Can antiprotons make stable bounds with halogens? Halogens are known for being highly electronegative. That means their electron dipole moment are high enough that they want to share other atoms electrons. 
I'm wondering If two Halogen atoms could share a single antiproton behaving as some kind of pseudo-alkali atom? It occurs to me that such antiproton might be kept stable against annihilation by the repulsive force from the electron cloud, but I might be oversimplifying this. Also, chemistry is far from my comfort zone
 A: Since the anti-proton and electrons are different particles there is no Pauli principle requiring them to stay apart. In effect we get a set of electronic orbitals and a set of anti-protonic orbitals. These will all be approximately hydrogenic, though their exact form will be perturbed away from the hydrogenic orbitals by the repulsion between negative charges.
So the antiproton will occupy a $1s$ like orbital, but given the high mass of the antiproton this will be far more compact than the electron orbitals. You'd still get a $Cl^-$ ion, but with the anti-proton buried down near the nucleus. In fact given the high overlap of the anti-proton's orbital and the nucleus the anti-proton will annihilate very quickly.
A: This is not an answer, I just place here a picture for a comment on the covalent bond.

A: Before asking if two halogen atoms could share an anti-proton, ask if they can share an electron. 
As far as I remember the chemical bonds between two atoms are so as to form in both atoms a complete shell. 
For instance, in the molecule of salt, NaCl, the Na atom has a superfluous electron (see the electron shells of Na in the periodic table of elements, http://www.chemicalelements.com/elements/na.html), while the Cl atom needs an electron to complete a stable shell. Thus, the Na atom "donates" its electron to the Cl atom. 
What you suggest with the anti-proton is not similar. A single anti-proton won't create a molecule of two halogens. What is needed for such a molecule should be two antiprotons. So, consider the anti-proton in the vicinity of a single halogen atom.
Since the antiproton is a different particle than the electron, the Pauli repulsion from the other electron on the last shell of the Cl, won't act. As to the electrical repulsion, I am not sure that you can count on it. The anti-proton mass is cca 1650 time bigger than the electron mass. So, the radius of the orbital of the anti-proton in the halogen is bound to be smaller than that of the additional electron needed. So, the anti-proton orbital would be quite close to the nucleus - which makes the annihilation quite probable.
A: The relationship between energy, angular momentum, and shape of the orbital are all strongly dependent on the mass of the particle. This will be VERY different for antiprotons than for electrons. For example, for conventional atoms

You can see the term $a_\mu$ appear in the denominator several times: that's the mass of the electron. Depending on the angular momentum, the radius will be much, much smaller with an antiproton.
Now since the smallest halogen is is Fluorine (unless you want to count Hydrogen, but that would be unconventional), you are looking to complete the "outer shell" of the atom with an antiproton. But a proton would want to be in a much tighter orbital, and there would be almost no overlap between the proton orbital in one atom and the other atom.
In other words - there would be no "bridge" for the antiproton to make it from one atom to the other and form a bond.
