Different countries have different constitutions and they follow different rules and regulations to deal with crimes. Some nations are quite rigid in dealing with some particular crimes and they follow law and order like tooth for a tooth and eye for an eye.
Before talking about the essential role of the death penalty, you have to think about the meaning, and the purpose, of any kind of punishment. If you consider that the purpose is to prevent the guilty from being nasty again, you can be seduced by an argumentation in favour of the suppression of capital punishment.