Question

Cohesive energy of a crystal is the energetic cost that holds all atoms together in a crystal. It can be determined both experimentally and theoretically. Explain, based on your knowledge on the quantum mechanical nature of non–covalent interactions, why the following statement is incorrect:

Because silicon crystal are bonded together by strong covalent bonds between silicon atoms, non– covalent interactions, in particular, dispersion interactions, play NO role in determining the cohesive energy in silicon crystals.

Answer 1

The cohesive energy of a crystal refers to the energy required to separate the constituent atoms apart from each other and bring them to an assembly of neutral free electrons. In case of a Si crystal too,the amount required to separate it's constituent atoms, corresponds to the cohesive energy of the Si crystal. The value of the cohesive energy for silicon nano particles usually varies form -4 to -5 eV. Now, cohesive energy is potentially the net energy, comprising of various other different energy contributions.

Now dispersion interaction is a phenomenon which arises from the fluctuations in the electron density distribution of the corresponding crystal. So, it's contribution to the total or net cohesive energy is quite significant. Electrons aren't equally distributed throughout the entire crystal. The density varies and is maximum in the ground states. So, according to the electron density distribution the minimum amount of energy required to separate it's atoms also varies. So, apart from the contribution of covalent forces, non covalent forces also play a major part in determining the cohesive energy of Silicon. Hence, the claimed statement is incorrect. Apart from dispersion interactions, various other non covalent interactions like, Van Der Walls interaction, various other hydrophobic effects, etc also play a major part in determining the cohesive energy of the crystal.