As soon as I got home, I went to watch this video because honestly, I had never seen it. It is "A Thousand Years" by Christina Perri.
She wrote the song just for Bella and Edward after falling in love with the first movie and books. In the final movie, she has a 2nd version with Steve Kazee. It is just as beautiful. I was hoping they would have another video with clips from 'Breaking Dawn, Part 2', but I haven't found one yet.
If you are interested in the piano music for either of them, here is where I found the cheapest print-at-home versions of these two songs:
"A Thousand Years" ($5.25)
"Turning Page"- ($3.50)
I hope you will enjoy them too!