Hi cm
I personally think an email explaining things is a good idea. It may give both of you some form of closure.
I wouldn't go into too much ad would avoid throwing in too much blame. Just keep it simple and to the point
Hi ex
Im sorry how I behaved the other night. I was upset and didn't handle it well.
I feel that we can no longer be together because I can no longer deal with xyz.
I realise that I have played a part in the relationship ending up how it did.
I think that we need to give each other room to heal.
All the best.
cm
Or something like that.
You wont get any closure from dragging everything up in a vent. You may even end up feeling bad about it.
I sent something similar to my exgf. I never got an apology but did get a thank you (of sorts

).
Just a thought and purely based on my relationship dynamics.