I had actually been wondering about this recently. People define a psychopath as someone with no empathy, and then jump to "therefore, they have no morals." But it doesn't seem impossible to value something or someone as a terminal value without empathizing with them. I don't see why you couldn't even be a psychopath and an extreme rational altruist, though you might not enjoy it. Is the word "psychopath" being used two different ways (meaning a non-empathic person and meaning a complete monster), or am I missing a connection that makes these the same thing?
The nearest term used in contemporary psychiatry is antisocial personality disorder. AFAIK some forensic psychiatrists use the term psychopath, but the criteria are not clear and it's not a recognized diagnosis. Forget about the press the term gets.
Lack of empathy certainly isn't sufficient for either label, and can be caused by other psychiatric conditions.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.