What you describe really does seem like a love hate relationship. Sometimes when this is true people get almost addicted to the intensity of the relationship the way it is and see a stable long term relationship without this turmoil as almost boring. If her psychiatric diagnosis contains some sort of mood disturbance this can also influence the intensity of the relationship. You can only make changes particular to you because of course you cannot change someone else. This means that you can only reach out in the hopes that she doesn't want closure. Your efforts regardless of the mode that you use to communicate are only going to be as successful as she allows them to be. You have to consider that she has to be receptive to your efforts. If she is then any effort to reach out will be successful whether that is calling, texting, emailing or any other form of communication.
If she truly is determined to keep you away then that sends a powerful message. Sometimes people get very close before they realize they are incompatible. The tension may just be petty differences or it could be total incompatibility. Anyone can be receptive even after tension but if she is an unforgiving person that will make your efforts more ineffective. Being kind doesn't create a relationship in and of itself.
I would make an effort and then accept the situation that follows. You can't make this work by yourself but to have closure you should make whatever efforts you find most comfortable.
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