The impact of spurious imaginary phonon modes on thermal properties of Metal-organic Frameworks

Abstract

Metal-organic Frameworks (MOFs) have emerged as potential candidates for direct air capture (DAC) of green house gases and water. Thermal properties of MOFs, such as their heat capacity, are used to determine the energy penalty associated with the adsorbent retrieval during the Temperature Swing Adsorption process. To aid exploration of the vast experimental design space of MOFs for such applications, computational methods like Density Functional Theory (DFT) or surrogate machine learning models trained on DFT data have been developed for obtaining phonon-derived heat capacities of MOFs. However, the high cost of explicit phonon computation in large and flexible nanoporous MOFs often necessitates the use of small supercells or lower convergence criteria which decrease predictive accuracy. These approximations often result in spurious imaginary phonon modes which are commonly ignored in practice. At present, there is no clear consensus in the literature on what magnitude of negative frequency or what fraction of imaginary modes can be considered acceptable. Here, we systematically demonstrate that spurious imaginary phonon modes can introduce substantial errors in heat capacity estimates, leading to incorrect ranking of MOFs in thermal-property-based screening. We further show that benchmarking machine learning interatomic potentials (MLIPs) against DFT datasets containing spurious imaginary modes can misrepresent models that predict physically meaningful phonon spectra for dynamically stable MOFs. Finally, we introduce a simple, rapid post-processing workflow that can be applied to standard phonon calculations to effectively correct heat capacity estimates and account for spurious imaginary modes in MOFs.

Figures (6)

• Figure 1: (a)The density of states (DOS) of the two phonon spectra obtained with and without spurious imaginary modes from Moosavi et al.Moosavi and Wieser Wieser2024et al. respectively on a $11\times11\times11$ mesh with the linear tetrahedron approach with a pitch of 0.01 THz.(b) The % deviations in $C_v$ obtained from DFT data with 1.03% spurious imaginary modes relative to 0% shows a strong temperature dependence. $\theta_D$ is the proxy Debye temperature of MOF-74 as per equation \ref{['eq:debye']}
• Figure 2: The phonon band diagram for MOF-74 obtained from the force constants reported in Moosavi et al.Moosavi using the primitive unit cell and relatively loose convergence criteria produces imaginary phonon modes for the branches corresponding to 3 acoustic and the lowest optical phonon mode.
• Figure 3: (a)The % deviations in $C_v$ obtained from DFT data with 1.03% spurious imaginary modes relative to 0% become significantly lower at $T \gg \theta_D$ after adding corrections (b) A constant underestimation $\sim 2\%$ can be seen in $C_v$ at temperatures around 300K due to the imaginary modes in the red curve. Accounting for the imaginary modes in the corrected contribution curve leads to a nearly perfect overlap with the blue 0% Imaginary Modes Curve.
• Figure 4: (a) The deviations (%) in $C_v$ obtained from DFT data with increasing spurious imaginary modes in different MOFs relative to the 0% imaginary-modes data from MACE-MP-MOF0. (b) The deviations (%) in the corrected $C_v$ obtained from post-processing the DFT data are $10\times$ smaller for all MOFs relative to the 0% imaginary-modes data from MACE-MP-MOF0.
• Figure 5: The $C_v$ curve from DFT data containing 1.03% spurious imaginary modes shows a constant underestimation relative to other DFT Wieser2024 and MACE-MP-MOF0 data containing $\sim$ 0% imaginary modes. The corrected contribution to the DFT data bridges this gap