## Topics in Computational Materials ScienceThis book describes the state-of-the-art research topics in theoretical materials science. It encompasses the computational methods and techniques which can advance more realistic calculations for understanding the physical principles in new growth methods of optoelectronic materials and related surface problems. These principles also govern the photonic, electronic, and structural properties of materials which are essential for device applications. They will also provide the crucial ingredients for the growth of future novel materials. |

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### Contents

Advances in Algorithmic Development in | 1 |

Linear scaling algorithms | 37 |

Summary | 52 |

Acknowledgments | 54 |

Plane Wave Pseudopotential Electronic Structure | 61 |

Evaluation of HY | 68 |

Benchmark timings | 82 |

Illustrative fortran subroutines | 88 |

Examples of the method | 191 |

Summary | 207 |

First Principles Studies of Stability | 214 |

Calculating the cluster expansion interaction energy | 227 |

Lowtemperature longrange order | 236 |

Stability of superlattices and other complex structures | 244 |

Conclusion | 256 |

Simulation of Semiconductor Growth Mechanisms | 263 |

FirstPrinciples Theory of Electron Excitation | 96 |

Some illustrative results | 110 |

A Mixedspace imaginary time formulation | 134 |

Photonic Band Structure | 143 |

Transfer matrix method TMM | 156 |

Finite difference time domain FDTD method | 162 |

TightBinding Parametrization of FirstPrinciples | 169 |

SlaterKoster parametrization of band structures | 175 |

SlaterKoster method for compounds | 181 |

Quantum mechanical calculations | 270 |

Kinetic Monte Carlo simulations | 287 |

Discussion and conclusions | 296 |

a Lattice Gas Approach | 306 |

Application of the BSM to the Pt 111 system | 325 |

Conclusion | 354 |

364 | |

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### Common terms and phrases

2DBSM 3DBSM activation energy adatoms adsorbate Ag-Au algorithm alloy approach approximation band gap band structure binding energies bond strength Brillouin zone calculations cluster expansion clusters computational configurations crystal density functional density functional theory density matrix determine dielectric diffusion discussed electron density electronic structure energy difference enthalpy equation exchange-correlation experimental Figure finite first-principles geometry Green's function Green's-function grid group-V growth Hamiltonian interactions Kohn-Sham lattice layer Lett matrix elements metals method meV/atom monovacancies nearest neighbor newly deposited atoms non-orthogonal obtained operator orbitals orthogonal parameters Pd-Pt phase photoemission photonic band Phys potential predicted processor pseudopotential quasiparticle quasiparticle energies real-space Rh-Pt S. G. Louie self-energy semiconductors shown in Fig simulations Slater-Koster solid stability step energies subspace superlattices surface surfactant temperature terraces theory tight-binding total energy trimer unit cell vacancy valence vector space wavefunction Zunger