Equilibrium nuclear quadrupole coupling constants associated with the di-halogen molecule XY in each of 60 complexes B⋯XY (where B is one of the Lewis bases N2, CO, HCN, H2O, H2S, HCCH, C2H4 PH3, NH3 or (CH3)3N and XY is one of the di-halogens Cl2, BrCl, Br2, ICl, IBr or I2) have been calculated ab initio. The Townes-Dailey model for interpreting the changes in the coupling constants when XY enters the complex was used to describe the electron redistribution in the di-halogen molecule in terms of the fraction δi of an electron transferred from the Lewis base B to atom X and the fraction δp of an electron transferred simultaneously from atom X to atom Y. Systematic relationships between the δi values for the six series are established. It is shown that, in reasonable approximation, δi decays exponentially as the first ionisation energy IB of the Lewis base B increases, that is δi = A exp (– b IB). It is concluded from the results for the series B⋯BrCl, B⋯Br2, B⋯ICl, B⋯IBr and B⋯I2 that the coefficients A and b in regression fits to the corresponding logarithmic version ln(δi) = ln(A) – b (IB) of the equation are not strongly dependent on either the halogen atom X directly involved in the halogen bond in B⋯XY or, for a given X, on the nature of Y. The behaviour of PH3 as a Lewis base appears to be anomalous. Values of δi and δp calculated by the quantum theory of atoms-in-molecules and natural bond orbital methodologies give results very close to those from application of the Townes-Dailey approach described.