Magnetic Aromaticity from NICS to Bond Magnetizability
by
Cina Foroutan-Nejad
Nucleus Independent Chemical Shift, NICS, is one of the most employed probes for measuring the so-called "magnetic
aromaticity", whatever it is!1
NICS has been used for measuring and comparing the "aromaticity" among different classes of
molecules containing main-group and transition-metal atoms. But, to what extent NICS really measures the "electronic ring
current", which is assumed to be the source of magnetic aromaticity.
We performed a systematic study to probe the influence of various factors on the magnitude of the NICS values.
Our investigations suggest that NICS values might be contaminated by two main factors; the local electron density 2
and the
size of aromatic rings. 3
Measuring the influence of ρ(r) on the magnetic shielding of arbitrary points in molecular space, i.e. NICS, is not a trivial
task. We assumed the following form for the influence of ρ(r) on the non-atom centered shielding, i.e. NICS:
ρ eq. 1
Here, the g(r) measures pure contribution of the electronic currents at a point in space and the F [ρ(r)] is an unknown
functional of ρ(r) which measures the influence of electronic matter at the same point of space. This equation is a mixed
equation; composed of a ground state, ρ(r), and a responseproperty, g(r). The real indicator of aromaticity in this equation is
the g (r), which results from the electronic currents. Since the proper form of F [ρ(r)] is unknown, one may remove the
ground state contribution by studying the NICSzz in the limit of zero electron density.
( ) eq. 2
On the other hand, we proposed a classical ring current model to measure the "ring current intensity", I, which can be related
to the magnetic aromaticity. Some models have been proposed for simulating electronic currents in aromatic rings.4
However, these models are not capable of reproducing the ring currents in π-MOs. Indeed, the π-electron density of a planar
aromatic molecule should be zero on the ring plane; a successful model must reflect this simple fact. Accordingly, we
employed a double current loop model for measuring the π-ring current intensity as follows:
(( ) ( )) eq. 3
In the equation 3 σπ, μ0, Iπ, Bext, R, z and r represent the π-magnetic shielding, the permeability of vacuum, π-ring current
intensity, the strength of external applied field, the π-current loop radius, the direction perpendicular to the ring plane and the
height of the current loop radius above (and below) the ring plane of the molecule, respectively. This model clearly showed
that the ring radius is an important factor on the magnitude of non-atom centered magnetic shieldings, e.g. NICS values.
The bond magnetizability, defined within the context of the quantum theory of atoms in molecules, QTAIM, was the latest
probe that we employed for evaluating our assumption regarding the NICS. The bond magnetizability, χ(Ω|Ω'), measures the
extent of the contribution of the induced electronic current flux that passes through the inter-atomic surface between two
neighboring atoms, Ω and Ω'.5
This is in close analogy with the "flux of current density" that is used by Monaco et al. for
probing aromaticity among various aromatic systems.6
Surprisingly, these three approaches for measuring the magnetic aromaticity converge into the same conclusion; this
convergence between three independent methods demonstrates validity of the initial proposal about the nature of NICS.
1. Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta and P. v. R. Schleyer, Chem. Rev., 2005, 105, 3842.
2. (a) C. Foroutan-Nejad, S. Shahbazian, P. Rashidi-Ranjbar, Phys. Chem. Chem. Phys., 2010, 12, 12630; (b) C. Foroutan-Nejad, S.
Shahbazian, P. Rashidi-Ranjbar,Phys.Chem. Chem. Phys., 2011,13,12655; (c) C. Foroutan-Nejad, Z. Badri, S. Shahbazian, P. RashidiRanjbar,
J. Phys. Chem. A, 2011, 115, 12708.
3. C. Foroutan-Nejad, S. Shahbazian, F. Feixas, P. Rashidi-Ranjbar, M. Sola, J. Compute. Chem., 2011, 32, 2422.
4. J. Juselius, D. Sundholm, Phys. Chem. Chem. Phys., 1999, 1, 3429.
5. C. Foroutan-Nejad, J. Phys. Chem. A, 2011, 115, 12555.
6. G. Monaco, R. Zanasi, S. Pelloni, P.Lazzeretti, J. Chem. Theory Compute., 2010, 6,3343.