There's also Nuclear winter to contend with. 100 or more cities being destroyed throwing dust and soot into the air is enough to lead to problems with food production, leading to widespread famine. Still not enough to eliminate human life entirely, but severely unpleasant to undergo. For that, you'd need up look into a significantly larger explosion, enough to crack the Earth's crust and unbalance its orbit. It might be easier to deorbit the moon and crash it into the Earth.