氧化鎳(NiO)與氧化鈷(CoO)是一強關聯的系統且為標準的Mott絕緣體。非共振非彈性X光散射實驗中發現氧化鎳與氧化鈷的d-d軌域之躍遷呈現很強之動量轉換相依(q-dependence)的特性，且此激子(exciton)的能量分布在準粒子能隙(quasiparticle band gap)之中。為了研究此局域化的躍遷行為，我們發展了局域化、有對稱性、能量可解析之Wannier函數。經由對Wannier電子電洞對的Fourier轉換之解析，我們了解此強動量轉換相依的起源且發現一新的選擇定則。進一步，我們提出一個稱為TDLDA+U的方法來解Bethe-Salpeter方程式用以描述電子電洞對間的吸引力來得出此能量分布在能隙中的激子。經由此方法，我們發現氧化鎳中的激子強烈混成在Mott能隙中。在Hartree-Fock近似下，一個有趣的動量轉換相依現象將被討論。另一方面，鈦酸鉛(PbTiO3)為一鐵電性材料，我們利用密度泛函微擾理論(DFPT)研究其晶體振動之特性。經由計算零溫下鈦酸鉛的聲子頻譜與彈性波速，我們確定了鈦酸鉛在低溫下的鐵電結構。更重要的，我們詳細分析鈦酸鉛在立方(cubic)與四方(tetragonal)晶體結構下的橫向光頻(TO)與縱向光頻(LO)振動模式間的偶合。不像立方結構中所發現的橫向光頻與縱向光頻間之巨大分裂，四方結構呈現正常的橫向與縱向振動模式之偶合關係。根據此發現，我們重新解釋了在鈦酸鉛摻雜鈣原子(Pb1-xCaxTiO3)下所發現的橫向與縱向之光頻分裂行為。最後我們將討論實驗上所觀測到鈦酸鉛摻雜鈣原子所發生之結構相變的成因，並預測低溫下新結構相變之發生。

We investigate the Frenkel excitons in NiO and CoO, the standard prototype of Mott insulator, within the diagrammatic picture of density-density response function. Recently immobile excitons showing up in the Mott gap from d-d excitations of NiO and CoO found by non-resonant inelastic X-ray scattering possess strong q-dependence and large binding energies. To study the local excitations, a new localized, symmetry-respecting, energy-resolved Wannier function is developed to perform the calculation. A novel TDLDA+U method is proposed to solve the relevant Bethe-Salpeter equation and the attraction of electron-hole pairs of corresponding real-space Wannier functions is well included. Strongly hybridized Frenkel excitons of NiO are found in the Mott gap via this approach and the local Hartree-Fock interaction reveals an interesting q-dependence in NiO and CoO due to the effect of quantum interference of excitons.
    Electronic structure calculations from first principles in density functional perturbation theory are made to elucidate the lattice dynamic properties of tetragonal PbTiO3. At low temperatures, the mechanical stability of ferroelectric PbTiO3 is identified by obtaining full calculated phonon dispersion curves and sound velocities. Most importantly, a normal coupling characteristic between transverse optical (TO) and longitudinal optical (LO) phonon modes are found in the stable tetragonal PbTiO3, unlike the giant LO-TO splitting in cubic perovskites, as determined by studying correlation matrices. Based on this information, the essentials of the analysis of LO-TO splitting are emphasized to examine the effect of doping in mixed Pb1-xCaxTiO3. Finally, we discuss the mechanism of structural phase transition observed by experiment in Pb1-xCaxTiO3 and predict a new phase transition (cubic-orthorhombic) for cubic Pb0.5Ca0.5TiO3 at low temperatures.

Chapter 0  Introduction                                   1
Chapter 1  Linear Density Response                        3
1.1 Non-Relativistic Hamiltonian                          3
   1.1.1 The Lagrangian for many-body systems             3
   1.1.2 Canonical momentum                               3
   1.1.3 Non-relativistic Hamiltonian                     4
   1.1.4 Quantization of the electromagnetic field        4
   1.1.5 Intrinsic spin in the magnetic field             5
   1.1.6 Born-Oppenheimer approximation                   5
   1.1.7 Model Hamiltonian for electrons                  6
1.2 Non-Resonant Inelastic Photon Scattering              7
   1.2.1 Time dependent perturbation theory (TDPT)        7
   1.2.2 Inelastic photon scattering                      8
1.3 Linear Density Response                              12
   1.3.1 Density-density response function               12
   1.3.2 Excitation energy of N-particle system          14
   1.3.3 Connection with dynamic structure factor        16
1.4 Time-Dependent Density-Functional Theory             18
   1.4.1 Density-functional theory (DFT)                 18
   1.4.2 Kohn-Sham response function                     21
   1.4.3 Meaning of Kohn-Sham response function          23
   1.4.4 Application to phonon calculation               25
Chapter 2  Excitons in NiO and CoO                       28
2.1 Introduction                                         28
2.2 Geometric structure                                  30
2.3 Electronic structure                                 31
   2.3.1 LDA+U method                                    31
   2.3.2 Band structure                                  33
   2.3.3 Wannier function                                42
2.4 Excitons                                             45
   2.4.1 Experimental results                            45
   2.4.2 Property of excitons                            48
   2.4.3 Angular dependence                              50
   2.4.4 Energy of exciton in NiO                        54
   2.4.5 Energy of exciton in CoO                        69
2.5 Summary                                              83
Chapter 3  Phonons in PbTiO3 and Related Mixing Material 84
3.1 Introduction                                         84
3.2 Geometric structure                                  86
3.3 Computational method                                 88
3.4 Results and Discussion                               89
   3.4.1 Structural detail                               89
   3.4.2 Lattice dynamics of tetragonal PbTiO3           90
   3.4.3 Dynamical effective charge analysis of PbTiO3   93
   3.4.4 Doping effect in Pb1-xCaxTiO3                  103
   3.4.5 Phase transitions in Pb1-xCaxTiO3              105
3.5 Summary                                             107
Chapter 4  Conclusion                                   108
Bibliography                                            110
List of Tables
Table 2.1 Fractional coordinates of selected k points for band-structure plots of NiO and
CoO 42
Table 3.1 Calculated (Type I, Type II (see in the text) and GGA[82]) and observed
(Expt.[82]) lattice constants (in a.u.), c/a ratios, and internal parameters (in
fractional coordinates along the z direction (u)) for tetragonal PTO. O1, O2 and
O3 denotes the oxygen atom on the yz, xz, and xy face of the unit cell,
respectively. 90
Table 3.2 Optimized internal parameters for tetragonal Pb0.75Ca0.25TiO3 corresponding to
experimental lattice constants. O1, O2 and O3 denotes the oxygen atom on the
yz, xz, and xy face of the unit cell, respectively. 90
Table 3.3 Elastic constants cμν in GPa; piezoelectric constants i eν in C/m2, and
dielectric constants ij ε (with phonon contribution) for tetragonal PTO.
Corresponding calculated data with respect to theoretical optimized lattice
constants are presented in parentheses. 92
Table 3.4 Born effective charges, the shortest Ti-O bondlength dTi-O (in a.u.) and the
enthalpy difference (in meV) with respect to the cubic (C) phase for the
tetragonal (T) phase of tetragonal PTO at different lattice volumes. The
calculated value of hydrostatic pressure corresponding to each smaller cell
volume is also given for reference. 95
Table 3.5 Correlation matrix and mode effective charges for cubic and tetragonal PTO at
experimental lattice constants. The data in parentheses for cubic and tetragonal
phases are obtained from the literature[80] and theoretical optimized lattice
constants, respectively. 96
Table 3.6 Dielectric constant along c-axis (ε 33(∞)) and Born effective charges ( Z* & ) for
Pb1-xCaxTiO3 and a fictitious tetragonal CaTiO3 (see in the text). All data are
obtained at experimental lattice constants. Effective charges Z* & refer to atom
displacements parallel to c-axis. The oxygen at the bottom of TiO5 in tetragonal
PTO is represented as O3 and the others are denoted by O1. 96
List of Figures
Fig. 1.1 Kohn-Sham response function KS(x,x'; ) σσ χ K K ω , ' KS 0
σ σ χ ≠ = . 21
Fig. 1.2 Connection between many-body and Kohn-Sham response functions. 24
Fig. 2.1 Rhombohedral structure of NiO (CoO). Anti-ferromagnetic order is constructed
from (111) planes composed of Ni (Co) atoms along the [111] direction in rocksalt
structure denoted schematically by small arrows. 30
Fig. 2.2 LDA+U band structure of NiO. The bands with s-orbital character of (a) spin-up
Ni1 (b) spin-down Ni1 (c) spin-up Ni2 (d) spin-down Ni2 are highlighted by open
circles. 34
Fig. 2.3 LDA+U band structure of NiO. The bands with p-orbital character of (a) spin-up
Ni1 (b) spin-down Ni1 (c) spin-up Ni2 (d) spin-down Ni2 are highlighted by open
circles. 35
Fig. 2.4 LDA+U band structure of NiO. The bands with d-orbital character of (a) spin-up
Ni1 (b) spin-down Ni1 (c) spin-up Ni2 (d) spin-down Ni2 are highlighted by open
circles. 36
Fig. 2.5 LDA+U band structure of NiO. The bands with s-orbital character of (a) spin-up O
(b) spin-down O and p-orbital character of (c) spin-up O (d) spin-down O are
highlighted by open circles. 37
Fig. 2.6 LDA+U band structure of CoO. The bands with s-orbital character of (a) spin-up
Co1 (b) spin-down Co1 (c) spin-up Co2 (d) spin-down Co2 are highlighted by
open circles. 38
Fig. 2.7 LDA+U band structure of CoO. The bands with p-orbital character of (a) spin-up
Co1 (b) spin-down Co1 (c) spin-up Co2 (d) spin-down Co2 are highlighted by
open circles. 39
Fig. 2.8 LDA+U band structure of CoO. The bands with d-orbital character of (a) spin-up
Co1 (b) spin-down Co1 (c) spin-up Co2 (d) spin-down Co2 are highlighted by
open circles. 40
Fig. 2.9 LDA+U band structure of CoO. The bands with s-orbital character of (a) spin-up O
(b) spin-down O and p-orbital character of (c) spin-up O (d) spin-down O are
highlighted by open circles. 41
Fig. 2.10 Selected k paths for band-structure plots of NiO. 42
Fig. 2.11 Energy levels of d-character Wannier functions in NiO and CoO. 43
Fig. 2.12 Comparison between LDA+U within RPA and non-resonant inelastic X-ray
scattering experiment for NiO at small momentum transfer (q~0.7Å-1) at absolute
unit. The low energy part in panel (a) is enlarged in panel (b). 45
Fig. 2.13 Dynamical structure factors found by non-resonant inelastic X-ray scattering
experiment for NiO and CoO. High-resolution (0.3 eV) measurements of (a) the
q-dependence of the d-d peak intensities for NiO in the [111] direction; (b) the
q-orientation dependence in CoO at q=7 Å-1. Panel (c) and panel (d) represent the
q-orientation dependence for q=3.5 Å-1 in NiO and q=3.75 Å-1 in CoO,
respectively. 46
Fig. 2.14 Low-resolution (1.1 eV) non-resonant inelastic X-ray scattering measurements
and LDA+U/RPA calculations of the dynamical structure factor for NiO and CoO:
(a) measurements along the [100] and [111] directions for NiO; (b) similar
measurements on CoO; (c) calculations for NiO along the [100] and [111]
directions; (d) similar calculations for CoO. 47
Fig. 2.15 Density fluctuation propagator in the many-body electron system. 48
Fig. 2.16 Bethe-Salpeter equation. 49
Fig. 2.17 A two-band ladder example for the Bethe-Salpeter equation. 49
Fig. 2.18 (a) q-dependence of transition probability of e’g to eg for NiO (3.5Å-1 at white
line). Averaging over cubic equivalent anti-ferromagnetic domain is imposed. (b)
and (c) are the polar plots of the calculated and measured d-d spectral weights,
respectively. 50
Fig. 2.19 q-dependence of transition probability of e’g to eg for pure cubic symmetry.
Averaging over cubic equivalent anti-ferromagnetic domain is imposed. 51
Fig. 2.20 q-dependence of transition probability of ag to eg for NiO. Averaging over cubic
equivalent anti-ferromagnetic domain is imposed. 51
Fig. 2.21 (a) q-dependence of transition probability of e’g to eg for CoO (3.5Å-1 at white
line). Averaging over cubic equivalent anti-ferromagnetic domain is imposed. (b)
and (c) are the polar plots of the calculated and measured d-d spectral weights,
respectively. 52
Fig. 2.22 q-dependence of transition probability of e’g to ag for CoO. Averaging over cubic
equivalent anti-ferromagnetic domain is imposed. 52
Fig. 2.23 Wannier functions of eg states in (a) NiO and (b) CoO. Note the bulge distortion
for CoO (at arrow) compared to the nearly cubic-symmetry shape for NiO. 53
Fig. 2.24 Wannier functions of e’g states in (a) NiO and (b) CoO. Note the slightly less
nodal shape for CoO (at arrow) compared to the nearly cubic-symmetry shape for
NiO. 53
Fig. 2.25 Illustration of (a) Fock and (b) Hartree interaction diagrams in Bethe-Salpeter
equation. 55
Fig. 2.26- 2.27 The real (dashed line) and imaginary (solid line) parts of polarization
propagator L for the L0 case in NiO. The corresponding diagram is presented
inside the plot. 56- 57
Fig. 2.28- 2.30 The real (dashed line) and imaginary (solid line) parts of polarization
propagator L for the Local case in NiO. The corresponding diagram is presented
inside the plot. 57- 58
Fig. 2.31- 2.35 The real (dashed line) and imaginary (solid line) parts of polarization
propagator L for the Fock case in NiO. The corresponding diagram is presented
inside the plot. 59- 61
Fig. 2.36- 2.40 The real (dashed line) and imaginary (solid line) parts of polarization
propagator L for the Hartree-Fock case in NiO. The corresponding diagram is
presented inside the plot. 61- 63
Fig. 2.41 χ (q~7Å-1,q~7Å-1;ω ), the results of the L0 case weighting by the Fourier
transforms of Wannier functions at q~7Å-1 for NiO. The zero intensity along
<100> direction reflects the nodal direction. 65
Fig. 2.42 χ (q~7&Aring;-1,q~7&Aring;-1;ω ), the results of the Local case weighting by the Fourier
transforms of Wannier functions at q~7&Aring;-1 for NiO. The zero intensity along
<100> direction reflects the nodal direction. 65
Fig. 2.43 χ (q~7&Aring;-1,q~7&Aring;-1;ω ), the results of the Fock case weighting by the Fourier
transforms of Wannier functions at q~7&Aring;-1 for NiO. The zero intensity along
<100> direction reflects the nodal direction. 66
Fig. 2.44 χ (q~7&Aring;-1,q~7&Aring;-1;ω ), the results of the Hartree-Fock case weighting by the
Fourier transforms of Wannier functions at q~7&Aring;-1 for NiO. The zero intensity
along <100> direction reflects the nodal direction. 66
Fig. 2.45 q-dependence of the imaginary parts of χ for the L0 case in NiO with the
energies at (a) 6.81eV and (b) 7.74eV. Averaging over cubic equivalent
anti-ferromagnetic domain is imposed. 67
Fig. 2.46 q-dependence of the imaginary parts of χ for the Local case in NiO with the
energies at (a) 1.65eV and (b) 1.95eV. Averaging over cubic equivalent
anti-ferromagnetic domain is imposed. 67
Fig. 2.47 q-dependence of the imaginary parts of χ for the Fock case in NiO with the
energies at (a) 1.43eV and (b) 1.95eV. Averaging over cubic equivalent
anti-ferromagnetic domain is imposed. 68
Fig. 2.48 q-dependence of the imaginary parts of χ for the Hartree-Fock case in NiO with
the energies at (a) 1.72eV and (b) 2.61eV. Averaging over cubic equivalent
anti-ferromagnetic domain is imposed. 68
Fig. 2.49- 2.50 The real (dashed line) and imaginary (solid line) parts of polarization
propagator L for the L0 case in CoO. The corresponding diagram is presented
inside the plot. 70
Fig. 2.51- 2.53 The real (dashed line) and imaginary (solid line) parts of polarization
propagator L for the Local case in CoO. The corresponding diagram is presented
inside the plot. 71- 72
Fig. 2.54- 2.61 The real (dashed line) and imaginary (solid line) parts of polarization
propagator L for the Fock case in CoO. The corresponding diagram is presented
inside the plot. 72- 76
Fig. 2.62- 2.68 The real (dashed line) and imaginary (solid line) parts of polarization
propagator L for the Hartree-Fock case in CoO. The corresponding diagram is
presented inside the plot. 76- 79
Fig. 2.69 χ (q~7&Aring;-1,q~7&Aring;-1;ω ), the results of the L0 case weighting by the Fourier
transforms of Wannier functions at q~7&Aring;-1 for CoO. 80
Fig. 2.70 χ (q~7&Aring;-1,q~7&Aring;-1;ω ), the results of the Local case weighting by the Fourier
transforms of Wannier functions at q~7&Aring;-1 for CoO. 80
Fig. 2.71 χ (q~7&Aring;-1,q~7&Aring;-1;ω ), the results of the Fock case weighting by the Fourier
transforms of Wannier functions at q~7&Aring;-1 for CoO. 81
Fig. 2.72 χ (q~7&Aring;-1,q~7&Aring;-1;ω ), the results of the Hartree-Fock case weighting by the
Fourier transforms of Wannier functions at q~7&Aring;-1 for CoO. 81
Fig. 2.73 q-dependence of the imaginary parts of χ for the Hartree-Fock case in CoO
with the energies at (a) 1.37eV , (b) 2.32eV, (c) 2.81eV, and (d) 3.17eV. Averaging
over cubic equivalent anti-ferromagnetic domain is imposed. 82
Fig. 3.1 Cubic structure of PbTiO3. 86
Fig. 3.2 Tetragonal structure of PbTiO3. 86
Fig. 3.3 Tetragonal structure of Pb0.75Ca0.25TiO3. 87
Fig. 3.4 Primitive unit cell of cubic Pb0.5Ca0.5TiO3. 87
Fig. 3.5 Phonon dispersion curves of tetragonal PTO corresponding to Type I and Type II
calculations (see in the text) are shown as solid and dotted curves, respectively.
Open symbols (circles, triangles)[85] and solid symbols (circles[71],
diamonds[83], squares[84]) denote various experimental data. 91
Fig. 3.6 Sound velocities of longitudinal (L) and two shear waves (S1 and S2) of tetragonal
PTO in (a) a-b and (b) a-c planes. Shear wave polarizes nearly perpendicular
(parallel) to the plane is represented as S1 (S2). Brillouin scattering experiment
data[72] and calculations based on experimental and theoretical relaxed
geometries are plotted as dashed, solid and dotted lines, respectively. 93
Fig. 3.7 TO1 mode of cubic PbTiO3 with frequency 215i cm-1. The direction of wave vector
q is pointed out on the right-hand side of the plot. 97
Fig. 3.8 LO3 mode of cubic PbTiO3 with frequency 600.9 cm-1. The direction of wave
vector q is pointed out on the right-hand side of the plot. 97
Fig. 3.9 TO2 mode of cubic PbTiO3 with frequency 63.0 cm-1. The direction of wave vector
q is pointed out on the right-hand side of the plot. 98
Fig. 3.10 LO1 mode of cubic PbTiO3 with frequency 62.7 cm-1. The direction of wave
vector q is pointed out on the right-hand side of the plot. 98
Fig. 3.11 TO3 mode of cubic PbTiO3 with frequency 442.5 cm-1. The direction of wave
vector q is pointed out on the right-hand side of the plot. 99
Fig. 3.12 LO2 mode of cubic PbTiO3 with frequency 414.1 cm-1. The direction of wave
vector q is pointed out on the right-hand side of the plot. 99
Fig. 3.13 TO1 mode of tetragonal PbTiO3 with frequency 145.8 cm-1. The direction of wave
vector q is pointed out on the right-hand side of the plot. 100
Fig. 3.14 LO1 mode of tetragonal PbTiO3 with frequency 188.7 cm-1. The direction of wave
vector q is pointed out on the right-hand side of the plot. 100
Fig. 3.15 TO2 mode of tetragonal PbTiO3 with frequency 360.2 cm-1. The direction of wave
vector q is pointed out on the right-hand side of the plot. 101
Fig. 3.16 LO2 mode of tetragonal PbTiO3 with frequency 443.2 cm-1. The direction of wave
vector q is pointed out on the right-hand side of the plot. 101
Fig. 3.17 TO3 mode of tetragonal PbTiO3 with frequency 646.4 cm-1. The direction of wave
vector q is pointed out on the right-hand side of the plot. 102
Fig. 3.18 LO3 mode of tetragonal PbTiO3 with frequency 784.8 cm-1. The direction of wave
vector q is pointed out on the right-hand side of the plot. 102
Fig. 3.19 Difference between square of A1(3LO) and A1(3TO) phonon frequencies for
tetragonal Pb1-xCaxTiO3 from Raman experiment[68]. 103
Fig. 3.20 Eigendisplacement of the softest mode in cubic Pb0.5Ca0.5TiO3. 106

1. A Modern Approach to Quantum Mechanics, John S. Townsend, chapter 14, University Science Books (2000)
2. Zur Quantentheorie der Molekeln (On the Quantum Theory of Molecules), M. Born and R. Oppenheimer, Ann. d. Physik 84, 457 (1927)
3. Resonant Raman scattering by charge-density and single-particle excitations in semiconductor nanostructures: A generalized interband-resonant random-phase-approximation theory, Daw-Wei Wang and S. Das Sarma, Phys. Rev. B 65, 125322 (2002).
4. Quantum Many-Particle Systems, John. W. Negele and Henri Orland, chapter 5, Westview Press (2001)
5. Quantum Theory of Many-Particle Systems, Alexander L. Fetter and John Dirk Walecka, chapter 5, Dover Publications (2003)
6. A Guide to Feynman Diagrams in the Many-Body Problem, Richard D. Mattuck, Dover Publications (1992)
7. Advanced Solid State Physics, Philip Phillips and Phil Phillips, chapter 4, Westview Press (2002)
8. New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem, Lars Hedin, Phys. Rev. 139, A796 (1965)
9. First-Principles Theory of Quasiparticles: Calculation of Band Gaps in Semiconductors and Insulators, Mark S. Hybertsen and Steven G. Louie, Phys. Rev. Lett. 55, 1418 (1985); Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies, Mark S. Hybertsen and Steven G. Louie, Phys. Rev. B 34, 5390 (1986)
10. Accurate Exchange-Correlation Potential for Silicon and Its Discontinuity on Addition of an Electron, R. W. Godby, M. Schlüter, and L. J. Sham, Phys. Rev. Lett. 56, 2415 (1986); Self-energy operators and exchange-correlation potentials in semiconductors, R. W. Godby, M. Schlüter, and L. J. Sham, Phys. Rev. B 37, 10159 (1988)
11. Metal-insulator transition in Kohn-Sham theory and quasiparticle theory, R. W. Godby and R. J. Needs, Phys. Rev. Lett. 62, 1169 (1989)
12. First-principles calculations of many-body band-gap narrowing at an Al/GaAs(110) interface, J. P. A. Charlesworth, R. W. Godby, and R. J. Needs, Phys. Rev. Lett. 70, 1685 (1993)
13. Quasiparticle energies in small metal clusters, Susumu Saito, S. B. Zhang, Steven G. Louie, and Marvin L. Cohen, Phys. Rev. B 40, 3643 (1989)
14. Inhomogeneous Electron Gas, P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964)
15. Self-Consistent Equations Including Exchange and Correlation Effects, W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965)
16. Generalized gradient approximation for the exchange-correlation hole of a many-electron system, John P. Perdew, Kieron Burke, and Yue Wang, Phys. Rev. B 54, 16533 (1996); Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation, John P. Perdew, J. A. Chevary, S. H. Vosko, Koblar A. Jackson, Mark R. Pederson, D. J. Singh, and Carlos Fiolhais, Phys. Rev. B 46, 6671 (1992)
17. Generalized Gradient Approximation Made Simple, John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)
18. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients, M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Rev. Mod. Phys. 64, 1045 (1992)
19. Solid State Physics, Neil W. Ashcroft and N. David Mermin, chapter 8, Brooks Cole (1976)
20. Density-Functional Theory for Time-Dependent Systems, Erich Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984).
21. Excitation Energies from Time-Dependent Density-Functional Theory, M. Petersilka, U. J. Gossmann, and E. K. U. Gross, Phys. Rev. Lett. 76, 1212 (1996)
22. TIME-DEPENDENT DENSITY FUNCTIONAL THEORY, M.A.L. Marques and E.K.U. Gross, Annu. Rev. Phys. Chem. 55, 427 (2004).
23. Electronic excitations: density-functional versus many-body Green’s-function approaches, Giovanni Onida, Lucia Reining, Angel Rubio, Rev. Mod. Phys. 74, 601 (2002)
24. Many-Body Diagrammatic Expansion in a Kohn-Sham Basis: Implications for Time-Dependent Density Functional Theory of Excited States, I. V. Tokatly and O. Pankratov, Phys. Rev. Lett. 86, 2078 (2001)
25. Many-body diagrammatic expansion for the exchange-correlation kernel in time-dependent density functional theory, I. V. Tokatly, R. Stubner, and O. Pankratov, Phys. Rev. B 65, 113107 (2002)
26. Exchange-correlation kernel in time-dependent density functional theory, F. Aryasetiawan and O. Gunnarsson, Phys. Rev. B 66, 165119 (2002)
27. Ab initio calculation of the exchange-correlation kernel in extended systems, Gianni Adragna, Rodolfo Del Sole, and Andrea Marini, Phys. Rev. B 68, 165108 (2003)
28. Excitonic effects in time-dependent density-functional theory:   An analytically solvable model, R. Stubner, I. V. Tokatly, and O. Pankratov, Phys. Rev. B 70, 245119 (2004)
29. Ab initio calculation of phonon dispersions in semiconductors, Paolo Giannozzi, Stefano de Gironcoli, Pasquale Pavone, and Stefano Baroni, Phys. Rev. B 43, 7231 (1991)
30. Phonons and related crystal properties from density-functional perturbation theory, Stefano Baroni, Stefano de Gironcoli, Andrea Dal Corso, and Paolo Giannozzi, Rev. Mod. Phys. 73, 515 (2001)
31. Non-Resonant Inelastic X-Ray Scattering and Energy-Resolved Wannier Function Investigation of d-d Excitations in NiO and CoO, B. C. Larson, J. Z. Tischler, Wei Ku, Chi-Cheng Lee, O. D. Restrepo, A. G. Eguiluz, P. Zschack, and K. D. Finkelstein, accepted in Phys. Rev. Lett. (2007)
32. Magnitude and Origin of the Band Gap in NiO, G. A. Sawatzky and J. W. Allen, Phys. Rev. Lett. 53, 2339 (1984)
33. Quasiparticle energy bands of NiO in the GW approximation, Je-Luen Li, G.-M. Rignanese, and Steven G. Louie, Phys. Rev. B 71, 193102 (2005) 
34. Electronic Structure of NiO in the GW Approximation, F. Aryasetiawan and O. Gunnarsson, Phys. Rev. Lett. 74, 3221 (1995)


35. Quasiparticle energy bands of transition-metal oxides within a model GW scheme, S. Massidda, A. Continenza, M. Posternak, and A. Baldereschi, Phys. Rev. B 55, 13494 (1997)
36. Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators, A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Phys. Rev. B 52, R5467 (1995)
37. Density-functional theory and NiO photoemission spectra, V. I. Anisimov, I. V. Solovyev, M. A. Korotin, M. T. Czyżyk, and G. A. Sawatzky, Phys. Rev. B 48, 16929 (1993)
38. First-principles calculation of NiO valence spectra in the impurity-Anderson-model approximation, Vladimir I. Anisimov, Pieter Kuiper, and Joseph Nordgren, Phys. Rev. B 50, 8257 (1994).
39. Ab Initio Calculations of the Quasiparticle and Absorption Spectra of Clusters: The Sodium Tetramer, Giovanni Onida, Lucia Reining, R. W. Godby, R. Del Sole, and Wanda Andreoni, Phys. Rev. Lett. 75, 818 (1995). 
40. Ab initio calculation of the quasiparticle spectrum and excitonic effects in Li2O, Stefan Albrecht, Giovanni Onida, and Lucia Reining, Phys. Rev. B 55, 10278 (1997). 
41. Ab Initio Calculation of Excitonic Effects in the Optical Spectra of Semiconductors, Stefan Albrecht, Lucia Reining, Rodolfo Del Sole, and Giovanni Onida, Phys. Rev. Lett. 80, 4510 (1998). 
42. Optical Absorption of Insulators and the Electron-Hole Interaction: An Ab Initio Calculation, Lorin X. Benedict, Eric L. Shirley, and Robert B. Bohn, Phys. Rev. Lett. 80, 4514 (1998). 
43. Electron-Hole Excitations in Semiconductors and Insulators, Michael Rohlfing and Steven G. Louie, Phys. Rev. Lett. 81, 2312 (1998); Electron-hole excitations and optical spectra from first principles, Michael Rohlfing and Steven G. Louie, Phys. Rev. B 62, 4927 (2000). 
44. Magnetic ordering and exchange effects in the antiferromagnetic solid solutions MnxNi1-xO, A. K. Cheetham and D. A. O. Hope, Phys. Rev. B 27, 6964 (1983)

45. First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+ U method, Vladimir I Anisimov, F Aryasetiawan, and A I Lichtenstein, J. Phys.: Condens. Matter 9, 767 (1997) 
46. Self-interaction correction to density-functional approximations for many-electron systems, J. P. Perdew and Alex Zunger, Phys. Rev. B 23, 5048 (1981)
47. Density-functional calculation of effective Coulomb interactions in metals, V. I. Anisimov and O. Gunnarsson, Phys. Rev. B 43, 7570 (1991)
48. 2p x-ray absorption of 3d transition-metal compounds: An atomic multiplet description including the crystal field, F. M. F. de Groot, J. C. Fuggle, B. T. Thole, and G. A. Sawatzky, Phys. Rev. B 42, 5459 (1990)
49. Band theory and Mott insulators: Hubbard U instead of Stoner I, Vladimir I. Anisimov, Jan Zaanen, and Ole K. Andersen, Phys. Rev. B 44, 943 (1991)
50. Wien2k package (all-electron with linearized augmented plane wave basis), http://www.wien2k.at/
51. Insulating Ferromagnetism in La4Ba2Cu2O10: An Ab Initio Wannier Function Analysis, Wei Ku, H. Rosner, W. E. Pickett, and R. T. Scalettar, Phys. Rev. Lett. 89, 167204 (2002)
52. d-d Excitations in Manganites Probed by Resonant Inelastic X-Ray Scattering, S. Grenier, J. P. Hill, V. Kiryukhin, W. Ku, Y.-J. Kim, K. J. Thomas, S-W. Cheong, Y. Tokura, Y. Tomioka, D. Casa, and T. Gog, Phys. Rev. Lett. 94, 047203 (2005)
53. Coexistence of Gapless Excitations and Commensurate Charge-Density Wave in the 2H Transition Metal Dichalcogenides, Ryan L. Barnett, Anatoli Polkovnikov, Eugene Demler, Wei-Guo Yin, and Wei Ku, Phys. Rev. Lett. 96, 026406 (2006)
54. Maximally localized generalized Wannier functions for composite energy bands, Nicola Marzari and David Vanderbilt, Phys. Rev. B 56, 12847 (1997)
55. Maximally localized Wannier functions for entangled energy bands, Ivo Souza, Nicola Marzari, and David Vanderbilt, Phys. Rev. B 65, 035109 (2001)
56. Ab initio transport properties of nanostructures from maximally localized Wannier functions, Arrigo Calzolari, Nicola Marzari, Ivo Souza, and Marco Buongiorno Nardelli, Phys. Rev. B 69, 035108 (2004)
57. Electron density distribution in paramagnetic and antiferromagnetic NiO:  A  -ray diffraction study, W. Jauch and M. Reehuis, Phys. Rev. B 70, 195121 (2004)
58. Principles and Applications of Ferroelectrics and Related Materials, M. E. Lines and A. M. Glass, Clarendon Press, Oxford (1977)
59. Observation of coupled magnetic and electric domains, M. Fiebig, Th. Lottermoser, D. Fröhlich, A. V. Goltsev and R. V. Pisarev, Nature 419, 818 (2002)
60. Origin of ferroelectricity in perovskite oxides, Ronald E. Cohen, Nature 358, 136 (1992)
61. Ferroelectricity of Perovskites under Pressure, Igor A. Kornev, L. Bellaiche, P. Bouvier, P.-E. Janolin, B. Dkhil, and J. Kreisel, Phys. Rev. Lett. 95, 196804 (2005)
62. Raman Studies of Underdamped Soft Modes in PbTiO3, Gerald Burns and B. A. Scott, Phys. Rev. Lett. 25, 167 (1970)
63. Effect of pressure on the zone-center phonons of PbTiO3 and on the ferroelectric-paraelectric phase transition, F. Cerdeira, W. B. Holzapfel, and D. Bäuerle, Phys. Rev. B 11, 1188 (1975)
64. High-pressure Raman study of zone-center phonons in PbTiO3, J. A. Sanjurjo, E. López-Cruz, and Gerald Burns, Phys. Rev. B 28, 7260 (1983)
65. Pressure dependence of optical absorption in PbTiO3 to 35 GPa: Observation of the tetragonal-to-cubic phase transition, C. S. Zha, A. G. Kalinichev, J. D. Bass, C. T. A. Suchicital, and D. A. Payne, J. Appl. Phys. 72, 3705 (1992)
66. Pressure-Induced Anomalous Phase Transitions and Colossal Enhancement of Piezoelectricity in PbTiO3, Zhigang Wu and Ronald E. Cohen, Phys. Rev. Lett. 95, 037601 (2005)
67. Effect of the Ca content on the electronic structure of Pb1–xCaxTiO3 perovskites, J. C. Jan, K. P. Krishna Kumar, J. W. Chiou, H. M. Tsai, H. L. Shih, H. C. Hsueh, S. C. Ray, K. Asokan, W. F. Pong, M.-H. Tsai, S. Y. Kuo, and W. F. Hsieh, Appl. Phys. Lett. 83, 3311 (2003)
68. Lattice dynamics of perovskite PbxCa1–xTiO3, Shou-Yi Kuo, Chung-Ting Li, and Wen-Feng Hsieh, Phys. Rev. B 69, 184104 (2004)

69. X-ray and optical studies on phase transition of PbTiO3 at low temperatures, J. Kobayashi, Y. Uesu, and Y. Sakemi, Phys. Rev. B 28, 3866 (1983)
70. First-principles study of stability and vibrational properties of tetragonal PbTiO3, Alberto García and David Vanderbilt, Phys. Rev. B 54, 3817 (1996)
71. Lattice dynamics of ferroelectric PbTiO3 by inelastic neutron scattering, J. Hlinka, M. Kempa, J. Kulda, P. Bourges, A. Kania, and J. Petzelt, Phys. Rev. B 73, 140101(R) (2006)
72. Elastic properties of tetragonal PbTiO3 single crystals by Brillouin scattering, A. G. Kalinichev, J. D. Bass, B. N. Sun, and D. A. Payne, J. Mater. Res. 12, 2623 (1997)
73. Giant LO-TO splittings in perovskite ferroelectrics, W. Zhong, R. D. King-Smith, and David Vanderbilt, Phys. Rev. Lett. 72, 3618 (1994)
74. Dielectric tensor, effective charges, and phonons in α-quartz by variational density-functional perturbation theory, Xavier Gonze, Douglas C. Allan, and Michael P. Teter, Phys. Rev. Lett. 68, 3603 (1992)
75. Phonons and related crystal properties from density-functional perturbation theory, Stefano Baroni, Stefano de Gironcoli, Andrea Dal Corso, and Paolo Giannozzi, Rev. Mod. Phys. 73, 515 (2001)
76. First-principles computation of material properties: the ABINIT software project, X. Gonze, J.-M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.-M. Rignanese, L. Sindic, M. Verstraete, G. Zerah, F. Jollet, M. Torrent, A. Roy, M. Mikami, Ph. Ghosez, J.-Y. Raty, and D. C. Allan, Comput. Mater. Sci. 25, 478 (2002)
77. Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory, M. Fuchs and M. Scheffler, Comput. Phys. Commun. 119, 67 (1999)
78. First-principles responses of solids to atomic displacements and homogeneous electric fields: Implementation of a conjugate-gradient algorithm, Xavier Gonze, Phys. Rev. B 55, 10337 (1997)


79. Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory, Xavier Gonze and Changyol Lee, Phys. Rev. B 55, 10355 (1997)
80. Ab initio statistical mechanics of the ferroelectric phase transition in PbTiO3, U. V. Waghmare and K. M. Rabe, Phys. Rev. B 55, 6161 (1997)
81. First-principles study of barium titanate under hydrostatic pressure, Eric Bousquet and Philippe Ghosez, Phys. Rev. B 74, 180101(R) (2006)
82. First-Principles Study of Piezoelectricity in PbTiO3, Gotthard Sághi-Szabó, Ronald E. Cohen, and Henry Krakauer, Phys. Rev. Lett. 80, 4321 (1998)
83. Lattice dynamics of tetragonal PbTiO3, Izumi Tomeno, Yoshinobu Ishii, Yorihiko Tsunoda, and Kunihiko Oka, Phys. Rev. B 73, 064116 (2006)
84. Soft Ferroelectric Modes in Lead Titanate, G. Shirane, J. D. Axe, J. Harada, and J. P. Remeika, Phys. Rev. B 2, 155 (1970)
85. Anharmonicity of the lowest-frequency A1(TO) phonon in PbTiO3, C. M. Foster, Z. Li, M. Grimsditch, S.-K. Chan, and D. J. Lam, Phys. Rev. B 48, 10160 (1993)
86. Lattice dynamics of BaTiO3, PbTiO3, and PbZrO3: A comparative first-principles study, Ph. Ghosez, E. Cockayne, U. V. Waghmare, and K. M. Rabe, Phys. Rev. B 60, 836 (1999)
87. Phonons and static dielectric constant in CaTiO3 from first principles, Eric Cockayne and Benjamin P. Burton, Phys. Rev. B 62, 3735 (2000)
88. Ab initio studies of phonons in CaTiO3, K. Parlinski, Y. Kawazoe, and Y. Waseda, J. Chem. Phys. 114, 2395 (2001)
89. Phonon Stability and LO-TO Splitting in Tetragonal PbTiO3 and Related Mixing Material, Chi-Cheng Lee, W. F. Pong, and H. C. Hsueh, submitted to Phys. Rev. B (2007)