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We investigated application of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculation of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities.Several different schemes to decompose the bath spectral density are employed: 1.The multiple Brownian oscillator model that can be obtained by fitting the model spectral density; 2.The combined Debye and oscillatory Debye model that can be constructed by fitting the bath correlation functions; 3.A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism.