Dear Sankush,

Generally speaking, the electronic band structure calculation methods can be grouped into two general categories, namely:

📷 ab initio Methods,

📷 Empirical (Approximate) Methods

The ab initio methods such as the Density Functional Theory (DFT) and NEGF, calculate the electronic structure from first principles, without the need for empirical fitting parameters.

On the other hand , there exist two basic approximate (or empirical) methods, which are widely used for the calculation of energy bands in solids, namely:

📷 The quasi-free electron (QFE) model, and

📷 The tightly bound electron (TB) model.

Both of the above approximate methods use the perturbation theory. But they differ in their zero approximation.

Sometimes, the TB is used in conjunction with DFT or NEGF or both.

For more details, refer to my downloadable Chapter:

Chapter Energy Band Theory & Classification of Solids

Dr. Sankush Krishna Maheshuni, I agree with Prof. Muhammad Hamza El-Saba answer.

In solid-state physics, there are ab initio methods that are used to calculate the electronic structure and help to explain the physical properties of crystals, one of those is DFT which involves the solution of the Schrodinger equation, but is not the only one.

On the other hand, my experience with the tight bind method in the fitting of low-temperature kinetic properties taught me that the use of the tight-binding (t, t´ and mu) parameters is important to fit experiments & to match with theories.

The average over the Fermi surface can be done with a rather few parameters using tight binding.

Best Regards.

Thank you sir Pedro L. Contreras E. Muhammad Hamza El-Saba for your answers.