A former graduate student under [Ivar Waller], Löwdin formulated in 1950 the symmetric orthogonalization scheme for molecular orbital calculations. This scheme is the basis of the zero-differential overlap (ZDO) approximation used in semiempirical theories.
The famous 'Löwdin pairing theorem' used in ROHF, UHF and RES-GVB theories is not his. According to himself, George G. Hall and King made the formal proposition after an informal suggestion by Löwdin.
He was also a very active teacher, starting the Summer Schools of Quantum Chemistry at Uppsala around 1958. In 1959-1960 Löwdin started the Quantum Theory Project at the University of Florida as a sister project to the Uppsala Quantum Chemistry Group. In 1964 he was joined by John C. Slater from MIT. The International Winter Institutes (held initially at Sanibel Island, and later at Gainesville) provided the initiation of hundreds of Latin American young scientists during the eighties and nineties. In 1960 he founded the Sanibel Symposium in conjunction with the Winter Institute. They have been held every year since 1960 with the 47th symposium held in 2007.
Löwdin was a member of the committee for the Nobel Prize in physics for many years, and the founder of the International Journal of Quantum Chemistry and of the series Advances in Quantum Chemistry. He was a foundation member of the International Academy of Quantum Molecular Science.