Igoris progress

Ref: Depp's portrait by Annie Leibovitz. Looks like classical Rembrandt lighting.

If you look carefully at the sculpted head its chin and nostrils have a strong shadow underneath. The right eye socket and right cheek have a weak shadow. 

Another variant with more uniform shadows

Ref: Hitchcock's portrait by Philippe Halsman. This one's tricky. I suspect it was lit by a strip softbox in front and slightly to the left of the subject. Looking at other Halsman's works there probably was a lot of masking during printing as well.

Try using an area light, this will give you a softer light. Place it adjacent to the camera and screen right, to have more light on the face.

Hope this helps!

Softer shadows and more light on the face. Don't like the look of the chin though, seems like a bit of light is leaking there and giving it a weird look. Next attempt would be to block it with masks

Ref: a still from "Full Metal Jacket", light coming through a window + fill light to soften the shadows a bit

Actually, increasing contrast makes it much better and a bit closer to the original

Another variant with a more "nocturnal" look

I am sorry, Dave