I don't think

The subtle difference is that the first is natural. Native speakers normally place the negation in the matrix clause ('I don't think...')

Thanks. I see that the first is natural.What puzzles me is how the second sentence makes native speakers feel unnatural. Could you please expain that?

I already have. Please read my original post again.

I am afraid you just expained how and when we should use “the transfer of nagation”,which I actually didn't mean.Thank you all the same.

You asked why native speakers feel it is unnatural and I explained that it is because we do not say it that way.

Hello, Yiduo:

May I add my two cents' worth to the excellent answer that you have already received?

I have checked my books (as we non-experts are warned to do before posting), and I believe that the topic of your question is called transferred negation (or "negative raising"). May I suggest that when you have time, you google that term. I did. There are many interesting

Thank you for your careful explanation.
I usually prefer using "I don't think you've met my wife" than "I think you haven't met my wife." I know how to use it.I am here to find the reason.May I suppose it is because of something like euphemism? I have this kind of feeling.
Thank you again.

yiduo We say "I don't think you are right". Then how about "I think you are not right" I can't feel the subtle difference between them.

I agree that the second is unnatural. Regarding the 'subtle' difference---

I remember seeing a post by a proficient speaker

Thanks to Prajwalkr's excellent link, I think (or, at least, imagine) that one of them is less harsh or confrontational:

Woman to bad boy: Excuse me. I don't think that you should do that.

Man to bad boy: Hey, dude! I think that you should not do that -- or else!

Maybe it has to do with the distance between "not" and "should do."

Thank you for your links.
I think that's just what i would like to find out.