Unsolicited request for a scientific collaboration
Be specific and brief, with a clear action item.

bad:

My name is X and I'm interested in Y, and I'm hoping you'd be interested in working with me.


slightly better:

My name is X, and I'm interested in Y. I read your recent papers on Foo1, foo2, and foo3, and I was wondering whether you thought Theorem eleventy-seven in your paper on foo2 could apply to the problem of Y''.


much better:

My name is X, and I'm interested in Y. I read your recent papers on Foo1, foo2, and foo3. I had an idea about how to apply theorem eleventy-seven in your foo2 paper to Y'', by inserting the well known lemma Bar1, and Bar2. I was wondering if you were aware of approaches that have tried this? I looked at refs 1–157 and didn't see anything relevant.
I'd love to chat more about this if you're interested.



Again, your mileage may vary. There are cultural variations, personal variations and so on. But I’ve had success with emails of this kind.