The Orthogonal Plane Wave (OPW) method is considered complete because it provides a complete basis set for the expansion of any wave function in a periodic crystal lattice. This means that any wave function can be expressed as a linear combination of OPWs, making it a powerful and versatile tool for studying the electronic properties of materials.
The OPW method involves solving the Schrödinger equation for a plane wave in a periodic potential. This results in a set of Bloch waves, which are then used to construct the OPWs. These OPWs are orthogonal to each other and form a complete basis set, allowing for the expansion of any wave function.
The OPW method has several advantages, including its ability to accurately describe the electronic properties of materials in both the valence and conduction bands. It is also computationally efficient and allows for the inclusion of effects such as spin and relativistic corrections.
While the OPW method is a powerful tool, it does have some limitations. It is most suitable for studying periodic systems and may not accurately describe the electronic properties of materials with strong localizations or disorder. It also requires a large number of Bloch waves to achieve high accuracy.
The completeness of the OPW method is verified by comparing the results obtained using the method with experimental data or with other accurate theoretical methods. If the results match closely, it can be concluded that the OPW method is complete in describing the electronic properties of the material under study.