Among the current best-performing SMMs, magnetic hysteresis has been observed as high as 80 K for [Dy(Cp*)(Cp i Pr5)][B(C6F5)4] (Cp* = pentamethyl-cyclopentadienyl), and more recently for the mixed-valence Cp iPr5 DyI3DyCp iPr5 (Cp iPr5 = pentaisopropyl-cyclopentadienyl) which shows strong magnetic exchange coupling mediated by the Ln-Ln half-𝜎 bond. In both cases, a large axial magnetic anisotropy is imposed by the cyclopentadienyl ligands, leading to large Ueff values and slow Orbach relaxation. For [Dy(Cp ttt )2][B(C6F5)4] (Cp ttt = C5H2-1,2,4t Bu) it has been demonstrated that the comparatively slow spin dynamics in the Raman regime for this class of materials results from a separation in energy between the very high-energy optical phonons (due to the conjugated five-membered rings being the only ligands in the first coordination sphere) and low-energy pseudo-acoustic phonons (due to the soft intermolecular potential energy of the bulky cation-anion pair). Variation of the cyclopentadienyl substituents can have a significant effect on the spin dynamics since it impacts both the magnetic anisotropy and the vibrational spectrum. Despite these successes, control of the spin dynamics through chemical modification remains an open challenge for the design of improved SMMs, and indeed any molecular spin system, and given the vastness of the chemical space, strategies employing machine learning are likely to be particularly promising. To this end, a number of research groups have recently started to develop ab initio methods for calculating molecular spin-phonon coupling and modelling spin dynamics. Such methods are crucial to leverage the computational materials design procedures that have proven very successful in solid-state chemistry, if we are to discover new and improved molecular materials with desirable spin dynamics. However, for this to be a viable approach, the calculations must approach experimental accuracy. Just recently, Lunghi and co-workers presented a landmark study: the first fully-ab initio simulation of Raman spin dynamics for an SMM. Taking inspiration from their work, we herein introduce a number of further developments, resulting in the most accurate ab initio simulation of molecular spin dynamics to date. We focus on the high performance Dy(III) SMM, [Dy(bbpen)Br] (1, Figure ), chosen because of its small unit-cell size, relatively high-symmetry space group (C2221), and excellent SMM performance, and consider two computational aspects that can affect the spin dynamics by orders of magnitude: the choice of phonon linewidth and the treatment of the electrostatic (Madelung) potential of the infinite crystal lattice. We perform the first ab initio calculation of the phonon linewidths for a molecular magnet to show that phonon lifetimes are orders of magnitude shorter than the spin lifetimes in this compound, justifying the commonly assumed Born-Markov approximation for molecular spin-dynamics, and that the phonon linewidths are highly energy-and wavevector-dependent, with full-width-at-half-maximum (FWHM) values varying between 0.1 -40 cm -1 at 300 K. We find that the spin dynamics are relatively insensitive to the choice of linewidth model, with similar results obtained using a fixed linewidth or a thermodynamic approximation, and thus our work suggests that the burden of performing expensive phonon linewidth calculations for other molecules may not be required to obtain accurate spin dynamics simulations. We find that the truncation of a crystal in finite-slab methods leads to significant errors in the electrostatic potential and electronicstructure calculations, and we implement a computationally inexpensive and accurate method to calculate the infinite crystalline electrostatic potential, including its effect on spin-phonon coupling terms, which vastly improves agreement with experiment. This work thus paves the way for accurate and efficient spin-phonon calculations on solid-state molecular systems, with applicability beyond molecular magnetism.