not to or to not

[Allthewayanime]

Some of the books I read use not to, the others(others or the others?) use to not.

Are there any differences between not to and to not?

e.g.I warned him not to/to not touch the pot.
He asked her not to/ to not give up on hope .
I want him not to/ to not come anywhere near my daughter.

[Dozy]

I think, as a general rule, when "not to" and "to not" both work, and both have the desired meaning, "not to" is the most usual and natural word order in conversational English. You may see "to not" more in formal English. However, the two are not always interchangeable.

I warned him not to touch the pot. -- OK.
I warned him to not touch the pot. -- Doesn't seem right.

He asked her not to give up on hope. -- OK.
He asked her to not give up on hope. -- Also possible, but less usual.

I want him not to come anywhere near my daughter.
I want him to not come anywhere near my daughter.
Neither sentence is very natural. You would say "I don't want him to come anywhere near my daughter.