One aim of the Manhattan Project was increasing the availability of concentrated radioactive and stable isotopes, in particular C, S, P, and deuterium for heavy water. Harold Urey, Nobel laureate physical chemist known for his discovery of deuterium, became its head of isotope separation research while a professor at Columbia University. In 1945, he joined The Institute for Nuclear Studies at the University of Chicago, where he continued to work with chemist Jacob Bigeleisen and physicist Maria Mayer, both also veterans of isotopic research in the Manhattan Project. In 1946, Urey delivered the Liversidge lecture at the then-Royal Institute of Chemistry, where he outlined his proposed model of stable isotope fractionation. Bigeleisen and Mayer had been working on similar work since at least 1944 and, in 1947, published their model independently from Urey. Their calculations were mathematically equivalent to a 1943 derivation of the reduced partition function by German physicist Ludwig Waldmann.