schaefer was awarded the american chemical society's acs award in pure chemistry in 1979 "for the development of computational quantum chemistry into a reliable quantitative field of chemistry and for prolific exemplary calculations of broad chemical interest". the pure chemistry award is given to the outstanding chemist in america under the age of 35. in 1983 he received the leo hendrik baekeland award for the most distinguished north american chemist under the age of 40. in 1992, he was awarded the centenary prize of the royal society of chemistry, london, with a citation that included "the first theoretical chemist successfully to challenge the accepted conclusion of a distinguished experimental group for a polyatomic molecule, namely methylene."