The Independent n -Electron Assumption

The implicit inclusion of interelectronic interactions is possible because we never actually write down a detailed expression for the n one-electron hamiltonian operator Hjt (i). (We cannot write it down because it results from a 7r-a separability assumption and an independent rr-electron assumption, and both assumptions are incorrect.) H (i) is considered to be an effective one-electron operator—an operator that somehow includes the important physical interactions of the problem so that it can lead to a reasonably correct energy value Ei. A key point is that the HMO method ultimately evaluates Ei via parameters that are evaluated by appeal to experiment. Hence, it is a semiem-pirical method. Since the experimental numbers must include effects resulting from 

It was pointed out in Chapter 5 that, when the independent electron approximation [Eqs. (8-8)-(8-ll)] is taken, all states belonging to the same configuration become degenerate. In other words, considerations of space-spin symmetry do not affect the energy in that approximation. Therefore, the HMO method can make no explicit use of spin orbitals or Slater determinants, and so il/jt is normally taken to be a single product function as in Eq. (8-8). The Pauli principle is provided for by assigning no more than two electrons to a single MO. 

EXAMPLE 8-1 If O2 were treated by the HMO method, what would be the form of the wavefunction and energy for the ground state  

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