Are you talking about the Roman Empire or the city of Rome?

The city still exists and was never completely abandoned but having its population drop from 1 million to less than 50000 is a significant change. I guess, if you consider this change a "collapse" depends if you think it dropped fast enough.

How much the fall of the (western) Roman Empire was due to or was accelerated by environmental factors is still up to debate. Was the migration period caused by climate changes? Or what role did the deforestation of the Italian peninsula play?

Rome did not collapse at all, it just entered a long slow decline period where the central power became less and less effective while independent city states thrived and created numerous works of art, developed scientifically and commercially and militarily, and generally weren’t particularly aware that there was a “collapse” going on.