  We investigate the impact of various levels of approximation in density
functional theory calculations for the structural and binding properties of the
prototypical halide perovskite MAPbI$_3$. Specifically, we test how the
inclusion of different correction schemes for including dispersive
interactions, and how in addition using hybrid density functional theory,
affects the results for pertinent structural observables by means of comparison
to experimental data. In particular, the impact of finite temperature on the
lattice constants and bulk modulus, and the role of dispersive interactions in
calculating them, is examined by using molecular dynamics based on density
functional theory. Our findings confirm previous theoretical work showing that
including dispersive corrections is crucial for accurate calculation of
structural and binding properties of MAPbI$_3$. They furthermore highlight that
using a computationally much more expensive hybrid density functional has only
minor consequences for these observables. This allows for suggesting the use of
semilocal density functional theory, augmented by pairwise dispersive
corrections, as a reasonable choice for structurally more complicated
calculations of halide perovskites. Using this method, we perform molecular
dynamics calculations and discuss the dynamic effect of molecular rotation on
the structure of and binding in MAPbI$_3$, which allowed for rationalizing
microscopically the simultaneous occurrence of cubic octahedral symmetry and MA
disorder.
