Does melting a metal affect its electronic band stucture? Given that the band structure of a metal emerges from the periodicity of the crystalline lattice and the corresponding symmetry arguments, what happens to the band structure as the metal is melted into its liquid state? Would some form of a limited band structure remain due to atomic clustering or would this not exist at all?
In addition, would melting the metal completely remove interband transitions due to the degradation of the band structure?
 A: What really emerges from the periodicity of the crystalline lattice and symmetry arguments is the so-called dispersion of the energy bands, i.e., the introduction of a (vector) parameter for the electronic states, the wavevector ${\bf k}$, labeling the electronic states that are simultaneously eigenstates of the Hamiltonian and the lattice translation operators.
The concept of energy bands is related but more general than the ${\bf k}$-space dispersion. It clearly emerges from any experiment probing the energy density of states (EDOS) in amorphous and liquid systems, as well as in their crystalline phases.
In every system, including metallic systems, the melting may affect the EDOS to a larger or lesser extent, depending on the ionic rearrangement accompanying the melting. For example, in metallic systems like Nickel, Copper, or Gold, the passage from a compact fcc crystalline structure to a dense simple-liquid structure, almost preserving the number of nearest neighbors, does not introduces dramatic changes in the EDOS. Of course, features specifically related to the ${\bf k}$-space dispersion, like the van-Hove singularities, disappear.
In other cases, like Si and Ge, undergoing a transition from an open crystal structure and a semiconducting behavior to a higher coordinated metallic liquid, the EDOS shows the gap's closing.
An example of the changes induced by the melting on the EDOS can be seen in calculations like this.
