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We present basic properties of primary stars that initiate a common envelope(CE) in a binary, while on the giant branch. We use the population-synthesiscode described in Politano et al. (2010) and follow the evolution of apopulation of binary stars up to the point where the primary fills its Rochelobe and initiates a CE. We then collect the properties of each system, inparticular the donor mass and the binding energy of the donor's envelope, whichare important for the treatment of a CE. We find that for most CEs, the donormass is sufficiently low to define the core-envelope boundary reasonably well.We compute the envelope-structure parameter {\lambda_\mathrm{env}} from thebinding energy and compare its distribution to typical assumptions that aremade in population-synthesis codes. We conclude that {\lambda_\mathrm{env}}varies appreciably and that the assumption of a constant value for thisparameter results in typical errors of 20--50%. In addition, such an assumptionmay well result in the implicit assumption of unintended and/or unphysicalvalues for the CE parameter {\alpha_\mathrm{CE}}. Finally, we discuss accurateexisting analytic fits for the envelope binding energy, which make theseoversimplified assumptions for {\lambda_\mathrm{env}}, and the use of{\lambda_\mathrm{env}} in general, unnecessary.

Masses and envelope binding energies of primary stars at the onset of a common envelope