  Despite recent advances in quantum sciences, a quantum master equation that
accurately and simply characterizes open quantum dynamics across extremely long
timescales and in dispersive environments is still needed. In this study, we
optimize the computation of the fourth-order time-convolutionless master
equation to meet this need. Early versions of this master equation required
computing a multidimensional integral, limiting its use. Our master equation
accounts for simultaneous relaxation and dephasing, resulting in coefficients
proportional to the system's spectral density over frequency derivative. In
sub-Ohmic environments, this derivative induces infrared divergence in the
master equation, invalidating the second-order Bloch-Redfield master equation
findings. We analyze the approach to a ground state in a generic open quantum
system and demonstrate that it is not reliably computed by the Bloch-Redfield
equation alone. The optimized fourth-order equation shows that the ground-state
approach is accurate to second order in bath coupling regardless of the
dispersion, even though it can diverge in the fourth order at zero temperature.
