Some states have it on the books, and it is carried out frequently.
No state carries it out frequently. Texas probably has the greatest frequency of any state, both percentage of murder wise and actual numbers wise. And even Texas only executes a very small fraction of the murders that occur in The State of Texas.
Consider this: In 2009 there were 1,328 recorded murders in the State of Texas; and in 2009 there were 24 executions in the State of Texas. (Even considering the executions were for murders occurring in earlier years, this data gives you a very good idea how few murderers are executed even in Texas.)
And herein lies the problem. What good is the death penalty when its application is almost nil — even in the state its most famous for! Few people realize this reality.
Once you fix this issue, and apply the penalty across the board for murder, you’re a long way towards solving this issue. This is the only just penalty for murder, even aside from any possible deterrent effect.