Despite the fruitful progresses, our analytic expressions and numerical simulations have certain limitations. First, the analytic expressions are empirical and with ad hoc corrections. The UP linewidth expression works only when FGR is valid, which might break down in certain parameter regimes. With regard to the numerical exact simulations, the computational cost increases drastically with N , which limits us to exploring only a small number of molecules. Moreover, the HEOM method is usually restricted to certain forms of spectral density functions . Future theoretical efforts are needed to address these problems.