A former graduate student under Ivar Waller, Löwdin formulated in 1950 the symmetric orthogonalization scheme for atomic and molecular orbital calculations, greatly simplifying the tight-binding method.
In 1956 he introduced the canonical orthogonalization scheme, which is optimal for eliminating approximate linear dependencies of a basis set.
[4][5] The famous 'Löwdin's pairing theorem' used in restricted open-shell Hartree–Fock (ROHF), unrestricted Hartree–Fock (UHF) and generalized valence bond (RES-GVB) theories is not his.
According to himself, George G. Hall and King made the formal proposition after an informal suggestion by Löwdin.
[citation needed] His Löwdin partitioning technique for quantum chemistry problems is best appreciated through the series of 14 papers on perturbation theory published between 1963 and 1971.