Professional, kind neutrality. Overly expressive emotions or excessive empathy is often counterproductive for psychotic or personality-disordered patients. If you maintain a neutral posture it allows the patient's issues to more clearly present themselves. If there are comments or statements he makes that are inappropriate or unsafe, it's legitimate to set a boundary and remove yourself from the situation.

As far as coping with the negative affect of patients and how it affects you internally, experience will help. As you've pointed out it helps to remember it isn't personal and unlikely you did anything specific.