@anthonyteacher has a great post at his site discussing the patterns “not to VERB” and “to not VERB”. He writes about his students’ reactions to the constructions, his own view, and some findings from Google N-grams and COCA. You should read his post in full.
I basically agree with everything he says, with one point he makes that I would like to extend a little bit. So I’d like to highlight this paragraph from his post, and especially the statement I put in red:
All of this data tells me several things. First, “to not” is on the rise, most likely due to the fact that the ability to separate an infinitive has become more accepted and “to not” has probably rolled in through a snowball effect. Second, the placement of “not” does not necessarily imply emphasis, as can be seen in the sentences above. Third, while my speech may make some of the older generations shake their first with anger, possibly telling me I am killing English, I can now reply confidently that my speech is the vanguard of an English where “not” is as placement-fluid as “they” is gender-fluid. My speech may be a speech that is likely to boldly go where few have gone before. Or to not boldly go, because language change is really unpredictable, and this is just a tiny thing.
I chose to highlight this section because I felt that sometimes my own choices regarding placement of “not” are definitely, if not necessarily, done for emphasis, but after thinking about it I don’t think it is a matter of placing emphasis per se. Rather, it is about restricting possible meanings/uses.
Let me explain. Here are two partial lines from COCA (query terms: not to mention):
1) … He would talk only if I promised not to mention he lived in …
2) … But tours and marketing materials, not to mention data on the average student, won’t tell you if that college will …
In the first line, I, personally, would probably phrase that as “to not mention”, though not necessarily. The point is that both constructions feel natural to me. However, I can’t imagine myself saying that about the second line. To me, and the way I’m processing these constructions, the first line’s meaning is straightforward, but the second line’s meaning is based on my understanding of “not to mention” as a fixed or partially fixed expression in this instance.
In this case, the construction is not simply negating the mentioning of something (in fact, the thing in question is explicitly and necessarily mentioned/understood). Indeed, the online Cambridge Dictionary, for example, defines “not to mention” as a phrase used when you want to emphasize something that you are adding to a list.
So, generally speaking, I process “to not VERB” as basically interchangeable with “not to VERB” (with a personal preference for “to not VERB”) when the meaning is straightforward (i.e. negating the verb). But “not to VERB”, perhaps because of it’s associations with certain fixed expressions, seems to me to have a broader range of usage. Something like this:
“not to VERB”: can negate the verb or have idiomatic/figurative meaning and usage
“to not VERB”: restricted to negating the verb
All the “to not VERB” uses here have meanings that can be understood as simply negating the verb. I suspect it would be this way throughout all the lines.
At least, until the language changes some more 😉
If I have said something glaringly, obviously wrong please tell me. Or if you have evidence of “to not VERB” used in an idiomatic/figurative way, please share it. Or if you have better choices for terminology etc. etc. etc. …