Black - He isn't exactly a psycho, but he is a grim reaper so he has no compassion for humans.
Cheese in the Trap - There is definitely something off about the ml, and he is very interested in fl.
Cruel City - Ml is basically a crime boss, and although he doesn't want to he finds himself falling for fl. Very dark.
Flower of Evil - Ml doesn't really care about anyone other than his wife and daughter.
Lust, Caution - The ml is definitely evil in this one. Not a great guy. This is also a movie, and if you're under 18 you probably shouldn't watch it. If you're interested in it, I recommend reading the tags before deciding to watch it or not.
Moon Lovers - Ml is definitely on the darker side of morally grey in this one. At least in the beginning. But he loves the fl.
Terius Behind Me - He isn't evil, but he is a pretty cold dude and he softens up a lot when it comes to fl and her child.
The Master's Sun - Again, absolutely isn't evil, but he does lack a sense of empathy and care towards others. Which obviously changes when he meets fl. Though it takes him some time to warm up to her.
The Smile Has Left Your Eyes - Personally I didn't really like this one, but a lot of people did and it seems to fit your critera.
