<p>Nowadays first-principles calculations have achieved considerable reliability for the prediction of the properties of materials. These calculations are based on the density functional theory. In the present work, we have obtained a large number of enthalpies of formation of binary intermetallic compounds of rare-earth metals (Sc, Y, and lanthanides) with Al, Ga, In, and Tl elements. This work was initiated with a study of binary rare-earth-boron systems. The <i>ab initio</i> values have been calculated with the Vienna <i>ab initio</i> simulation package in the generalized gradient approximation. We have compared the calculated enthalpies of formation of compounds to the values obtained with calorimetric methods. Good agreement is observed in the cases of aluminium and gallium based compounds. A less good agreement is observed with the In, and Tl based compounds. In the case of the In and Tl based compounds, we always observe that the experimental values are more negative than the calculated ones. All the results show similar behaviour of Sc and Lu on one hand and of Y and Gd on the other hand with the <i>p</i> subshell elements. The evolution of the enthalpies of formation along the rare-earth series has been discussed. The behaviour of a given rare-earth element with <i>p</i> elements belonging to a same column has also been discussed.</p>