Computing the melting temperature by using the free energy difference
between the liquid and solid phases is exactly what we've been using to
compute melting points. You can find more details about this method in J.
Chem. Phys 127, 214504 (2007). This method has been implemented in lammps
and will be released soon. In Ind. Eng. Chem. Res, 49, 559-571 (2010), we
used this implementation in LAMMPS to compute melting points. It should be
trivial to extend this method to Si.
If desired, I can send the routines to you.