Chemical Communications RSC
COMMUNICATION
This journal is © The Royal Society of Chemistry 2012 Chem. Commun., 2015, 00, 1-3 | 1
How does relativity affect magnetically induced
currents?
R. J. F. Berger,
a
* M. Repisky
b
and S. Komorovsky
b
*
Magnetically induced probability currents in molecules are
studied in relativistic theory. Spinorbit coupling (SOC)
enhances curvature and gives rise to a previously
unobserved current cusp in AuH or small bulgelike
distortions in HgH
2
at the proton positions. The origin of
this curvature is magnetically induced spindensity arising
from SOC in the relativistic description.
Under terrestrial conditions magnetic fields are omnipresent and
even in environments free of external magnetic fields nuclear
magnetic moments are present. The magnetically induced probability
current density (j
B
) is the fundamental property in the description of
the magnetic response of a molecule. Various programs for the
computation of numerical approximations to j
B
have been
developed,
[1,2,3]
and exemplary studies have been reviewed some
years ago.
[4]
Other magnetic response properties like the magnetic
susceptibility, induced magnetic multipole0moments or even
chemical shieldings can directly be calculated from j
B
.
[5]
j
B
can be
determined experimentally, as it was shown in two conceptional
studies using polarized neutron diffraction.
[6,7]
Two of us (SK, MR)
have developed in the framework of the program ReSpect
[8]
methods
for a fully relativistic four0component treatment (FR) capable to
calculate j
B
in polyatomic molecules. In this current version of
ReSpect also a physically consistent determination of the influence
of solely the relativistic spin0orbit coupling (SOC) contribution to j
B
is possible. This is one of the first investigations where particular
SOC contributions to FR molecular currents are reported. The only
other work where a FR method was employed to analyze the SOC
contribution to j
B
involved the Sternheim approximation
[9]
to the
diamagnetic contribution of the response current.
[10]
Later Sulzer and
coworkers overcame this approximation by using the simple
magnetic balance approach but they have not regarded the specific
nature of the SOC contributions they yielded.
[11]
In this work we are
using a computationally efficient solution based on the restricted
magnetic balance framework.
[12]
We have chosen gold(I)hydride
(AuH) and mercury(II)bishydride (HgH
2
) as subjects of this study
due to their simplicity and since they are in the non0relativistic (NR)
framework single reference singlets.
Not taking SOC into account (computational details are described in
the Electronic Supplementary Information), AuH sustains one large
gold centered diatropic (inductively weakening the external field B)
current loop (see Fig. 1 b) with a distinct extension directed to the
proton. At the FR level (Fig. 1 a) the current topology remains
unchanged, however, it appears that the current loops contain
considerably more curvature around the atomic cores and most
notably a kind of current cusp appears at the position of the proton,
which without regarding SOC effects (non0SOC) is passed over by a
smooth current. Such a cusp structure in molecular ring currents, to
the best of our knowledge is previously unobserved. The current
difference plot (FR minus non0SOC, Fig. 1 c) shows that this cusp
originates solely from SOC, causing a strongly localized ring current
around the proton. It can be easily seen, that a ring current of
suitable orientation when added to a smooth current field with little
curvature, yields a total current of such a cusp shape. However, it is
required that the strength of the ring current contribution in the area
of the cusp is approximately constant and equal in strength to the
smooth current field contribution. Apparently, these conditions are
met in case of AuH. In a homogeneous magnetic field of 1 T
strength the total current of the SOC induced vortex around the
hydrogen atom integrates (see ESI for computational details) to 1.6
nA (see ESI for computational details). This additional diatropic
vortex causes an SOC induced high field shift in the chemical shift
of the proton of about 019 ppm compared to the non0SOC calculation
(FR shielding: 54 ppm, non0SOC shielding: 35 ppm). The
corresponding difference (FR minus non0SOC) of only the z
components of the shielding tensor, which can be directly (without
taking into account directional averaging) related to the integrated
and plotted j
B
field, is 030 ppm. To quantify the additional curvature
of the current field in the region around the hydrogen atom one can
calculate the radius of a circular loop of an infinitely thin wire,
causing a field of 030 ppm of 1 T (3.0 10
07
T) at the center of the
loop (hydrogen atom position) and sustaining a current of 1.6 nA
using the Biot0Savart law. This yields a loop radius of 0.35 Å or a
curvature (reciprocal radius) of 2.9 Å
01
.
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