  We have investigated interlayer interactions in the bilayer PtTe$_{2}$
system, which influence the electronic energy bands near the Fermi levels. Our
diffusion Monte Carlo (DMC) calculations for the high-symmetry bilayer
stackings (AA, AB, AC) manifest distinct interlayer binding characteristics
among the stacking modes by revealing significantly different interlayer
separations depending on the stackings, which is critical to understanding the
interlayer coupling of the twisted bilayers consisting of various local
stacking arrangements. Furthermore, a comparison between the interlayer
separations obtained from DMC and density functional theory (DFT) shows that
meta-GGA-based vdW-DFT results agree with DMC for different layer stackings,
including twisted bilayers, but only the ground-state AA stacking matches well
with GGA-based DFT predictions. This underscores the importance of accurate
exchange-correlation potentials even for capturing the stacking-dependent
interlayer binding properties. We further show that the variability in
DFT-predicted interlayer separations is responsible for the large discrepancy
of band structures in the 21.79$^{\circ}$-twisted bilayer PtTe$_{2}$, affecting
its classification as metallic or semiconducting. These results demonstrate the
importance of obtaining a correct description of stacking-dependent interlayer
coupling in modeling delicate bilayer systems at finite twists.
