culations on very accurate global potential energy surfaces. This was for instancedone for the well–studied exothermic exchange reaction F + H 2 → HF + H inRef. 565 . Other gas phase reactions studied were Li(2p) + H 2 → LiH( 1 Σ) + H( 1 S)in Ref. 387 , F + C 2 H 4 → C 2 H 3 F + H in Ref. 83 , 2O 3 → 3O 2 in Ref. 170 , F − +CH 3 Cl → CH 3 F + Cl − in Ref. 605 , hydroxyl radical with nitrogen dioxide radical165 , formaldehyde radical anion with CH 3 Cl in Ref. 700 , the reduction of OH •with 3-hexanone 215 or the hydrolysis (or solvolysis, S N 2 nucleophilic substitution)of methyl chloride with water 2,3 . Photoreactions of molecules slowly become accessibleto ab <strong>initio</strong> <strong>dynamics</strong>, such as for instance the cis–trans photoisomerizationin ethylene 46 , excited–state <strong>dynamics</strong> in conjugated polymers 71 , bond breakingin the S 8 ring 562 , transformations of diradicales 195,196 , or the S 0 → S 1 photoisomerization of formaldimine 214 .In addition to allowing to study complex gas phase chemistry, ab <strong>initio</strong> <strong>molecular</strong><strong>dynamics</strong> opened the way to simulate reactions in solution at finite temperatures.This allows liquid state chemistry to take place in the virtual laboratory wherethermal fluctuations <strong>and</strong> solvation effects are included. Some applications out ofthis emerging field are the cationic polymerization of 1,2,5–trioxane 146,147 , theinitial steps of the dissociation of HCl in water 353,354 , the formation of sulfuricacid by letting SO 3 react in liquid water 421 or the acid–catalyzed addition of waterto formaldehyde 422 .Proton transfer is a process of broad interest <strong>and</strong> implications in many fields.Intra<strong>molecular</strong> proton transfer was studied recently in malonaldehyde 695,47 , a Mannichbase 182 , <strong>and</strong> formic acid dimers 427 . Pioneering ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong>simulations of proton <strong>and</strong> hydroxyl diffusion in liquid water were reported in themid nineties 640,641,642 . Related to this problem is the auto–dissociation of purewater at ambient conditions 628,629 . Since recently it became possible to studyproton motion including nuclear quantum effects 645,410,412 by using the ab <strong>initio</strong>path integral technique 395,399,644,404 , see Sect. 4.4.<strong>Ab</strong> <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong> also allows chemical reactions to take place in solidphases, in particular if a constant pressure methodology is used 56 , see Sect. 4.2.For instance solid state reactions such as pressure–induced transformations ofmethane 13 <strong>and</strong> carbon monoxide 54 or the polymerization 57 <strong>and</strong> amorphization 56of acetylene were investigated.5.10 Catalysis <strong>and</strong> ZeolitesThe polymerization of olefines is an important class of chemical reactions that isoperated on the industrial scale. In the light of such applications the detailed underst<strong>and</strong>ingof these reactions might lead to the design of novel catalysts. Drivenby such stimulations several catalysts were investigated in detail such as metalalkyles 609 , platinum–phospine complexes 141 , or Grubbs’ ruthenium–phosphinecomplexes 1 , metallocenes 696 . In addition, elementary steps of various chemicalprocesses were the focus of ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong> simulations. Amongthose are chain branching <strong>and</strong> termination steps in polymerizations 696 , ethylenemetathesis 1 , “living polymerization” of isoprene with ethyl lithium 522 , Ziegler–Natta heterogenous polymerization of ethylene 79,80 , Reppe carbonylation of Ni–125
CH=CH 2 using Cl(CO) 2 20 , or Sakakura–Tanaka functionalization 382 . As in thereal laboratory, side reactions can occur also in the virtual laboratory, such as e.g.the β–hydrogen elimination as an unpredicted reaction path 383 . A digression onusing finite–temperature ab <strong>initio</strong> <strong>dynamics</strong> in homogeneous catalysis research canbe found in Ref. 697 .Zeolites often serve as catalysists as well <strong>and</strong> are at the same time ideal c<strong>and</strong>idatesfor finite–temperature ab <strong>initio</strong> simulations in view of their chemical complexity.A host of different studies 559,100,268,614,545,206,560,598,207,315,208,209,546 contributedgreatly to the underst<strong>and</strong>ing of these materials <strong>and</strong> the processes occurringtherein such as the initial stages of the methanol to gasoline conversion 599 . Heterogenouscatalysts are often poisoned, which was for instance studied in the caseof hydrogen dissociation on the Pd(100) surface in the presence adsorbed sulfurlayers 257 .5.11 Biophysics <strong>and</strong> BiochemistryApplications of ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong> to molecules <strong>and</strong> processes of interestin life sciences begin to emerge 18,113 . Investigations related to these interests areinvestigations of the crystal structure of a hydrated RNA duplex (sodium guanylyl–3’–5’–cytidine nona–hydrate) 311 , structure models for the cytochrom P450 enzymefamily 547,548,549 , nanotubular polypeptides 112 , a synthetic biomimetic model ofgalactose oxidase 523 , aspects of the process of vision in form of the 11–cis toall–trans isomerization in rhodopsin 67,68,474 , interconversion pathways of the protonatedβ–ionone Schiff base 615 , or of the binding properties of small moleculesof physiological relevance such as O 2 , CO or NO to iron–porphyrines <strong>and</strong> its complexes527,528,529 .Proton transport throught water wires is an important biophysical process inthe chemiosmotic theory for biochemical ATP production. Using the ab <strong>initio</strong>path integral technique 395,399,644,404 the properties of linear water wires with anexcess proton were studied at room temperature 419 . Amino acids are importantingredients as they are the building blocks of polypeptides, which in turn formchannels <strong>and</strong> pores for ion exchange. Motivated by their ubiquity, glycine <strong>and</strong>alanine as well as some of their oligopeptides <strong>and</strong> helical (periodic) polypeptideswere studied in great detail 323 .5.12 Outlook<strong>Ab</strong> <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong> is by now not only a st<strong>and</strong>ard tool in academic researchbut also becomes increasingly attractive to industrial researchers. Analysisof data bases, see caption of Fig. 1 for details, uncovers that quite a few companiesseem to be interested in this methodology. Researchers affiliated to Bayer, Corning,DSM, Dupont, Exxon, Ford, Hitachi, Hoechst, Kodak, NEC, Philips, Pirelli, Shell,Toyota, Xerox <strong>and</strong> others cite the Car–Parrinello paper Ref. 108 or use ab <strong>initio</strong><strong>molecular</strong> <strong>dynamics</strong> in their work. This trend will certainly be enhanced by theavailability of efficient <strong>and</strong> general ab <strong>initio</strong> <strong>molecular</strong> <strong>dynamics</strong> packages which arecommercially available.126
- Page 1 and 2:
John von Neumann Institute for Comp
- Page 4:
2500Number200015001000CP PRL 1985AI
- Page 7 and 8:
The goal of this section is to deri
- Page 9:
¡the Newtonian equation of motion
- Page 13 and 14:
Ehrenfest molecular dynamics is cer
- Page 15 and 16:
the Car-Parrinello approach 108 , s
- Page 17:
According to the Car-Parrinello equ
- Page 20 and 21:
Figure 4. (a) Comparison of the x-c
- Page 22 and 23:
Up to this point the entire discuss
- Page 24 and 25:
parameters are those used to repres
- Page 26 and 27:
in terms of a linear combination of
- Page 28 and 29:
structure calculations, see e.g. Re
- Page 30 and 31:
“unbound electrons” dissolved i
- Page 32 and 33:
Table 1. Timings in cpu seconds and
- Page 34 and 35:
stressed that the energy conservati
- Page 36 and 37:
see e.g. the discussion following E
- Page 38 and 39:
from a set of one-particle spin orb
- Page 40 and 41:
is used, which represents exactly a
- Page 42 and 43:
2.8.3 Generalized Plane WavesAn ext
- Page 44 and 45:
disposable parameters that can be o
- Page 46 and 47:
The index i runs over all states an
- Page 48 and 49:
f(G) are related by three-dimension
- Page 50 and 51:
where j l are spherical Bessel func
- Page 52 and 53:
andE self = ∑ I1√2πZ 2 IR c I.
- Page 54 and 55:
¢££¤¤¢¢¢n tot (G)inv FTn to
- Page 56 and 57:
correlation energyΩ ∑E xc = ε x
- Page 58 and 59:
3.4 Total Energy, Gradients, and St
- Page 60 and 61:
3.4.3 Gradient for Nuclear Position
- Page 62 and 63:
The local part of the pseudopotenti
- Page 64 and 65:
¢¢¢¢¢i = 1 . . .N b¢c i (G)¢
- Page 66 and 67:
¢¢¢¢¢c i (G)123g, E self∆V I
- Page 68 and 69:
where G c is a free parameter that
- Page 70 and 71:
and a matrix form of the Gram-Schmi
- Page 72 and 73:
The two sets of equations are coupl
- Page 74 and 75:
introducing different masses for di
- Page 76 and 77: The Lagrange multiplier have to be
- Page 78 and 79: Table 3. Relative size of character
- Page 80 and 81: of the G vectors, and only real ope
- Page 82 and 83: CALL SGEMM(’T’,’N’,M,N b ,2
- Page 84 and 85: ing standard communication librarie
- Page 86 and 87: over processors. All processors sho
- 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
- Page 92 and 93: are the improved load-balancing for
- Page 94 and 95: situations where• it is necessary
- Page 96 and 97: espectively), but completely analog
- Page 98 and 99: 4.2.3 Imposing Pressure: BarostatsK
- Page 100 and 101: in the previous section. The isobar
- Page 102 and 103: 4.3.2 Many Excited States: Free Ene
- Page 104 and 105: down the generalization of the Helm
- Page 106 and 107: free energy functional discussed in
- Page 108 and 109: Figure 16. Four patterns of spin de
- Page 110 and 111: and electrons r = {r i } can be wri
- Page 112 and 113: The effective classical partition f
- Page 114 and 115: up e.g. in Refs. 132,37,596,597,428
- Page 116 and 117: The eigenvalues of A when multiplie
- Page 118 and 119: frequency of the electronic degrees
- Page 120 and 121: 5.2 Solids, Polymers, and Materials
- Page 122 and 123: the penetration of the oxidation la
- Page 124 and 125: in terms of their electronic struct
- 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.