Is expiation incumbent upon someone who swore an oath in a state of extreme anger and then retracted it, and is it permissible for the expiation to be merely an intention to pay a sum of money to six needy persons?

If the other person does not do what you swore an oath upon, then there is no expiation (kaffarah) for you, as there is no breach of the oath. As for an oath of divorce, if a person swears to another that they will or will not do something, and ties their divorce to it, then the person sworn upon does what was sworn upon, there are two cases:

1. If the person sworn upon is someone whose actions can be prevented by the oath (like a wife or child), and they did the action forgetfully, unknowingly, or intentionally, then the oath is breached only in terms of divorce. 2. If the person sworn upon is someone whose actions cannot be prevented, and they did the action, then the oath is breached absolutely, in terms of divorce and otherwise.

In both cases, divorce occurs, and neither intention nor giving money in lieu of expiation is sufficient.