Date a Live, Vol. 1 (Light Novel): Dead-End Tohka, Paperback/Koushi Tachibana

A little meet-cute in a decimated city April 10. The first day of school. Shido Itsuka is rudely awoken by his personal alarm clock--his little sister. It's shaping up to be another typical day...well, as typical as it gets on a planet plagued by massive spatial quakes. Little does Shido know, however, his life is about to take a sudden turn when he encounters the source of this destructive phenomenon--a girl his age, apparently known as a Spirit. Turns out, there are only two ways he can stop her from unleashing hell on the world: Eliminate her by force or placate her...by taking her out on a date and making her fall in love with him