What factors determine the melting point of a substance? What factors regulate how high or low melting points of different chemical elements are?
Given that the pressure is ambient, what are other factors to consider when choosing an element with a desired melting point?
This wiki article on melting point seems to indicate that the symmetrical arrangement of atoms in a molecule is a factor. Another one, as I gather from that article, is how much free space atoms have around them to freely vibrate when being heated. Are these two, besides the pressure, the only know factors that define the melting point of a substance?
 A: An equilibrium phase transition occurs when the chemical potentials of the two phases are equal. The chemical potential is also the molar Gibbs free energy $g\equiv h-Ts$, with molar enthalpy $h$, temperature $T$ and molar entropy $s$, so we have
$$h_\mathrm{liquid}-T_\mathrm{melting}s_\mathrm{liquid}=h_\mathrm{solid}-T_\mathrm{melting}s_\mathrm{solid},$$
or
$$T_\mathrm{melting}=\frac{\Delta h}{\Delta s},$$
referring to the difference in enthalpies and entropies between the two phases. Thus, better bonding in the solid state promotes a higher melting temperature, and greater entropy (e.g., more accessible molecular configurations) in the liquid state promotes a lower melting temperature. This tradeoff arises everywhere: Nature prefers* both strong bonding and high entropy, and the temperature mediates whether the former or the latter predominates. As low temperatures, we encounter solids (strong bonding), and at high temperatures, we encounter gases (high entropy).
*The reason is that high entropy offers many possible arrangements, so we're more likely to see one of them. Strong bonding releases energy that heats the rest of the universe, raising its entropy correspondingly; the same reasoning applies.
