By Holtje, Hans-Dieter

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**Example text**

However, the major disadvantage of the UHF technique is that unlike the true and also the ROHF wave function, a UHF Slater determinant is no longer an eigenfunction of the total spin operator, Sˆ 2 . The more the 〈Sˆ 2 〉 expectation value of a Slater determinant deviates from the correct value – i. , S(S+1) where S is the spin quantum number representing the total spin of the system – the more this unrestricted determinant is contaminated by functions corresponding to states of higher spin multiplicity and the less physically meaningful it obviously gets.

3-2) 10 r 2 r12 The importance of this equation is not so much how well it is able to really describe the energy of an atom (actually it is only of limited use in that respect because TTF is only a very coarse approximation to the true kinetic energy and exchange and correlation effects are completely neglected), but that the energy is given completely in terms of the electron H density ρ( r ) . Thus, we have the first example of a genuine density functional for the enH ergy! In other words, equation (3-2) is a prescription for how to map a density ρ( r ) onto an energy E without any additional information required.

Two spin orbitals χp and χq share the same spatial orbital φp connected with an α and a β spin function, respectively and have the same orbital energy. If we impose this double occupancy right from the start, we arrive at the restricted Hartree-Fock approximation, RHF for short. Situations where the RHF picture is inadequate are provided by any system containing an odd number of electrons (the methyl radical or even the hydrogen atom with its single electron fall into this category) or by systems with an even number of electrons, but where not all of these electrons occupy pair-wise one spatial orbital – i.