1. General discussions of and references to ab initio calculations are found in: (a) Levine IN (2014) Quantum chemistry, 7th edn. Prentice Hall, Engelwood Cliffs; (b) Lowe JP (1993) “Quantum chemistry”, 2nd edn. Academic Press, New York; (c) Pilar FL (1990) Elementary quantum chemistry”, 2nd edn. McGraw-Hill, New York; (d) An advanced book: Szabo A, Ostlund NS (1989) “Modern quantum chemistry”. McGraw-Hill, New York; (e) Foresman JB, Frisch Æ (1996) “Exploring chemistry with electronic structure methods”. Gaussian Inc., Pittsburgh; (f) Leach AI (2001) “Molecular modelling, 2nd edn”. Prentice Hall, Essex, England; (g) A useful reference is still: Hehre WJ, Radom L, Schleyer PVR, Pople JA (1986) “Ab initio molecular orbital theory”. Wiley, New York; (h) An evaluation of the state and future of quantum chemical calculations, with the emphasis on ab initio methods: Head-Gordon M (1996). J Phys Chem 100, 13213; (i) Jensen F (2007) Introduction to computational chemistry, 2nd edn. Wiley, Hoboken, New Jersey; (j) Dewar MJS (1969) The molecular orbital theory of organic chemistry. McGraw-Hill, New York. This book contains many trenchant comments by one of the major contributors to computational chemistry; begins with basic quantum mechanics and ab initio theory, although it later stresses semiempirical theory. (k) Young D (2001) Computational chemistry. A practical guide for applying techniques to real world problems. Wiley, New York; (l) Cramer CJ (2004) “Essentials of computational chemistry”, 2nd edn. Wiley, Chichester
2. Regarding the first use of the term in chemistry: Dewar casts aspersions on this (Dewar MJS (1992) “A semiempirical life”, profiles, pathways and dreams series. In: Seeman JI (ed). American Chemical Society, Washington, D.C., p. 129) by saying that in the paper in which it evidently first appeared (Parr RG, Craig DP, Ross IG (1950). J Chem Phys 18 1561 it merely meant that the collaboration of Parr on the one hand with Craig and Ross on the other had been carried through from the start in Parr’s lab. However, the PCR paper states “The computations, which are heavy, were carried through independently ab initio by RGP on the one hand, and DPC and IGR on the other.” In this author’s view this means either that both groups did the calculations independently from the beginning, or it is conceivably a nod to the complexity of evaluating complicated integrals without semiempirical assistance in those pre-computer days, and may then indeed be taken as being consonant with the current meaning of the term. Rudenberg states (Rudenberg K, Schwarz WHE (2013) Chapter 1 in “Pioneers of quantum chemistry”, ACS Symposium Series 1122, Eds. E. T. Strom, A. K. Wilson, American Chemical Society, Washington, DC, p. 36) that he recalled the use of ab initio by Mulliken in a lecture at the University of Chicago sometime in 1953–1955. The first appearance in print in its unambiguous modern sense seems to be Chen TC (1955). J Chemical Physics 23 2200, where it is explicitly contrasted with the term semiempirical.
3. Hartree DR (1928) Proc Cambridge Philos Soc 24:89
4. (a) The relativistic one-electron Schrödinger equation is called the Dirac equation. It can be used with the Hartree-Fock approach to do Dirac-Fock (Dirac-Hartree-Fock) calculations; see Levine IN (2014) Quantum chemistry, 7th edn. Prentice Hall, Engelwood Cliffs, section 16.11; (b) For a brief discussion of spin-orbit interaction see Levine IN (2014) Quantum chemistry, 7th edn. Prentice Hall, Engelwood Cliffs, section 11.6
5. The many-body problem in chemistry has been reviewed: Tew DP, Klopper W, Helgaker T (2007). J Comp Chem 28 1307