Barring this numerical challenge, importantly the adiabatic representation also introduces incompatibility challenges for propagating the coupled electronic and nuclear degrees of freedom. This is because many quantum dynamics approaches, such as the spin-mapping approaches used in this work, are instead formulated in the diabatic representation {|D µ } are incompatible with the output obtained in the adiabatic representation. Within the diabatic representation {|D µ }, the NACV vanishes by definition,