1. Many important contributions in this connection were published by Löwdin as technical reports of the Quantum Chemistry Group of Uppsala University between 1957 and 1962.
2. Among the papers by P.-O. Löwdin, we have in mind mainly his fundamental review cited below. The background and initial phase of his interest in orthogonality is well presented by John C. Slater in his famous treatise on the Quantum Theory of Molecules and Solids (New York: McGraw-Hill 1963)), where he refers in particular to the seminal paper of Löwdin’s master G. Wannier, “Structure and Electronic Excitation Levels in Insulating Crystals,” Phys. Rev. 52(1937), 191, and to Löwdin’s papers “On the Nonorthogonality Problem connected with the use of Atomic Wave Functions in the Theory of Molecules and Crystals,” J. Chem. Phys. 18(1950), 365 and “Note on Orthogonal Atomic Orbitals,” J. Chem. Phys. 19(1951), 220.
3. Wolfgang Weber, Walter Thiel: “Orthogonalization corrections for semiempirical methods,” Theor. Chem. Acc. 103(2000), 495–506.Most of the recent work on orthogonality was cited in Weber and Thiel’s paper.
4. Per-Olov Löwdin: “Quantum theory of cohesive properties of solids,” Phil Mag. Suppl. 5(1956), 1–172.
5. L. Pauling, The Nature of the Chemical Bond (Ithaca, N.Y.: Cornell U. Press 1960), p. 9lff.