My answer is colored by the fact that my AXH was emotionally abusive and an emotional manipulator who used every interaction as a way to try to "get me back" into the marriage.
I don't think you have any responsibility toward him whatsoever. None. I know I have to treat my AXH in a very behavioristical manner: What I say to him means jack sh*t; it's what I do that gets through. So every time he sent me an e-mail calling me names and telling me what an evil person I was, I ignored it and didn't respond. I only responded to direct questions ("Is DD taking trumpet lessons?" "No"). After a while, his e-mails dwindled to direct questions. (Well, until he completely lost his mind, but that's another ballgame...)
I don't get the comparison with a parent. With a parent or a child, I would want them to know why I've stopped communicating. With an ex I don't have children with, all I feel he needs to know is that it's over. He's out of my life, I don't care one whit what he thinks about me.