explain or explanation and others

  1. He has left the room without explaining/ explanation.

  2. They left the house in a frightening/ frightful mess.

I see it as follows:

  1. He has left the room without explanation.–OK He has left the room without explaining [not finished. You need a follow-up here:…explaining himself\how much he loves her\how he got there.]

  2. –Expected wording here is a ‘frightful mess’. (‘frightful’ used for emphasis, especially of something bad). ‘Frightening’ (= terrifying) would sound differently—you’d expect to find something really stressful in such a house: damaged gas pipes\ heating system out of order (in freezing temperatures)\ deformed walls etc.