Quantum-Classical Adaptive Resolution Simulation
The adaptive method applied to systems where one of the resolution is at quantum level has a different conceptual meaning compared to the classical case. In fact in this case not only the degrees of freedom change but also the physical laws by which they are governed are different. So far the adaptive idea applied to systems with electrons has been (in my view) highly unsatisfactory. The sentence "Quantum-Classical" adaptive, for the case of electrons, has been misused or misunderstood.
In fact what has been done in reality is to use electronic structure calculations to update on the fly a classical force field and then couple this latter to a larger system with a (given) standard classical force field. A real "Quantum-Classical" adaptive would instead imply that we couple the quantum region to a large classical reservoir and the electronic properties in the quantum region are the same as those in an equivalent region of a full quantum calculation. The development of such an algorithm is the major challenge I see in the future of adaptive resolution methods. Instead, when there are no electrons involved in the problem, and one wants to consider the quantum effects of spatial delocalization of particles (e.g. hydrogen), then the adaptive resolution idea can be applied in a rather rigorous way. In fact atoms are described through the formalism of Path Integral which leads to the "effective" treatment of them as classical polymer rings. A polymer ring fluctuates and this fluctuation describes (statistically) the delocalization of the atom in space.
For the adaptive resolution then to interface a quantum and a classical region is equivalent to interface two effective classical regions, one where the atoms are represented with polymer rings and another where they are classical spheres (or even coarse-grained molecules); this means that we can use AdResS as for the classical case.
This idea has been successfully applied to the delicate case of parahydrogen at extreme thermodynamic conditions. Next step will consist of analysing the effect of hydrogen delocalization in the hydrogen bonding network for water and its relevance for solvation properties.
Selected References:
A.B.Poma and L.Delle Site
Phys.Rev.Lett. 104, 250201 (2010)
A.Agarwal and L.Delle Site:
J.Chem.Phys.143, 094102 (2015)
A.Agarwal and L.Delle Site:
Comp.Phys.Comm. 206, 26-34 (2016)