Introduction

The discussion up to this point has revolved essentially around the “standard” ab initio molecular dynamics methodologies. The notion “standard” means in particular that classical nuclei evolve adiabatically in the electronic ground state in the microcanonical ensemble. In addition, it is assumed that the electronic structure of all constituents of the system is treated on an equal footing. This combination allows already a multitude of applications, but many circumstances exist where the underlying approximations or restrictions break down or are unsatisfactory. Among these cases are situations where:

1. It is necessary to keep the temperature and/or pressure constant, such as during journeys in phase diagrams or in the investigation of solidstate phase transitions.

2. Pronounced free energy barriers have to be surmounted in rather short simulation times, such as during chemical reactions, conformational changes or phase transitions with high activation energies.

3. There is a sufficient population of excited electronic states, such as in materials with a small or vanishing electronic gap, or nonadiabatic dynamics involving a few specific excited states occurs, such as in dye molecules or chromophores after photoexcitation events.

4. Light nuclei are involved in crucial steps of a process, such as in studies of proton transfer in hydrogen-bonded systems or muonium impurities in crystals.

5. The system is too large to be fully described quantum-mechanically, such as enzymes, where a large “biomatrix” hosts a small “hot spot” to carry out a biochemical reaction or in the field of surface chemical reactions and heterogeneous catalysis.