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[edoc]
<+B><:#568,9360><:f480,,><+!>

<+B><:#568,9360><+!><:f480,,>Contents<-!><:f>

<:S+-2><:#420,9360>

<:s><:S+-2><:#420,9360>

<:s><:S+-2><:#420,9360>

<:S+-2><:#492,9360><:f280,,><+!>I. An Introduction to Pseudopotentials and Total Energy Calculations<-!><:f>

<:s><:S+-2><:#492,9360><+!><:f280,,>

<:S+-2><:#432,9360><:f240,,><-!><+!>  I.1. Overview of Chapters <-!>--<:f>---------------------------------------------------------------- I-1

<:S+-2><:#432,9360><:f240,,><+!>  I.2. Background Information: Essential<-!><+!> Theory of Pseudopotential<-!><:f>-----------------I-3

<:S+-2><:f200,,><+!>        I.2.0. What Is A Pseudopotential and How Is It Used ?<-!> 
<:f>-------------------------------------- I-4

<:S+-2><:#420,9360><:f200,,><+!>        I.2.1. The OPW (Orthogonalised Plane Wave) View Point<-!><:f> ---------------------------------- I-5

<:S+-2><:#420,9360><:f200,,><-!><+!>        I.2.2 <+">Ab initio<-"> Pseudopotentials from Pseudising and<-!><+!><:f200,2Times New Roman,0,0,0> Inverting 
<-!><:f200,,><+!>Wave Functions<-!> <:f>------------ I-6

<:S+-2><:#420,9360><:f200,2Times New Roman,0,0,0><+!>        I.2.4 Unscreening Pseudopotentials<-!><:f> ---------------------------------------------------------- I-8

<:S+-2><:#420,9360><:f200,2Times New Roman,0,0,0><+!>        I.2.5 Norm-conserving<-!><+!><:f200,2Times New Roman,0,0,0> Pseudopotentials<-!><:f> ----------------------------------------------------- I-9

<:S+-2><:#420,9360><:f200,2Times New Roman,0,0,0><+!>        I.2.6 The Kleinman-Bylander<-!><+!><:f200,2Times New Roman,0,0,0> Form of A Pseudopotential<-!><:f200,,> 
<:f> ---------------------------------- I-12

<:S+-2><:f200,2Times New Roman,0,0,0><+!>        I.2.<-!><+!>7.<-!><+!> BHS Table for Excited States<-!><+!><:f200,2Times New Roman,0,0,0>, and Comments<-!><:f200,,> 
<:f> ------------------------------------------ I-14

<:S+-2><:#432,9360><:f240,,><+!>  I.3. Total Energy Calculation<-!><:f> ------------------------------------------------------------- I-15

<:s><:S+-2><:#420,9360>

<:s><:S+-2><:#420,9360>

<:s><:S+-2><:#492,9360><:f280,,><+!>

<:s><:S+-2><:#492,9360><+!><:f280,,>II.<:f280,,> <+!>Optimised Pseudopotentials with Kinetic Energy Filter Tuning<-'><-'><-!><:f><-'>

<:s><:S+-2><:#432,9360><:f240,,><+!>

<:S+-2><:#432,9360><+!><:f240,,>  II.1. Introduction <-!><:f>--------------------------------------------------------------------------- II-2

<+@><:S+-2><:#432,9360><:f240,,><+!>  II.2. The <+">Q<-"><+'>c<-'> Tuning Method<-!><:f> -------------------------------------------------------------- II-7

<+@><:S+-2><:#432,9360><:f240,,><+!>  II.3. Generation  and Test of Some Pseudopotentials 
<-!><:f>------------------------------- II-9

<:S+-2><:#432,9360><:f240,,><+!>  II.4. Discussion and  Conclusion<-!><:f> -------------------------------------------------------- II-10

<:s><:S+-2><:#420,9360>

<:s><:S+-2><:#420,9360>

<:s><:S+-2>

<:S+-2><:#492,9360><:f280,,><+!>III. Non-local Projector Reduction in Optimised Pseudopotentials<-!><:f>

<:s><:S+-2><:#420,9360>

<:S+-2><:#432,9360><:f240,,><+!>  III.1. Introduction<:f240,,> <-!><:f>---------------------------------------------------------------------- III-1

<:S+-2><:#432,9360><:f240,,><+!>  III.2. The Projector Reduction Method and Examples<-!><:f> -------------------------- III-4

<:S+-2><:#432,9360><:f240,,><+!>  III.3. Atomic and Solid State Test<-!><:f> --------------------------------------------------- III-7

<:S+-2><:#432,9360><:f240,,><+!>  III.4. Discussion<-!><:f> ------------------------------------------------------------------------- III-9

<:S+-2><:#432,9360><:f240,,><+!>  III.5. Conclusion<-!><:f> ------------------------------------------------------------------------ III-10

<:s><:S+-2><:#420,9360>

<:s><:S+-2><:#420,9360>

<:s><:S+-2><:#492,9360><:f280,,><+!>IV. Local and Partly Local Pseudopotentials <-!><+!>from 
<-!><+!>A Non-local Method<-!><-!><:f>

<:s><:S+-2><:#420,9360><:f240,,>

<:S+-2><:#432,9360><:f240,2Times New Roman,><+!>  IV.1. Introduction<-!><-!><:f> ---------------------------------------------------------------------- IV-1

<:S+-2><:#432,9360><+!><:f240,,>  IV.2. <:f240,2Times New Roman,>Reducing The Non-locality in Different Cases<-!><:f> ----------------------------- IV-5

<:S+-2><:#432,9360><+!><:f240,2Times New Roman,>  IV.3. Case Studies of Al, Si and Ge<-!><:f> ------------------------------------------------- IV-7

<:S+-2><:#432,9360><+!><:f240,2Times New Roman,>  IV.4. Discussion <-!><+!>and Conclusion<-!><:f> ---------------------------------------------------- IV-12

<:s><:S+-2><:#420,9360>

<:s><:S+-2><:#420,9360>

<:s><:S+-2><:#492,9360><:f280,2Times New Roman,><+!>V.<:f280,2Times New Roman,> Pseudopotentials Generated 
<-!><+!><:f280,2Times New Roman,>and <-!><+!><:f280,2Times New Roman,>Tested for Collaborations<-!><+!><:f>

<:s><:S+-2><:#420,9360>

<:S+-2><:#432,9360><:f240,,><+!>  V.1. The Art<-!><+!> of Generating Pseudopotentials<-!><:f> ------------------------------------- V-2

<:S+-2><:#432,9360><:f240,2Times New Roman,><+!>  V.2. A List of Working Pseudopotential<-!><:f> ------------------------------------------- V-4

<:s><:S+-2><:#420,9360>

<:s><:S+-2><:#420,9360>

<:s><:S+-2><:#492,9360><:f280,,><+!>VI. Ideas for Further Research<-!><:f>

<:s><:S+-2><:#432,9360><:f240,,><+!>

<:S+-2><:#432,9360><+!><:f240,,>  VI.1. Pseudo Core Overlap<-!><:f> ---------------------------------------------------------- VI-2

<:S+-2><:#432,9360><:f240,,><+!>  VI.2. Softer Si Pseudopotentials<-!><:f> ---------------------------------------------------- VI-5

<:S+-2><:#432,9360><:f240,,><+!>  VI.3. The Special Cases of the I-A and II-A Elements<-!><:f> -------------------------- VI-7

<:s><:S+-2><:#420,9360>

<:s><:S+-2>

<:s><:S+-2>

<:S+-2><:f280,,><+!>VII.<:f280,,> The Origin<-!><+!> of Disorder in <:f280,2Symbol,0,0,0>g<:f280,,>-Al<+'>2<-'>O<+'>3<-!><-'><:f>

<:s><:S+-2>

<+@><:S+-2><:f240,,><+!>  VII.1. Introduction<-!> -<:f>-------------------------------------------------------------------- VII-1

<:S+-2><:f240,,><+!>  VII.2.<-!><+!> Background<-!><+!> Experimental<-!><+!> Information<-!><:f> ------------------------------------ VII-4

<:S+-2><:f240,2Times New Roman,0,0,0><-!><+!>  VII.3. Configuration Energies from First Principles Calculations<-!><:f> ------------ VII-7

<:S+-2><:f240,,><+!>  VII.4. The Model Hamiltonian<-!><:f> ------------------------------------------------------- VII-11

<:S+-2><:f200,2Times New Roman,0,0,0><+!>             VII.4.1. Constructing a Simplified<-!><+!><:f200,2Times New Roman,0,0,0> Model Hamilton<-!><:f> --------------------------------- VII-11

<:S+-2><:f200,2Times New Roman,0,0,0><+!>             VII.4.2. Determine The Parameters in Model Hamiltonian<-!><:f> ------------------------- VII-13

<:S+-2><:f240,2Times New Roman,0,0,0><+!>  VII.5. Simulation of Structures and Comparison with Experiments<-!><:f> --------- VII-14

<:S+-2><:f240,,><+!>  VII.6. Discussion :<-!><+!> Geometrical Interpretation of Results<-!><:f> --------------------- VII-19

<:S+-2><:f240,,><+!>  VII.7. Plans for Possible Further<-!><+!> Work<-!><:f> ------------------------------------------- VII-22

<:s><:S+-2>

<:s>


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