Psychopathy refers to a range of traits primarily including Antisocial, Borderline, and Narcississtic behavior. Superficially charming, a Psychopath frequently has a good first impression on other people and usually come across as a normal person. They have a notable, if not complete lack of ability to feel remorse, empathize, love, or even establish meaningful relationships, in combination with their immense egocentricity.
This category will include both Psychopaths and Sociopaths, since, in fiction, it's difficult to distinguish the two.
Psychopaths arean't always serial killers, murderers, or violent criminals. In fact, there are many who are highly capable business(wo)men but have a notable lack of guilt and difficulty with socialization.
To be classed as a Psychopath, the character in question must have at least one personality disorder from Cluster B (Borderline, Narcissistic, or Antisocial Disorders). Psychopaths may or may not have all 3, or they can have only one, or a combination of two of those disorders.