polarisation process, not the process itself. As a result, when used in a molecular
dynamics simulation, QCTFF renders immediately the energies of all atoms in
response to a given nuclear configuration. There is no need to iteratively converge
towards a self-consistent field at each simulation step.
2.5 An Invitation to Falsification
As announced in the Introduction there is a need for more falsification in the area of
chemical interpretation by means of quantum mechanical tools. In a first stage
contradictions need to be spotted: when are two methods providing (semi)-quantitatively or qualitatively different interpretations? The second stage is more challenging: how can an experiment judge one interpretation to be right and the other
wrong? A valiant but strongly disputed [87] example of this kind of scientific
activity was published [88] in 2009 where it was claimed that experiment could
disprove QTAIM’s interpretation of an attractive interaction between the two
hydrogens in the bay region of phenanthrene.
With regards to the second stage, one could broaden the decision process, not
through experiment, but by teasing out a clash with a theoretical principle or
another theoretical interpretation that is more firmly established. For example, a
number of electronegativity scales all agree that boron is a very electropositive
element. One may then ask how it is possible that a population analysis allocates a
negative net charge to boron. Yet this happens. For example, in 1995 Siegbahn
allocated a net charge −0.26e to boron in (BH 3 NH 3 ) 2 using the Mulliken population
analysis. Of course the QTAIM charge of boron is emphatically positive. Another
candidate for a falsifiable case study is that of 1, 2-difluoroethene, which was
discussed in a 2009 publication [89] comparing the IQA method (i.e. QCT) with the
non-QCT method EDA and NBO, in connection with interpreting stereo-electronic
effects. IQA rules that there is significant FF’ delocalisation in the cis isomer, which
is “not easily found in NBO” according to the article. This is a fine example of one
method spotting an effect and the other not. The challenge is to exploit this difference, either via an experiment that can confirm one or the other method, or
demonstrate that guidance (in synthesis for example) is more reliable by one
method than by the other.
A final example is that of diborane. A pivotal question is: can QTAIM and hence
QCT extract a Lewis diagram from a given molecular wave function? A very recent
study, published [70] in 2013, set out to answer precisely this question, and the
answer is yes. It is possible by inspecting motives in calculated V
AB
exch values, and
this 2013 work systematically investigated V
AB
exch values, for all atom-atom interactions in 31 small covalent molecules (including ions) and 3 van der Waals
complexes. For the first time, clear clusters were revealed in the values of V
AB
exch ,
clusters separated by almost an order of magnitude in energy, starting with hundreds of kilojoules per mole, and decreasing in a stepwise manner to less than
2 On Quantum Chemical Topology
45
dynamics simulation, QCTFF renders immediately the energies of all atoms in
response to a given nuclear configuration. There is no need to iteratively converge
towards a self-consistent field at each simulation step.
2.5 An Invitation to Falsification
As announced in the Introduction there is a need for more falsification in the area of
chemical interpretation by means of quantum mechanical tools. In a first stage
contradictions need to be spotted: when are two methods providing (semi)-quantitatively or qualitatively different interpretations? The second stage is more challenging: how can an experiment judge one interpretation to be right and the other
wrong? A valiant but strongly disputed [87] example of this kind of scientific
activity was published [88] in 2009 where it was claimed that experiment could
disprove QTAIM’s interpretation of an attractive interaction between the two
hydrogens in the bay region of phenanthrene.
With regards to the second stage, one could broaden the decision process, not
through experiment, but by teasing out a clash with a theoretical principle or
another theoretical interpretation that is more firmly established. For example, a
number of electronegativity scales all agree that boron is a very electropositive
element. One may then ask how it is possible that a population analysis allocates a
negative net charge to boron. Yet this happens. For example, in 1995 Siegbahn
allocated a net charge −0.26e to boron in (BH 3 NH 3 ) 2 using the Mulliken population
analysis. Of course the QTAIM charge of boron is emphatically positive. Another
candidate for a falsifiable case study is that of 1, 2-difluoroethene, which was
discussed in a 2009 publication [89] comparing the IQA method (i.e. QCT) with the
non-QCT method EDA and NBO, in connection with interpreting stereo-electronic
effects. IQA rules that there is significant FF’ delocalisation in the cis isomer, which
is “not easily found in NBO” according to the article. This is a fine example of one
method spotting an effect and the other not. The challenge is to exploit this difference, either via an experiment that can confirm one or the other method, or
demonstrate that guidance (in synthesis for example) is more reliable by one
method than by the other.
A final example is that of diborane. A pivotal question is: can QTAIM and hence
QCT extract a Lewis diagram from a given molecular wave function? A very recent
study, published [70] in 2013, set out to answer precisely this question, and the
answer is yes. It is possible by inspecting motives in calculated V
AB
exch values, and
this 2013 work systematically investigated V
AB
exch values, for all atom-atom interactions in 31 small covalent molecules (including ions) and 3 van der Waals
complexes. For the first time, clear clusters were revealed in the values of V
AB
exch ,
clusters separated by almost an order of magnitude in energy, starting with hundreds of kilojoules per mole, and decreasing in a stepwise manner to less than
2 On Quantum Chemical Topology
45