I made an account so I could contribute what I've found.
The way he played it at the Grammys last night was something like this,
Capo 7
First chord, F/Dm (1, 0, 0, 2, 3, 1)
Second chord I'm not as certain about. It appears that he moves his thumb off the fretboard for this chord, but it sounds to be and F (1, 0, 3, 2, 1, x). The way he has his hands positioned, it doesn't look as if he's playing the high F. I don't hear it, so I think he has it muted.
The third I'm not certain of either, but I believe it's a F/Bbsus2 (1, 1, 3, 3, 1, x). He frets both the F and the Bb with his thumb for this chord.
The chords when Rihanna come in are "the same", but they have different voicings. It looks like he goes up somewhere around the fourth fret, but I can't be certain. The fact that they hardly show the front of the guitar after Rihanna comes in makes it much more difficult to discern. Hopefully I can get back to you all on the rest, if someone doesn't before me.
Actually, that first chord appears to be incorrect, at least the second time he plays it. His index finger definitely isn't on the first fret like I thought. My guess now is F/Dm (1, 0, 0, 2, 3, x). I dunno, the chords are easy enough, but the voicings is where it gets complicated.