The density response matrix occurs in 10 total terms (A 5 , B 6 , A 9 , B 9 , A 11 , A 12 , B 12 , A 13 , A 14 , B 14 ). We will first consider those terms where ρ contains one target index (A 11 , A 16 , A 18 , A 24 ), which can be written as: