Dear Sikander Azam,

FPLAPW method

The augmented plane wave (APW) method and in particular its linearized form, the LAPW method, enables accurate calculations of electronic and magnetic properties

of poly-atomic systems using density-functional theory (DFT) . One successful implementation of the full-potential LAPW (FP-LAPW) method is the program package WIEN, a code developed by Blaha, Schwarz and coworkers. It has been successfully applied to a wide range of problems such as electric field gradients and systems such as high-temperature superconductors, minerals, surfaces of transition metals, or anti-ferromagnetic oxides and even molecules . Minimizing the total energy of a system by relaxing the atomic coordinates for complex systems became possible by the implementation of atomic forces, and even molecular dynamics became feasible. Up to now the main drawback of the FP-LAPW-method compared to the pseudopotential plane-wave (PPW) approach has been its higher computational expense.

http://arxiv.org/pdf/cond-mat/9902277v1.pdf

Pseudopotential , LMTO, KKR Green function methods

The pseudopotential is an attempt to replace the complicated effects of the motion of the core (i.e. non-valence) electrons of an atom and its nucleus with an effective potential, or pseudopotential, so that the Schrödinger equation contains a modified effective potential term instead of the Coulombic potential term for core electrons normally found in the Schrödinger equation.

The muffin-tin approximation is a shape approximation of the potential field in an atomistic environment. It is most commonly employed in quantum mechanical simulations of electronic band structure in solids. The approximation was proposed by John C. Slater. Augmented plane wave method is a method which uses muffin-tin approximation. It is a method to approximate the energy states of an electron in a crystal lattice. The basis approximation lies in the potential in which the potential is assumed to be spherically symmetric in the muffin-tin region and constant in the interstitial region. Wave functions (the augmented plane waves) are constructed by matching solutions of the Schrödinger equation within each sphere with plane-wave solutions in the interstitial region, and linear combinations of these wave functions are then determined by the variational method[ Many modern electronic structure methods employ the approximation. Among them are the augmented plane wave (APW) method, the linear muffin-tin orbital method (LMTO) and various Green's function methods. One application is found in the variational theory developed by Korringa (1947) and by Kohn and Rostoker (1954) referred to as the KKR method. This method has been adapted to treat random materials as well, where it is called the KKR coherent potential approximation.

In its simplest form, non-overlapping spheres are centered on the atomic positions. Within these regions, the screened potentialexperienced by an electron is approximated to be spherically symmetric about the given nucleus. In the remaining interstitial region, the potential is approximated as a constant. Continuity of the potential between the atom-centered spheres and interstitial region is enforced.

In the interstitial region of constant potential, the single electron wave functions can be expanded in terms of plane waves. In the atom-centered regions, the wave functions can be expanded in terms of spherical harmonics and the eigenfunctions of a radial Schrödinger equation. Such use of functions other than plane waves as basis functions is termed the augmented plane-wave approach (of which there are many variations). It allows for an efficient representation of single-particle wave functions in the vicinity of the atomic cores where they can vary rapidly (and where plane waves would be a poor choice on convergence grounds in the absence of a pseudopotential).

References:

Duan, Feng; Guojun, Jin (2005). Introduction to Condensed Matter Physics 1. Singapore: World Scientific. ISBN 978-981-238-711-0.

Slater, J. C. (1937). "Wave Functions in a Periodic Potential". Physical Review 51 (10): 846–851. Bibcode:1937PhRv...51..846S. doi:10.1103/PhysRev.51.846.

 Kaoru Ohno, Keivan Esfarjani, Yoshiyuki (1999). Computational Materials Science. Springer. p. 52. ISBN 3-540-63961-6.

 Vitos, Levente (2007). Computational Quantum Mechanics for Materials Engineers: The EMTO Method and Applications. Springer-Verlag. p. 7. ISBN 978-1-84628-950-7.

Richard P Martin (2004). Electronic Structure: Basic Theory and Applications. Cambridge University Press. pp. 313 ff. ISBN 0-521-78285-6.

 U Mizutani (2001). Introduction to the Theory of Metals. Cambridge University Press. p. 211. ISBN 0-521-58709-3.

 Joginder Singh Galsin (2001). "Appendix C". Impurity Scattering in Metal Alloys. Springer. ISBN 0-306-46574-4.

 Kuon Inoue, Kazuo Ohtaka (2004). Photonic Crystals. Springer. p. 66. ISBN 3-540-20559-4.

 I Turek, J Kudrnovsky & V Drchal (2000). "Disordered Alloys and Their Surfaces: The Coherent Potential Approximation". In Hugues Dreyssé. Electronic Structure and Physical Properties of Solids. Springer. p. 349. ISBN 3-540-67238-9.

Slater, J. C. (1937). "An Augmented Plane Wave Method for the Periodic Potential Problem". Physical Review 92 (3): 603–608. Bibcode:1953PhRv...92..603S. doi:10.1103/PhysRev.92.603.

Summary:  FPLAPW method is more accurate and more expensive than  LMTO and KKR Green function methods.

Hoping this will be helpful,

Rafik

Resp Rafik Karaman Sir

Thank you so much sir.

Regards

Sikander

Thank you very much Rafik Karaman

Best regards

Thank you so much Rafik Karaman sir.

Regards

Manjula

thanks Sir Rafik Karaman

thank you a lot for this informations

Thank you for the information