I am interested in the underlying physics of the concept of a melting point, a temperature at which an object tends to gain enough energy to break the bonds that hold it together and be in a liquid state. Or the other way around, a freezing point.
What I am interested is... Since temperature is basically a measure of the kinetic energy of particles within, when they actually start to vibrate enough they break apart. And the changes in temperature in the surrounding medium is due to them transferring heat during "impact" with the solid object, be it air or some other medium at a certain temperature.
So, if we know all that, why do we depend upon experimental data? Why isn't there some logical way to deduce what is the melting point of some matter under some variable pressure?