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But in most situations in crystals, nuclei are more heavier than electron cloud. So, we consider no motion of nuclei and thus internuclear distances will be the same. Thus, the hamiltonian will get reduced to:
Now further we are interested in slater's determinant (a multi fermionic representation) representation, which is considered to be the best way of representing wave functions and allows us to work in a computational mode even. Now comes the real challenge, when we have to construct wave function for multi- electron system, so it is not easy to put forward an ansatz because of closer analysis, which reveals that electron–electron interactions are to be present and the equations need iterative solutions as direct solutions are not possible though. So, thus another approach can be done by approximating the wave functions mainly MOs as a linear combination of some basic functions resembling to isolated atoms and then we come at LCAO approximation where :
Further we will look at what basis functions are!!
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