Ab initio molecular dynamics: Theory and Implementation

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5.2 Solids, Polymers, and MaterialsThe first application of Car–Parrinello molecular dynamics 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 and off–center displacements of the Cu along the (111) directionswere found to be important to describe the crystal structure as a functionof temperature and pressure 64 . Various properties of solid nitromethane 647 ,crystalline nitric acid trihydrate 602 , solid benzene 420 , stage–1 alkali–graphite intercalationcompounds 286,287 , and of the one-dimensional intercalation compound2HgS•SnBr 2 530 were determined based on first principles. The molecular solid HBrundergoes various phase transitions upon compression. The dynamical behavior ofone of these phases, disordered HBr–I, could be clarified using ab initio moleculardynamics 313 . Structure, phase transitions and short–time dynamics of magnesiumsilicate perovskites were analyzed in terms of ab initio trajectories 670 . The A7 tosimple cubic transformation in As was investigated using ab initio molecular dynamicsat constant–pressure 568 . By applying external pressure the hydrogen sublatticewas found to undergo amorphization in Mg(OH) 2 and 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 and compared to experiment 514 .Ab initio simulations of the graphitization of flat and 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 generatedand analyzed in terms of atomistic rearrangements 432 . Microfracture in a sampleof amorphous silicon carbide was induced by uniaxial strain and 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 dynamics of atoms in solids 93 . Using the ab initio path integraltechnique 395,399,644,404 , see Sect. 4.4 the preferred sites of hydrogen and 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 and self–interstitials was simulated by ab initio molecular dynamics178 . The classical diffusion of hydrogen in crystalline GaAs was followed interms of diffusion paths 668 and 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 . Ab initio dynamics 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 and Y–doped SrCeO 3 , is studied via ab initio molecular dynamics, whereis it found that covalent OH–bonds are formed during the process 561 . Ionic diffusionin a ternary superionic conductor was obtained by ab initio dynamics 677 .Proton motion and isomerization pathways of a complex photochromic molecular119
crystal composed of 2–(2,4–dinitrobenzyl)pyridine dyes was generated by ab initiomethods 216 .Also materials properties of polymers are investigated in quite some detail.Early applications of semiempirical zdo molecular dynamics 666 were devoted todefects in conducting polymers, in particular to solitons, polarons and alkali dopingin polyacetylene 666,667 as well as to muonium implanted in trans and cis polyacetylene200 . More recent are calculations of Young’s modulus for crystalline polyethylene271 , soliton dynamics 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 strand 534 , orion diffusion in polyethylene oxide 456 .5.3 Surfaces, Interfaces, and AdsorbatesA host of studies focusing on atoms and in particular on molecules interactingwith surfaces appeared over the years. Recent studies focussed for instance onC 2 H 2 , C 2 H 4 , and 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 , and sulfuricacid adsorbed on ZrO 2 (101) and ZrO 2 (001) 269 .Specific to ab initio molecular dynamics is its capability to describe alsochemisorption as well as dynamical processes on (and of) surfaces including surfacereactions 500 . The ab initio calculations of surface phonons in semiconductor surfacescan be based on the frozen–phonon, linear–response or nowadays moleculardynamics approaches, see Ref. 218 for a discussion and comparison. A review onthe structure and energetics of oxide surfaces including molecular processes occurringon such surfaces is provided in Ref. 235 , whereas Ref. 256 concentrates on theinteraction of hydrogen with clean and adsorbate covered metal and semiconductorsurfaces.Recent applications in surface science include the transition from surface vibrationsto liquid–like diffusional dynamics 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) and the low–temperature dynamicsof 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 and reactions on Si(100) 691 ,molecular motion of NH 3 on MgO 358 , dynamics and reactions of hydrated α–alumina surfaces 289 , molecular 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, and finally premelting was observed in ab initio 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 molecular 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 84 and 85: ing standard communication librarie
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Page 88 and 89: ab = 2 * sdot(2 * N p D ,A(1),1,B(1
Page 90 and 91: ENDCALL ParallelFFT3D("INV",scr1,sc
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Page 128 and 129: AcknowledgmentsOur knowledge on ab
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.
Page 144 and 145: 502. L. M. Ramaniah, M. Bernasconi,
Page 146 and 147: 562. F. Shimojo, K. Hoshino, and Y.
Page 148 and 149: 620. A. Tongraar, K. R. Liedl, and
Page 150: 682. R. M. Wentzcovitch, Phys. Rev.
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