Computational Chemistry

for implementing them (1964, 1965). It is not far from the truth to say that the use of
DFT in chemistry began, with this method, in the 1960s. The first such calculation
was on atoms (1966) [4], with molecular DFT calculations picking up steam in the
1970s [5], and starting to become routine ca. 1990 [6].
The reason for the delay is that it took the Kohn–Sham approach to initiate
practical DFT calculations on molecules, and time was needed to “experiment”
with techniques for improving the accuracy of calculations [7]. As for why the
Hohenberg–Kohn theorems and the Kohn–Sham insight came not until 40 years
after the wavefunction and electron density concepts, one can only speculate;
perhaps scientists were mesmerized by the peculiarities of the wavefunction [8],
or perhaps it simply took the creativity of specific individuals to usher in the era of
widespread density functional calculations.

References

1. The Schr€odinger equation applied the wave concept of particles to a classical wave equation
   yielding wavefunctions as solutions: Schr€odinger E (1926) Ann Phys 81:109


2. The interpretation of the square of the wavefunction as a measure of electron density in atoms
   and molecules arose from a slightly different suggestion by Max Born: Born M (1926) Z Phys
   37:863. See Moore W (1989) Schr€odinger. Life and thought. Cambridge University Press,
   Cambridge, UK, pp 219–220, 225–226, 240, 436–436


3. Both the early molecular orbital and the early valence bond approaches used wavefunctions: (a)
   Molecular orbital, e.g. Pauling L (1928) Chem Rev 5:173. Lennard-Jones E (1929) Trans
   Faraday Soc 25:668. (b) Valence bond: Heitler W, London F (1927) Z Phys 44:455


4. Tong BY, Sham LJ (1966) Phys Rev 144:1


5. A search of Chemical Abstracts with SciFinder using the article title words “density functional”
   gave for 1950–1970, only one publication, but for 1971–1979, 111 publications, and for 1980,
   45 publications


6. Borman S (1990) Chemical and Engineering News, April 9, p 22


7. For a short exposition of the evolution from the local-density approximation to the local-spin-
   density approximation and gradient-corrected and hybrid functionals, see Levine IN (2000)
   Quantum chemistry, 5th edn. Prentice Hall, Upper Saddle River, NJ, pp 581–592


8. E.g. (a) Baggott J (1992) The meaning of quantum theory. Oxford Science Publications,
   Oxford. (b) Whitaker A (1996) Einstein, Bohr and the quantum dilemma. Cambridge Univer-
   sity Press, Cambridge, UK

Chapter 7, Harder Questions, Answers

Q10

For a spring or a covalent bond, the concepts of force and force constant can be
expressed in terms of first and second derivatives of energy with respect to
extension. If we let a “charge space”Nrepresent the real space of extension of
the spring or bond, what are the analogous concepts to force and force constant?
Using the SI, derive the units of electronegativity and of hardness.

Answers 645