Is it safe to drink water from a 2 liter bottled left open for a day?

Carcinogens are not a problem, since the water was in that bottle for a long time before you opened it. Plastics have a bad reputation, but you can be fairly sure the bottler does not want to kill his customers.

The problem is that bugs and dust may have entered the bottle. You can see any drowned bugs (unlikely), and the danger of dust is very small. I mean if such a small amount of dust can kill you, you need to abandon that area right away. (Mold in the walls of the house would justify that.)

General advice: Stop living in fear. Learn a few things about stuff you have to live with.

It is not advisable to drink water which remained open for long time. Nobody knows what happened with it during that period. As it is a matter of risk for our health, we should not compromise.