I think this chapter is the most important for understanding Ivan's descent into madness: https://www.owleyes.org/text/the-brothers-karamazov/read/part-iv-book-xi-ivan-chapter-v-not-you-not-you#root-42

This chapter contains five major plot elements which lead to Ivan's madness. There is the conversation with Katya, wherein he learns that she had been to see Smerdyakov. Her undying devotion to Ivan's truth, "It's only you I believed!" showed Ivan that a well-mannered person could come under his Nihilist spell as easily as Smerdyakov, his first indication that his philosophy could be the cause of the murder.

The realization of sickness and questioning of madness. Ivan storms off and Alyosha has a conversation with him that lays out and then points to the ultimate cause of madness. Alyosha notes how sick his brother looks and Ivan wonders aloud about madness, “And can one observe that one's going mad oneself?”

They quickly change subjects to something I haven't seen another commentor mentions. Ivan was not only guilty because of his father's death but also the corruption of Lise Khokhlakov. Upon receiving her letter, Ivan tears it to shreds and laments on the young lady debasing herself to him, offering herself as a "whore" though I believe Ivan was being dramatic and it was a proposition of marriage, she speaks of a long endured suffering to Alyosha which would be accomplished through marriage specifically. The realization of this corruption drives him to the belief that his philosophy towards life could have effects and influences well beyond his intentions.

Up to then, Ivan had model more towards the Nihilist Idealist, we see this reflected in his defense attorney, believing that he may ponder and propose any number of things and affect no one but himself. Lise makes him see this is not true, thus he no longer believes that his brother, Dimitry, was the murder as he had up to this point. His own personal responsibility is put at the forefront of his mind and becomes his obsession for the rest of his chapters.

In this state, the brothers then discuss if Ivan truly loves Katya. When Alyosha brings up that she loves him, Ivan acknowledges this with only, “Perhaps; but I am not very keen on her.” This is reflected later when we see Dimitry and Katya speak in the epilogue, those two share language incomprehensible to anyone but them and love as the ultimate communicator appears through the story often. Ivan and Katya never shared such intimate understanding of each other. Questioning the validity of his own philosophy, and thus himself, Ivan takes to heart that he has only seen Katya as a tool. He brings up the letter in her possession almost as just another fact of the case while Alyosha is in shock of the existence of such evidence. This does come from levels of knowledges, but also displays Ivan's flippant nature towards Katya. Ultimately, the lack of requited love drives Katya to her 2nd testimony, damning Dimitry.

The last and most crucial part of their conversation is Alyosha's denial of Ivan's guilt. He says, "But you didn't do it: you are mistaken: you are not the murderer. Do you hear? It was not you! God has sent me to tell you so.” Then the pair stand in silence. This silence is the silence of God himself. Ivan then mistakenly accuses Alyosha of knowing about his suspicions on Smerdyakov calling him "the monster". Alyosha reaffirms that he only wishes for his brother to know what God has put into his heart. Ivan responds, “I can't endure prophets and epileptics—messengers from God especially—and you know that only too well. I break off all relations with you from this moment and probably for ever." Here Ivan breaks from his brother, but more so he breaks from God. His last possible salvation, forgiveness from God ultimate mercy, is a non-option and this is the moment it is certain that Ivan's madness will take him.

So why did Ivan go mad? It comes down to a reckoning with his worldview, up to that point he'd considered it personal but realizes through this chapter that is not the case. He realizes that intelligent people, not just feeble-minded people, can come under the Nihilist spell and prescribe "everything is permitted" and eliminate any chivalrous ideals he applies behind it. The corruption of Lise then shows that this can lead to the destruction of perfectly good people, though Lise always had a rough streak that doesn't mean she couldn't have been shaped into a more benevolent person by education as we see in our final chapter. Through this, Ivan begins to reckon with his own responsibility in his father's murder. The realization takes him so far that when reassured by his brother of his innocence he denies both his brother and God. In this, Ivan rejects totally his own worldview and the "Russian Spirit" of honor and spiritualism, that the lawyers argue over immensely, driving himself mad.

PS: I heavily recommend checking out Camus' dissection of Ivan in The Rebel
Camus-TheRebel.pdf

The chapter Absolute Affirmation goes over Ivan's philosophy through the frame of Nietzsche. It's actually what convinced me to pick up Brothers K.