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We present synthetic dust polarization maps of simulated molecular clouds(MCs) with the goal to systematically explore the origin of the relativeorientation of the magnetic field ($\bf{B}$) with respect to the MCsub-structures identified in density ($n$; 3D) and column density ($N$; 2D).The polarization maps are generated with the radiative transfer code POLARIS,including self-consistently calculated efficiencies for radiative torquealignment. The MCs are formed in two sets of 3D MHD simulations: in (i)colliding flows (CF), and (ii) the SILCC-Zoom simulations. In 3D, for the CFsimulations with an initial field strength below $\sim$5 $\mu$G, $\bf{B}$ isoriented parallel or randomly with respect to the $n$-structures. For CF runswith stronger initial fields and all SILCC-Zoom simulations, which have aninitial field strength of 3 $\mu$G, a flip from parallel to perpendicularorientation occurs at high densities of $n_\text{trans}$ $\simeq$ 10$^2$ -10$^3$ cm$^{-3}$. We suggest that this flip happens if the MC's mass-to-fluxratio, $\mu$, is close to or below the critical value of 1. This corresponds toa field strength around 3 - 5 $\mu$G. In 2D, we use the Projected RayleighStatistics (PRS) to study the orientation of $\bf{B}$. If present, the flip inorientation occurs at $N_\text{trans}$ $\simeq$ 10$^{21 - 21.5}$ cm$^{-2}$,similar to the observed transition value from sub- to supercritical magneticfields in the ISM. However, projection effects can reduce the power of the PRSmethod: Depending on the MC or LOS, the projected maps of the SILCC-Zoomsimulations do not always show the flip, although expected from the 3Dmorphology. Such projection effects can explain the variety of recentlyobserved field configurations, in particular within a single MC. Finally, we donot find a correlation between the observed orientation of $\bf{B}$ and the$N$-PDF.

From parallel to perpendicular -- On the orientation of magnetic fields in molecular clouds