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Accurately predicting the formation energy of a compound, which describes itsthermodynamic stability, is a key challenge in materials physics. Here, weemploy many-body quantum Monte Carlo (QMC) with single-reference trialfunctions to compute the formation energy of two electronically disparatecompounds, the intermetallic VPt$_2$ and the semiconductor CuI, for whichstandard density functional theory (DFT) predictions using both thePerdew-Burke Ernzerhof (PBE) and the strongly constrained and appropriatelynormed (SCAN) density functional approximations deviate markedly from availableexperimental values. For VPt$_2$, we find an agreement between QMC, SCAN, andPBE0 estimates, which therefore remain in disagreement with the much lessexothermic experimental value. For CuI, the QMC result agrees with neither SCANnor PBE pointing towards DFT exchange-correlation biases, likely related to thelocalized Cu $3d$ electrons. Compared to the behavior of some densityfunctional approximations within DFT, spin-averaged QMC exhibits a smaller butstill appreciable deviation when compared to experiment. The QMC result isslightly improved by incorporating spin-orbit corrections for CuI and solidI$_2$, so that experiment and theory are brought into imperfect but reasonableagreement within about 120~meV/atom.

Assessing the accuracy of compound formation energies with quantum Monte Carlo