the penetration of the oxidation layer into the bulk. Similarly, the growth of anoxide layer was generated on an Si(100) surface 653 .The water–Pd(100), water–O/Pd(100) <strong>and</strong> water–Si(111) interfaces were simulatedbased on ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong> 336,655 . Water covering the surface ofa microscopic model of muscovite mica is found to form a two–dimensional networkof hydrogen bonds, called two–dimensional ice, on that surface 447 . The metal–organic junction of monolayers of Pd–porphyrin <strong>and</strong> perylene on Au(111) was analyzedusing an ab <strong>initio</strong> approach 355 . An interesting possibility is to compute thetip–surface interactions in atomic force microscopy as e.g. done for a neutral silicontip interacting with an InP(110) surface 619 or Si(111) 481,482 .5.4 Liquids <strong>and</strong> SolutionsMolecular liquids certainly belong to the classic realm of <strong>molecular</strong> <strong>dynamics</strong> simulations.Water was <strong>and</strong> still is a challenge 581 for both experiment <strong>and</strong> simulationsdue to the directional nature <strong>and</strong> the weakness of the hydrogen bonds which leadsto delicate association phenomena. Pioneering ab <strong>initio</strong> simulations of pure waterat ambient 352 <strong>and</strong> supercritical conditions 205 were reported only a few yearsago. More recently, these gradient–corrected density functional theory–based simulationswere extended into several directions 587,573,575,576,579,118 . In the mean time(minimal–basis) Hartree–Fock ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong> 291 as well as more approximateschemes 455 were also applied to liquid water. Since chemical reactionsoften occur in aqueous media the solvation properties of water are of utmost importanceso that the hydration of ions 403,620,621,377,502 <strong>and</strong> small molecules 353,354,433was investigated. Similarly to water liquid HF is a strongly associated liquid whichfeatures short–lived hydrogen–bonded zig–zag chains 521 . Another associated liquid,methanol, was simulated at 300 K using an adaptive finite–element method 634in conjunction with Born–Oppenheimer <strong>molecular</strong> <strong>dynamics</strong> 635 . In agreement withexperimental evidence, the majority of the molecules is found to be engaged in shortlinear hydrogen–bonded chains with some branching points 635 . Partial reviews onthe subject of ab <strong>initio</strong> simulations as applied to hydrogen–bonded liquids can befound in the literature 586,406,247 .The ab <strong>initio</strong> simulated solvation behavior of “unbound electrons” in liquidammonia at 260 K was found to be consistent with the physical picture extractedfrom experiment 155,156 . Similarly,ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong> of dilute 553,203 <strong>and</strong>concentrated 569 molten K x·(KCl) 1−x mixtures were performed at 1300 K enteringthe metallic regime. The structure of liquid ammonia at 273 K was investigatedwith a variety of techniques so that limitations of using classical nuclei, simple pointcharge models, small systems, <strong>and</strong> various density functionals could be assessed 164 .<strong>Ab</strong> <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong> is also an ideal tool to study other complex fluidswith partial covalency, metallic fluids, <strong>and</strong> their transformations as a function oftemperature, pressure, or concentration. The properties of water–free KF • nHFmelts depend crucially on polyfluoride anions H m F − m+1 <strong>and</strong> solvated K+ cations.<strong>Ab</strong> <strong>initio</strong> simulations allow for a direct comparison of these complexes in the liquid,gaseous <strong>and</strong> crystalline phase 515 . The changes of the measured structure factorof liquid sulfur as a function of temperature can be rationalized on the atomistic121
level by various chain <strong>and</strong> ring structures that can be statistically analyzed in ab<strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong> simulations 631 . Liquid GeSe 2 is characterized by strongchemical bonds that impose a structure beyond the usual very short distances dueto network formation 416 . Zintl–alloys such as liquid NaSn 552 or KPb 556 have veryinteresting bonding properties that manifest themselves in strong temperature– <strong>and</strong>concentration dependences of their structure factors (including the appearance ofthe so–called first sharp diffraction peak 555 ) or electric conductivities.Metals are ideal systems to investigate the metal–insulator transition upon expansionof the liquid 346,63 or melting 689 . Liquid copper was simulated at 1500 K:structural <strong>and</strong> dynamical data were found to be in excellent agreement with experimental464 . Transport coefficients of liquid metals (including in particular extremeconditions) can also be obtained from first principles <strong>molecular</strong> <strong>dynamics</strong> using theGreen–Kubo formalism 571,592 . The microscopic mechanism of the semiconductor–metal transition in liquid As 2 Se 3 could be rationalized in terms of a structuralchange as found in ab <strong>initio</strong> simulations performed as a function of temperature<strong>and</strong> pressure 563 . The iii–v semiconductors, such as GaAs, assume metallic behaviorwhen melted, whereas the ii–vi semiconductor CdTe does not. The differentconductivities could be traced back to pronounced structural dissimilarities of thetwo systems in the melt 236 .5.5 Glasses <strong>and</strong> Amorphous SystemsRelated to the simulation of dynamically disordered fluid systems are investigationsof amorphous or glassy materials. In view of the severe limitations on systemsize <strong>and</strong> time scale (<strong>and</strong> thus on correlation lengths <strong>and</strong> times) ab <strong>initio</strong> <strong>molecular</strong><strong>dynamics</strong> can only provide fairly local information in this sense. Within these inherentconstraints the microscopic structure of amorphous selenium 304 <strong>and</strong> tetrahedralamorphous carbon 384 , the amorphization of silica 684 , boron doping in amorphousSi:H 181 or in tetrahedral amorphous carbon 227 , as well as the Raman spectrum 465<strong>and</strong> dynamic structure factor 466 of quartz glass <strong>and</strong> their relation to short–rangeorder could be studied.The properties of supercooled CdTe were compared to the behavior in the liquidstate in terms of its local structure 237 . Defects in amorphous Si 1−x Ge x alloysgenerated by ab <strong>initio</strong> annealing were found to explain ESR spectra of this system329 . The infrared spectrum of a sample of amorphous silicon was obtained<strong>and</strong> found to be in quantitative agreement with experimental data 152 . The CO 2insertion into a model of argon–bombarded porous SiO 2 was studied 508 . In particularthe electronic properties of amorphous GaN were investigated using ab <strong>initio</strong>methods 601 .Larger systems <strong>and</strong> longer annealing times are accessible after introducing moreapproximations into the first principle treatment of the electronic structure thatunderlies ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong>. Using such methods 551 , a host of differentamorphous carbon nitride samples with various stoichiometries <strong>and</strong> densities couldbe generated <strong>and</strong> characterized in terms of trends 675 . Similarly, the pressure–induced glass–to–crystal transition in condensed sodium was investigated 22 <strong>and</strong> twostructural models of amorphous GaN obtained at different densities were examined122
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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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and a matrix form of the Gram-Schmi
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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.
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- Page 150: 682. R. M. Wentzcovitch, Phys. Rev.