i would recommend Vapor Snag over Murder because Vapor Snag is 1 mana instead of 3 and also Go for the Throat and Doom Blade

Maybe Trepanation Blade if you want to go further ahead with Undead Alchemist . For now he's just sitting there - a lonely 4x creature. Doesn't really do much for him. There are so many delicious black zombies, that even have undying, that would fit with him in your sideboard. :)

one of the things i'd watch out for is running two copies of Nephalia Drownyard . You've got quite a few 2 color requirement cards like Murder and Dissipate . I found the drownyards were really slow and in the long game I think you'd end up using the Sands of Delirium over those lands anyway. Check out a kind of similar build I made, What, no cards?, using red instead of black. I tried to make it really draw-heavy with card:Jace's Erasure and it works quite well because it tends to restock your hand while simultaneously milling your opponent.

@mattil

Undead Alchemist is a tool to be used with the milling. It's just really fun to use! I already have another deck with him and Trepanation Blade and I love it.