One-Electron Properties Electric-Dipole Moments

Generally speaking, one-electron expectation values obtained by the SCF method are expected to be in good agreement with experiment. 

in its primitive form, the Brillouin theorem applies to closed-shell systems only. Its extension to open-shell systems is not straightforward, because the extension of the SCF method itself can be done in different ways, leading to various restricted, unrestricted or extended Hartree-Fock theories (see e.g. (25)). 

for one-electron properties given by a perturbation formula, there is a relatively large freedom in constructing the appropriate excited states, since they are not necessarily given by a variational calculation, 

if the magnitude of a physical property in a certain molecule is small with respect to its usual value in standard compounds, the SCF method may give spurious results, even for the sign (if any) of the observable, because the calculation becomes too sensitive to the approximations made, e.g. those related to the nature and the size of the basis set etc., and the second-order correlation correction may be larger than the SCF zero-order value. 

In the case of typical molecules, the coefficient of the first weakly occupied natural orbital is about 0.1, so that the corresponding occupation number, with which it contributes to the electron density is (0.1)2 = 

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