I was in a relationship with a psychopath. Love does not matter to these people. Your emotions do not matter to these people. Your intentions do not matter to these people. The only thing that matters to a psychopath is their own ego and self-aggrandizement. You're taking an incredibly naive view that will likely leave you completely taken advantage of and hurt. It doesn't matter how much love you show a psychopath, it won't ever be enough. They will try to manipulate you to make you feel like you're not doing enough for them. They will be the victim when it suits them and helps their argument, or they will be the victor when it suits them.
Love does not matter to a psychopath. I gave her every ounce of love I had available to me, every ounce of understanding and care. It might as well have not happened. She still thinks (I'm not sure if she genuinely believes this, or is just trying to be manipulative) that I was a horrible boyfriend who was too selfish to give her what she needed (I paid for her to live in my apartment, I paid for about 95% of her food, I helped her find her first job, I helped her move cities).
Love does not matter to a psychopath. The only way to win that game is not to play.