The Chebyshev expansion allows efficient dynamics propagation by accurately calculating the action of the unitary propagator on an arbitrary vector. However, there is still a numerical challenge in simulating quantum dynamics with the HTC model. In Eq. 34, the phase factor in the Chebyshev expansion, Eq. 32, depends on the approximate absolute magnitude of the lower eigenvalue ϵ min . Thus, if the eigenvalue has a large absolute magnitude, the accuracy of this method is reduced due to the noise that builds up from the highly oscillating term coming from the high absolute magnitude of ϵ min , especially if we are simulating both ground state and single excitations (or further including the double excitation) where these values are on the order of eV, and the difference between ϵ