What type of murder gets you on death row?

My history teacher told us what types of murders can get you on death row... Like if you walk in on your wife cheating you can kill the guy and you won't get put on death row because it wasn't premeditated. I wasn't really paying attention though, I was upset because he was very pro-death penalty and my best friend at the time was a schizophrenic attempted murderer, who I thought was the sweetest guy ever and shouldn't be on death row if he had completed the (very much premeditated) murder... Yeah I realized how bad an idea it was to be his friend and dropped him. I still hate the death penalty, But whatever. What gets you on death row? Its been killing me trying to think of it.