orderrbcan be defined in terms of the electron density, and the bond orderbABfor
two particular atoms A and B is then defined by an empirical equation obtained by
fittingrbto a few accepted A–B bond orders [ 279 ]. For example, for nitrogen/
nitrogen bonds a linear equationbAB¼aNNrbþbNNcorrelatesbABandrbfor, say,
H 2 N–NH 2 , HN¼NH and NN; from this equation bond orders can be assigned to
other nitrogen/nitrogen bonds from theirrbvalues. The main application of AIM
has been to investigate whether, in questionable cases, there really is a bond
between certain atoms. Recent (2006–2009) examples of this are studies of: the
differences between results from AIM and from other methods of population
analysis [ 280 ], hydrogen bonding top-donors [ 281 ], hydrogen bonding tos-donors
[ 282 ], and secondary interactions (i.e. weak bonding) in Diels–Alder reactions
[ 283 ]. Other recent applications are studies of strain energies in small rings [ 284 ]
and of electron distribution in protonated nitriles [ 285 ].
AIM theory and applications, and the inextricable question of the virtues and
defects of the wavefunction versus the electron density, have engendered an
entertaining series of polemics. Frenking censuredGillespie and Popelier for
being enamored with electron densityandslightingwavefunctions[ 286 ], eliciting
aspiritedreplyfromthoseauthors[ 287 ]andthenadefenceofhisreviewby
Frenking [ 288 ]. Bader jumped into the fray with a rather spirited appeal to
fundamental physics, defending what he took to be Schr€odinger’s prescient
view that the wavefunction should be regarded as a mathematical abstraction en
route to the electron density [ 289 ](amoresedatedefenceofAIMcalculationof
atom charges rebutted criticisms of charges as being not observable or not unique
[ 290 ]). A return to polemics wasseenwhenKovacsetal.[ 291 ]allegedly[ 292 ]
used “wrong physics” in interpreting the Laplacian of the electron density. This
educed a rebuke of (in a certain contextat least) “orthodox understanding of
physics” and an assertion that “Chemical research begins where the physics of
Richard Bader ends.” [ 293 ]. Another, almost anticlimactic, thread sprung from an
AIM analysis by Bader and coworkers that inferred bonding betweenortho-
hydrogens in planar biphenyl [ 294 ]. This was criticised by Poater et al. [ 295 ],
defended by Bader [ 296 ], and again criticised by Poater et al. with an interesting
reference to the apparent (accordingto AIM) bonding of helium trapped in an
adamantane cage [ 297 ].
There are many technical terms, qualifications, and fine points which could not
be gone into here. The reader will gather that the correct use of the AIM method can
be tricky, and one is urged to consult review papers and books for more details, and
to proceed with caution, especially if one is sensitive to criticism.
5.5.5 Miscellaneous Properties – UV and NMR Spectra,
Ionization Energies, and Electron Affinities
A few other properties that can be calculated by ab initio methods are briefly treated
here.
5.5 Applications of the Ab initio Method 359