Microscopic Modelling of Correlated Low-dimensional Systems

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Chapter 2: Method 27 g(ɛ) = 2 VBZ � � n δ(ɛ − ɛ n k )dk (2.44) The function g(ɛ) is called the Density of states DOS, which is the number of states per unit of energy. δ is the Dirac delta function, k is any vector in the first Brillouin zone that corresponds to a plane wave that is commensurate with the macroscopic crystal. VBZ is the volume of the first Brillouin zone, and the integral is over the first Brillouin zone. The factor 2 is included to account explicitly for (degenerate) spin.
Chapter 2: Method 28 2.3 An overview on classical ab initio and molecular dynamics Part of this work was developed as interdisciplinary projects between experimentalist and theoreticians from the chemistry and physics areas. Due to the complexity and diversity of the studied compounds, it was necessary in some cases, to develop a procedure which combine different approaches. This will be presented in Section 5.1. This procedure includes ab initio classical techniques and molecular dynamics relaxation. This section is dedicated to present the general ideas about these methods. 2.3.1 The DREIDING force field methods A force field is a mathematical function which returns the energy of a system as a function of the conformation of the system. The idea is to consider a molecule as a collection of atoms held together by elastic forces, these forces can be written in terms of potential energy functions of various structural features such as bond lengths, bond angle, non- bonded interactions and so on. The force field is a combination of these potential energy terms. Force field methods were developed with the philosophy of carrying out simulations for describing molecular structures and properties in an accurate way within a reasonable amount of computational time and applicable to a large variety of systems. Different force field methods have been developed, every one for specific materials, in this work we have used the simple generic DREIDING force field [80], which is useful for predicting structures and dynamics of organic, biological and main-group inorganic molecules. It writes the force field of a system based on simple hybridization considerations. It needs only 4 input parameters namely, the atom type (N, B, etc.), the hybridization or geometry (1=linear (sp 1 ), 2=trigonal (sp 2 ), 3=tetrahedral (sp 3 )), the oxidation state and the number of implicit hydrogens. Then, the force field is written as E = Eval + Enb (2.45) where Eval and Enb contains the valence interactions and the non-bonded interaction terms respectively. In DREIDING the valence interactions consist of Eval = EB + EA + ET + EI (2.46)
Page 1 and 2: Microscopic Modelling of Correlated
Page 3 and 4: I declare that I wrote this work my
Page 5 and 6: Abstract v description of their low
Page 7 and 8: Contents vii 5 Results and Discussi
Page 9 and 10: List of Figures ix 4.7 (above) (a)
Page 11 and 12: List of Figures xi 5.16 Cu Wannier
Page 13 and 14: List of Tables 4.1 Bond lengths and
Page 15 and 16: List of Abbreviations 1D . . . . .
Page 17 and 18: Dedicated to Fernando-Andres Salgue
Page 19 and 20: Chapter 1: Introduction 2 are being
Page 21 and 22: Chapter 1: Introduction 4 external
Page 23 and 24: Chapter 2 Method Our understanding
Page 25 and 26: Chapter 2: Method 8 system at any t
Page 27 and 28: Chapter 2: Method 10 The functional
Page 29 and 30: Chapter 2: Method 12 and to use it
Page 31 and 32: Chapter 2: Method 14 2.2.2 Orbital-
Page 33 and 34: Chapter 2: Method 16 linearized for
Page 35 and 36: Chapter 2: Method 18 and relativist
Page 37 and 38: Chapter 2: Method 20 the fact that
Page 39 and 40: Chapter 2: Method 22 The basis func
Page 41 and 42: Chapter 2: Method 24 • If these b
Page 43: Chapter 2: Method 26 LAPW and LMTO
Page 47 and 48: Chapter 2: Method 30 2.4 Effective
Page 49 and 50: Chapter 2: Method 32 HSO = λ(L ·
Page 51 and 52: Chapter 3 Crystal structures of the
Page 53 and 54: Chapter 3: Crystal structures of th
Page 55 and 56: Chapter 3: Crystal structures of th
Page 57 and 58: Chapter 4 Low dimensional spin syst
Page 59 and 60: Chapter 4: Low dimensional spin sys
Page 89 and 90: Chapter 5 Results and Discussion 5.
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Chapter 5: Results and Discussion 7
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Chapter 6 Summary and Outlook The t
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Chapter 6: Summary and Outlook 150
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Chapter 6: Summary and Outlook 152
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Appendix A: Atomic coordinates for
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Appendix A: Atomic coordinates for
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Appendix B: Atomic coordinates for
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Appendix C Atomic coordinates for t
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Bibliography [1] F. H. Allen, O. Ke
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Bibliography 170 [34] R. C. Dickins
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Bibliography 172 [75] M. D. Lumsden
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Bibliography 174 [116] R. L. Wither
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Zusammenfasung Niedrigdimensionale
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Zusammenfasung 178 Quantenspinssyst
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Zusammenfasung 180 Clustern zeigen,
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Experience: Curriculum vitae Name:
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I would like to thank: Acknowledgme
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Microscopic Modelling of Correlated Low-dimensional Systems

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