Extent of Melting of Bonds or Intermolecular Forces

I'm currently having a revisit on the subject of periodicity of the periodic table, and I came across an issue that is kind of bugging me.


If we take a look at the melting and boiling point trends of just the second and third periods:


[![1](https://i.stack.imgur.com/kiuCl.png)](https://i.stack.imgur.com/kiuCl.png)


We can see that the difference in melting and boiling points for metals is much larger than that of molecular substances. I've heard two different versions of this:


1. The extent of breaking of metallic bond is much lower than the extent of breaking of other forces
2. The extent of breaking of non-directional forces is much lower than the extent of breaking of directional forces (This one doesn't seem plausible to me as hydrogen bonds are directional yet it plays an important role in determining the physical properties of liquids)


Now I want to clear one thing up first before I get to the point: I know that a lot of textbooks state that the stronger the bond/intermolecular forces, the more energy is needed to break them and the higher the melting/boiling point, and the data does support it. But is this kind of misleading? Since we know that it is the latent heat that breaks the attraction between atoms/molecules, and the only reason why temperature is related is because ∆S = L/T by the Clausius-Clapeyron Equation, where ∆S is more or less similar between substances at room pressure. (Please correct me if I'm not getting this right)


Therefore for the main question, I would be using enthalpy of fusion and vaporisation instead of melting/boiling temperatures to represent the extent of breaking of forces.


Now as I have said, I couldn't find any material online that shows how many bonds/intermolecular forces are broken (compared to when all of them are broken when boiling), so I tried to find out the trend from real data. I tried to quantify the extent of bond breaking with:


\begin{equation}
Extent of Melting = \frac{∆H\_{f}}{∆H\_{f}+∆H\_{v}}
\end{equation}


And plotted the data in Desmos (using data from [this website](https://periodictable.com/)):
[![3](https://i.stack.imgur.com/2Fyk1.png)](https://i.stack.imgur.com/2Fyk1.png)


To me, there doesn't seem to be any pattern I can see other than the fact that metallic bond does seem to be pretty low in its extent of bond breaking.


So the main question I'm asking is: **What kind(s) of atomic property(ies) can explain the above trend?**


P.S. I'm pretty sure the method I used above is completely wrong, as the bonds are probably not broken only during the process of change in phase so as to satisfy the virial theorem (though I don't quite understand how the theorem is obeyed during phase change as KE seem to only depend on temperature only if we derive the KE term from the boltzmann factor, but that's a question for another day), and so if you believe what I did above is wrong, please also provide me the correct trend of "extent of melting" while answering the question. Thank you.


