Many-body electronic structure of LaScO$_3$ by real space quantum Monte Carlo.

We present real space quantum Monte Carlo (QMC) calculations of the scandate LaScO$_3$ that proved to be challenging for traditional electronic structure approaches due to strong correlation effects resulting in inaccurate band gaps from DFT and $GW$ methods when compared with existing experimental data. Besides calculating an accurate QMC band gap corrected for supercell size biases and in agreement with numerous experiments, we also predict the cohesive energy of the crystal using the standard fixed-node QMC without any empirical or non-variational parameters. We show that promotion (optical) gap and fundamental gap agree with each other illustrating a clear absence of significant excitonic effects in the ideal crystal. We obtained these results in perfect consistency in two independent tracks that employ different basis sets (plane wave vs. localized gaussians), different codes for generating orbitals (\textsc{Quantum Espresso} vs. \textsc{Crystal}), different QMC codes (\textsc{Qmcpack} vs. \textsc{Qwalk}) and different high-accuracy pseudopotentials (ccECPs vs. Troullier-Martins) presenting the maturity and consistency of QMC methodology and tools for studies of strongly correlated problems.