Ab initio molecular dynamics: Theory and Implementation

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 initio dynamics, such as for instance the cis–trans photoisomerizationin ethylene 46 , excited–state dynamics 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 initio moleculardynamics 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 and 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 and implications in many fields.Intramolecular proton transfer was studied recently in malonaldehyde 695,47 , a Mannichbase 182 , and formic acid dimers 427 . Pioneering ab initio molecular dynamicssimulations of proton and 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 initiopath integral technique 395,399,644,404 , see Sect. 4.4.Ab initio molecular dynamics 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 and carbon monoxide 54 or the polymerization 57 and amorphization 56of acetylene were investigated.5.10 Catalysis and 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 understandingof 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 initio molecular dynamics simulations. Amongthose are chain branching and 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