The dipolar contribution to the Helmholtz energy FD has been determined for dipolar two-center Lennard-Jones molecules of increasing elongation at one corresponding state point in the liquid. The calculation is based on the dipole–dipole energy obtained from simulations and subsequent integration according to the λ-coupling technique. It results, that at fixed values of the reduced dipole moment μ*2=μ2/(εσ3) with ε and σ being the Lennard-Jones site–site interaction parameters, the dipolar free energy FD is nearly constant as function of the molecular elongation. Keeping the effective dipole moment μ̃2=μ2(ρp/Tp) constant with Tp and ρp being the critical temperature and density obtained from WCA-type perturbation theory, FD increases somewhat with the elongation.