Hermione's intelligence allows her to understand Snape's complex nature. She can analyze his actions and words more deeply than others. For instance, when Snape is being particularly harsh in class, Hermione realizes it's often because he's under a lot of pressure or has high standards. So she can comfort him by saying she understands his intentions. Her knowledge also helps her to find solutions to problems that are bothering Snape. If there's an issue with a potion or a magical object, Hermione can use her vast knowledge to fix it, which in turn comforts Snape as it eases his stress.
Hermione's intelligence means she can quickly spot flaws in Snape's statements. So, she can correct him, which annoys him. For example, if Snape makes a small error in a potion ingredient amount, Hermione will point it out right away.
Snape's brooding and mysterious personality might work in Hermione's favor. His intimidating presence alone could deter some of her enemies. People in the wizarding world might be afraid to cross him, so they would think twice before harming Hermione if they knew Snape was protecting her.
In the fanfiction, the relationship may start off with Snape being rather cold and distant towards Hermione as his familiar. However, as Hermione proves herself time and again, perhaps by using her unique skills to solve problems that Snape couldn't on his own, he starts to warm up to her. Their relationship then develops into a more complex one, where they have a mutual respect and a sort of unspoken understanding. This could involve Snape sharing some of his own magical knowledge with Hermione in a way that he would never do with other students, and Hermione in turn, helping Snape with his personal and professional matters, such as dealing with the other Hogwarts faculty or protecting the school from hidden threats.
She might give him cold stares in class. Hermione is not one to shy away from showing her emotions through her expressions. So, every time Snape is in her line of sight, she could fix him with a withering glare that clearly shows her displeasure.
Well, it often starts with a lot of misunderstandings. Snape has his own preconceived notions about Hermione as a Gryffindor student, and Hermione has her own view of Snape as a strict and often unfair teacher. However, as they live together, small moments start to change their relationship. For example, when Hermione is having trouble with a particularly difficult spell, Snape doesn't scold her but instead patiently guides her. This gradually builds trust between them, and they form a unique bond that is different from the typical student - teacher relationship or even a normal father - daughter relationship.
Snape might initially be shocked. He's not one to show much emotion openly, but internally he could be very disturbed. He might start investigating what happened to Hermione immediately, using his skills in potions and magic to try and find a cure or at least understand the cause.
It often changes the perception of Snape among other characters. When Hermione stands up for him, some characters who previously disliked or distrusted Snape start to question their own views. For example, in a fanfic, after Hermione's defense, Ron might start to see Snape in a new light and be less hostile towards him.
She might initially be shocked and scared. But then she would start to think rationally and try to find a way to outwit Snape. For example, she could start to gather evidence against Snape's own wrongdoings, if there are any, so that she can turn the tables on him.
She might use her extensive knowledge of magic. For example, she could brew a complex potion that cures a deadly curse Snape has been afflicted with. Hermione is known for her academic excellence in potions, so it's very likely she'd use this skill to save him.
One possible heartwarming scene could be when Hermione finds Snape in a moment of self - doubt. She might offer him words of affirmation about his skills as a potions master, reminding him how many students have actually learned a great deal from him. For example, she could say that his strict teaching methods, while intimidating, have made her and others more precise in their potion - making. Another scene could be Hermione using her intelligence to solve a problem that has been plaguing Snape for a long time, like a mystery regarding a potion ingredient's origin. This not only eases his worry but also makes him see Hermione in a new light. And perhaps there is a moment where Hermione simply sits with Snape in silence when he's had a particularly rough day, just being there as a comforting presence.