In Veronika Decides To Die, what is the name of the beautiful piece of music played on the piano?

I want to know the name of the piece and the composer's
name/performer's name if at all possible. I want to know the name of
the first piece played on the piano by 'Sarah Michelle
Gellar/Veronika' when it is raining outside. The piece is this one on
Youtube, I would like to find an official, un-movie version.
http://www.youtube.com/watch?v=Uys5onjQTsg

This question will be open until it gets the right answer. Please feel
free to answer this question or comment until the end of time, I will
always want to know what this piece of music is. Thankyou in advance
for all your trouble and help, please don't post useless or demeaning
responses.

Thanks.