The free energy of binding of deuterium to a surface silicon atom is o
btained directly from our previously reported experiment. However, com
parison with first-principles calculations of the surface Si-D bond en
ergy requires an estimation of the contribution to the free energy fro
m the vibrational entropy S-vib. Herring and Van de Walle determine a
value of 2.99 eV for the bond energy at 800 degrees C from our data, u
sing a harmonic oscillator model to estimate S-vib Our method of estim
ating S-vib from Solubility measurements gives a lower Si-D bond energ
y of 2.49 eV. These values are both lower than the bond energy from Va
n de Walle's first-principles calculation. Uncertainties involved in c
omparing theory with experiment are discussed.