Does divorce occur in the following situations: when the husband threatens his wife by saying, "If you don't tell me tomorrow, I will do as so-and-so did and marry a female student of knowledge—no, rather, I will divorce you," with the intention of motivation, not enacting divorce; or when the idea of divorce comes to mind while searching for information about it; or when writing the word "we divorce you" while searching for its ruling, especially given the husband's suffering from obsessive-compulsive disorder?

Firstly, your statement to your wife, "If you don't tell me tomorrow, I will do as so-and-so did and marry a student of knowledge, no, rather I will divorce you then marry a student of knowledge," is a threat, and divorce does not occur by it unless you actually carry it out. If it was a conditional divorce intended to encourage her to memorize, then you would owe an expiation for an oath if she did not recite the categories of Tawhid (definition). However, she recited the categories that very night with your help, so divorce does not occur. You erred in using divorce as a threat and in your method of teaching.

Secondly, the obsessive thoughts (waswasa) you mentioned do not result in divorce. The cure for obsessive thoughts is repentance, increasing good deeds, and ignoring them.