Ab initio molecular dynamics: Theory and Implementation

in terms of their electronic structure 601 .5.6 Matter at Extreme ConditionsA strong advantage of ab initio simulations is their predictive power also at extremeconditions, an area where molecular dynamics relying on fitted potentialmodels might encounter severe difficulties. Thus, high pressures and / or high temperaturessuch as those in the earth’s core, on other planets, or on stars can beeasily achieved in the virtual laboratory. This opens up the possibility to studyphase transformations and chemical reactions at such conditions 56 . Furthermore,conditions of geophysical and astrophysical interest can nowadays be produced inthe real laboratory, using techniques based on diamond anvil cells, shock waves, orlasers. The limitations of these experimental approaches are, however, not so muchrelated to generating the extreme conditions as one might expect, but rather tomeasuring observables.In the virtual laboratory this information is accessible and the melting ofdiamond at high pressure 222 , the phase transformation from the antiferromagneticinsulating δ–O 2 phase to a nonmagnetic metallic molecular ζ–O 2 phase 557 ,the phase diagram of carbon at high pressures and temperatures 261 as well astransformations of methane 13 , carbon monoxide 54 , molecular CO 2 267,558 , waterice 363,364,58,50,51,52 , solid 305,337,65,66,333 and hot fluid 5 hydrogen, solid Ar(H 2 ) 253under pressure could be probed. Along similar lines properties of a liquid Fe–S mixtureunder earth’s core conditions 11 , the viscosity of liquid iron 690,592 , the soundvelocity of dense hydrogen at conditions on jupiter 6 , the phase diagram of waterand ammonia up to 7000 K and 300 GPa 118 , the laser heating of silicon 570,572and graphite 574 etc. were investigated at extreme state points. A review on abinitio simulations relevant to minerals at conditions found in the earth’s mantle isprovided in Ref. 683 .5.7 Clusters, Fullerenes, and NanotubesInvestigations of clusters by ab initio molecular dynamics were among the firstapplications of this technique. Here, the feasibility to conduct finite–temperaturesimulations and in particular the possibility to search globally for minima turnedout to be instrumental 302,31,303,550,517,519 , see e.g. Refs. 16,321,32 for reviews.Such investigations focus more and more on clusters with varying composition518,293,199,348,349,161 . Cluster melting is also accessible on an ab initio footing84,531,525,526 and molecular clusters, complexes or cluster aggregates are activelyinvestigated 612,645,613,70,596,597,133,701,524 .Iii–v semiconductor clusters embedded in sodalite show quantum confinementand size effects that can be rationalized by ab initio simulations 625,95 . Supportedclusters such as Cu n on an MgO(100) surface are found to diffuse by “rolling” and“twisting” motions with very small barriers 438 . The diffusion of protonated heliumclusters in various sodalite cages was generated using ab initio dynamics 198 . Photo–induced structural changes in Se chains and rings were generated by a verticalhomo → lumo excitation and monitored by ab initio dynamics 306 . With thediscovery and production of finite carbon assemblies ab initio investigations of the123