In the late 1950s and early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. In outer-sphere reactions an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several useful expressions, one of which has come to be known as the Marcus cross-relation or the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel prize in chemistry.