Contents

I. An Introduction to Pseudopotentials and Total Energy Calculations

I.1. Overview of Chapters ------------------------------------------------------------------ I-1

I.2. Background Information: Essential Theory of Pseudopotential-----------------I-3

I.2.0. What Is A Pseudopotential and How Is It Used ? -------------------------------------- I-4

I.2.1. The OPW (Orthogonalised Plane Wave) View Point ---------------------------------- I-5

I.2.2 Ab initio Pseudopotentials from Pseudising and Inverting Wave Functions ------------ I-6

I.2.4 Unscreening Pseudopotentials ---------------------------------------------------------- I-8

I.2.5 Norm-conserving Pseudopotentials ----------------------------------------------------- I-9

I.2.6 The Kleinman-Bylander Form of A Pseudopotential ---------------------------------- I-12

I.2.7. BHS Table for Excited States, and Comments ------------------------------------------ I-14

I.3. Total Energy Calculation ------------------------------------------------------------- I-15

II. Optimised Pseudopotentials with Kinetic Energy Filter Tuning

II.1. Introduction --------------------------------------------------------------------------- II-2

II.2. The Q_c Tuning Method -------------------------------------------------------------- II-7

II.3. Generation and Test of Some Pseudopotentials ------------------------------- II-9

II.4. Discussion and Conclusion -------------------------------------------------------- II-10

III. Non-local Projector Reduction in Optimised Pseudopotentials

III.1. Introduction ---------------------------------------------------------------------- III-1

III.2. The Projector Reduction Method and Examples -------------------------- III-4

III.3. Atomic and Solid State Test --------------------------------------------------- III-7

III.4. Discussion ------------------------------------------------------------------------- III-9

III.5. Conclusion ------------------------------------------------------------------------ III-10

IV. Local and Partly Local Pseudopotentials from A Non-local Method

IV.1. Introduction ---------------------------------------------------------------------- IV-1

IV.2. Reducing The Non-locality in Different Cases ----------------------------- IV-5

IV.3. Case Studies of Al, Si and Ge ------------------------------------------------- IV-7

IV.4. Discussion and Conclusion ---------------------------------------------------- IV-12

V. Pseudopotentials Generated and Tested for Collaborations

V.1. The Art of Generating Pseudopotentials ------------------------------------- V-2

V.2. A List of Working Pseudopotential ------------------------------------------- V-4

VI. Ideas for Further Research

VI.1. Pseudo Core Overlap ---------------------------------------------------------- VI-2

VI.2. Softer Si Pseudopotentials ---------------------------------------------------- VI-5

VI.3. The Special Cases of the I-A and II-A Elements -------------------------- VI-7

VII. The Origin of Disorder in g-Al₂O₃

VII.1. Introduction --------------------------------------------------------------------- VII-1

VII.2. Background Experimental Information ------------------------------------ VII-4

VII.3. Configuration Energies from First Principles Calculations ------------ VII-7

VII.4. The Model Hamiltonian ------------------------------------------------------- VII-11

VII.4.1. Constructing a Simplified Model Hamilton --------------------------------- VII-11

VII.4.2. Determine The Parameters in Model Hamiltonian ------------------------- VII-13

VII.5. Simulation of Structures and Comparison with Experiments --------- VII-14

VII.6. Discussion : Geometrical Interpretation of Results --------------------- VII-19

VII.7. Plans for Possible Further Work ------------------------------------------- VII-22