Two-dimensional (2D) post-transition metal chalcogenides (PTMC) have attracted attention due to their suitable band gaps and lower exciton binding energies, making them more appropriate for electronic, optical and water-splitting devices than graphene and monolayer transition metal dichalcogenides (TMDs). Of the predicted 2D PTMCs, GaSe has been reliably synthesized and experimentally characterized. Despite this fact, quantities such as lattice parameters and band character vary significantly depending on which density functional theory (DFT) functional is used. Although many-body perturbation theory (GW approximation) has been used to correct the electronic structure and obtain the excited state properties of 2D GaSe, and solving the Bethe-Salpeter equation (BSE) has been used to find the optical gap, we find that the results depend strongly on the starting wavefunction. In attempt to correct these discrepancies, we employed the many-body Diffusion Monte Carlo (DMC) method to calculate the ground and excited state properties of GaSe because DMC has a weaker dependence on the trial wavefunction. We benchmark these results with available experimental data, DFT [local-density approximation, Perdew-Burke-Ernzerhof (PBE), strongly constrained and appropriately normed (SCAN) meta-GGA, and hybrid (HSE06) functionals] and GW-BSE (using PBE and SCAN wavefunctions) results. Our findings confirm monolayer GaSe is an indirect gap semiconductor (Gamma-M) with a quasiparticle electronic gap in close agreement with experiment and low exciton binding energy. We also benchmark the optimal lattice parameter, cohesive energy and ground state charge density with DMC and various DFT methods. We aim to present a terminal theoretical benchmark for pristine monolayer GaSe, which will aide in the further study of 2D PTMCs using DMC methods.
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