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This study investigates the predictive capabilities of common DFT methods(GGA, GGA+$U$, and GGA+$U$+$V$) for determining the transition temperature ofantiferromagnetic insulators. We utilize a dataset of 29 compounds and deriveHeisenberg exchanges based on DFT total energies of different magneticconfigurations. To obtain exchange parameters within a supercell, we havedevised an innovative method that utilizes null space analysis to identify andaddress the limitations imposed by the supercell on these exchange parameters.With obtained exchanges, we construct Heisenberg Hamiltonian to computeTransition temperatures using classical Monte Carlo simulations. To refine thecalculations, we apply linear response theory to compute on-site ($U$) andintersite ($V$) corrections through a self-consistent process. Our findingsreveal that GGA significantly overestimates the transition temperature (by~113%), while GGA+$U$ underestimates it (by ~53%). To improve GGA+$U$ results,we propose adjusting the DFT results with the $(S+1)/S$ coefficient tocompensate for quantum effects in Monte Carlo simulation, resulting in areduced error of 44%. Additionally, we discover a high Pearson correlationcoefficient of approximately 0.92 between the transition temperaturescalculated using the GGA+$U$ method and the experimentally determinedtransition temperatures. Furthermore, we explore the impact of geometryoptimization on a subset of samples. Using consistent structures with GGA+U andGGA+U+V theories reduced the error.

A Benchmark of Density Functional Theory on the Prediction of Antiferromagnetic Transition Temperature