Disagree, I believe first degree murderers should get the death penalty. If your action was premeditated, you should pay your externality (in the same way I believe a thief should be fined proportional to the amount they stole).
There will always be the possibility that someone is wrongfully convicted and executed. Even if just one person had ever been wrongfully executed, that is one too many.
Suppose 1 person is wrongly executed for every 19 people correctly executed. Furthermore, suppose that executing 1 person deters 0.1 first degree murders on average. Then, the total number of innocent people dead would be smaller with the death penalty. The problem is that there are no perfect solutions.
The death penalty does not deter murderers.