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Contents
Preface .........................................................................................................................v
List of Publications ....................................................................................................vii
Part 1 Improving Self-consistent Field Convergence.................................................1
1.1 Introduction .....................................................................................................................1
1.2 The Self-consistent Field Method....................................................................................2
1.3 A Survey of Methods for Improving SCF Convergence .................................................5
1.3.1 Energy Minimization.............................................................................................6
1.3.2 Damping and Extrapolation...................................................................................7
1.3.3 Level Shifting......................................................................................................11
1.4 Development of SCF Optimization Algorithms ............................................................12
1.4.1 Dynamically Level Shifted Roothaan-Hall .........................................................13
1.4.1.1 RH Step with Control of Density Change..............................................13
1.4.1.2 The Trust Region RH Level Shift ..........................................................15
1.4.1.3 DIIS and Dynamically Level Shifted RH ..............................................16
1.4.1.4 Line Search TRRH.................................................................................18
1.4.1.5 Optimal Level Shift without MO Information.......................................19
1.4.1.6 The Trace Purification Scheme..............................................................23
1.4.2 Density Subspace Minimization..........................................................................25
1.4.2.1 The Trust Region DSM Parameterization..............................................25
1.4.2.2 The Trust Region DSM Energy Function ..............................................26
1.4.2.3 The Trust Region DSM Minimization ...................................................27
1.4.2.4 Line Search TRDSM..............................................................................29
1.4.2.5 The Missing Term..................................................................................30
1.4.3 Energy Minimization Exploiting the Density Subspace .....................................32
1.4.3.1 The Augmented RH Energy model........................................................33
1.4.3.2 The Augmented RH Optimization .........................................................34
1.4.3.3 Applications ...........................................................................................36
1.5 The Quality of the Energy Models for HF and DFT .....................................................37
1.5.1 The Quality of the TRRH Energy Model............................................................39
1.5.2 The Quality of the TRDSM Energy Model.........................................................42
1.6 Convergence for Problems with Several Stationary Points...........................................44
1.6.1 Walking Away from Unstable Stationary Points ................................................46
1.6.1.1 Theory....................................................................................................46
1.6.1.2 Examples................................................................................................47
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