'decide not to' or 'decide to not' ? [duplicate]

I came up with this question when I received an email from a committee with a sentence 'We have decided not to publish it', which seems really strange to me because the grammar I learned in English classes is 'decide not to do something' and 'decide to not do' was told incorrect.

I searched for answers to this problem online, but did not find a clear as well as persuasive answer. In terms of grammar, is 'decide not to do' correct ? If it is incorrect, is there a reason why people say 'decide not to do' even in official letters ?

Solution 1:

Each of decide not to do, decide to not do, and not decide to do is correct. But the last one means something different from the other two.

• If you have decided not to do X then you have decided. (And presumably you will not do X.) And deciding not to do X is the same as deciding to not do X.

• If you have not decided to do X then you have not made a decision about doing X.