Chapter 7, Harder Questions, Answers
Q8
The multielectron wavefunctionCis a function of the spatial and spin coordinates
of all the electrons. Physicists say thatCfor any system tells us all that can be
known about the system. Do you think the electron density functionrtells us
everything that can be known about a system? Why or why not?
Although the wavefunctionCseems to contain more information than the
electron density functionr(question 1), it ought to be possible in principle to
calculate any property of a system fromr, because different states – different
geometries, different electronic states, etc. – must have different electron distribu-
tions (or they would not be different). The problem is to transform the calculated
rto an energy (question 5).
Extraction of information fromrmay not be as elegant as fromC. For example,
the Woodward–Hoffmann rules follow fairly transparently from the symmetries of
molecular orbitals (wavefunctions), but deriving them fromrrequires using a “dual
descriptor” function [1].
Reference
- Ayers PW, Morell C, De Proft F, Geerlings P (2007) Chem Eur J 13:8240
Chapter 7, Harder Questions, Answers
Q9
If the electron density function is mathematically and conceptually simpler than the
wavefunction concept, why did DFT come later than wavefunction theory?
The wavefunction [1] and electron density [2] concepts came at about the same
time, 1926, but the application of wavefunction theory to chemistry began in the
1920s [3], while DFT was not widely used in chemistry until the 1980s (see below).
Why?
The DFT concept of calculating the energy of a system from its electron density
seems to have arisen in the 1920s with work by Fermi, Dirac, and Thomas.
However, this early work was useless for molecular studies, because it predicted
molecules to be unstable toward dissociation. Much better for chemical work, but
still used mainly for atoms and in solid-state physics, was the Xamethod, intro-
duced by Slater in 1951. Nowadays the standard DFT methodology used by
chemists is based on the Hohenberg–Kohn theorems and the Kohn–Sham approach
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