One can be rational "based on or in accordance with reason or
  logic." and also have justification ""the action of showing
  something to be right or reasonable." for murder. Sane
  "sensible, practical, advisable, responsible, realistic,
  prudent, wise, reasonable, rational, levelheaded,
  commonsensical, judicious, politic" shares the word rational.
  However, it's meaning is akin to a "reasonable person" and _not_
  necessarily Logic. One can use Logic and Reason to Justify
  Murder. They will consider themselves Sane, because Logic is
  Rational. But in that case, they will not fit the definition of
  a "Reasonable Man", which defines Rational differently than
  Logic. Pure Logic does not imply Sanity. Nor does it imply
  Insanity. it is unrelated. Care must be taken in defining the
  term Rational properly. It means something quite different in
  different contexts. Many a logical murderer has become confused
  at being referred to as Insane when they were being perfectly
  logical. They, in fact, were insane: "in a state of mind that
  prevents normal perception, behavior, or social interaction" -
  because they lacked what is considered "normal perception,
  behavior", etc. Social norms apply. A rational insane person can
  exist, should the rational person be rational by virtue of Logic
  rather than by what is considered "A reasonable man". However,
  all that being said: "What is a reasonable person?" really?
  That's where things get even trickier. Personally, my opinion is
  that the concept of the reasonable person should be scrapped
  entirely and replaced with "social norms". it's far more honest
  that way. I don't believe a Reasonable Man exists; and attempts
  to gauge "true intent" are quite difficult. Cognitive Science
  will slowly chip away at "free will" until there is
  justification provided (however 'insane' as it may be) that free
  will simply does not exist. Once free will does not exist, then
  no one is culpable for ANY crime. It's a slippery slope,
  externalism combined with brain scans. Remove the impetus from
  the man, and the man has no responsibility. But it's the
  direction things are going. Oh well. Eventually Science will
  likely take over the courts and i don't necessarily see that as
  a good thing. Science is not ready to be in charge of society
  just yet.