What factors determine whether a proton-bound homodimer has a symmetric or an asymmetric hydrogen bond?

What factors determine whether a proton-bound homodimer with a central [X ··· H ··· X]+ moiety has a symmetric or an asymmetric hydrogen bond? Although hydrogen bonding may be considered the incipient step of protonation, quantum chemical computations indicate that the proton affinity of the base is not the governing influence as to whether the hydrogen bond is symmetric or asymmetric. Instead, the primary factor appears to be the electronegativity of the hydrogen-bonded heavy atom X, with a more electronegative X usually facilitating the formation of a symmetric hydrogen bond. Additional influences arise from the increased weakening of the X–H bond in the protonated monomer upon dimer formation for less electronegative X, as well as from stabilizing or destabilizing interactions involving more distant atoms that do not directly participate in the [X ··· H ··· X]+ hydrogen bond.