in detail the relative merits of a wavefunction and an electron density approach to
chemical structure and bonding requires a pretty deep knowledge of quantum
chemistry. There is no question that electron density is a valid and useful concept
in chemistry, and that it is more easily grasped intuitively than the wavefunction.
But logically, there is no basis for thinking that ease of understanding is correlated
positively with the likelihood of physical reality. Is electron density physically
more real than a wavefunction? Electron density in molecules is certainly physi-
cally real: it can be measured by X-ray crystallography [12] or electron scattering
[13]. Is the wavefunction real or is it a mathematical abstraction? This is controver-
sial, and pursuing it would take us well into physics and even perhaps philosophy.
In the orthodox interpretation of quantum mechanics (QM), from the Copenhagen
school of Bohr and Heisenberg, observation of a system causes “collapse of the
wavefunction” [14], implying that it is real. This school was practically unchal-
lenged for decades, but alternative interpretations of QM are now being given a
hearing [14], and in some there is no wavefunction collapse, such as with quantum
decoherence [15] and (de Broglie and more recently Bohm) the pilot wave concept
[16]. A reaction to all interpretations of QM is an article entitled “Quantum theory
needs no ‘interpretation’” [17].
As chemists we can pose a simple, focussed question: how do the Woodward–
Hoffmann rules (WHR) [18] arise from a purely electron density formulation of
chemistry? The WHR for pericyclic reactions were expressed in terms of orbital
symmetries; particularly transparent is their expression in terms of the symmetries
of frontier orbitals. Since the electron density function lacks the symmetry proper-
ties arising from nodes (it lacks phases), it appears at first sight to be incapable of
accounting for the stereochemistry and allowedness of pericyclic reactions. In
fact, however, Ayers et al. [19] have outlined how the WHR can be reformulated
in terms of a mathematical function they call the “dual descriptor”, which encapsu-
lates the fact that nucleophilic and electrophilc regions of molecules are mutually
friendly. They do concede that with DFT “some processes are harder to describe than
others” and reassure us that “Orbitals certainly have a role to play in the conceptual
analysis of molecules”. The wavefunction formulation of the WHR can be pictorial
and simple, while DFT requires the definition of and calculations with some
nonintuitive (!) density function concepts. But we are still left uncertain whether
the successes of wavefunctions arises from their physical reality (do they exist “out
there”?) or whether this successes is “merely” because their mathematical form
reflectsan underlying reality – are they merely the shadows in Plato’s cave? [20].
References
- Frenking G (2003) Angew Chem Int Ed 42:143
- Gillespie RJ, Popelier PLA (2001) Chemical bonding and molecular geometry from Lewis to
electron densities. Oxford University Press, New York - Gillespie RJ, Popeleir PLA (2003) Angew Chem Int Ed 42:3331
- Frenking G (2003) Angew Chem Int Ed 42:3335
- Bader RFW (2003) Int J Quant Chem 94:173
638 Answers