-level shift, and the charge entrapment and polarization induced by crystal size reduction. Introducing the effect of CN imperfection in the surface skin to the convention of an extended solid evolves the entire band stmcture of a nanometric semiconductor. This approach allows one to discriminates the contribution from crystal binding from the effect of e-p coupling in determining the Eq expansion and PL blueshift. 

As already mentioned, the d and d, -y orbitals of the Ti atoms are no longer equivalent in the square crystal field of the four nonmetal atom neighbors. The Tit -3rf 2 orbitals extend toward the vacancy and cannot form pd bonds with the X-2p orbitals. Therefore, the number of pda bonds is reduced compared with the stoichiometric compounds. More information can be gained from Tables 4 and 5, which list the splitting of the Ti(3d/)-like charge into its components. The Ti -3fi 22 and T - idxz, idyz components are greatly reduced in the p bands of the substoichiometric compounds but furnish the biggest contributions to the DOS in the vacancy band. From the reduction of the number of Ti -3 /22 states in the p bands of the substoichiometric compounds it can be concluded that the number of pda bonds is reduced. In a similar way, the... 

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