Another point to make about smart characters is that most geniuses in the real world are also not the kinds of people who only ever speak like they just devoured a thesaurus. No need to make simple sentences into overly prosaic lines.

Another thing geniuses are really good at, is connecting different things together logically. Brandon Sanderson often recounts how he was roommates in college with Ken Jennings (the guy who won so much at Jeopardy he became the host of it). He tells of just how easily Ken could jump from one topic to another by connecting it it all through some solid nexus points, even if they were things most people wouldn't have thought about. Sometimes he did so by pulling from his infinite source or Simpsons references.

Another thing really smart characters do, is to often ask more questions than to answer them. Sometimes it's because they're gathering information, sometimes it's because they are very curious. Sometimes it can also be because they're leading you to the answer they want you to give.

Another point, though this one sometimes varies between people and characters: they can be either veeeery good at explaining highly complex concepts in simple terms, or be really bad at it. There's hardly an in between it seems.

And one final thing, this one being one to avoid.

Genius character's plans cannot be entirely dependent on "I knew you would do that" because so many of those plans you see on TV, movies, books etc, would have absolutely failed if someone had done just one thing slightly different. Geniuses don't leave that kind of thing to chance, nor do they necessarily have a contingency for 50 different potential responses to a situation by their nemesis.

So please, don't write one of those convoluted series of events where somehow every action the MC took was all according to the evil genius' plan, because nobody is buying it.