He was wrongly portrayed in the comedy The Clouds. He does believe in the gods, therefore he is not a Natural Philosopher; and he does not influence others by lecturing in a one-sided manner, therefore he is not a Sophist. His name was only used in the play due to name recognition. Socrates name was well known during that time period, and was friends with Aristophanes. The comedy The Clouds portrays Sophists as teaching people to win an argument, such as Socrates use of right and wrong; and portrays Natural Philosophers as atheists who explain the world's phenomenon's through science instead of the gods, such as how Socrates says "no Zeus." This play is a comedy, which means that it is supposed to be humorous and be entertaining to people. The play is not about the life of Socrates, the play is about Sophists and Natural Philosophers; both of these groups are active during this time period and the play takes aim at them.
Mellitus convicted Socrates of not believing in the gods. The comedy the Clouds portrays Natural Philosophers as not believing in the gods, and this is probably where Mellitus gets the notion of that. If this was true then the journey of Socrates to the Delphic oracle was proof of his not-believing in the gods? The oracle was asked if anyone was wiser than himself, Socrates. The answer was no, there was no man wiser. Socrates found out that there was no one wiser, because he could admit that he did not know anything. This proves that he does believe in the gods and therefore could not be guilty of this crime.
Mellitus also convicts Socrates as being a Sophist. The Clouds portrays Sophists as teachers of the art of right and wrong to use against people in any argument, and says that Socrates does indeed do this. Socrates is a teacher, he is a teacher of Philosophy, his ways might have been deemed odd by some people but he was a teacher none the less of different ways to see things; not to winning arguments.