i guess you want to know the reasons that why somee organic chemicals are resistance in the environment. The reasons might include high chemical stability (to UV, radical, O2, heat and others), high toxicity to organisms, and low bioavailability (biodegradation).

Persistent organic pollutants (POPs) are, by definition, organic compounds that are highly resistant to degradation by biological, photolytic or chemical means and thus remains in the environment for a long period of time (many years).

I don't think this can be a general formula for all POPs but i believe most POPs have high octanol/water partition coefficiens (Kow). On a log scale, it is likely that most POPs have Log Kow > 4 or even 5. Thus they tend to bioaccumulate, be toxic, etc. As i said, this is just a very broad approach but at least it might help you conduct a preliminary screening. 

thanks to all for your views