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Why is spin-contamination, introduced by e.g. Unrestricted Hartree Fock, undesirable, and to which problems further on can it lead?

The only problem I currently see myself is that spin-contamined orbitals cannot be used in spectroscopy, because the selection rules don't hold.

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    $\begingroup$ Not an expert on this, but my understanding is that if you have spin contamination, you know your wavefunction must be wrong in some way as the true wavefunction is an eigenfunction of the total spin operator. $\endgroup$ – Tyberius Aug 1 '18 at 3:30
  • $\begingroup$ But then 'restricted' methods such as RHF usually give you only an approximate wavefunction too, so why is the fact that it is approximate worse with UHF? $\endgroup$ – GingerBadger Aug 1 '18 at 9:59
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    $\begingroup$ In a nutshell, if you have spin contamination, your energy-optimised solution is a mixture of two or more distinct spin states, which will probably have quite different properties for anything related to spin, so any derived quantities that you compute from such a wavefunction are suspect and may have little or nothing to do with the actual wavefunction and derived properties for the ground state of that system. $\endgroup$ – user41033 Aug 1 '18 at 10:23
  • $\begingroup$ Thanks. Could you please give me examples of any properties related to spin and how they are useful in chemistry? $\endgroup$ – GingerBadger Aug 1 '18 at 10:24
  • $\begingroup$ Just to clarify, I’m trying to get a sense of the scope of chemistry problems for which I can use UHF. $\endgroup$ – GingerBadger Aug 1 '18 at 14:18

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