Ab initio molecular dynamics: Theory and Implementation

subsequent analysis of its electronic properties is performed using different Hamiltonians.Several attempts to treat also the electrons in the path integral formulation –instead of using wavefunctions as in the ab initio path integral family – werepublished 606,119,488,449,450 . These approaches are exact in principle, i.e. non–adiabaticity and full electron–phonon coupling is included at finite temperatures.However, they suffer from severe stability problems 121 in the limit of degenerateelectrons, i.e. at very low temperatures compared to the Fermi temperature, whichis the temperature range of interest for typical problems in chemistry and materialsscience. Recent progress on computing electronic forces from path integral MonteCarlo simulations was also achieved 708 .More traditional approaches use a wavefunction representation for both theelectrons in the ground state and for nuclear density matrix instead of path integrals.The advantage is that real–time evolution is obtained more naturallycompared to path integral simulations. A review of such methods with the emphasisof computing the interactions “on–the–fly” is provided in Ref. 158 . An approximatewavefunction–based quantum dynamics method which includes severalexcited states and their couplings was also devised and used 385,386,387,45 . An alternativeapproach to approximate quantum dynamics consists in performing instantonor semiclassical ab initio dynamics 325,47 . Also the approximate vibrationalself–consistent field approach to nuclear quantum dynamics was combined with“on–the–fly” MP2 electronic structure calculations 122 .5 Applications: From Materials Science to Biochemistry5.1 IntroductionAb initio molecular dynamics was called a “virtual matter laboratory” 234 , a notionthat is fully justified in view of its relationship to experiments performed in thereal laboratory. Ideally, a system is prepared in some initial state and than evolvesaccording to the basic laws of physics – without the need of experimental input.It is clear to every practitioner that this viewpoint is highly idealistic for morethan one reason, but still this philosophy allows one to compute observables withpredictive power and also implies a broad range of applicability.It is evident from the number of papers dealing with ab initio molecular dynamics,see for instance Fig. 1, that a truly comprehensive survey of applicationscannot be given. Instead, the strategy chosen is to provide the reader with a wealthof references that try cover the full scope of this approach – instead of discussingin depth the physics or chemistry of only a few specific applications. To this endthe selection is based on a general literature search in order to suppress personalpreferences as much as possible. In addition the emphasis lies on recent applicationsthat could not be covered in earlier reviews. This implies that several olderkey reference papers on similar topics are in general missing.118