CLOPW: a mixed basis set full potential electronic structure method


Bekker, Hermie Gerhard (1997) CLOPW: a mixed basis set full potential electronic structure method. thesis.

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Abstract:This thesis is about the development of the full potental CLOPW package for electronic structure calculations. Chapter 1 provides the necessary background in the theory of solid state physics. It gives a short overview of the effective one particle model as commonly used in solid state physics. It also shows the reasons for the development of CLOPW and the role CLOPW plays in the discrete cellular project. Chapter 2 forms the main part of the thesis. It shows how to calculate all relevant quantities with the CLOPW basis functions for the self consistent calculation. First the basis functions are introduced. The expressions for the matrix elements for the secular equation are derived and the effective one particle potential is constructed. It is shown that the mathematical nature of the CLOPW basis functions allows a numerically efficient evaluation of all relevant integrals. Chapter 3 reports the results of a feasibility study. The CLOPW basis set has been used to calculate eigenvalues and eigenfunctions of an external self consistent potential generated by a LMTO-ASA programme. The results for materials like Copper, Silicon, Lithium Hydride (LiH) and Aluminum were found to match very well with the LMTO-ASA results and other results from literature. This showes that the CLOPW basis functions are able to accurately represent electronic states in free electron, d-band, covalent and ionic materials. Finally Chapter 4 contains the results from calculations done with the full potential self consistent CLOPW package. We have studied charge transfer in binary compounds which were of past and/or present interest in the discrete cellular project. We have also calculated an important intermediate quantity, the joint density of states polarizability, in the calculation of the optical properties of Silicon and Diamond. It turns out that this quantity which is easily calculated gives a good qualitative indication for the behaviour of the true polarizability. We further showed that the combination of analytical hydrogenlike orbitals and plane waves is unable to give an accurate enough representation of the core states. We suspect that this causes an inaccurate calculation of the kinetic energy of the core electrons and therefore an inaccurate calculation of the total energy.
In the appendices we give some mathematical derivations and a short introduction in the use of the CLOPW package.
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