Direct Spectroscopic Evidence of Orbital
Magnetism of Essentially Free Ion
Magnitude in a Rigorously Linear TwoCoordinate High-Spin Fe (II) Compound
W. M. Reiff,a A. M. LaPointe,b and C. E. Schulzc
aDepartment
of Chemistry, Northeastern University, Boston MA 02115, USA, bSymyx
Technologies Inc., Santa Clara, CA 95051, USA, and cDepartment of Physics, Knox
College, Galesburg IL, 61401, USA, w.reiff@neu.edu
Substantial first order orbital contributions are important to the ground state magnetic
behavior of certain first transition series metal ions in six coordination. Thus nominal Oh
symmetry ground states such as 2T2g (Ti3+, low-spin Fe3+), 5T2g(high-spin Fe2+ and Co3+),
4T (high-spin Co2+) and 3T (Ni2+in T ) are well established examples. In practice, such
1g
1
d
orbital angular momentum is largely quenched by any of low symmetry ligand field
components, crystal packing effects or more fundamentally, the linear Jahn-Teller Effect
(vide infra: top half of slide number (6)). The limit of such quenching effects is so-called
spin-only magnetism as illustrated for high-spin Fe2+ in the following slide, (3).
Kahn, O. Molecular Magnetism,VCH-Wiley:New York,1993, 31-52
Jahn, H. A.; Teller, E. Proc.Roy. Soc., 1937, A161, 220-226.
One can plausibly assume that complexes having minimal regular ligation, e.g. rigorously
linear two coordination should afford maximal orbital effects, and depending on the overall
symmetry essentially those of the corresponding free gas phase ion (slide (4), high-spin
Fe2+). Significantly, in this (linear) situation, there is no requirement for a Jahn-Teller
distortion effect, slide (6) bottom half . Higher order non-linear terms in the vibronic
coupling interaction can lead to distortion ( bending in the present context ) and lift orbital
degeneracy. However, bulky, stereochemically demanding ligands that stabilize
coordinative unsaturation are precisely those that vitiate bending effects in the solid state.
One sees that complex 1, slide (7), has all of these characteristics leading to true orbital
ground state degeneracy or quasi degeneracy, slide (8)) and extraordinary orbital
magnetism. Mössbauer spectroscopy uniquely highlights this magnetism in terms of the
highly symmetry sensitive orbital contribution, HL, to Hinternal.
Classically and depending on the symmetry, increasing coordination number enhances
the overall ability of ligands to impede the free orbital circulation of electrons and leads
to a decrease in L
J
Fe2+ exhibits the largest free ion magnetic moment of the first transition series metal ions.
For real compounds that are highly coordinatively unsaturated (2 or 3 coordinate), this is
a particularly propitious situation in the context of directly investigating orbital angular
momentum effects. An isotope specific spectroscopic technique such as the Mossbauer
Effect can more readily discern these effects in terms of the contributions to Hinternal as
opposed to classical bulk powder susceptibility methods.
The spin-only value of  for a fictitious S= 3 cation is 6.93 . Thus, the present orbital effect
is more or less equivalent to adding ~ two full spins to the magnetism of Fe2+, i.e. S= 4/2
6/2, arguably a very large effect.
6.71
High density near random powder average SQUID data. These data indicate very large first
order orbital angular momentum for complex 1, slide 7, and close to the free gas phase ion
value of slide 4. The characteristic temperature dependence of  is typical of depopulation of
spin-orbit states for  <0, with ~1 and no distortion.
Figgis, B. N.; Lewis, J.; Mabbs, F. E.; Webb, G. A.: J. Chem.Soc (A)(1967), 442-447.
The above will generally lead to partial if not complete loss of
first order orbital angular momentum.
Bis(tris(trimethylsilyl)methyl)Fe(II)
LaPointe, A. M.; Inorg. Chimica. Acta, 2003, 345, 359-362
1
C------Fe------C=180.0°
Fe--------Fe ~9Å
DIHEDRAL ANGLE = 60°, Ideal Staggered D3d Symmetry
The ground (Eg) orbital doublet wave functions leads to the maximum orbital angular
momentum for dn configurations in view of the ml values of the spherical harmonics linearly
combined to produce the real dxy and dx2-y2 pair. The degeneracy of this pair in combination
with the C8 symmetry element (slide 8) connecting them is essential to manifestation of the
orbital momentum. More classically, for rigorously linear two coordination there are no in plane ligands (only axial) to impede the orbital circulation of the electrons.
CRYSTAL FIELD SPLITTING
DIAGRAM FOR IDEAL LINEAR TWO COORDINATION WITH HOMOLEPTIC LIGATION
IN D3d SYMMETRY
The C8 symmetry element transforms dxy into dx2-y2 with which it is
degenerate
L
L
L
C8(45)
L
Sketches of Four of the Five Real Spherical Harmonics for L=2
The orbital ground state of 1 in local Dh symmetery is 5g.
5 (  ls)
various spin–orbit states.
g
The ground spin-orbit state is the “pure” Mj= ± 4 spin-orbit doublet.
Since, mj = ±8 for this doublet, transitions within this doublet are highly forbidden and
lead to slow relaxation. Hence, we expect 1 to be ESR silent and exhibit hyperfine
splitting in zero external field as shown in the following two slides.
 ~0.4 mm/s
E~ 1.2 mm/s
Complex 1 undergoes gradual slow relaxation and Zeeman splitting over the
range 293 to 47 K. However, the broad resonances and trace rapidly relaxing
paramagnetic phase suggest that we are near but not quite at the infinitely slow
relaxation limit at 47 K. Analysis of the obvious quadrupole shift (s1-s2) of the
spectrum indicates that Hinternal relaxes parallel to the C3 axis of 1 as expected.
At 4.2K, 1 is clearly at the slow relaxation limit and exhibits, by far, the largest
value for the internal hyperfine field ever observed for iron!
Reiff, W. M.; LaPointe, A. M.; Witten, E., J. Am. Chem. Soc. 2004,126, 10206-10207.
{mI = 0 ( )}*
*
H0 = 0
*
The mI = 0 transitions have sin2 dependence ( = the angle between Eγ and Hint), Their intensities will
approach zero with increasing application of a longitudinal field, see the next slide.
A relatively small longitudinal external field (0.5 T) largely polarizes the sample magnetizaton
parallel to Eγ as expected for a simple paramagnet. For even larger applied fields (to 9 T)
Heff increases confirming a dominant orbital contribution to Hnternal
*
*
*
6
4
6
{
-LINEAR
THE INTEGERS TO THE UPPER LEFT OF THE FIRST THREE ENTRIES ARE
THE COORDINATION NUMBERS OF THE IRON CHROMPHORES FOR THESE
COMPOUNDS.
Conclusion
the results of the preceding table are entirely consistent with the comments
of this narrative. Clearly, the absence of the Jahn- and Renner-Teller effects
for the linear coordination of two bulky ligands in the solid state is shown to
have an enormous effect on the magnitude of internal hyperfine field
primarily through the increased magnitude of the orbital contribution.
Recall that, Hint = Hf+Hd+Hl where Hf is the Fermi contact term (~ -12.5 T/spin for
iron) and Hd the usually small dipolar term that can be positve or negative and
that is neglected herein. Hence from the result of slide 12:
152 T ~ -50 T + ~0 + HL implying HL is ~200 T. This is a remarkable result for two
sigma bonding, non-delocalizing, hard Lewis base carbanion ligands in the
rigorously linear geometry of complex 1, slide 7. The results of this work also
imply that for appropriate geometry real compounds can exhibit magnetic
properties very close to that of the corresponding free ion.