Computational Chemistry

These values are somewhat better than the ab initio MP2 energy difference values,
and are considerably better than MP2 Koopmans’ theorem IEs. Rough estimates of
electron affinities can be obtained from the negative LUMOs from LSDA func-
tionals (gradient-corrected functionals give much worse estimates). For conjugated
molecules, HOMO-LUMO gaps from hybrid functionals agreed well with the
p!p* UV transitions. The mutually related concepts of electronic chemical poten-
tial, electronegativity, hardness, softness, and the Fukui function are usually dis-
cussed within the context of DFT. They are readily calculated from ionization
energy, electron affinity, and atom charges.

References....................................................................

1. (a) Whitaker A (1996) Einstein, Bohr and the quantum dilemma. Cambridge University Press,
   Cambridge (b) Yam P (June 1997) Scientific American, p 124 (c) Albert DZ (May 1994)
   Scientific American, p 58 (d) Albert DZ (1992) Quantum mechanics and experience. Harvard
   University Press, Cambridge, MA (e) Bohm D, Hiley HB (1992) The undivided universe.
   Routledge, New York (f) Baggott J (1992) The meaning of quantum theory. Oxford, New York
   (g) Jammer M (1974) The philosophy of quantum mechanics. Wiley, New York


2. Bader RFW (1990) Atoms in molecules. Oxford, New York


3. Reference 2, pp 7–8


4. Shusterman GP, Shusterman AJ (1997) J Chem Educ 74:771


5. Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford, New
   York, p 53


6. (a) Wilson E (1998) Chem Eng News October 19:12 (b) Malakoff D (1998) Science 282:610


7. See e.g. Diacu F (1996) Mathematical Intelligencer 18:66


8. Kohn W (1951) Phys Rev 84:495


9. Cf. Levine IN (2000) Quantum chemistry, 5th edn. Prentice Hall, Upper Saddle River, NJ,
   p 422, equation (13.130); cf. p 624, problem 15.67, for the Kohn–Sham orbitals. The
   multielectron wavefunction is treated on pp 421–423


10. L€owdin P-O (1955) Phys Rev 97:1474


11. Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford,
    New York


12. Koch W, Holthausen M (2000) A chemist’s guide to density functional theory. Wiley-VCH,
    New York


13. Levine IN (2000) Quantum chemistry, 5th edn. Prentice Hall, Upper Saddle River, NJ, pp
    573–592


14. Friesner RA, Murphy RB, Beachy MD, Ringnalda MN, Pollard WT, Dunietz BD, Cao Y
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15. Kohn W, Becke AD, Parr RG (1996) J Phys Chem 100:12974


16. Parr RG, Yang W (1995) Annu Rev Phys Chem 46:701


17. Cramer CJ (2004) Essentials of computational chemistry, 2nd edn. Wiley, New York,
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18. Jensen F (2007) Introduction to computational chemistry, 2nd edn. Wiley, New York,
    Chapter 6


19. E.g. Griffiths DJ (1995) Introduction to quantum mechanics. Prentice-Hall, Engelwood
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20. Earlier work (1927) by Fermi was published in Italian and came to the attention of the
    physics community with a paper in German: Fermi E (1928) Z Phys 48:73. This appears
    in English translation in March NH (1975) Self-consistent fields in atoms. Pergamon, Oxford

512 7 Density Functional Calculations