We note that the space smoothening extend the density artificially to a slightly wider interval than the actual wave function, but of course only for meaningful values of the coordinates. As will be discussed in Section 2.3.1, mildly expanding the density with low weight into the area where it "might go" soon is actually an advantage as it improves safety and stability. A hard limit for coordinate minimum and maximum may be relevant in some coordinates and can easily be introduced. The smoothening of densities backwards in time may be only over a small previous time interval or all the way from the beginning of the computation. This can be used to tune the PES construction for what is important right now at time t for small N t values or being focused on the full domain of where the wave function has propagated in its history for large N t values.