Things that probably help: give a reason why so they wont break their head over the why.
And tell them it has nothing to do with how they acted and that they could not have prevented you in any way because your mind was set. Saves them some worry that they COULD have done something. I would not just leave a note, but also maybe a delayed letter, in case the police takes the letter for whatever research. Even if its delayed a month. Agree with the closure thing.