Ab initio molecular dynamics: Theory and Implementation

situations where• it is necessary to keep temperature and /or pressure constant (such as duringjourneys in phase diagrams or in the investigation of solid–state phase transitions),• there is a sufficient population of excited electronic states (such as in materialswith a small or vanishing electronic gap) or dynamical motion occurs in a singleexcited states (such as after photoexcitation events),• light nuclei are involved in crucial steps of a process (such as in studies ofproton transfer or muonium impurities).In the following subsections techniques are introduced which transcede these limitations.Thus, the realm of ab initio molecular dynamics is considerably increasedbeyond the basic setup as discussed in general terms in Sect. 2 and concerningits implementation in Sect. 3. The presented “advanced techniques” are selectedbecause they are available in the current version of the CPMD package 142 , but theirimplementation is not discussed in detail here.4.2 Beyond Microcanonics4.2.1 IntroductionIn the framework of statistical mechanics all ensembles can be formally obtainedfrom the microcanonical or NV E ensemble – where particle number, volume andenergy are the external thermodynamic control variables – by suitable Laplacetransforms of its partition function; note that V is used for volume when it comesto labeling the various ensembles in Sect. 4 and its subsections. Thermodynamicallythis corresponds to Legendre transforms of the associated thermodynamicpotentials where intensive and extensive conjugate variables are interchanged. Inthermodynamics, this task is achieved by a “sufficiently weak” coupling of theoriginal system to an appropriate infinitely large bath or reservoir via a link thatestablishes thermodynamic equilibrium. The same basic idea is instrumental ingenerating distribution functions of such ensembles by computer simulation 98,250 .Here, two important special cases are discussed: thermostats and barostats, whichare used to impose temperature instead of energy and / or pressure instead ofvolume as external control parameters 12,445,270,585,217 .4.2.2 Imposing Temperature: ThermostatsIn the limit of ergodic sampling the ensemble created by standard molecular dynamicsis the microcanonical or NV E ensemble where in addition the total momentumis conserved 12,270,217 . Thus, the temperature is not a control variable in the Newtonianapproach to molecular dynamics and whence it cannot be preselected andfixed. But it is evident that also within molecular dynamics the possibility to controlthe average temperature (as obtained from the average kinetic energy of thenuclei and the energy equipartition theorem) is welcome for physical reasons. Adeterministic algorithm of achieving temperature control in the spirit of extended93