Calling police may be overreaction that would have huge implications for his home life.
Calling the Police and them actually having a word with him, and letting him know that this is unacceptable will be better for his "home life" than him actually following through on his threat to the OP!
His threatening messaging is actually, right now, having huge implications for the OP's home life. She's scared, has contacted the Police, got a friend round, is too frightened to sleep, in her own home where she should be able to feel safe, and is making plans to stay elsewhere for a couple of nights.
Will people stop making excuses for this man and minimising his behaviour?! He is quite deliberately doing this, at the very least, to unsettle the OP.
She says that he is an intelligent, articulate man who works in a senior position. He knows full well that his attentions are not welcomed by the OP.
Women are damned if we do and damned if we don't. A direct unambiguous rejection can lead to verbal or physical violence, and indirect rejection - which the OP has used - can lead to verbal and physical violence and has already led, in this case, to intimidation and threat of violence.