  Ab initio methods for electronic structure of molecules have reached a
satisfactory accuracy for calculation of static properties, but remain too
expensive for quantum dynamical calculations. We propose an efficient
semiclassical method for evaluating the accuracy of a lower level quantum
dynamics, as compared to a higher level quantum dynamics, without having to
perform any quantum dynamics. The method is based on dephasing representation
of quantum fidelity and its feasibility is demonstrated on the
photodissociation dynamics of CO2. We suggest how to implement the method in
existing molecular dynamics codes and describe a simple test of its
applicability.
