computational chemistry - Why do post-Hartree-Fock methods fail to predict the direction of the dipole moment of carbon monoxide?

In carbon monoxide the dipole moment (negative to positive) points towards the oxygen, as I explained it in How can the dipole moment of carbon monoxide be rationalised by molecular orbital theory?

A calculation using density functional approximation, the level of theory is BP86/def2-QZVPP, yields the correct direction: \begin{align} \ce{{}^{\ominus}\!:C#O:^{\oplus}} && \text{Dipole:}~|\mathbf{q}|=0.19~\mathrm{D} && \text{Direction:}~\longrightarrow \end{align}

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 Center     Atomic      Atomic             Coordinates (Angstroms)
 Number     Number       Type             X           Y           Z
 ---------------------------------------------------------------------
      1          6           0        0.000000    0.000000   -0.648987

      2          8           0        0.000000    0.000000    0.486740
 ---------------------------------------------------------------------
[...]
 Dipole moment (field-independent basis, Debye):
    X=              0.0000    Y=              0.0000    Z=              0.1907  Tot=              0.1907

Using Møller-Plesset Perturbation Theory of second order, i.e. MP2/def2-QZVPP, we obtain \begin{align} \ce{{}^{\ominus}\!:C#O:^{\oplus}} && \text{Dipole:}~|\mathbf{q}|=0.30~\mathrm{D} && \text{Direction:}~\longleftarrow \end{align}

 ---------------------------------------------------------------------
 Center     Atomic      Atomic             Coordinates (Angstroms)

 Number     Number       Type             X           Y           Z
 ---------------------------------------------------------------------
      1          6           0        0.000000    0.000000   -0.648450
      2          8           0        0.000000    0.000000    0.486337
 ---------------------------------------------------------------------
[...]
 Dipole moment (field-independent basis, Debye):
    X=              0.0000    Y=              0.0000    Z=             -0.3002  Tot=              0.3002

There is no improvement going to other post-Hartree_Fock methods, as the following table indicates. A positive value means that the dipole is directed towards the carbon; the used basis set is in all cases def2-QZVPP. \begin{array}{lr} \text{Method} & \mathbf{q}(\overrightarrow{\ce{CO}})\\\hline \text{Experimental}^1 & 0.11\\\hline \text{HF} & -0.14\\\hline \text{MP2} & -0.30\\ \text{MP3} & -0.22\\ \text{MP4(SDQ)} & -0.27\\ \text{MP4(SDTQ)//MP4(SDQ)} & -0.27\\ \text{CCSD} & -0.25\\ \text{CCSD(T)//CCSD} & -0.25\\ \text{CISD} & -0.22\\ \text{QCISD} & -0.26\\ \hline \text{BP86} & 0.19\\ \text{PBE0} & 0.12\\ \text{M11} & 0.06\\ \text{B3LYP} & 0.10\\ \hline \text{B2PLYP} & -0.07\\ \hline \end{array}

This failure probably already starts with Hartree-Fock. Where does the deficiency lie in the HF description in this particular case? And why is this deficiency not corrected by post-HF methods? Even the double hybrid functional B2PLYP cannot predict the direction of the dipole moment correctly.

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1. According to Gernot Frenking, Christoph Loschen, Andreas Krapp, Stefan Fau, and Steven H. Strauss, J. Comp. Chem., 2007, 28 (1), 117-126. the value can be found in J. S. Muenter. J. Mol. Spectrosc. 1975, 55, 490. (I don't have access to that publication.)

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Sample Input for Gaussian 09

#p MP2/def2QZVPP
scf(tight) opt(verytight,maxcycle=100)

symmetry(loose)
gfinput gfoldprint iop(6/7=3)

carbon monoxide

0 1
C   0.0 0.0 1.135
O   0.0 0.0 0.0