Neither of them are natural English.
Student or Learner
I decided that with my free will.
I wanted that with my free will.
Are these sentences correct?
The second has an unnatural collocation of "want" and "free will".
"I decided that of my own free will" or "I did that of my own free will" work for the first.
I've read/heard "of one's own accord".
I think it means the same as "of one's own free will".
So which one is more useful in real life?
I've just changed "one's" to "my" in 'of one's own accord':
I find "based on" much less natural than "of" there.
So do I- based on is used with the thinking and reasoning, which is not the same. You free will implies that you made the decision without outside interference or pressure.