## 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 | 53 |

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 Pt111 system | 325 |

Conclusion | 354 |

364 | |

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### Common terms and phrases

2DBSM adatoms adsorbate algorithm alloy applications approach approximation assume atoms band band gap basis binding bond calculations clusters compared computational configuration constant coordination corrections corresponding crystal defined density dependent deposited described determine dielectric diffusion direction discussed effects electron elements energy equation example exchange experimental Figure finite first-principles formation function geometry give given ground growth Hamiltonian interactions islands lattice layer Lett lower materials matrix measured metals method meV/atom neighbor Note obtained operator orbitals orthogonal pair parallel parameters performed periodic phase Phys Physics position potential predicted principle problem processor properties quantum mechanical quasiparticle representation respectively scaling semiconductors shown shows similar simulations solid solution space stability step structure substrate surface Table temperature theory tight-binding total energy unit cell vacancy values variational vector wave