Why use "to not V"? Why not use "not to V"?

[Sitifan]

look through somebody/something (phrasal verb)
to not notice or pretend not to notice someone you know, even though you see them
http://www.ldoceonline.com/dictionary/look_1
look through sb
to not notice someone that you know, or to pretend that you have not noticed someone, even though you are looking directly at them
http://dictionary.cambridge.org/define.asp?key=look.through*2+0&dict=P

Why use "to not V"? Why not use "not to V"?
What's the difference in meaning or style between the above two structures?
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Thank you very much for your reply.

[Jamie (K)]

You're supposed to use "not to V". "To not V" would be ungrammatical in speech or writing.