AIMD procedures

A rapid development of the field was initiated by the formulation of the AIMD by Car and Parrinello based on a DF procedure employing a plane wave expansion of the electronic wavefunction. Related approaches based on the rigorous BO approximation for separation of nuclear and electronic degrees of freedom have been proposed. At the same time other AIMD procedures have been developed in the framework of the HF (AIMD-HF) (cf. Ref. 17 and references therein), the generalized valence bond, and recently the nonlocal density functional (AlMD-B-LYP) methods. All these approaches employ Gaussian basis sets localized at the nuclei. 

Of special importance to AIMD are the enhanced sampling methods termed elastic band and string methods. Michaelides and coworkers explained in their excellent free-energy method assessment article that special considerations have to be taken when rare event simulations are done within AIMD. As the iterative SCF procedure has an impact on the calculation of the forces in contrast to the exact forces in empirical simulations, the convergence tolerance of the SCF procedure has to be chosen carefully, especially for reactive situations [61]. 

Compared to ordinary quantum chemical approaches, the AIMD free-energy calculations have significant advantage as entropic effects and anharmonicity are explicitly included in the calculation. In contrast, a normal static DFT procedure requires that the vibrational entropy be added via harmonic frequency calculations and the computational demands may be quite substantial for large molecular systems. Furthermore, the harmonic approximation may not even be valid in situations where weak interactions are dominant. 

Therefore we combined the idea of AIMD, which was initiated by Car and Parrinello [35] in connection with a density functional (DF) procedure employing a plane waves expansion, with the quantum-chemical calculations of energies and gradients in the framework of the HF [25-27] or GDF [28, 29] procedures employing the AO basis sets. 

The idea of AIMD, originally initiated by Car and Parrinello in connection with a DF procedure employing a plane waves expansion, is here revisited... 

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