Magnetization Slow Dynamics in Ferrocenium Complexes

Article abstract of DOI:10.1002/chem.201900799

The single-molecule magnet (SMM) properties of a series of ferrocenium complexes, [Fe(η⁵-C₅R₅)₂]⁺ (R=Me, Bn), are reported. In the presence of an applied dc field, the slow dynamics of the magnetizati

Full text of DOI:10.1002/chem.201900799

A Journal of
Accepted Article
Title: Magnetization Slow Dynamics in Ferrocenium Complexes
Authors: Mei Ding, Anne K. Hickey, Maren Pink, Joshua Telser,
David L. Tierney, Martin Amoza, Mathieu Rouzières, Tarik J.
Ozumzerzifon, Wesley A. Hoffert, Matthew P. Shores, Eliseo
Ruiz, Rodolphe Clérac, and Jeremy M Smith
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To be cited as: Chem. Eur. J. 10.1002/chem.201900799
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Magnetization Slow Dynamics in Ferrocenium Complexes
Mei Ding,[a] Anne K. Hickey,[a] Maren Pink,[a] Joshua Telser,*[b] David L. Tierney,[c] Martin Amoza,[d]
Mathieu Rouzières,[e],[f] Tarik J. Ozumzerzifon,[g] Wesley A. Hoffert,[g] Matthew P. Shores,[g] Eliseo
Ruiz,*[d] Rodolphe Clérac*[e],[f] and Jeremy M. Smith*[a]
Abstract: The Single-Molecule Magnet (SMM) properties of a series
of ferrocenium complexes, [Fe(η5-C5R5)2]+ (R = Me, Bn), are reported.
In the presence of an applied dc field, the slow dynamics of the
magnetization in [Fe(η5-C5Me5)2]BArF are revealed. Multireference
quantum mechanical calculations show a large energy difference
between the ground and first excited states, excluding the commonly
invoked, thermally activated (Orbach-like) mechanism of relaxation.
In contrast, a detailed analysis of the relaxation time highlights that
both direct and Raman processes are responsible for the SMM
properties. Similarly, the bulky ferrocenium complexes, [Fe(η5-
C5Bn5)2]BF4 and [Fe(η5-C5Bn5)2]PF6, also exhibit magnetization slow
dynamics, however an additional relaxation process is clearly
detected for these analogous systems.
defined redox properties have led to an enormous number of
ferrocene-containing ligands, molecules and materials.[2-5]
Amazingly, over sixty years since its discovery, fundamental
discoveries regarding ferrocene and its derivatives are still being
reported, as exemplified by the recent isolation of the remarkable
Fe(IV) complex, [Fe(η5-C5Me5)2]2+.[6]
It is notable that the canonical d-orbital manifold for metallocenes
resembles that for four-coordinate complexes in three-fold
symmetry (Figure 1),[7] where the degenerate dxz, dyz orbitals are
strongly antibonding, dz2 is largely a non-bonding orbital and the
degenerate dx2-y2
, dxy are bonding orbitals. The electronic
structure of this latter class of complexes can lead to remarkable
magnetic properties, such as spin-crossover, Single-Molecule
Magnet (SMM), or photoinduced SMM properties for example for
iron(II) tris(carbene)borate complexes.[8-11] More recently, we
have found that the low spin d3 (S = ½) Mn(IV) complex
Introduction
2
PhB(MesIm)3Mn≡N, which has an E ground state,[12] displays
slow relaxation of the magnetization, and thus can be classified
as an SMM.[13] Theoretical investigations revealed that this
behavior originates from an anisotropic ground doublet that is
stabilized by spin–orbit coupling. In light of the analogous
electronic structures (Figure 1), we hypothesized that
metallocene complexes with the appropriate d-electron count may
likewise show SMM properties.
As the commonly accepted progenitor of organometallic
chemistry, ferrocene has seen a myriad of applications since the
report of its discovery in 1951.[1] The synthetic flexibility and well-
[a]
Dr. M. Ding, Dr. A.K. Hickey, Dr. M. Pink, Prof. J.M. Smith
Department of Chemistry,
Indiana University
800 E. Kirkwood Ave., Bloomington, Indiana 47401, United
States.
E-mail: smith962@indiana.edu
Prof. J. Telser
e1g
e
dxz
d
,
yz
[b]
X
Department of Biological, Chemical and Physical Sciences
Roosevelt University
Chicago, Illinois 60605 United States
E-mail: jtelser@roosevelt.edu
Prof. D.L. Tierney
Department of Chemistry and Biochemistry
Miami University
M
a1g
a1
e
M
dz
2
~90°
D5d
C3
v
e2g
dx
d
,
2-y2 xy
[c]
[d]
Oxford, Ohio 45056, United States
M. Amoza, Prof. E. Ruiz
Figure 1. Canonical d-orbital manifold for metallocenes (left, in staggered
geometry) and certain three-fold symmetric complexes with tripodal ligands
Departament de Química Inorgànica i Orgànica, Institut de
Recerca de Química Teòrica i Computacional
Universitat de Barcelona
(right). Note that lower two energy levels may have
ordering.[7]
a different relative
Diagonal 645, Barcelona, 08028 Spain
E-mail: jtelser@roosevelt.edu
[e]
[f]
M. Rouzières, Dr. Hab. R. Clérac
CNRS, CRPP, UMR 5031, 33600 Pessac, France
E-mail: clerac@crpp-bordeaux.cnrs.fr
M. Rouzières, Dr. Hab. R. Clérac
Univ. Bordeaux
CRPP, UMR 5031, 33600 Pessac, France.
T.J. Ozumzerzifon, W.A. Hoffert, Prof. M.P. Shores
Department of Chemistry
Ferrocene and its derivatives can be readily and reversibly
oxidized to low spin d5 (S = ½) ferrocenium cations, [Fe(η5-
C5R5)2]+. Magnetic susceptibility[14,15] and EPR[16,17] experiments
have established the electronic ground state of ferrocenium to be
2E [(a )2(e )3], where the relative energies of the a and e2g
levels has changed from the canonical electronic structure. The
orbital degeneracy of this electronic configuration gives rise to
highly anisotropic g values, which are observed in the EPR
spectra of ferrocenium cations. This four-fold degenerate
g
2
1g
2g
1g
[g]
Colorado State University
Fort Collins, Colorado 80523, United States.
Supporting information for this article is given via a link at the end
of the document.
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10.1002/chem.201900799
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electronic state is split into two Kramers doublets by the combined
action of the spin-orbit coupling (SOC) interaction and a low
symmetry perturbation. Since this latter perturbation is only
slightly larger than the SOC, it is only partially quenched. This
unquenched SOC leads to magnetic moments that are
significantly larger than the S = ½ spin only value.
counterions, allowing the magnetic centers to be well-separated
in the solid state. Specifically, the bulky cyclopentadienyl ligands
in [Fe(η5-C5Bn5)2]X (X = BF4- and PF6-)[26] and the large counterion
in [Fe(η5-C5Me5)2]BArF
are expected to provide long Fe…Fe
[27]
separations in the solid state (Scheme 1).
Understanding the magnetization dynamics of a paramagnetic
complex requires an accurate knowledge of the various
mechanisms involved. For a paramagnetic metal complex, four
mechanisms are generally used to describe the magnetization
relaxation in the solid state, each of which has a characteristic
temperature (T) and dc-field (H) dependence. The global
relaxation rate (denoted τ-1 with τ being the relaxation time) is
then usually described by a combination of all or some of these
mechanisms, specifically Orbach, direct, quantum tunneling
(QTM) and Raman processes, although other processes have
been proposed:[18]
Ph
Ph
Ph
Ph
Ph
X-
Fe
Fe
Ph
Ph
Ph
Ph
Ph
-
BF4 PF
,
6
-
-
=
H2 4
C6
X
]
)
[B(3,5-(CF3)2
5-C
5-C
5Bn
η
η
5Me
[Fe(
5 2]BArF
)
[Fe(
5 2]X
)
Scheme 1. Ferrocenium complexes investigated in this work.
(1)
Results and Discussion
where ∆ is the magnetic anisotropy barrier, τ0 is an attempt time,
and a, b1, b2, d, e, f and n are reduced parameters linked to the
different relaxation pathways (see reference [18]). The last
contribution, which includes the Brons-van Vleck term[19] as a
prefactor, describes both the field and temperature dependence
of the Raman process at low magnetic fields. In zero field, this
Raman term is equivalent to the commonly used dTn expression,
e.g. in EPR spectroscopy (it is worth noting that the d parameter
corresponds to the zero-field relaxation). The e parameter is
highly dependent on the paramagnetic center concentration and
introduces the relaxation of the interacting spins while the f
parameter indicates the effect of the external field to suppress the
spin relaxation. It is also interesting to mention the resemblance
of the Brons-van Vleck term to the QTM term. For an S = ½
Kramers ion such as ferrocenium, which has no barrier, tunneling
can contribute to the spin relaxation just by the transition between
two states with opposite spin.
The spin-lattice relaxation dynamics of ferrocenium ions have
been investigated spectroscopically. At temperatures above 80 K,
the spin-lattice relaxation dynamics of ferrocenium-containing
materials was proposed to follow an Orbach-like mechanism, as
determined by 57Fe Mössbauer spectroscopy.[20-24] However, the
solid state relaxation dynamics of some very bulky ferrocenium
salts do not follow a simple Orbach-like mechanism at lower
temperatures.[20-23] At very low temperatures, the relaxation of
some bulky ferrocenium complexes is observed to be slow on the
Mössbauer timescale, as evidenced by the appearance of
hyperfine interactions in the spectrum,[20-23] which was first
observed for [Fe(η5-(1,3-Me3Si)2C5H3)2]OTf.[25]
Synthesis, Structural and Spectroscopic Characterization
The bulky ferrocene, Fe(η5-C5Bn5)2, was prepared from
pentabenzylcyclopentadienyl lithium and anhydrous FeCl2,
similarly to literature procedures.[28,29] As previously reported,
oxidation to the ferrocenium complexes, [Fe(η5-C5Bn5)2]BF4 and
[Fe(η5-C5Bn5)2]PF6, was accomplished using NOBF4 and AgPF6
oxidants, respectively.[25] The molecular structure of [Fe(η5-
C5Bn5)2]BF4 was determined by single-crystal X-ray diffraction,
revealing the anticipated ferrocenium complex (Figure 2) that
crystallizes along with interstitial CH2Cl2 molecules. As previously
observed,[25] the cyclopentadienyl rings are staggered, with Fe-C
(2.100(4) – 2.114(4) Å) and cyclopentadienyl C-C distances
1.427(7)
– 1.446(6) Å that are typical for ferrocenium
complexes.[30] The angle between the cyclopentadienyl rings is
0.47°. Importantly and as expected, the paramagnetic iron
centers are well-separated in the solid state, with the nearest
Fe…Fe distance being 11.208(1) Å.
In this paper, we report a detailed analysis of the magnetization
dynamics in some ferrocenium-based materials. To reduce the
possible effects of dipolar magnetic interactions on the
magnetization dynamics, we chose to investigate ferroceniums
having bulky cyclopentadienyl ring substituents and/or large
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Magnetic Properties
The magnetic properties of the ferrocenium complexes have been
studied by dc and ac techniques (see Supporting Information).
Since the dc magnetic data could not be fit to a simple model, they
were simulated using the results of the theoretical calculations
(see below). As illustrated for [Fe(η5-C5Me5)2]BArF, the χT product
at 270 K has a value of 1.06 cm3 K mol−1, in agreement with a
magnetically isolated low-spin (S = ½) Fe(III) center with
substantial spin-orbit coupling (Figure 3). The large deviation
from the spin-only value has been previously noted.[14,15,20-23,31] As
the temperature is lowered, the χT product decreases linearly,
followed by a downturn around 60 K to reach 0.79 cm3 K mol−1 at
1.85 K. The field dependences of the magnetization below 8 K for
[Fe(η5-C5Me5)2]BArF are in good agreement with an S = ½ species
with a magnetization that reaches 1.33 µB at 7 T & 1.85 K (Figure
3 inset). These experimental M versus H data can be fitted
qualitatively well to an S = ½ Brillouin function providing an
average g factor around 2.65(5). Similar results, shown in the
Supporting Information, are observed for the other ferrocenium
Figure 2. X-ray crystal structure of [Fe(η5-C5Bn5)2]BF4. Thermal ellipsoids
shown at 50% probability, hydrogen atoms and cocrystallized CH2Cl2 solvent
omitted for clarity. Black, orange, pink and lime ellipsoids represent C, Fe, B
and F atoms, respectively.
complexes [Fe(η5-C5Bn5)2]BF4 (g
C5Bn5)2]PF6 (g = 2.40(5)).
=
2.33(5)) and [Fe(η5-
Unfortunately, while we were able to determine the connectivity
for the cation in [Fe(η5-C5Bn5)2]PF6, the diffraction data were too
weak to obtain any meaningful metrical information. On the other
hand, the structure of [Fe(η5-C5Me5)2]BArF was previously
reported.[26] The iron atoms are also well-separated in this
structure, with the nearest Fe…Fe distance being 9.6116 Å. The
angle between cyclopentadienyl rings is 2.72°, suggesting a
slightly lower local symmetry than for [Fe(η5-C5Bn5)2]BF4. These
three complexes were characterized by low temperature EPR
spectroscopy, while [Fe(η5-C5Bn5)2]BF4 was also characterized
by variable temperature 57Fe Mössbauer spectroscopy (Figures
S3 and S4). On decreasing the temperature, the single absorption
signal in the spectrum at 80 K (δ = 0.57 mm/s) resolves into six
lines at 4.5 K, indicative of slow relaxation of the magnetization
on the timescale of the Mössbauer experiment. Similar behavior
has been reported for other bulky ferrocenium complexes.[20-23]
The magnetization dynamics of the three ferrocenium complexes
have been probed by ac susceptibility measurements. In the
absence of a dc field and above 1.8 K, no significant out-of-phase
component of the ac susceptibility for frequencies up to 10 kHz
was observed for any of the complexes. However, application of
a dc field leads to the appearance of frequency dependent signals
in both components of the ac susceptibility, revealing the slow
dynamics of the magnetization. As shown for [Fe(η5-C5Me5)2]BArF
(Figure 4), a maximum in the out-of-phase component becomes
detectable for an applied dc field of 100 Oe. At all fields, the χ’
versus ν and χ” versus ν data can be fit to a generalized Debye
model (Figure 4) with a small α coefficient (< 0.4; Figure S8)
indicating a narrow distribution of the relaxation time (τ).
The field dependence of the characteristic relaxation frequency at
2 K reveals that relaxation time, τ, is maximum for an optimum
applied dc field of 1500 Oe (Figure 4 inset and Figure S8).
Variable–frequency and –temperature ac susceptibility data for
this complex were thus collected under 1500 Oe between 1.9 and
15 K (Figure 5 and Figure S9) to determine the temperature
dependence of the relaxation time. The observed curvature of the
resulting τ versus T−1 plot (at 1500 Oe) in Figure 6 suggests the
presence of competing relaxation processes. A rapid analysis of
the temperature dependence of the relaxation time (Figure 6)
could conclude (i) at an exponential behavior (thermally activated)
above 4 K suggesting an Orbach-like mechanism[32] of relaxation
(first term of equation 1: τ0 = 5.7(5) × 10−7 s; ∆/kB = 17.6(5) K (12.2
cm−1)) and (ii) below 4 K to the effect of the quantum tunneling of
the relaxation (second term of equation 1). But as shown by the
electronic structure calculations (vide infra), an Orbach-like
relaxation mechanism is not relevant in the present Kramers
systems. Similar ac susceptibility measurements for [Fe(η5-
C5Bn5)2]BF4 and [Fe(η5-C5Bn5)2]PF6 (see Supporting Information;
Figures S10-S17) also reveal that the relaxation time is strongly
both dc-field and temperature dependent.
Figure 3. Temperature dependence of the χT product at 0.1 T for [Fe(η5-
C5Me5)2]BArF (χ is defined as magnetic susceptibility equal to M/H per mole of
[Fe(η5-C5Me5)2]BArF). Inset: field dependence of the magnetization below 8 K
for [Fe(η5-C5Me5)2]BArF (8–280 mT min-1). Solid lines are simulations using the
NEVPT2 results discussed in the text (see Electronic Structure Calculations
section).
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Figure 6. Temperature dependence of the relaxation time (τ) shown in
semilogarithm τ vs. T-1 plot (Arrhenius plot) for [Fe(η5-C5Me5)2]BArF constructed
from the generalized Debye fits of the χ′ vs. ν (red dots) and χ″ vs. ν (blue dots)
obtained under a dc field of 1500 Oe.
Figure 4. Frequency dependence of the real (χ′, top) and imaginary (χ″, bottom)
components of the ac susceptibility at 2 K at different dc fields between 0 and 1
T for a polycrystalline sample of [Fe(η5-C5Me5)2]BArF. Solid lines are the best
fits of the experimental data to the generalized Debye model (see Supporting
Information). Inset: Field dependence of the characteristic ac frequency (ν)
deduced from the generalized Debye model fits of the χ′ vs. ν (red dots) and χ″
vs. ν (blue dots) data. The solid lines are guides for the eyes.
Electronic Structure Calculations
At first glance, the canonical metallocene electronic structure as
in Figure 1 is not consistent with the relatively large easy-axis
character found experimentally, for example by EPR (Figure S5).
4
1
The suggested electronic e2g a1g configuration leads to first
excitation energies between dx2 2/dxy (ml = ±2) and dz2 (ml = 0)
-y
that cannot provide significant spin-orbit contributions (due to the
+2 difference of |ml| values for the orbitals involved in such
excitations). In order to explain this discrepancy, we performed
spin-orbit CASSCF calculations on the crystal structure of the
[Fe(η5-C5Me5)2]+ molecule (Orca 4.0 code[39,40] with a def2-TZVP
basis set[41,42]). The use of a relatively large active space of 10
orbitals with 9 electrons to include the five Fe 3d orbitals, the two
occupied M-L bonding ligand orbitals and three empty orbitals
provides an S = ½ ground state in agreement with the
experimental data. A smaller active space considering only the
five orbitals results in an incorrect (S = 5/2) ground state (note that
manganocene, [Mn(η5-C5H5)2], does have this high spin ground
state[43]). This problem can also be solved for the smaller active
space by adding dynamic correlation, for instance with the
NEVPT2 approach.[44] The results for the [Fe(η5-C5Bn5)2]+
complex (see Supporting Information) are qualitatively similar to
those of the [Fe(η5-C5Me5)2]+ system, thus, we will focus the
discussion in the main text in this latter system. The presented
results correspond to the NEVPT2 calculations including spin-
orbit effect (quasi-degenerate perturbation theory, QDPT) using
the 5-orbitals active space by calculating all 75 doublet, 24
quadruplet and one sextet state (to give a total of 252 microstates).
The 5-orbital active space was finally selected because it allows
to perform an Ab Initio ligand field (AILFT) calculation after the
NEVPT2/QDPT. This approach gives a high-quality d orbital
energy splitting that helps to describe the magnetic anisotropy of
the system (see Figure 8). The local magnetic anisotropy of this
S = ½ system is illustrated in the calculated g-tensor with gz = 5.42
and gx = gy = 0.99 (gave = 2.47) eigenvalues indicating the
relatively large uniaxial magnetic anisotropy (see Figure 7
showing that gz is almost perpendicular to the (η5-C5Me5) planes).
Figure 5. Temperature (left) and frequency (right) dependences of the real (χ′,
top) and imaginary (χ″, bottom) components of the ac susceptibility, between
1.9 and 15
C5Me5)2]BArF in a 1500-Oe dc field. Solid lines are visual guides on the left part
of the figure; they are the best fits of the experimental data to the generalized
Debye model (see Supporting Information) on the right part of the figure.
K
and between 10 and 10000 Hz respectively, for [Fe(η5-
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same |ml| number (see Figure 8) and consequently supports the
presence of a large uniaxial anisotropy found experimentally in
the [Fe(η5-C5Me5)2]+ system and analogous complexes.[45,46] This
anomalous occupancy of the d orbitals, i.e. filled a1g (dz2) orbital
at slightly higher in energy than the partially filled e2g (dxy, dx2-y2
)
orbitals, indicates a smaller electronic repulsion (lesser pairing
energy) in the former orbital. Finally, it is worth noting that the
[Fe(η5-C5Bn5)2]+ system (see Table S6) is less distorted than the
[Fe(η5-C5Me5)2]+ one. The first excitation is related to the Jahn-
Teller splitting of the 2E2g state, thus, the value for [Fe(η5-C5Bn5)2]+
is smaller (841 cm-1) and consequently, it should have larger axial
character (see g components in Table S5).
Origin of the Magnetization Relaxation
Figure 7. Representation of the NEVPT2 calculated gz component of the g-
tensor for [Fe(η5-C5Me5)2]+. The z eigen-direction of the g-tensor is almost
perpendicular to the (η5-C5Me5) planes (i.e., aligned with the C5 axis).
Based on the above electronic structure calculations and the
estimated position of its first excited state above 1000 K in energy,
Orbach-like processes with an energy barrier as small as
17.6(5) K (as suggested by the temperature dependence of the
spin relaxation time shown in Figure 6) can be unambiguously
eliminated as being responsible for the slow dynamics of the
magnetization in [Fe(η5-C5Me5)2]BArF. Moreover, an Orbach-like
mechanism should not be considered for this system as it
possesses an isolated S = 1/2 Kramers’ doublet ground state, i.e.
a two-level scheme, for which an energy barrier cannot be defined.
On the other hand, quantum tunneling contribution is kept in the
analysis as spin-spin dipolar interactions might be relevant in
these compounds.[47] Thus, Equation 1 may be simplified to only
three terms as shown in Equation 2.
The simulation of the experimental data in Figure 3 gives slightly
overestimated values in the case of both M vs H and χT vs T. At
1.85 K, the magnetization reaches experimentally an almost
saturation value of 1.33 µB at 7 T while the simulation leads to a
value closer to 1.5 µB. Likewise, in the case of the magnetic
susceptibility, the simulated χT product has a minimum of 0.97
cm3K/mol at 1 K and a maximum at 300 K of 1.11 cm3K/mol,
compared to the respective experimental values of 0.80 and 1.05
cm3K/mol. Importantly, the analysis of the calculated NEVPT2
ground state reveals the participation of two determinants that
3
correspond mainly to the e2g a1g2 electron configuration (weighted
values of 0.70 and 0.24). These two determinants correspond to
(dx2 2)2(dxy)1(dz2)2
and
(dx2 2)1(dxy)2(dz2)2
configurations,
-y
-y
respectively.
(2)
In order to minimize the possible effects of overparametrization in
the fitting procedure, the field dependence of the relaxation time
at 2 K was first independently fitted to Equation 2. As shown in
Figure 9 (left part), Equation 2 is able to reproduce very well the
experimental data for [Fe(η5-C5Me5)2]BArF by considering only
direct and Raman terms with a = 2.0(2) 104 K-1T-4s-1, e = 280(20)
T-2, f = 8.1(1) 105 T-2, 2nd = 3.8(1) 106 s-1. Notably, tunneling and
field-dependent Raman terms are relatively similar and can both
fit the low-field region. However, only the Raman term with the
obtained values from the field dependence of the relaxation time
can reproduce the temperature dependence (vide infra). Thus, at
low fields (typically below 0.15 T), a Raman process induces an
increase in the relaxation time, while the decrease at higher fields
is attributed to the increasing importance of the direct process in
applied dc field. The temperature dependence of the relaxation
time at 0.15 T was analyzed analogously according to Equation
2 (without the QTM term) fixing the a, d, e and f parameters to the
values deduced from the field dependence of τ at 2 K. Therefore,
the experimental τ vs T data (Figure 9, right part) were fitted but
with only n as an adjustable parameter. Remarkably, this simple
approach reproduces extremely well the experimental data with
the exponent (n) of 3.8(1) for the Raman term, suggesting that
relaxation involves both optical and acoustic phonons.[48] It is
Figure 8. Energy splitting of the iron d orbitals calculated at NEVPT2 level using
the AILFT (ab initio ligand field theory) approach.
Furthermore, the first excited state (959 cm-1 above the ground
state, equivalent to 1380 K) has the same composition as the
ground state but with an inversion of their two weighted coefficient
values. Thus, the first excitation energies correspond to
transitions between the dx2 2 and dxy orbitals which possess the
-y
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worth mentioning that while Kramers ions are expected to have n
= 9,[32] smaller n values have been observed in a number of S =
½ transition metal complexes which display slow relaxation of the
magnetization.[13,49-55]
that the overall fits are of lower quality, which potentially supports
the presence of an additional relaxation mechanisms.
Overall, the analysis of both field and temperature dependences
of the relaxation time below 6 K and 1 T confirms that direct and
Raman mechanisms are mainly responsible for the relaxation of
the magnetization in [Fe(η5-C5Me5)2]BArF. However, since the
addition of other processes in our analysis will lead to
overparametrization, the presence of other active relaxation
pathways cannot be totally excluded.
Figure 10. Field (left, at 1.85 K) and temperature (right, at 0.02 T) dependences
of the average relaxation time for [Fe(η5-C5Bn5)2]BF4 estimated from Figures
S10 and S12. The red lines are the best fits obtained with the theoretical
approach developed in the text.
Conclusions
We have shown that a series of bulky ferrocenium ions display
slow relaxation of the magnetization, i.e. Single-Molecule Magnet
properties, with a characteristic relaxation time that is strongly dc-
field and temperature dependent. In the case of [Fe(η5-
C5Me5)2]BArF, multireference quantum mechanical computations
reveal an energy gap of over 1000 K between the ground and first
excited states, excluding an Orbach-like mechanism as being the
origin of the observed SMM properties. A detailed analysis of the
field and temperature dependence of the relaxation time supports
the theoretical calculations, revealing that both direct and Raman
processes are responsible for the slow dynamics of the magnetization.
In the case of [Fe(η5-C5Bn5)2]BF4 and [Fe(η5-C5Bn5)2]PF6, a similar
analysis reveals the presence of an additional relaxation
mechanism detectable at low magnetic fields, which has been
attributed to quantum tunneling. The analysis of the electronic
structure of the [Fe(η5-C5Me5)2]+ system indicates a complex
multireferential character in the ground state. The orbital energy
splitting assuming a simple, monodeterminant approach indicates
that the dz2 orbital should be the SOMO bearing the unpaired
electron, but such electronic configuration [(e2g)4(a1g)1] is not in
agreement with the experimental magnetic properties. By contrast,
NEVPT2 calculations including spin-orbit coupling effects reveal
that, due to the different electronic repulsion of the orbitals, the
ground state and first excited states correspond to the single-
Figure 9. Field (left, at 2 K) and temperature (right, at 0.15 T) dependences of
the average relaxation time for [Fe(η5-C5Me5)2]BArF estimated from Figures 4
and 5. The red lines are the best fits obtained with the theoretical approach
developed in the text using Equation 2 (without the QTM term).
Interestingly, the observed magnetization dynamics in [Fe(η5-
C5Bn5)2]BF4 and [Fe(η5-C5Bn5)2]PF6 differs from that of [Fe(η5-
C5Me5)2]BArF. While a unique maximum in the field dependence
of the relaxation time is seen for [Fe(η5-C5Me5)2]BArF at around
0.15 T (Figure 9), a similar maximum is observed at 0.015 T, with
a shoulder around 0.3 T for both [Fe(η5-C5Bn5)2]+ salts (Figures
10 and S18 for [Fe(η5-C5Bn5)2]BF4 and [Fe(η5-C5Bn5)2]PF6
respectively), suggesting the presence of an additional relaxation
process. While we were unable to fit the experimental τ vs H data
from 0 to 1 T to only Raman and direct processes as for Fe(η5-
C5Me5)2]BArF, it is mandatory for these two salts to include the
tunneling term to fit the more complex low-field region below 0.3 T
(Equation 2). Despite the similar field dependence of QTM and
field-dependent Raman terms, it is reasonable to assume that the
effect of the tunneling appears at lower fields than the Raman
mechanism (as assumed in Figure 10 for [Fe(η5-C5Bn5)2]BF4).
Thus, under the presence of a small external field, the degeneracy
is lifted and consequently, the probability of relaxation through the
QTM pathway is reduced. The obtained parameters are then
a = 1.3(2) 104 K-1T-4s-1, b1=2.1(2) 103 s-1, b2=4.4(9) 104 T-2, e =
1.9(5) 103 T-2, f = 4.5(5) 102 T-2, 1.85nd = 252(20) s-1 (Figure 10),
and a =4.2(7) 103 K-1T-4s-1, b1=8.4(9) 102 s-1, b2=72(5) 103 T-2, e =
4.2(5) 102 T-2, f = 2.6(5) 102 T-2, 4nd = 6.1(4) 102 s-1 (Figure S18),
for Fe(η5-C5Bn5)2]BF4 and [Fe(η5-C5Bn5)2]PF6 respectively.
Similarly to the case of [Fe(η5-C5Me5)2]BArF, these parameters
can be used to fit the temperature dependence with only n as an
adjustable parameter (n = 2.6(1) and 3.7(1)), however it is clear
occupancy of the dx2 2/dxy orbitals, respectively while the dz2
-y
orbital is doubly-occupied in both states. These unexpected
electronic configurations of the ground and first excited states
[(a1g)2(e2g)3] are in agreement with the relatively large magnetic
anisotropy found experimentally.
Our experimental results demonstrate the critical importance of
analyzing the field and temperature dependence of the relaxation
time. Although a naïve analysis of the temperature dependence
of relaxation for these ferrocenium complexes suggests the
presence of Orbach-like and quantum tunneling pathways, the
field dependence shows that the relaxation is indeed dominated
by a combination of direct and Raman processes. The multiple
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[13] M. Ding, G. E. Cutsail III, D. Aravena, M. Amoza, M. Rouzières, P.
Dechambenoit, Y. Losovyj, M. Pink, E. Ruiz, R. Clérac and J. M. Smith,
Chem. Sci., 2016, 7, 6132-6140.
relaxation pathways that are available to paramagnetic
compounds make such analyses critical for understanding
magnetization dynamics, e.g. diagnosing SMM behavior.
[14] D. N. Hendrickson, Y. S. Sohn and H. B. Gray, Inorg. Chem., 1971, 10,
1559-1563.
[15] Y. S. Sohn, D. N. Hendrickson and H. B. Gray, J. Am. Chem. Soc., 1970,
92, 3233-3234.
Acknowledgements
[16] R. Prins, Mol. Phys., 1970, 19, 603-620.
[17] R. Prins and F. J. Reinders, J. Am. Chem. Soc., 1969, 91, 4929-4931.
[18] K. N. Shrivastava, Phys. Stat. Sol. A, 1983, 117, 437-458.
[19] J. H. Van Vleck, Phys. Rev., 1940, 57, 426-447.
M.D., A.K.H. and J.M.S. acknowledge funding from Indiana
University and the NSF (CHE-1112299). R.C. and M.R. thank the
University of Bordeaux, the Conseil Regional de Nouvelle
Aquitaine, the CNRS, the GdR MCM-2 and the MOLSPIN COST
action CA15128 for financial support. T.J.O., W.A.H., and M.P.S.
thank the National Science Foundation (CHE-1363274) for
support. M.A and E.R. thank Spanish Ministerio de Economía y
Competitividad (MINECO) for the grant PGC2018-093863-B-C21
and the computer resources, technical expertise and assistance
provided by the CSUC. E.R. acknowledges Generalitat de
Catalunya for an ICREA Academia award. M. A. thanks the
Spanish "Ministerio de Educación y Formación Profesional for a
graduate FPU fellowship. We thank Prof. Brian M. Hoffman,
Northwestern University, for use of the low temperature X- and Q-
band EPR spectrometers, which is supported by the NIH (GM
111097 to B.M.H.).
[20] M. Abraham, H. H. Klauß, W. Wagener, F. J. Litterst, A. Hofmann and M.
Herberhold, Hyperfine Interact., 1999, 120/121, 253-256.
[21] R. H. Herber, I. Felner and I. Nowik, Hyperfine Interact., 2016, 237, 100.
[22] I. Nowik and R. H. Herber, Inorg. Chim. Acta, 2000, 310, 191-195.
[23] H. Schottenberger, K. Wurst, U. J. Griesser, R. K. R. Jetti, G. Laus, R. H.
Herber and I. Nowik, J. Am. Chem. Soc., 2005, 127, 6795-6801.
[24] M. Reiners, D. Baabe, P. Schweyen, M. Freytag, P. G. Jones and M. D.
Walter, Eur. J. Inorg. Chem., 2017, 388-400.
[25] A. Houlton, R. A. Brown, J. R. Miller, R. M. G. Roberts, J. Silver and M.
Thomas, J. Organomet. Chem., 1992, 431, C17-C20.
[26] P. Zanello, A. Cinquantini, S. Mangani, G. Opromolla, L. Pardi, C. Janiak
and M. D. Rausch, J. Organomet. Chem., 1994, 471, 171-177.
[27] I. Chávez, A. Alvarez-Carena, E. Molins, A. Roig, W. Maniukiewicz, A.
Arancibia, V. Arancibia, H. Brand and J. Manuel Manrıquez, J.
́
Organomet. Chem., 2000, 601, 126-132.
[28] J. W. Chambers, A. J. Baskar, S. G. Bott, J. L. Atwood and M. D. Rausch,
Organometallics, 1986, 5, 1635-1641.
Keywords: metallocences • magnetic properties • electronic
[29] H. Schumann, C. Janiak, R. D. Köhn, J. Loebel and A. Dietrich, J.
Organomet. Chem., 1989, 365, 137-150.
structure • ab initio calculations
[30] C. R. Groom, I. J. Bruno, M. P. Lightfoot and S. C. Ward, Acta Cryst.,
2016, B72, 171-179.
[1]
[2]
T. J. Kealy and P. L. Pauson, Nature, 1951, 168, 1039-1040.
I. R. Butler and D. Thomas, in Comprehensive Organometallic Chemistry
III, Elsevier, 2007, pp. 185-220.
[31] K. D. Warren, Inorg. Chem., 1974, 13, 1317-1324.
[32] A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of
Transition Ions, Dover, New York, 1986.
[3]
[4]
[5]
[6]
[7]
Chiral Ferrocenes in Asymmetric Catalysis: Synthesis and Applications,
(Eds.: L.-X. Dai and X.-L. Hou), Wiley-VCH, Weinheim, 2010.
Ferrocenes: Ligands, Materials and Biomolecules, (Ed.: P. Štěpnička)
John Wiley & Sons., New York, 2008.
[33] F. Aquilante, L. De Vico, N. Ferré, G. Ghigo, P.-Å. Malmqvist, P.
Neogrády, T. B. Pedersen, M. Pitonak, M. Reiher, B. O. Roos, L.
Serrano-Andrés, M. Urban, V. Veryazov and R. Lindh, J. Comput. Chem.,
2010, 31, 224-247.
Ferrocenes: Compounds, Properties and Applications, (Ed: E. S. Philips ),
Nova Science Publishers, New York, 2011.
[34] G. Karlström, R. Lindh, P.-Å. Malmqvist, B. O. Roos, U. Ryde, V.
Veryazov, P.-O. Widmark, M. Cossi, B. Schimmelpfennig, P. Neogrady
and L. Seijo, Comput. Mater. Sci., 2003, 28, 222-239.
M. Malischewski, K. Seppelt, M. Adelhardt, J. Sutter and K. Meyer,
Science, 2016, 353, 678-682.
[35] V. Veryazov, P.-O. Widmark, L. Serrano-Andrés, R. Lindh and B. O.
Roos, Int. J. Quantum Chem., 2004, 100, 626-635.
For both classes of complex, the energy separation of between the a1g
(a1) and lower lying e2g (e) levels is small and may have a different
relative energy ordering, depending on the metal and oxidation state. For
metallocenes, see for example, T.A. Jackson, J. Krzystek, A. Ozarowski,
G.B. Wijeratne, B.F. Wicker, D.J. Mindiola and J. Telser, Organometallics
2012, 31, 8265-8274 and T.A. Jackson, J. Krzystek, A. Ozarowski, G.B.
Wijeratne, B.F. Wicker, D.J. Mindiola and J. Telser, Organometallics
2014, 33, 1325-1325 (addendum). For pseudotetrahedral complexes,
see for example, L. Bucinsky, M. Breza, W.-T. Lee, A.K. Hickey, D.A.
Dickie, I. Nieto, J.A. DeGayner, T.D. Harris, K. Meyer, J. Krzystek, A.
Ozarowski, J. Nehrkorn, A. Schnegg, J. Holldack, R.H. Heber, J. Telser,
and J.M. Smith, Inorg. Chem. 2017, 56, 4751-4768.
[36] B. O. Roos, R. Lindh, P.-A. Malmqvist, V. Veryazov and P.-O. Widmark,
J. Phys. Chem. A., 2004, 108, 2851-2858.
[37] B. O. Roos, R. Lindh, P.-Å. Malmqvist, V. Veryazov, P.-O. Widmark and
A. C. Borin, J. Phys. Chem. A., 2008, 112, 11431-11435.
[38] P.-O. Widmark, P.-Å. Malmqvist and B. O. Roos, Theor. Chim. Acta,
1990, 77, 291-306.
[39] F. Neese, Wiley Interdiscip. Rev. Comput. Mol. Sci., 2012, 2, 73-78.
[40] F. Neese, Wiley Interdiscip. Rev. Comput. Mol. Sci., 2018, e1327.
[41] A. Schäfer, H. Horn and R. Ahlrichs, J. Chem. Phys., 1992, 97, 2571-
2577.
[42] F. Weigend and R. Ahlrichs, Phys. Chem. Chem. Phys., 2005, 7, 3297.
[43] M. E. Switzer, R. Wang, M. F. Rettig and A. H. Maki, J. Am. Chem. Soc.,
1974, 96, 7669-7674.
[8]
[9]
M. Ding, M. Rouzières, Y. Losovyj, M. Pink, R. Clérac and J. M. Smith,
Inorg. Chem., 2015, 54, 9075-9080.
H.-J. Lin, D. Siretanu, D. A. Dickie, D. Subedi, J. J. Scepaniak, D. Mitcov,
R. Clérac and J. M. Smith, J. Am. Chem. Soc., 2014, 136, 13326-13332.
[44] C. Angeli, R. Cimiraglia, S. Evangelisti, T. Leininger and J. P. Malrieu, J.
Chem. Phys., 2001, 114, 10252-10264.
[10] C. Mathonière, H.-J. Lin, D. Siretanu, R. Clérac and J. M. Smith, J. Am.
Chem. Soc., 2013, 135, 19083-19086.
[45] S. Gómez-Coca, D. Aravena, R. Morales and E. Ruiz, Coord. Chem.
Rev., 2015, 289-290, 379-392.
[11] J. J. Scepaniak, T. D. Harris, C. S. Vogel, J. r. Sutter, K. Meyer and J. M.
Smith, J. Am. Chem. Soc., 2011, 133, 3824-3827.
[46] S. Gomez-Coca, E. Cremades, N. Aliaga-Alcalde and E. Ruiz, J. Am.
Chem. Soc., 2013, 135, 7010-7018.
[12] G. E. Cutsail III, B. W. Stein, D. Subedi, J. M. Smith, M. L. Kirk and B. M.
Hoffman, J. Am. Chem. Soc., 2014, 136, 12323-12336.
[47] D. Aravena, J. Phys. Chem. Lett., 2018, 9, 5327-5333.
[48] A. Singh and K. N. Shrivastava, Phys. Stat. Sol. B., 1979, 95, 273-277.
This article is protected by copyright. All rights reserved.

10.1002/chem.201900799
Chemistry - A European Journal
FULL PAPER
[49] M. Atzori, E. Morra, L. Tesi, A. Albino, M. Chiesa, L. Sorace and R.
Sessoli, J. Am. Chem. Soc., 2016, 138, 11234-11244.
[53] L. Tesi, E. Lucaccini, I. Cimatti, M. Perfetti, M. Mannini, M. Atzori, E.
Morra, M. Chiesa, A. Caneschi, L. Sorace and R. Sessoli, Chem. Sci.,
2016, 7, 2074-2083.
[50] M. Atzori, L. Tesi, S. Benci, A. Lunghi, R. Righini, A. Taschin, R. Torre,
L. Sorace and R. Sessoli, J. Am. Chem. Soc., 2017, 139, 4338-4341.
[51] R. Boča, C. Rajnák, J. Titiš and D. Valigura, Inorg. Chem., 2017, 56,
1478-1482.
[54] L. Tesi, A. Lunghi, M. Atzori, E. Lucaccini, L. Sorace, F. Totti and R.
Sessoli, Dalton Trans., 2016, 45, 16635-16643.
[55] S.-Q. Wu, Y. Miyazaki, M. Nakano, S.-Q. Su, Z.-S. Yao, H.-Z. Kou and
O. Sato, Chem. Eur. J., 2017, 23, 10028-10033.
[52] W. Lin, T. Bodenstein, V. Mereacre, K. Fink and A. Eichhöfer, Inorg.
Chem., 2016, 55, 2091-2100.
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Multireference quantum chemical
computations and a detailed analysis
of the magnetization relaxation time
reveal that both direct and Raman
processes are responsible for the
SMM properties of bulky ferrocenium
complexes.
Mei Ding, Anne K. Hickey, Maren Pink,
Joshua Telser,* David L. Tierney, Martin
Amoza, Mathieu Rouzières, Tarik J.
Ozumzerzifon, Wesley A. Hoffert,
Matthew P. Shores, Eliseo Ruiz,*
Rodolphe Clérac* and Jeremy M. Smith*
Page No. – Page No.
Magnetization Slow Dynamics in
Ferrocenium Complexes
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