= 267 cm -1 is chosen as the minimum in the phonon density of states (DoS) above the lowenergy pseudo-acoustic peak (Figure ). The cut-off is applied to avoid divergences in the in the Raman rates, as the denominator of Equations 46 -49 in reference 58 goes to zero when ℏ𝜔 is resonant with a CF excitation, and the chosen value is sufficiently smaller than the first crystal field excitation of ca. 420 cm -1 . The double integral is transformed into a onedimensional integral due to the conservation of energy via the Dirac delta function, and is performed over anti-Lorentzian phonon lineshapes (Equation 11 in reference 58) to an equivalent range of 𝜇 ± 2𝜎 (95%) using the trapezoidal method with 40 equidistant steps; anti-Lorentzian lineshapes are used to ensure that the DoS goes to zero at zero energy.