Description of the Problem

Performing exact quantum dynamics of a molecular system, which has many electrons and many nuclear degrees of freedom is a formidable task. Thus, there exist a wide range of computationally inexpensive semi-classical and mixed-quantum classical methods for simulating quantum dynamics approximately. To perform direct on-the-fly quantum dynamics simulations of molecular systems one needs to combine these approximate quantum dynamics approaches with the outputs of an electronic structure approach. Unfortunately, most of the electronic structure approach provide outputs in the adiabatic representation while many of the quantum dynamics approaches are formulated in the diabatic representation, making them incompatible with each other. 

Our Solution: the Quasi-Diabatic Framework

The main idea behind our approach is that adiabatic states associated to a reference geometry (crude adiabats) can be used to construct a compact diabatic representation in the neighborhood of the reference geometry.  In other words, we can use the adiabatic states associated to the reference geometry to perform quantum dynamics simulations using any diabatic quantum dynamics approach for a short-time.  After this short-time as the nuclear geometry evolves outside of the neighborhood of the reference geometry, the corresponding crude adiabats no longer can be used to create a compact representation (unless we are using infinitely many). We must construct a new compact representation using adiabatic states associated to the a new reference geometry. 

This method works like a charm.