Importance of out-of-state spin-orbit coupling for slow magnetic relaxation in mononuclear FeII complexes

Article abstract of DOI:10.1021/ja203845x

Two mononuclear high-spin Fe^II complexes with trigonal planar ([Fe^II(N(TMS)₂)₂(PCy₃)] (1) and distorted tetrahedral ([Fe^II(N(TMS)₂)₂(depe)] (2) geometries are reported (TMS = SiMe₃, Cy = cyclohexyl, depe = 1,2-bis(diethylphosphino)ethane). The magnetic properties of 1 and 2 reveal the profound effect of out-of-state spin-orbit coupling (SOC) on slow magnetic relaxation. Complex 1 exhibits slow relaxation of the magnetization under an applied optimal dc field of 600 Oe due to the presence of low-lying electronic excited states that mix with the ground electronic state. This mixing re-introduces orbital angular momentum into the electronic ground state via SOC, and 1 thus behaves as a field-induced single-molecule magnet. In complex 2, the lowest-energy excited states have higher energy due to the ligand field of the distorted tetrahedral geometry. This higher energy gap minimizes out-of-state SOC mixing and zero-field splitting, thus precluding slow relaxation of the magnetization for 2.

Full text of DOI:10.1021/ja203845x

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Importance of Out-of-State SpinꢀOrbit Coupling for Slow Magnetic
Relaxation in Mononuclear FeII Complexes
Po-Heng Lin,†,‡ Nathan C. Smythe,§ Serge I. Gorelsky,†,‡ Steven Maguire,†,‡ Neil J. Henson,^ Ilia Korobkov,†
Brian L. Scott,|| John C. Gordon,§ R. Tom Baker,†,‡ and Muralee Murugesu*,†,‡
†Department of Chemistry and ‡Centre for Catalysis Research and Innovation, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
§Chemistry Division, ^Theoretical Division, and Materials Physics and Applications Division, Los Alamos National Laboratory,
MS J582, Los Alamos, New Mexico 87545, United States
S Supporting Information
b
levels are degenerate, as the dxy, dxz, and dyz orbitals can be inter-
ABSTRACT: Two mononuclear high-spin FeII complexes
converted by a rotation of 90ꢀ about the x-, y-, or z-axis. Thus,
with trigonal planar ([FeII(N(TMS)2)2(PCy3)] (1) and
in the ground state of these complexes, the orbital angular
momentum is not quenched by the ligand field, and the resulting
distorted tetrahedral ([FeII(N(TMS)2)2(depe)] (2) geo-
metries are reported (TMS = SiMe3, Cy = cyclohexyl, depe =
1,2-bis(diethylphosphino)ethane). The magnetic proper-
ties of 1 and 2 reveal the profound effect of out-of-state
spinꢀorbit coupling (SOC) on slow magnetic relaxation.
Complex 1 exhibits slow relaxation of the magnetization
under an applied optimal dc field of 600 Oe due to the
presence of low-lying electronic excited states that mix with
the ground electronic state. This mixing re-introduces
orbital angular momentum into the electronic ground state
via SOC, and 1 thus behaves as a field-induced single-
molecule magnet. In complex 2, the lowest-energy excited
states have higher energy due to the ligand field of the
distorted tetrahedral geometry. This higher energy gap
minimizes out-of-state SOC mixing and zero-field splitting,
thus precluding slow relaxation of the magnetization for 2.
strong “in-state” SOC can give rise to a sizable axial zero-field-
splitting (ZFS) parameter, |D|.1,5 In contrast, octahedral HS
MnIII complexes are an example of “out-of-state” SOC systems.
These complexes have an orbitally non-degenerate electronic
state, and, as a result, in-state SOC cannot contribute to nonzero
ZFS. However, SOC of the non-degenerate ground state with
low-lying excited states bearing angular momenta can produce
ZFS. Thus, SOC has a profound effect on the magnetic proper-
ties of molecular complexes.1
To fully understand magnetic anisotropy effects on slow
magnetic relaxation, it is important to investigate structurally
simple molecules that exhibit SOC. In order to assess how
significant out-of-state SOC contributions can be to ZFS, we
focused our attention on mononuclear HS FeII complexes with
ligand fields that produce structures with non-degenerate ground
states. Herein we report the synthesis of three- and four-coordinate
mononuclear FeII complexes, each containing two bis(trimethyl-
silyl)amide ligands along with monodentate tricyclohexylphosphine
(PCy3) or bidentate 1,2-bis(diethylphosphino)ethane (depe)
ligands. Detailed magnetic studies reveal significant differences
in the magnetic behavior of these three- and four-coordinate com-
plexes due to the difference in their electronic structures arising from
the disparate Fe coordination geometries.
n discrete molecular complexes, the combination of non-
I
negligible spin ground state S and uniaxial Ising-like anisotropy
2
|D| (taking into account the Hamiltonian, H = DSz ) gives rise to
1
an energy barrier U, defined as S2|D| and (S2 ꢀ /4)|D| for integer
and half-integer spins, respectively. Molecules with significant
U values exhibit slow relaxation of their magnetization, indicating
magnet-like behavior,1 and are termed single-molecule magnets
(SMMs).1,2 In an effort to increase the energy barrier in SMMs
for application purposes, much effort has been focused on obtain-
ing high-spin (HS) systems, without much success.3 Therefore,
in recent years many research groups have dedicated their efforts
toward controlling magnetic anisotropy (|D|) by looking to
highly anisotropic metal ions.4
The planar three-coordinate complex [FeII(N(TMS)2)2(PCy3)]
(1) was obtained from the reaction of PCy3 and FeCl2 (1:1) in
THF, followed by addition of potassium bis(trimethylsilyl)amide
(KN(TMS)2) (2 equiv) at ꢀ25 ꢀC. The detailed synthetic pro-
cedure can be found in the Supporting Information. Complex 1
crystallizes in the monoclinic space group P21/n as a mono-
nuclear FeII complex (Figure 1, left). The central FeII ion is coor-
dinated by one PCy3 and two N(TMS)2 ligands in a trigonal
planar arrangement (sum of angles, 359.9ꢀ). The coordinated
N1, N2 atoms (FeꢀN (1.95 Å)) and the P1 atom (FeꢀP (2.52 Å))
form a planar near isosceles triangle wherein the FeII center lies
only 0.03 Å above the plane. The N1ꢀFeꢀN2 angle of 128.5ꢀ
leads to a small distortion that can be seen in the N1ꢀFeꢀP1 and
N2ꢀFeꢀP1 angles of 115.2ꢀ and 116.3ꢀ, respectively. A close
inspection of the packing arrangement reveals layered ABAB
Magnetic anisotropy can be introduced into complexes with
unpaired electrons through structural distortions (such as
JahnꢀTeller splitting) and spinꢀorbit coupling (SOC) invol-
ving one or more electronic states.1,5 Two SOC effects can be
present: (a) SOC that involves an orbitally degenerate electronic
ground state, and (b) SOC that involves an orbitally non-
degenerate ground state with low-lying electronic excited states.
Typical examples of the first case are dn metal ion complexes
with coordination geometries that allow orbital degeneracy. For
instance, in an octahedral HS d6 complex, the partially filled t2g
Received: April 26, 2011
Published: September 06, 2011
r
2011 American Chemical Society
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Table 1. Selected Bond Lengths (Å) and Angles (ꢀ) of 1 and 2
1
2
1
2
FeꢀN1
1.95
1.99
FeꢀP1
2.52
2.60
2.59
78.4
99.2
126.2
FeꢀN2
1.95
1.99
FeꢀP2
N1ꢀFeꢀN2
N1ꢀFeꢀP1
N2ꢀFeꢀP1
128.5
115.2
116.3
120.9
129.1
98.3
P1ꢀFeꢀP2
N1ꢀFeꢀP2
N2ꢀFeꢀP2
FeII complexes exhibited clearly distinct magnetic behavior under
direct current (dc) and alternating current (ac) measurements. At
room temperature, χT values of 5.16 and 3.20 cm3 K molꢀ1 for
3
3
Figure 1. Molecular structures of (left) the three-coordinate complex
[FeII(N(TMS)2)2(PCy3)] (1) and (right) the four-coordinate complex
[FeII(N(TMS)2)2(depe)] (2). Hydrogen atoms and carbon atom labels
have been omitted for clarity.
1 and 2, respectively, were obtained (Figure 2). The latter value
for 2 is in good agreement with the expected theoretical spin-only
value of 3 cm3 K molꢀ1 for a non-interacting HS FeII ion (S = 2,
3
3
g = 2, χT = g2S(S + 1)/8). Conversely, the observed χT value for
1 is much higher than the expected spin-only value. This can be
attributed to the presence of a significant orbital contribution in
1, which makes the spin-only formula invalid for a HS d6 ion.
Therefore, it is important to take the orbital contribution into
account. The observed χT value of 5.16 cm3 K molꢀ1 is close to
3
3
the expected value of 5.6 cm3 K molꢀ1 for an FeII (5D4, S = 2,
3
3
L = 2, J = 4, g = /2, χT = g2J(J + 1)/8) ion with unquenched
orbital angular momentum.7 Similar observations have been re-
ported by Reiff et al. for a two-coordinate HS FeII complex with
significant SOC.5c,d
3
Upon lowering the temperature, the χT product remains
constant until 20 K for 2, whereas for 1, the χT product initially
decreases slightly before increasing back to 5.3 cm3 K molꢀ1
.
3
3
Overall, this slight variation of the χT product for 1 is in the
5.0ꢀ5.3 cm3 K molꢀ1 range. At temperatures below 50 K for 1
3
3
and 20 K for 2, a rapid decrease in χT can be observed with
minimum values of 3.59 and 1.97 cm3 K molꢀ1 at 2 K for 1 and
3
3
2, respectively. Complex 2 clearly obeys the expected Curieꢀ
Weiss-type behavior (c = 3.21 cm3 K molꢀ1; θ = ꢀ1.64)
3
3
(Figure S5), whereas the origin of the observed slight inflection
for 1 remains unclear. In the latter case, a physical torquing effect
can be ruled out, as the data are highly reproducible even under
different restraining matrices such as grease or eicosane. Single-
crystal X-ray studies reveal that the geometries of 1 at low (120 K)
and high (298 K) temperatures are nearly identical, and no spin
crossover or phase transition is observed. Although the inter-
molecular distances are significant, the low-temperature decrease
of the χT product could also be due to very weak antiferromag-
netic interactions for 1 and 2. The more pronounced decrease in
1 also suggests the presence of significant ZFS due to its trigonal
planar geometry (vide infra). To estimate the axial ZFS parameter
(D), fitting of the susceptibility data assuming a simple ZFS effect
was carried out (Figure S6).8 An excellent fit was obtained for 1
(below 50 K) and 2 (2ꢀ300 K range), with D values of ꢀ10.9
and +5.9 K, respectively.
The field dependenceof the magnetizationof 1 and 2 below 8 K
is shown in Figures 2 (inset), S7, and S8. The lack of saturation
and non-superposition on a single master curve of M vs H/T data
also suggests the presence of low-lying excited states (for 1 and 2)
and magnetic anisotropy (for 1) (vide infra). Several attempts to
fit the reduced magnetization data using the Magnet9 program
were unsuccessful, most likely due to low-lying excited states.
To probe possible SMM behavior in both complexes, studies
on the temperature and frequency dependence of the ac suscept-
ibility were carried out in the temperature range 2.2ꢀ15 K.
Figure 2. Temperature dependence of χT at 1000 Oe for 1 and 2. Inset:
M vs H/T plots at 3, 5, and 8 K for 1 (left) and 2 (right).
packing along the crystallographic c-axis (Figure S1), with the
shortest Fe Fe distance of 9.53 Å between adjacent molecules.
3 3 3
It is noteworthy that 1 joins a rare family of other reported three-
coordinate Fe complexes.6 As a consequence of its low coordina-
tion geometry and +2 oxidation state, 1 is extremely reactive and
readily oxidizes upon exposure to air. The four-coordinate
complex [FeII(N(TMS)2)2(depe)] (2) was obtained from the
reaction of LiN(TMS)2 and FeBr2 (2:1) in THF at ꢀ25 ꢀC,
followed by addition of depe (1 equiv). Complex 2 crystallizes in
the tetragonal space group P41 as a mononuclear FeII complex
(Figure 2, right). The coordination environment of the FeII center
reveals a distorted tetrahedral geometry with a P1ꢀFeꢀP2 angle
of 78.4ꢀ and an N1ꢀFeꢀN2 angle (120.9ꢀ) that is significantly
smaller than that of 1 (128.5ꢀ). The shortest Fe Fe distance of
3 3 3
10.04 Å between adjacent molecules is shown in the packing
arrangement along the a-axis (Figure S2). Such large separation
distances are generally inefficient for intermolecular magnetic
interactions. A comparison of selected bond distances and angles
for 1 and 2 is presented in Table 1, and further structural infor-
mation is given in Figures S3 and S4 and Tables S1ꢀS11.
Magnetic studies were carried out on powdered polycrystal-
line samples of 1 and 2 prepared in a glovebox. Both mononuclear
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Figure 4. TD-DFT calculated two lowest-energy excited states and the
β-spin molecular orbitals involved in the excitations for 1 (left) and 2
(right). The excited-state energies (cmꢀ1) from PBE and B3LYP
calculations are shown in black and blue, respectively. The percent
contributions of the Fe atom to the density of molecular orbitals are also
shown. H atoms are omitted for clarity.
Figure 3. Out-of-phase susceptibility (χ00) vs frequency ν (logarithmic
scale) for 1 in the temperature range 2.2ꢀ9 K under an applied optimum
dc field of 600 Oe. Inset: Relaxation time of the magnetization ln(τ) vs
T
ꢀ1 (Arrhenius plot using ac data). The solid line corresponds to the fit.
Under a zero dc field and a 3 Oe ac field oscillating at frequencies
between 1 and 1500 Hz, no ac signal was observed. When a static
dc field was applied, a frequency-dependent signal was observed
only for 1 (Figures 3, S9ꢀS11). Such behavior generally indicates
that slow relaxation of the magnetization is highly influenced by
quantum tunneling of the magnetization (QTM). This is most
likely due to the presence of rhombic anisotropy (E), causing the
mixing of the (2 levels with the (1 level, subsequently providing
the QTM pathway. Applying a static dc field will reduce QTM
through the spin reversal barrier via degenerate (Ms energy
levels; therefore, measurements at various applied dc fields will
lift the degeneracy.2g To shortcut the tunneling effect, we initially
carried out ac measurements under various dc fields to determine
the optimum field for which the QTM is minimized (Figures S12
and S13). Ac measurements under the applied optimum field of
600 Oe reveal a frequency-dependent signal (Figures 3 and S11)
with a clear out-of-phase (χ00) peak. Such behavior is indicative of
super-paramagnet-like slow magnetization relaxation of a SMM.
An anisotropic energy barrier (Ueff) can be obtained from the
high-temperature regime of the slow magnetization relaxation
whereitisthermally induced (Arrheniuslaw, τ = τ0 exp(Ueff/kT)).
The obtained value of Ueff = 42 K (τ0 = 6 ꢁ 10ꢀ7 s) (Figure 3
inset) is close to that previously reported for the trigonal
pyramidal [(tpaMes)Fe]ꢀ complex by Long, Chang, and co-
workers.5b By using the U = S2|D| equation and the obtained Ueff
value, we can deduce that D ≈ 10 K. A single relaxation
mechanism can be confirmed by fitting the ColeꢀCole plot
(Figure S14), and the obtained fits (α = 0.03ꢀ0.1) using the
Debye model1b are in good agreement with such behavior.
To further investigate the electronic structure of these mol-
ecules, and to understand why the SMM properties are only
present in the case of 1, nonrelativistic density functional theory
(DFT) calculations were carried out. Geometry optimization
calculations were performed on models of the molecular species
constructed using the crystal structure data as starting points and
employing the spin-unrestricted formalism to assess the effect of
differing spin states at the PBE10/TZVP11 level of theory. The
calculations were also repeated at the B3LYP12/TZVP level of
theory to confirm the results and to assess the sensitivity of the
results to the exchange-correlation potential (vide infra). For
both 1 and 2, the lowest energy d6 spin state is predicted to be HS
(quintet vs singlet and triplet). The HS structures reproduce the
experimental bond lengths and angles closely. Selected geo-
metric parameters are shown in Table S12 for the optimized
geometries. In the quintet state, most of the spin density is
localized on the FeII center (NPA13-derived atomic spin density
is 3.46 for 1 and 3.40for 2). The calculated Mayer bond orders14,15
for FeꢀP and FeꢀN bonds are 0.69 and 0.82 in 1 and 0.51ꢀ0.55
and 0.75ꢀ0.77 in 2, respectively. Thus, the metalꢀligand bonds
in 1 carry more covalency15 than the metalꢀligand bonds in 2 to
compensate for the lower coordination number in 1. Overall, the
NPA-derived atomic charges of the FeII center (+0.96 au in 1 and
+0.73 au in 2) indicate that this compensation through higher
metalꢀligand covalency was not quite complete, and, as a result,
the d orbital splitting due to metalꢀligand interactions in 1 can
be expected to be lower than in 2. Time-dependent DFT (TD-
DFT)16 calculations were used to calculate the energies of the
lowest-energy excited states for 1 and 2. TD-DFT calculations
performed using the hybrid B3LYP functional are in agreement
with the TD-DFT calculations performed using the PBE func-
tional (Figure 4).
Electronic transitions from the ground electronic state to four
lowest-energy quintet excited states of the complexes are dꢀd
(ligand-field)17 excitations from the β-spin highest occupied
molecular orbital (HOMO) to four β-spin lowest unoccupied
molecular orbitals (LUMOs) (Figure 4 and S15).
Due to trigonal planar geometry, 1 has the Fe dxz orbital (see
Figure S16 for the orientation of the Cartesian axes with respect
to the molecular frames) as the β-spin HOMO (Figure 4 left)
and two excited states with very low energies (∼2000 cmꢀ1 for
the first excited state (dy2ꢀz2) and ∼5000 cmꢀ1 for the second
excited state (dyz)). The two excited states that originate from the
electron excitations from the β-spin HOMO to the remaining
unoccupied Fe d orbitals have energies in the 10 000ꢀ14 000 cmꢀ1
range (Figure S15). Complex 2, with its distorted tetrahedral
geometry, has the dx2ꢀz2 orbital as the β-spin HOMO (Figure 4
right), and the two lowest excited states have significantly higher
energies (∼5000 cmꢀ1 for the first excited state (dyz) and
∼8000 cmꢀ1 for the second excited state (dxy)) than the two
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Journal of the American Chemical Society
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lowest excited states in 1. Since neither structure contains a
three- or four-fold symmetry axis and the orbital energy levels
in these systems are not degenerate, in-state SOC cannot be
present. Only out-of state SOC can contribute to nonzero ZFS.
The increase of the energies of the two lowest-energy excited
states when going from 1 to 2 should significantly decrease the
out-of-state SOC contribution to the ZFS. Indeed, no ac signal was
observed for 2, even under an applied field, indicating absence of
slow relaxation of the magnetization. This is consistent with
quenched orbital angular momentum and weak out-of-state SOC
in a distorted tetrahedral FeII complex. We can conclude that the
remarkable observation of slow relaxation of the magnetization
of 1 proves that it behaves as a field-induced SMM due to the
large intrinsic magnetic anisotropy arising from out-of-state SOC
in the trigonal planar complex.
The results described herein demonstrate that slow relaxation
of the magnetization in 1 arises from the intrinsic magnetic
anisotropy of the HS FeII ion within a three-coordinate environ-
ment. This gives rise to very low-lying excited states that couple
with the non-degenerate ground state via out-of-state SOC. The
related four-coordinate complex, 2, has a non-degenerate ground
state and excited states with higher energies; thus, it does not
exhibit magnetic anisotropy. We can conclude that out-of-state
spinꢀorbit coupling for systems with low-lying excited states
appear to be an important contributor to the slow magnetic
relaxation of mononuclear complexes. We believe this may provide
new avenues for conceiving polynuclear high-energy-barrier SMMs.
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’ ASSOCIATED CONTENT
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Supporting Information. Complete experimental and com-
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putational details (PDF); X-ray crystallographic files (CIF).
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’ AUTHOR INFORMATION
Corresponding Author
m.murugesu@uottawa.ca
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We thank the University of Ottawa (start-up), CCRI, CFI,
FFCR, NSERC (Discovery and RTI grants), ERA, and U.S. DOE
Office of Energy Efficiency and Renewable Energy for their support.
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