[23M] who has a [24F] toxic ex-girlfriend who won't stop emailing me despite my effort of cutting her out of my life

Calling this girl an ex-girlfriend is a stretch. She was in my life from July of last year to the end of January this year (~7 months). I had fallen in love with her, she told me the same, but the whole time it was toxic. Without going into details, she treated me with no respect and had effectively continued a relationship with her ex-boyfriend behind my back. I frequently would walk away and get suckered back in under the guise that she would change. One day we were arguing and she told me she never thought we would have worked out, even though she had previously told me the contrary. I left, blocked her on every form of social, and haven't spoken to her since (this was January 31).

She has been frequently trying to get back in contact with me. I have ignored texts, many emails, and comments from my friends that she's seen that she's asking for my number again. I've moved on. I've had a few flings since and am currently in the early stages of something new. Yesterday she emailed me the first cohesive (and likely sober) communication I've seen:

Hi [23M].

I know we haven’t talked in a long time. But I’d really like to grab a beer soon and talk. I know we’re both doing our own thing now, and I hope you’re happy. I just think it would be nice for both of us to get some closure. This is the only way I think I can contact you.

Please let me know. I think it would be really good for both of us.

Xoxo.

-[24F]

I'm looking for advise on if I should respond or not. I genuinely don't know if it is healthy or not to get back to her or continue to shut her out. I do not want to see her again as I know I will either get angry and vindictive or get suckered into her pity party. I don't feel the need for closure; I know what happened, I don't feel obliged to forgive her for anything, and I've acknowledged a long time ago that she isn't going to change. Am I being petty by continuing to ignore this girl?

tl;dr: Ex-girlfriend treated me poorly and was sleeping with her then ex-boyfriend during our time together. I walked away ~4 months ago and haven't spoken since. I've been ignoring her forms of contact. Am I at any obligation to respond?

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