5.2 Solids, Polymers, <strong>and</strong> MaterialsThe first application of Car–Parrinello <strong>molecular</strong> <strong>dynamics</strong> 108 dealt with silicon,one of the basic materials in semiconductor industry. Classic solid–state applicationof this technique focus on the properties of crystals, such as those of CuClwhere anharmonicity <strong>and</strong> off–center displacements of the Cu along the (111) directionswere found to be important to describe the crystal structure as a functionof temperature <strong>and</strong> pressure 64 . Various properties of solid nitromethane 647 ,crystalline nitric acid trihydrate 602 , solid benzene 420 , stage–1 alkali–graphite intercalationcompounds 286,287 , <strong>and</strong> of the one-dimensional intercalation compound2HgS•SnBr 2 530 were determined based on first principles. The <strong>molecular</strong> solid HBrundergoes various phase transitions upon compression. The dynamical behavior ofone of these phases, disordered HBr–I, could be clarified using ab <strong>initio</strong> <strong>molecular</strong><strong>dynamics</strong> 313 . Structure, phase transitions <strong>and</strong> short–time <strong>dynamics</strong> of magnesiumsilicate perovskites were analyzed in terms of ab <strong>initio</strong> trajectories 670 . The A7 tosimple cubic transformation in As was investigated using ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong>at constant–pressure 568 . By applying external pressure the hydrogen sublatticewas found to undergo amorphization in Mg(OH) 2 <strong>and</strong> Ca(OH) 2 a phenomenonthat was interpreted in terms of frustration 511 . Properties of solid cubane C 8 H 8were obtained in constant pressure simulations <strong>and</strong> compared to experiment 514 .<strong>Ab</strong> <strong>initio</strong> simulations of the graphitization of flat <strong>and</strong> stepped diamond (111) surfacesuncovered that the transition temperature depends sensibly on the type ofthe surface 327 .Sliding of grain boundaries in aluminum as a typical ductile metal was generated<strong>and</strong> analyzed in terms of atomistic rearrangements 432 . Microfracture in a sampleof amorphous silicon carbide was induced by uniaxial strain <strong>and</strong> found to induce Sisegregation at the surface 226 . The early stages of nitride growth on cubic siliconcarbide including wetting were modeled by depositing nitrogen atoms on the Si–terminated SiC(001) surface 225 .Classical proton diffusion in crystalline silicon at high temperatures was an earlyapplication to the <strong>dynamics</strong> of atoms in solids 93 . Using the ab <strong>initio</strong> path integraltechnique 395,399,644,404 , see Sect. 4.4 the preferred sites of hydrogen <strong>and</strong> muoniumimpurities in crystalline silicon 428,429 , or the proton positions in HCl • nH 2 O crystallinehydrates 516 could be located. The radiation–induced formation of H ⋆ 2 defectsin c–Si via vacancies <strong>and</strong> self–interstitials was simulated by ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong>178 . The classical diffusion of hydrogen in crystalline GaAs was followed interms of diffusion paths 668 <strong>and</strong> photoassisted reactivation of H–passivated Si donorsin GaAs was simulated based on first principles 430 . Oxygen diffusion in p–dopedsilicon can be enhanced by adding hydrogen to the material, an effect that couldbe rationalized by simulations 107 . <strong>Ab</strong> <strong>initio</strong> <strong>dynamics</strong> helped in quantifying thebarrier for the diffusion of atomic oxygen in a model silica host 279 . The microscopicmechanism of the proton diffusion in protonic conductors, in particular Sc–dopedSrTiO 3 <strong>and</strong> Y–doped SrCeO 3 , is studied via ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong>, whereis it found that covalent OH–bonds are formed during the process 561 . Ionic diffusionin a ternary superionic conductor was obtained by ab <strong>initio</strong> <strong>dynamics</strong> 677 .Proton motion <strong>and</strong> isomerization pathways of a complex photochromic <strong>molecular</strong>119
crystal composed of 2–(2,4–dinitrobenzyl)pyridine dyes was generated by ab <strong>initio</strong>methods 216 .Also materials properties of polymers are investigated in quite some detail.Early applications of semiempirical zdo <strong>molecular</strong> <strong>dynamics</strong> 666 were devoted todefects in conducting polymers, in particular to solitons, polarons <strong>and</strong> alkali dopingin polyacetylene 666,667 as well as to muonium implanted in trans <strong>and</strong> cis polyacetylene200 . More recent are calculations of Young’s modulus for crystalline polyethylene271 , soliton <strong>dynamics</strong> in positively charged polyacetylene chains 125 , chargelocalization in doped polypyrroles 140 , chain rupture of polyethylene chains undertensile load 533 , the influence of a knot on the strength of a polymer str<strong>and</strong> 534 , orion diffusion in polyethylene oxide 456 .5.3 Surfaces, Interfaces, <strong>and</strong> AdsorbatesA host of studies focusing on atoms <strong>and</strong> in particular on molecules interactingwith surfaces appeared over the years. Recent studies focussed for instance onC 2 H 2 , C 2 H 4 , <strong>and</strong> trimethylgallium adsorbates on the GaAs(001)–(2×4) surface 248 ,thiophene on the catalytically active MoS 2 (010) 512 or RuS 580 2 surfaces, smallmolecules on a nitric acid monohydrate crystal surface 624 , CO on Si(001) 314 , smallmolecules on TiO 554,41 2 , sulfur on Si(100) at various coverages 707 , <strong>and</strong> sulfuricacid adsorbed on ZrO 2 (101) <strong>and</strong> ZrO 2 (001) 269 .Specific to ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong> is its capability to describe alsochemisorption as well as dynamical processes on (<strong>and</strong> of) surfaces including surfacereactions 500 . The ab <strong>initio</strong> calculations of surface phonons in semiconductor surfacescan be based on the frozen–phonon, linear–response or nowadays <strong>molecular</strong><strong>dynamics</strong> approaches, see Ref. 218 for a discussion <strong>and</strong> comparison. A review onthe structure <strong>and</strong> energetics of oxide surfaces including <strong>molecular</strong> processes occurringon such surfaces is provided in Ref. 235 , whereas Ref. 256 concentrates on theinteraction of hydrogen with clean <strong>and</strong> adsorbate covered metal <strong>and</strong> semiconductorsurfaces.Recent applications in surface science include the transition from surface vibrationsto liquid–like diffusional <strong>dynamics</strong> of the Ge(111) surface 607 , the diffusion of Siadatoms on a double–layer stepped Si(001) surface 330 , the structure of chemisorbedacetylene on the Si(001)–(2×1) surface 423 , chemisorption of quinizarin on α–Al 2 O 212,213 3 , the diffusion of a single Ga adatom on the GaAs(100)–c(4×4) surface367 , homoepitaxial crystal growth on Si(001) <strong>and</strong> the low–temperature <strong>dynamics</strong>of Si(111)–(7×7) 595,611 , dissociation of an H 2 O molecule on MgO 358,359 , dissociationof Cl 2 on GaAs(110) 380 , chlorine adsorption <strong>and</strong> reactions on Si(100) 691 ,<strong>molecular</strong> motion of NH 3 on MgO 358 , <strong>dynamics</strong> <strong>and</strong> reactions of hydrated α–alumina surfaces 289 , <strong>molecular</strong> vs. dissociative adsorption of water layers onMgO(100) as a function of coverage 448 , oxidation of CO on Pt(111) 8,705 , thereaction HCl + HOCl → H 2 O + Cl 2 as it occurs on an ice surface 373 , or desorptionof D 2 from Si(100) 255 . Thermal contraction, the formation of adatom-vacancypairs, <strong>and</strong> finally premelting was observed in ab <strong>initio</strong> simulations of the Al(110)surface at temperatures up to 900 K 415 Early stages of the oxidation of a Mg(0001)surface by direct attack of <strong>molecular</strong> O 2 was dynamically simulated 96 including120
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John von Neumann Institute for Comp
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2500Number200015001000CP PRL 1985AI
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The goal of this section is to deri
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¡the Newtonian equation of motion
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Ehrenfest molecular dynamics is cer
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the Car-Parrinello approach 108 , s
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According to the Car-Parrinello equ
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Figure 4. (a) Comparison of the x-c
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Up to this point the entire discuss
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parameters are those used to repres
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in terms of a linear combination of
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structure calculations, see e.g. Re
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“unbound electrons” dissolved i
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Table 1. Timings in cpu seconds and
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stressed that the energy conservati
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see e.g. the discussion following E
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from a set of one-particle spin orb
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is used, which represents exactly a
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2.8.3 Generalized Plane WavesAn ext
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disposable parameters that can be o
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The index i runs over all states an
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f(G) are related by three-dimension
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where j l are spherical Bessel func
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andE self = ∑ I1√2πZ 2 IR c I.
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¢££¤¤¢¢¢n tot (G)inv FTn to
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correlation energyΩ ∑E xc = ε x
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3.4 Total Energy, Gradients, and St
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3.4.3 Gradient for Nuclear Position
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The local part of the pseudopotenti
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¢¢¢¢¢i = 1 . . .N b¢c i (G)¢
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¢¢¢¢¢c i (G)123g, E self∆V I
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where G c is a free parameter that
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- Page 130 and 131: 57. M. Bernasconi, G. L. Chiarotti,
- Page 132 and 133: Superiore di Studi Avanzati (SISSA)
- Page 134 and 135: 175. E. Ermakova, J. Solca, H. Hube
- Page 136 and 137: 244. H. Goldstein, Klassische Mecha
- Page 138 and 139: 313. T. Ikeda, M. Sprik, K. Terakur
- Page 140 and 141: 384. N. A. Marks, D. R. McKenzie, B
- Page 142 and 143: 442. S. Nosé and M. L. Klein, Mol.
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- Page 146 and 147: 562. F. Shimojo, K. Hoshino, and Y.
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