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This book is organized into nine chapters, starting with Chapter 1, which gives a general overview of computational science. Chapter 2 introduces MD methods based on classical mechanics: Its implementation into actual calculations follows in Chapter 3 with run examples of XMD and LAMMPS, respectively. Chapter 4 introduces first-principles methods based on quantum mechanics on a brief introductory level. Here, various illustrations and appropriate analogies will be presented to assist students to understand this tough subject. Chapter 5 is dedicated solely to the density functional theory (DFT) in detail, because this is the very first-principles method that can handle materials practically. Chapter 6 exclusively deals with solids and reveals how bulk materials can be represented with a handful of k-points. The chapter also provides how each orbital of electron leads to particular properties of solids such as total energy, band structure, and band gap. Finally, Chapters 7 through 9 implement the DFT into actual calculations with various codes such as Quantum Espresso, VASP, and MedeA-VASP, respectively. They cover from an atom to solids, and from simple GGA to GGA+U and hybrid methods. Chapter 9 specifically deals with advanced topics in DFT counting dispersion, +U, DFT with hybrid XC potentials, and ab initio MD by using a convenient GUI program, MedeA-VASP. Note that methods once considered as “too expensive” are now practical enough to treat materials, owing to the ever-increasing power of computers. Various postprocessing programs such as VESTA, VMD, and VTST will be exercised through the runs.

Preface ...............................................................................................................xix Author ............................................................................................................ xxiii Chapter 1 Introduction .................................................................................. 1 1.1 Computational materials science .......................................................... 1 1.1.1 Human beings versus matter ................................................... 1 1.1.2 Computational materials science ............................................ 3 1.1.2.1 Goals ........................................................................... 3 1.1.2.2 Our approach............................................................. 3 1.2 Methods in computational materials science ...................................... 4 1.2.1 Basic procedures of computational materials science .......... 5 1.2.2 Finite element analysis .............................................................. 5 1.2.3 Monte Carlo method ................................................................. 6 1.2.4 Molecular dynamics .................................................................. 7 1.2.5 First-principles methods (ab initio methods) .......................... 7 1.2.6 Remarks ...................................................................................... 7 1.3 Computers ................................................................................................ 8 Reference ............................................................................................................. 9 Chapter 2 Molecular dynamics ................................................................. 11 2.1 Introduction ............................................................................................ 12 2.1.1 Atomic model in MD............................................................... 12 2.1.2 Classical mechanics ................................................................. 13 2.1.3 Molecular dynamics ................................................................ 14 2.2 Potentials ................................................................................................. 15 2.2.1 Pair potentials .......................................................................... 17 2.2.2 Embedded atom method potentials ...................................... 19 2.2.3 Tersoff potential ....................................................................... 22 2.2.4 Potentials for ionic solids ........................................................ 23 2.2.5 Reactive force field potentials ................................................ 24 2.3 Solutions for Newton’s equations of motion ...................................... 24 2.3.1 N-atom system.......................................................................... 24 2.3.2 Verlet algorithm ....................................................................... 26 2.3.3 Velocity Verlet algorithm ........................................................ 27 2.3.4 Predictor–corrector algorithm ............................................... 27 2.4 Initialization ........................................................................................... 29 2.4.1 Pre-setups ................................................................................. 29 2.4.1.1 Potential cutoff ........................................................ 29 2.4.1.2 Periodic boundary conditions ............................... 31 2.4.1.3 Neighbor lists .......................................................... 32 2.4.2 Initialization ............................................................................. 32 2.4.2.1 Number of atoms (system size) ............................. 33 2.4.2.2 Initial positions and velocities .............................. 33 2.4.2.3 Timestep ................................................................... 33 2.4.2.4 Total simulation time ............................................. 34 2.4.2.5 Type of ensemble .................................................... 34 2.5 Integration/equilibration ...................................................................... 36 2.5.1 Temperature and pressure control ........................................ 36 2.5.2 Minimization in a static MD run .......................................... 37 2.5.2.1 Steepest-descent method ....................................... 37 2.5.2.2 Conjugate gradients method ................................. 38 2.6 Data production ..................................................................................... 38 2.6.1 Run analysis ............................................................................. 38 2.6.1.1 Conservation of energy .......................................... 38 2.6.1.2 Confirmation of global minimum ........................ 39 2.6.1.3 Time averages under the ergodic hypothesis ..... 39 2.6.1.4 Errors ........................................................................ 40 2.6.2 Energies .................................................................................... 40 2.6.3 Structural properties ............................................................... 41 2.6.3.1 Equilibrium lattice constant, cohesive energy .... 41 2.6.3.2 Bulk modulus .......................................................... 41 2.6.3.3 Thermal expansion coefficient .............................. 42 2.6.3.4 Radial distribution function .................................. 42 2.6.4 Mean-square displacement .................................................... 43 2.6.5 Energetics, thermodynamic properties, and others ........... 44 Homework ........................................................................................................ 44 References .......................................................................................................... 45 Further reading ................................................................................................. 46 Chapter 3 MD exercises with XMD and LAMMPS ............................. 47 3.1 Potential curve of Al .............................................................................. 47 3.1.1 Input files .................................................................................. 48 3.1.1.1 Run file ..................................................................... 48 3.1.1.2 Potential file ............................................................. 49 3.1.2 Run ........................................................................................ 50 3.1.3 Results ................................................................................... 50 3.1.3.1 Potential energy curve ....................................... 51 3.2 Melting of Ni cluster ............................................................................ 52 3.2.1 Run file ................................................................................. 52 3.2.2 Results ................................................................................... 53 3.2.2.1 Visualization with MDL ChimeSP6 ................. 54 3.3 Sintering of Ni nanoparticles ............................................................. 55 3.3.1 Input file ............................................................................... 55 3.3.2 Results ................................................................................... 57 3.4 Speed distribution of Ar gas: A computer experiment .................. 58 3.4.1 Input file ............................................................................... 60 3.4.2 Results ................................................................................... 61 3.5 SiC deposition on Si(001) ..................................................................... 62 3.5.1 Input file ............................................................................... 62 3.5.2 Results ................................................................................... 65 3.6 Yield mechanism of an Au nanowire ............................................... 66 3.6.1 Input file ............................................................................... 67 3.6.2 Results ................................................................................... 68 3.6.2.1 Snapshots ............................................................. 68 3.6.3 Conclusions .......................................................................... 69 3.7 Nanodroplet of water wrapped by a graphene nanoribbon ......... 69 3.7.1 Input files .............................................................................. 69 3.7.1.1 Positions file (data.C–H2O) ................................ 70 3.7.1.2 Input file .............................................................. 71 3.7.2 Results ................................................................................... 72 3.7.3 Conclusions .......................................................................... 73 3.8 Carbon nanotube tension ................................................................... 74 3.8.1 Introduction ......................................................................... 74 3.8.2 Input file ............................................................................... 75 3.8.3 readdata.CNT ....................................................................... 76 3.8.4 CH.old.airebo ....................................................................... 77 3.8.5 Results ................................................................................... 78 3.9 Si-tension ............................................................................................... 79 3.9.1 Introduction ......................................................................... 79 3.9.2 Input file ............................................................................... 79 3.9.3 Results ................................................................................... 82 3.10 Si–CNT composite under tension ...................................................... 83 3.10.1 Introduction ......................................................................... 83 3.10.2 Potentials .............................................................................. 85 3.10.3 Input files .............................................................................. 85 3.10.4 Run ........................................................................................ 89 3.10.5 Results .................................................................................. 89 3.10.6 Conclusions .......................................................................... 90 3.11 ZrO2-Y2O3-MSD .................................................................................... 91 3.11.1 Introduction .......................................................................... 91 3.11.2 Input files .............................................................................. 92 3.11.3 Run ........................................................................................ 94 3.11.4 Results ................................................................................... 94 Homework ........................................................................................................ 95 References .......................................................................................................... 96 Chapter 4 First-principles methods .......................................................... 99 4.1 Quantum mechanics: The beginning ............................................. 100 4.1.1 Niels Bohr and the quantum nature of electrons .......... 101 4.1.2 De Broglie and the dual nature of electrons .................. 103 4.1.3 Schrödinger and the wave equation ............................... 104 4.1.4 Heisenberg and the uncertain nature of electrons ........ 105 4.1.5 Remarks............................................................................... 106 4.2 Schrödinger wave equation .............................................................. 107 4.2.1 Simplifying the problem ................................................... 107 4.2.1.1 Forget about gravity, relativity, and time ...... 107 4.2.1.2 Forget about nuclei and spin ........................... 108 4.2.1.3 Forget about the excited states ........................ 109 4.2.1.4 Use of atomic units ........................................... 109 4.2.2 Time-independent electronic wave equation ................ 109 4.2.3 Energy operator: Hamiltonian H  .....................................110 4.2.4 Waves and wave function ................................................. 112 4.2.4.1 Plane wave ..........................................................113 4.2.4.2 Standing wave ....................................................114 4.2.4.3 Superposition principle of waves ....................114 4.2.4.4 Indistinguishability of electrons .....................115 4.2.5 Energy E ...............................................................................115 4.2.6 Solutions of Schrödinger wave equation: An electron in a well .................................................................116 4.2.6.1 An electron in a one-dimensional infinite well ......................................................................116 4.2.6.2 An electron in a one-dimensional well with a finite potential ........................................119 4.2.6.3 Hydrogen atom ..................................................119 4.2.6.4 Degenerate states .............................................. 120 4.3 Early first-principles calculations .................................................... 120 4.3.1 n-electron problem ............................................................ 120 4.3.2 Hartree method: One-electron model ............................ 121 4.3.3 Hartree–Fock method ....................................................... 122 4.3.3.1 Expression for Ψ(r) ........................................... 122 4.3.3.2 Orthonormality of wave functions ................ 123 4.3.3.3 Expression for E ................................................ 124 4.3.3.4 Calculation for E ................................................... 126 4.3.3.5 Variational approach to the search for the ground-state energy ............................................. 127 4.3.3.6 Self-consistent procedure..................................... 127 4.3.3.7 Remarks .................................................................. 128 Homework ...................................................................................................... 128 References ........................................................................................................ 129 Further reading ............................................................................................... 129 Chapter 5 Density functional theory ..................................................... 131 5.1 Introduction .......................................................................................... 132 5.1.1 Electron density ..................................................................... 133 5.1.1.1 Electron density in DFT ....................................... 135 5.1.2 Hohenberg–Kohn theorems ................................................. 135 5.1.2.1 Electron density as central player....................... 135 5.1.2.2 Search for the ground-state energy .................... 136 5.2 Kohn–Sham approach ......................................................................... 138 5.2.1 One-electron representations............................................... 138 5.2.2 One-electron system replacing n-electron system ............ 139 5.3 Kohn–Sham equations ........................................................................ 140 5.3.1 Energy terms ...........................................................................141 5.3.1.1 Kinetic energy ........................................................141 5.3.1.2 External energy ..................................................... 142 5.3.1.3 Hartree energy ...................................................... 142 5.3.1.4 Exchange-correlation energy .............................. 143 5.3.1.5 Magnitudes of each energy term ........................ 144 5.3.2 Functional derivatives ........................................................... 145 5.3.3 Kohn–Sham equations .......................................................... 147 5.3.3.1 KS orbitals .............................................................. 148 5.3.3.2 KS eigenvalues....................................................... 149 5.4 Exchange-correlation functionals ..................................................... 149 5.4.1 Exchange-correlation hole .................................................... 150 5.4.1.1 Exchange hole ........................................................ 151 5.4.1.2 Correlation hole ..................................................... 152 5.4.1.3 Exchange-correlation hole ................................... 152 5.4.2 Local density approximation ............................................... 153 5.4.2.1 Homogeneous electron gas ................................. 154 5.4.2.2 Exchange energy ................................................... 154 5.4.2.3 Correlation energy ................................................ 154 5.4.2.4 XC energy ............................................................... 155 5.4.2.5 Remarks .................................................................. 156 5.4.3 Generalized gradient approximation ................................. 156 5.4.3.1 PW91 ....................................................................... 158 5.4.3.2 PBE .......................................................................... 158 5.4.4 Other XC functionals ............................................................ 159 5.4.5 Remarks .................................................................................. 160 5.4.5.1 General trends of GGA ........................................ 160 5.4.5.2 Limitations of GGA: Strongly correlated systems ....................................................................161 5.4.5.3 Limitations of GGA: Band gap underestimation .....................................................161 5.5 Solving Kohn–Sham equations ..........................................................162 5.5.1 Introduction .............................................................................162 5.5.1.1 Self-consistency ......................................................162 5.5.1.2 Variational principle ............................................. 163 5.5.1.3 Constraints ............................................................. 163 5.5.2 Direct diagonalization .......................................................... 164 5.5.3 Iterative diagonalization ....................................................... 164 5.5.3.1 Total energy and other properties ...................... 165 5.6 DFT extensions and limitations ......................................................... 166 5.6.1 DFT extensions ....................................................................... 166 5.6.1.1 Spin-polarized DFT ...............................................167 5.6.1.2 DFT with fractional occupancies .........................167 5.6.1.3 DFT for excited states ............................................167 5.6.1.4 Finite-temperature DFT ....................................... 168 5.6.1.5 Time-dependent DFT ........................................... 168 5.6.1.6 Linear scaling of DFT ........................................... 169 5.6.2 DFT limitations ...................................................................... 169 Homework ...................................................................................................... 170 References ........................................................................................................ 171 Further reading ............................................................................................... 172 Chapter 6 Treating solids ......................................................................... 173 6.1 Pseudopotential approach ...................................................................174 6.1.1 Freezing the core electrons ................................................... 175 6.1.1.1 Core electrons ........................................................ 175 6.1.1.2 Valence electrons ................................................... 175 6.1.1.3 Frozen-core approximation ..................................176 6.1.2 Pseudizing the valence electrons .........................................176 6.1.2.1 Pseudizing procedure .......................................... 177 6.1.2.2 Benefits ................................................................... 178 6.1.3 Various pseudopotentials ..................................................... 179 6.1.3.1 Norm-conserving PPs .......................................... 179 6.1.3.2 Ultrasoft PPs .......................................................... 179 6.1.3.3 PAW potentials ...................................................... 180 6.2 Reducing the calculation size ............................................................ 181 6.2.1 Supercell approach under periodic boundary conditions ............................................................182 6.2.2 First Brillouin zone and irreducible Brillouin zone .......... 183 6.2.2.1 Reciprocal lattice ................................................... 183 6.2.2.2 The first Brillouin zone ........................................ 186 6.2.2.3 Irreducible Brillouin zone .................................... 186 6.2.3 k-points ................................................................................... 187 6.2.3.1 k-point sampling ................................................... 188 6.2.3.2 Monkhorst–Pack method ..................................... 189 6.2.3.3 Γ-point .................................................................... 189 6.3 Bloch theorem ...................................................................................... 189 6.3.1 Electrons in solid ................................................................... 190 6.3.2 Bloch expression with periodic function ........................... 190 6.3.3 Bloch expression with Fourier expansions ........................ 192 6.3.3.1 Fourier expansions ............................................... 192 6.3.3.2 Fast Fourier transformation ................................ 193 6.3.3.3 Matrix expression for the KS equations ............ 193 6.4 Plane wave expansions ....................................................................... 195 6.4.1 Basis set .................................................................................. 195 6.4.1.1 Local basis set ........................................................ 195 6.4.1.2 Plane wave basis set ............................................. 195 6.4.2 Plane wave expansions for KS quantities .......................... 196 6.4.2.1 Charge density ...................................................... 196 6.4.2.2 Kinetic energy ....................................................... 198 6.4.2.3 Effective potential ................................................. 198 6.4.2.4 KS equations .......................................................... 198 6.4.3 KS orbitals and bands ........................................................... 199 6.4.3.1 Band structure of free electron ........................... 200 6.4.3.2 Band structure of electrons in solids ................. 200 6.4.3.3 Density of states .................................................... 202 6.5 Some practical topics ........................................................................... 203 6.5.1 Energy cutoff .......................................................................... 203 6.5.1.1 Cutoff energy ......................................................... 203 6.5.2 Smearing ................................................................................. 204 6.5.2.1 Gaussian smearing ............................................... 205 6.5.2.2 Fermi smearing ..................................................... 205 6.5.2.3 Methfessel–Paxton smearing .............................. 205 6.5.2.4 Tetrahedron method with Blöchl corrections....... 206 6.6 Practical algorithms for DFT runs..................................................... 206 6.6.1 Electronic minimizations ..................................................... 206 6.6.1.1 Direct diagonalization ......................................... 207 6.6.1.2 Iterative Davidson method .................................. 207 6.6.1.3 RMM-DIIS method ............................................... 207 6.6.2 Ionic minimizations .............................................................. 209 6.6.2.1 Hellmann–Feynman forces ................................. 209 6.6.2.2 Minimization methods ........................................ 210 6.6.4 Car–Parrinello molecular dynamics ....................................211 6.6.4.1 CPMD for electronic minimization .....................211 6.6.4.2 CPMD for ionic minimization ............................ 212 6.6.5 Multiscale methods ............................................................... 213 6.6.5.1 Crack propagation in silicon ............................... 213 Homework .......................................................................................................214 References .........................................................................................................214 Further reading ............................................................................................... 215 Chapter 7 DFT exercises with Quantum Espresso ............................. 217 7.1 Quantum espresso ............................................................................... 217 7.1.1 General features ..................................................................... 217 7.1.2 Installation ............................................................................. 218 7.2 Si2 ........................................................................................................... 218 7.2.1 Introduction ............................................................................ 218 7.2.2 Si2.in ........................................................................................ 218 7.2.3 Si.pbe-rrkj.UPF ....................................................................... 220 7.2.4 Run .......................................................................................... 221 7.2.5 Si2.out ..................................................................................... 221 7.3 Si2-convergence test ............................................................................ 223 7.3.1 Introduction ............................................................................ 223 7.3.2 Si2-conE.in ............................................................................. 223 7.3.3 Results ..................................................................................... 223 7.3.4 Further runs ........................................................................... 224 7.4 Si2-band ................................................................................................. 227 7.4.1 Introduction ............................................................................ 227 7.4.2 Si2-scf ...................................................................................... 227 7.4.3 Si2-bands ................................................................................. 228 7.4.4 Results and discussion .......................................................... 229 7.5 Si7-vacancy ............................................................................................ 230 7.5.1 Introduction ............................................................................ 230 7.5.2 Si8-scf ...................................................................................... 231 7.5.3 Si7v-relax ................................................................................ 232 7.6 Si7-vacancy diffusion .......................................................................... 235 7.6.1 Introduction ............................................................................ 235 7.6.2 Calculation method ............................................................... 235 7.6.3 Step 1: First image .................................................................. 236 7.6.4 Step 2: Last image .................................................................. 236 7.6.5 Step 3: Si7v.NEB20.in ............................................................. 237 Homework ...................................................................................................... 241 References ........................................................................................................ 242 Chapter 8 DFT exercises with VASP ......................................................243 8.1 VASP ...................................................................................................... 245 8.1.1 General features of VASP ..................................................... 245 8.1.2 Flow of VASP .......................................................................... 245 8.1.2.1 Ten things you should not do in a VASP run ........ 246 8.2 Pt-atom .................................................................................................. 247 8.2.1 Input files ............................................................................. 247 8.2.1.1 INCAR .................................................................... 247 8.2.1.2 KPOINTS ................................................................ 248 8.2.1.3 POSCAR ................................................................. 248 8.2.1.4 POTCAR ................................................................. 249 8.2.2 Run .......................................................................................... 249 8.2.3 Results .................................................................................... 250 8.2.3.1 OSZICAR ................................................................ 250 8.2.3.2 OUTCAR ................................................................ 251 8.2.3.3 Continuous run ..................................................... 251 8.3 Pt-FCC .................................................................................................... 252 8.3.1 Input files ................................................................................ 252 8.3.1.1 INCAR .................................................................... 252 8.3.1.2 KPOINTS ................................................................ 254 8.3.1.3 POSCAR ................................................................. 254 8.3.2 Run .......................................................................................... 255 8.3.2.1 run.vasp .................................................................. 255 8.3.2.2 nohup.out ............................................................... 255 8.3.3 Results ..................................................................................... 256 8.3.3.1 CONTCAR ............................................................. 256 8.3.3.2 OUTCAR ................................................................ 257 8.4 Convergence tests ................................................................................ 257 8.4.1 Encut convergence ................................................................. 257 8.4.1.1 Shell script run.lattice........................................... 258 8.4.1.2 Run .......................................................................... 259 8.4.1.3 Results .................................................................... 259 8.4.2 k-points convergence ............................................................. 261 8.5 Pt-bulk ................................................................................................... 262 8.5.1 Cohesive energy of solid Pt .................................................. 262 8.5.1.1 Cohesive energy .................................................... 264 8.5.2 Vacancy formation energy of Pt .......................................... 265 8.5.2.1 Vacancy formation energy ................................... 265 8.5.2.2 CHGCAR plot ........................................................ 266 8.6 Pt(111)-surface ....................................................................................... 268 8.6.1 Pt(111)-slab .............................................................................. 268 8.6.1.1 INCAR .................................................................... 268 8.6.1.2 KPOINTS ................................................................ 269 8.6.1.3 POSCAR ............................................................... 269 8.6.1.4 Results ................................................................... 271 8.6.2 Adsorption energy ................................................................. 272 8.6.2.1 POSCAR ............................................................... 272 8.6.2.2 POTCAR ............................................................... 274 8.6.2.3 Results ................................................................... 274 8.6.3 Work function and dipole correction .................................. 275 8.6.3.1 Work function ...................................................... 275 8.6.3.2 Results ................................................................... 276 8.7 Nudged elastic band method ............................................................. 277 8.7.1 Principle of NEB method ...................................................... 278 8.7.2 Procedure of the NEB method ............................................. 278 8.7.2.1 Initial and final states ......................................... 278 8.7.2.2 Initial band ........................................................... 279 8.7.2.3 Nudging the band ............................................... 279 8.7.2.4 Force calculation .................................................. 279 8.7.2.5 NEB method with climb ..................................... 279 8.7.3 Pt(111)-O-NEB ........................................................................ 280 8.7.3.1 Pt(111)-slab-O-HCP ............................................. 280 8.7.3.2 Run NEB with VTST scripts .............................. 281 8.7.3.3 Results ................................................................... 282 8.8 Pt(111)-catalyst ..................................................................................... 284 8.8.1 Catalyst ................................................................................... 284 8.8.2 Density of states ..................................................................... 285 8.8.3 Pt(111)-slab-O-DOS ................................................................ 285 8.8.3.1 Static run............................................................... 285 8.8.3.2 DOS run ................................................................ 285 8.8.3.3 Results ................................................................... 286 8.9 Band structure of silicon ..................................................................... 287 8.9.1 Static run for Si ....................................................................... 288 8.9.2 Run for band structure of Si ................................................. 290 8.9.2.1 INCAR .................................................................. 290 8.9.2.2 KPOINTS .............................................................. 290 8.9.2.3 EIGENVAL ........................................................... 291 8.10 Phonon calculation for silicon............................................................ 293 8.10.1 Input files ................................................................................ 293 8.10.2 Phonon calculations .............................................................. 294 8.10.2.1 INPHON ............................................................... 295 Homework ...................................................................................................... 297 References ........................................................................................................ 297 Chapter 9 DFT exercises with MedeA-VASP .......................................299 9.1 MedeA-VASP ........................................................................................ 299 9.1.1 General features ..................................................................... 299 9.2 Si2-band-HSE06 .................................................................................... 300 9.2.1 Introduction ............................................................................ 300 9.2.2 Run steps ................................................................................ 301 9.2.3 Results ..................................................................................... 302 9.3 Si16-phonon .......................................................................................... 304 9.3.1 Introduction ............................................................................ 304 9.3.2 Ionic relaxation for supercell with displacements ............ 304 9.3.3 Results ..................................................................................... 304 9.4 W12C9-Co28-interface ......................................................................... 307 9.4.1 Introduction ............................................................................ 307 9.4.2 Surface models for WC and Co ............................................ 308 9.4.3 Interface model for WC–Co .................................................. 308 9.4.4 Results .................................................................................... 309 9.5 Mg4(Mo6S8)3-barrier energy .................................................................311 9.5.1 Introduction .............................................................................311 9.5.2 NEB run ...................................................................................314 9.5.3 Results ......................................................................................314 9.6 Si14-H2-ab initio MD .............................................................................314 9.6.1 Introduction .............................................................................314 9.6.2 Run steps ..................................................................................316 9.6.3 Results ..................................................................................... 317 References .........................................................................................................318 Appendix A: List of symbols and abbreviations ....................................... 319 Appendix B: Linux basic commands .......................................................... 323 Appendix C: Convenient scripts .................................................................. 325 Appendix D: The Greek alphabet ................................................................ 337 Appendix E: SI prefixes ................................................................................. 339 Appendix F: Atomic units ............................................................................. 341 Index ................................................................................................................ 343

June Gunn Lee is an emeritus research fellow at the Computational Science Center, Korea Institute of Science and Technology (KIST), Seoul, where he served for 28 years. He has also lectured at various universities in Korea for over 20 years. He has published about 70 papers both on engineering ceramics and computational materials science. Dr. Lee is a graduate of Hanyang University, Seoul, and acquired his PhD in materials science and engineering from the University of Utah. He has been involved in computational materials science ever since he was a visiting professor at Rutgers University, New Jersey, in 1993. Currently, he is lecturing at University of Seoul, Seoul.

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