Please see the disclaimer.

Have you ever thought about the difference between “not to do something” and “to not do something”? If you are a normal person, probably not.

But I am not a normal person, and misuse of the two is one of the things I notice. The hardest part is that I misuse them too!

But here is the difference: “not to” is supposed to be used in the subjunctive mood, to express a negative feeling, and “to not” is supposed to be used to negate an action.

Here is an example sentence that uses both correctly:

My goal is not to succeed, it's to not die.

Now you know.