Date a Live: Tohka Dead End

Shido Itsuka was born in a world where widespread catastrophes of varying size called spacequakes can happen anytime and anywhere, razing everything in the vicinity. When his city's alarm forewarns one impending, the teenager races to his sister Kotori in an attempt to rescue her. But upon his arrival, the spacequake transpires in that very spot, and standing in the middle of the destruction is a beautiful sword-wielding girl. Soon after, he learns she is one of many beings called "Spirits" who cause the disasters, and charming those like her is the solution to preventing them. Effective immediately, Shido must date Spirits and make them fall in love with him, because if he cannot, mankind's destruction may very well be inevitable.