History of Orbital Definition While presenting at the 1979 Sanibel Symposium I had the occasion to ask Per Olov L wdin for his definition of an orbital Without hesitation he told me that it was first used by Robert S Mulliken in 1925 as the English translation of Schroedinger s use of the German word Eigenfunktion Mulliken had been working in Germany in 1925 with many of the founders of Quantum Mechanics and particularly in 1927 with Friedrich Hund on the beginnings of molecular orbital theory Mulliken presented his work at that time in Physical Review L wdin told me to look there for the first use of a hydrogen orbital in English He also agreed that a suitable definition of an orbital would be a mathematical function that describes the wave like behavior of an electron I will edit the definition to reflect this usage of the term as a mathematical function but also connect it to the more general description of an orbital as a region of space that can be calculated from the function The advent of graphing calculators has enabled even high school students to grasp the definition of an orbital as a mathematical function I invite educators to have their students graph the simplified 1s orbital y exp abs Z x where Z 1 2 3 Atomic Number This simple exercise can display the effects of electronegativity and the fact that atoms and isoelectronic ions decrease their size in going to the right in a row in the periodic chart The bonding and antibonding sigma MO can also be displayed by y exp abs Zx 1 or exp abs Zx 1 After graphing functions students can grasp the idea of combining functions atomic orbitals to get other functions molecular orbitals and what is meant by the and signs or the red blue white gray colors of the orbitals As for some measure of proof please see Mulliken s 1966 Nobel acceptance speech I fully support your edits They are an improvement The source above does need adding however I was not at Sanibel in 1979 but I was in 1982 and 1990 and I recall some others