  The mapping approach addresses the mismatch between the continuous nuclear
phase space and discrete electronic states by creating an extended, fully
continuous phase space using a set of harmonic oscillators to encode the
populations and coherences of the electronic states. Existing quasiclassical
dynamics methods based on mapping, such as the linearised semiclassical initial
value representation (LSC-IVR) and Poisson bracket mapping equation (PBME)
approaches, have been shown to fail in predicting the correct relaxation of
electronic-state populations following an initial excitation. Here we
generalise our recently published modification to the standard quasiclassical
approximation for simulating quantum correlation functions. We show that the
electronic-state population operator in any system can be exactly rewritten as
a sum of a traceless operator and the identity operator. We show that by
treating the latter at a quantum level instead of using the mapping approach,
the accuracy of traditional quasiclassical dynamics methods can be drastically
improved, without changes to their underlying equations of motion. We
demonstrate this approach for the seven-state Frenkel-Exciton model of the
Fenna-Matthews-Olson light harvesting complex, showing that our modification
significantly improves the accuracy of traditional mapping approaches when
compared to numerically exact quantum results.
