Evaluating the Stability of 2D Compounds: Effects of Temperature, Mechanical Support and Vibrational Degrees of Freedom

Abstract The thermodynamic stability of two-dimensional (2D) materials remains a critical bottleneck in their synthesis and practical application. While Density Functional Theory (DFT) has revolutionized the characterization of these systems, standard 0 K computational protocols often overlook the complex interplay between thermal fluctuations and structural constraints. In this work, we investigate the stability of 2D MgO monolayers, examining how temperature, structural flexibility and mechanical support from a Pd substrate influence the material’s energy landscape. Our findings show that the thermodynamic behavior depends strongly on the structural degrees of freedom accessible in the simulations. Adequately large simulation cells are required to capture long-wavelength vibrational modes that significantly lower the free energy through entropic contributions. We demonstrate that while freestanding monolayers become unstable at finite temperatures, mechanical coupling with a substrate provides a crucial stabilizing effect while modifying the electronic band gap and atomic mobility. These results provide a more accurate framework for predicting the behavior of 2D compounds under realistic experimental conditions and highlight the importance of including vibrational entropy and substrate effects in computational studies of two-dimensional materials.