Typical (sub)system-bath quantum dynamical problems are often investigated by means of (approximate) reduced equations of motion. Wavepacket approaches to the dynamics of the whole system have gained momentum in recent years and there is hope that properly designed approximations to the wavefunction will allow one to correctly describe the subsystem evolution. The continuous-configuration time-dependent self-consistent field (CC-TDSCF) and local coherent-state approximation (LCSA) methods, for instance, use a simple Hartree product of bath single-particle-functions for each discrete variable representation (DVR) state introduced in the Hilbert space of the subsystem. Here we focus on the above two methods and replace the DVR states with the eigenstates of the subsystem Hamiltonian, i.e., we adopt an energy-local representation for the subsystem. We find that stable and semiquantitative results are obtained for a number of dissipative problems, at the same (small) computational cost of the original methods. Furthermore, we find that both methods give very similar results, thus suggesting that coherent-states are well suited to describe (local) bath states. As a whole, present results highlight the importance of the system basis-set in the selected-multiconfiguration expansion of the wavefunction. They suggest that accurate and yet computationally cheap methods may be simply obtained from CC-TDSCF/LCSA by letting the subsystem states be variationally optimized.
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