A linear cobalt(II) complex with maximal orbital angular momentum from a non-Aufbau ground state

Article abstract of DOI:10.1126/science.aat7319

Orbital angular momentum is a prerequisite for magnetic anisotropy, although in transition metal complexes it is typically quenched by the ligand field. By reducing the basicity of the carbon donor atoms in a pair of alkyl ligands, we synthesized a cobalt(II) dialkyl complex, Co(C(SiMe₂ONaph)₃)₂ (where Me is methyl and Naph is a naphthyl group), wherein the ligand field is sufficiently weak that interelectron repulsion and spin-orbit coupling play a dominant role in determining the electronic ground state. Assignment of a non-Aufbau (d_x2_–y2, d_xy)³(d_xz, d_yz)³(d_z2)¹ electron configuration is supported by dc magnetic susceptibility data, experimental charge density maps, and ab initio calculations. Variable-field far-infrared spectroscopy and ac magnetic susceptibility measurements further reveal slow magnetic relaxation via a 450–wave number magnetic excited state.

Full text of DOI:10.1126/science.aat7319

RESEARCH ARTICLES
Cite as: P. C. Bunting et al., Science
10.1126/science.aat7319 (2018).
A linear cobalt(II) complex with maximal orbital angular
momentum from a non-Aufbau ground state
Philip C. Bunting1, Mihail Atanasov2,3, Emil Damgaard-Møller4, Mauro Perfetti5, Iris Crassee6, Milan Orlita6,7,
Jacob Overgaard4, Joris van Slageren5, Frank Neese2, Jeffrey R. Long1,8,9
*
1Department of Chemistry, University of California, Berkeley, CA 94720, USA. 2Max-Planck-Insitut für Kohlenforschung, Mülheim an der Ruhr D-45470, Germany. 3Institute
of General and Inorganic Chemistry, Bulgarian Academy of Sciences, Academy Georgi Bontchev, Sofia 1113, Bulgaria. 4Department of Chemistry and Centre for Materials
Crystallography, Aarhus University, DK-8000 Aarhus C, Denmark. 5Institut für Physikalische Chemie and Center for Integrated Quantum Science and Technology (IQST),
Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany. 6Laboratoire National des Champs Magnétiques Intenses, CNRS-UGA-UPS-INSA-EMFL, 25 rue des
Martyrs, 38042 Grenoble, France. 7Institute of Physics, Charles University, Ke Karlovu 5, 12116 Praha 2, Czech Republic. 8Department of Chemical and Biomolecular
Engineering, University of California, Berkeley, CA 94720, USA. 9Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
*Corresponding author. Email: jrlong@berkeley.edu
Orbital angular momentum is a prerequisite for magnetic anisotropy, although in transition metal
complexes it is typically quenched by the ligand field. Here, by reducing the basicity of the carbon donor
atoms in a pair of alkyl ligands, we synthesize a cobalt(II) dialkyl complex, Co(C(SiMe2ONaphthyl)3)2,
wherein the ligand field is sufficiently weak that interelectron repulsion and spin-orbit coupling play a
2
dominant role in determining the electronic ground state. Assignment of a non-Aufbau (dx 2, dxy)3(dxz,
–y
2
dyz)3(dz )1 electron configuration is supported by dc magnetic susceptibility data, experimental charge
density maps, and ab initio calculations. Variable-field far-infrared spectroscopy and ac magnetic
susceptibility measurements further reveal slow magnetic relaxation via a 450 cm−1 magnetic excited
state.
All materials exhibiting a large magnetic anisotropy possess transition metal complexes have garnered interest of late be-
nonzero orbital angular momentum L arising from an cause they are energetically unaffected by Jahn-Teller distor-
electronic structure of partially-filled (but not half-filled) tions, allowing for the possibility of virtually unquenched
energetically degenerate orbitals. In trivalent lanthanide orbital angular momentum (2). Analogously to lanthanide
ions, the valence 4f orbitals are well-shielded and interact complexes, such transition metal systems with nonzero L are
little with their coordination environment, allowing for a best described by a total angular momentum J, which is split
nonzero L that couples with the total spin S to give rise to a by spin-orbit coupling and the ligand field into 2J + 1 MJ
total angular momentum of |L − S| ≤ J ≤ |L + S| and states. Two transition metal complexes that have been de-
potentially a large magnetic anisotropy. In the case of scribed using this formalism are the iron(II) complex
transition metals, however, the ligand field typically removes Fe(C(SiMe3)3)2 and the iron(I) complex [Fe(C(SiMe3)3)2]− (3,
any orbital degeneracy, leading to quenching of the orbital 4). Both complexes have ground states with L = 2 due to elec-
angular momentum (L = 0) and an appropriate description tronic configurations which place three electrons in the de-
2
2
of the ground state in terms of S only. When magnetic generate orbital pair dx -y and dxy, which arise from linear
anisotropy is present in such complexes, it is generally a weak combinations of the hydrogen-like d-orbitals with ml = 2. A
effect that arises from mixing of electronic ground and notable consequence of these electronic structures is that
excited states induced by spin-orbit coupling. Creating both complexes exhibit relatively large energy separations be-
unquenched orbital angular momentum in molecular tween their ground and first excited MJ states, making them
transition metal-based systems requires an exceptionally prone to single-molecule magnet behavior (5). Indeed, ac
weak ligand field and/or two or more orbitals that are nearly magnetic susceptibility data revealed that both molecules ex-
degenerate. In this context, perhaps the simplest hibit slow magnetic relaxation (the former complex under an
experimental system is a one-coordinate cobalt atom: applied dc field and the latter in zero applied field) with ef-
individual cobalt atoms on a MgO surface (referred to as fective spin-reversal barriers (Ueff) of 178 and 246 cm−1, re-
adatoms) were recently shown using scanning probe spectively (6)—values close to the calculated energy
9
3
microscopy to possess a J = /2 (L = 3, S = /2) ground state separations between their ground and first excited MJ states
and exhibit near maximal magnetic anisotropy in a half- (7, 8).
integer spin 3d system (1).
At first glance it may seem impossible to increase orbital
In the regime of molecules, linearly coordinated angular momentum for a transition metal complex beyond L
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release) 1

= 2. An L = 3 ground state requires two sets of degenerate (1).
2
orbitals, dx -y2, dxy (ml = 2) and dxz, dyz (ml = 1), with an odd
Our motivations to isolate a dialkyl cobalt(II) complex
number of electrons in each. The Aufbau principle describes were thus twofold: first, the proposed electronic structure vi-
the manner in which electrons fill orbitals, typically from olates the Aufbau principle and is analogous to what is com-
lowest to highest energy. A more rigorous consideration of monly seen for lanthanides; second, realizing maximal
electronic structure accounts for three main effects: ligand orbital angular momentum should afford a very large mag-
field stabilization, interelectron repulsion, and spin-orbit netic anisotropy, a property that has important applications
coupling. Ligand field effects typically dominate when con- in the study of magnetism. Here, we present the synthesis
sidering transition metal complexes. When the ligand field and characterization of such a dialkyl cobalt(II) complex and
stabilization and interelectron repulsion energies are similar confirm the proposed J = 9/2 ground state through direct elec-
in transition metal complexes, high spin electronic configu- tronic and spectroscopic measurements, ab initio modeling,
rations arise. For example, placing three electrons in the or- and magnetic susceptibility measurements. The energy sepa-
2
2
bitals (dx -y
,
dxy)(dxz, dyz) could give the low-spin ration between the MJ = 9/2 and 7/2 states leads to slow
configuration (dx -y2, dxy)3(dxz, dyz)0 if the energy separation be- magnetic relaxation at temperatures as high as 70 K and low-
2
tween orbital pairs is larger than the electron pairing energy, temperature magnetic hysteresis.
2
or the high-spin configuration (dx -y2, dxy)2(dxz, dyz)1 if the or-
Synthesis and structure of a linear cobalt dialkyl
bital pairs are relatively close in energy. For six electrons, the complex
2
expected Aufbau filling of these orbitals is (dx -y2, dxy)4(dxz,
Our attempts to synthesize Co(C(SiMe3)3)2 from metathe-
dyz)2, and as the sixth electron must be paired in either orbital sis reactions of [C(SiMe3)3]– salts and CoX2 (X = Cl, Br, I) gave
pair, there is no reason to assume there would be any stabili- only intractable amorphous black solids. Similar reactivity
zation from the non-Aufbau configuration, (dx2-y2, dxy)3(dxz, with [C(SiMe3)3]– was reported previously, but by switching
dyz)3.
to [C(SiMe2Ph)3]– it proved possible to isolate the dimer
Intriguingly, calculations on the hypothetical complex [Co(C(SiMe2Ph)3)]2, a product formed by the in situ reduction
Co(C(SiMe3)3)2 show a ground state with L = 3, which arises of cobalt(II) (10). Thus, at least one challenge in isolating a
2
from a non-Aufbau 3d-orbital filling of (dx -y2, dxy)3(dxz, dialkyl cobalt(II) complex is the strongly reducing nature of
dyz)3(dz2)1, and further predict a splitting between ground and the carbanion. Others have shown that substituting electron-
first excited MJ states of 454 cm–1 (9). Efforts to synthesize withdrawing alkoxides onto each silyl group significantly re-
this molecule both by our laboratory and others (10) were un- duces the basicity and electron density of the carbanion (17).
successful. Moreover, although nearly 70 two-coordinate, par- In an initial pursuit of this approach, we found that
amagnetic transition metal complexes have been synthesized [C(SiMe2OPh)3]– did support a dialkyl cobalt(II) complex,
(11), the only such compounds with alkyl ligands are of the Co(C(SiMe2OPh)3)2, but long-range Co···O interactions led to
type [M(C(SiMe3)3)2]0/1−, where M is Fe(II) (12), Fe(I) (4), a significantly bent C–Co–C axis (fig. S1). We next synthesized
Mn(II) (13) and Mn(I) (14). Several approximately linear co- a number of [C(SiMe2OR)3]– derivatives (R = various alkyl or
balt(II) complexes have been studied, however, and one such substituted phenyl groups) following the general reaction
molecule (sIPr)CoNDmp (where sIPr is an N-heterocyclic car- scheme outlined in Fig. 1A. Smaller substituents did not read-
bene and NDmp is an arylimido ligand) has a spin-reversal ily yield isolable products, and larger substituents supported
barrier of 413 cm−1, more than 1.5 times that measured for only dinuclear complexes of the type (R3CCo)2(μ-X)2 (where X
[FeI(C(SiMe3)3)2]–, despite both molecules possessing the is a halide), similar to the structure of ((PhMe2Si)3CZn)2(μ-
7
same total angular momentum of J = /2 (15). Correspond-
ingly, the increase in magnetic anisotropy for the Co(II) com-
plex must arise from an increase in the spin-orbit coupling
constant, a value which trends with effective nuclear charge.
In another example, bent [OCoO]– anions inserted into the
channels of an apatite-type structure were shown to have a
spin-reversal barrier of 387 cm−1 (16). A semi-empirical
method based on ligand field parameterization predicted that
Cl)2 (18). In an effort to reduce the nucleophilicity of the oxy-
gen atom, we also tried using electron withdrawing substitu-
ents such as perfluorophenyl, but found these ligands to be
susceptible to Si–O cleavage, a challenge also encountered
when trying to metallate other HC(SiMe2OR)3 complexes with
MeLi (19). Ultimately, we determined that only the naphthol
(R = Naph = C10H7) derivative yielded the requisite linear ge-
ometry.
The reaction of two equivalents of KC(SiMe2ONaph) with
CoBr2 in THF at 60°C affords a green solution. After removal
of the solvent in vacuo and redissolution into hexanes, dark
red crystals of Co(C(SiMe2ONaph)3)2 (1) emerged from the
green solution over the course of several days at room tem-
perature. Crystallization at −30°C formed green crystals that
9
such a barrier could arise from a J = /2 ground state, with
increasing mixing of MJ states (and a concomitant diminish-
ing of the barrier height) arising as the [OCoO]– anion be-
comes increasingly bent. In the extreme case of the cobalt
adatoms mentioned above, a separation of 468 cm−1 was de-
9
7
termined for the separation between MJ = /2 and /2 states
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release)
2

were not suitable for X-ray diffraction, but elemental analysis model molecule show that inclusion of the carbon σ-bonding
of the thoroughly dried crystals suggested the isolation of the electrons in the complete active space have only a very minor
solvated complex, Co(C(SiMe2ONaph)3)2(THF). Compound 1 effect (less than 3%) on the energies of both the non-relativ-
is insoluble in common organic solvents, and exposure to istic and relativistic states (tables S10 and S11).
4
THF led to formation of a green solution which is likely the
aforementioned solvated complex. The zinc congener,
Zn(C(SiMe2ONaph)3)2 (2), was obtained from the reaction of
KC(SiMe2ONaph) and ZnBr2 in Et2O. After removal of KBr by
filtration, colorless crystals of 2 grew from the Et2O solution
over the course of several days. Using the same reaction con-
ditions with a mixture of ZnBr2 and CoBr2(THF) further ena-
Ligand-field analysis of the calculations revealed the Φ
ground state to have the 3d-orbital filling (dx -y2, dxy)3(dxz,
2
dyz)3(dz2)1 (Fig. 2A), which deviates from the expected Aufbau
2
orbital filling of (dx -y2, dxy)4(dxz, dyz)2(dz2)1 (4Σ−) and can be ex-
plained by considering the competing effects of ligand field
stabilization and interelectron repulsion. In general, inter-
electronic repulsion is strongest for two electrons occupying
the same orbital (necessarily with opposite spin). Two elec-
trons with opposite spin in different orbitals alternatively ex-
perience medium-strong electron-electron repulsion, while
two electrons with parallel spin (necessarily in different or-
bitals) repel each other least strongly owing to the presence
of the Fermi-hole. Typically, only the electron pairing energy
component of interelectron repulsion is important for transi-
tion metal complexes, and whether a complex is high- or low-
spin is determined by considering whether the ligand field
strength is small or large compared to the pairing energy. In
the case of 1, the ligand field strength is so small that not only
does the molecule display a high-spin state, but it also max-
imizes its orbital angular momentum in keeping with the
Hund rule for free atoms and ions, thus leading to a non-Auf-
bled preparation of
a
magnetically dilute sample,
Co0.02Zn0.98(C(SiMe2ONaph7)3)2 (3).
Single crystal x-ray diffraction analysis revealed com-
pounds 1 and 2 to be isostructural, crystallizing in space
group R–3 (no. 148) and featuring a linear C–M–C axis im-
posed by the S6 site symmetry (Fig. 1, B and C). The Co–C and
Zn–C interatomic distances of 2.066(2) and 1.995(3) Å, re-
spectively, are similar to the Fe–C separation of 2.0505(14) Å
in Fe(C(SiMe3)3)2 (12) and the and Zn–C separation of 1.982(2)
Å in Zn(C(SiMe3)3)2 (20). In addition, the Co···O distance of
3.1051(11) Å and Zn···O distance of 3.1240(16) Å are signifi-
cantly longer than the sum of cobalt or zinc and oxygen ionic
radii (~2.2 Å), suggesting minimal interactions. Instead, the
staggered orientation of the ligands facilitates close sp3-
CH∙∙∙π and sp2-CH∙∙∙π contacts of 2.692 and 2.822 Å, re-
bau ground state configuration. Clearly, the (dx -y2, dxy)3(dxz,
2
spectively (fig. S3), which are in the range of weak CH-π in- dyz)3(dz2)1 configuration minimizes electron-electron repul-
teractions (21). This suggests that inter-ligand interactions sion relative to the alternative (dx -y2, dxy)4(dxz, dyz)2(dz2)1 con-
2
may help stabilize 1, consistent with reports of dispersion figuration that features an electronically crowded (dx -y2, dxy)4
2
forces stabilizing other two-coordinate complexes (22).
subshell. This stabilization is also reflected in the total orbital
Electronic structure calculations
angular momentum of the ground state that is an approxi-
Ab initio calculations performed on 1 using the crystal mately good quantum number in this system. Non-relativistic
structure geometry reveal that the 4F free ion state is split by ligand field calculations without interelectron repulsion
the linear ligand field into three doubly-degenerate states 4Φ,
show the expected ground state of 4Σ− (with L = 0). Using lig-
4Π, and 4Δ, and one non-degenerate state 4Σ− (here we employ and field parameters from ab initio NEVPT2 calculations and
C∞v point group notation). Due to the exceptionally weak lig- ligand field expressions for the S = 3/2 states under linear sym-
4
and field, the seven states of F parentage are split by less metry with interelectron repulsion, the high orbital angular
than 3000 cm−1 (accounting also for interelectron repulsion momentum Φ state (with L = 3) is stabilized by 1300 cm−1
4
relative to the 4Σ− state (Fig. 2B and table S9). Spin-orbit cou-
energy). This splitting is small even relative to that of other
two-coordinate complexes; for example, the 5D and 4F free ion
states of Fe(C(SiMe3)3)2 and [Fe(C(SiMe3)3)2]– are split by 5000
and 6000 cm−1, respectively (3, 4, 7). Excitations from the 4Φ
9
4
pling further stabilizes the MJ = /2 component of the Φ
ground state by 788 cm−1.
This situation is completely distinct from that of estab-
ground state of 1 to the 4Σ−(4P) and 4Π(4P) states were calcu- lished complexes with stronger ligand fields that can some-
lated to be spectroscopically accessible at 13,537 and 18,864 times have electronic ground states with significant
cm−1, and indeed are observed in the ultraviolet-visible (UV- contributions from non-Aufbau configurations. For example,
vis) diffuse reflectance spectrum at 12,000 and 15,000 cm−1 the iron(II) metallophthalocyanine complex (FePc) has a
(fig. S4). The splitting of the 4Φ ground state due to spin-orbit ground state with nearly equal contributions from Aufbau
coupling results in four sets of Kramers doublets, best de- and non-Aufbau configurations, wherein the non-Aufbau
scribed by MJ = 9/2, 7/2, 5/2, and 3/2, in order of increasing component arises from an accidental orbital near-degeneracy
energy. The total splitting of 4Φ is 1469 cm−1, while the calcu- (23). The essential difference between complex 1 and FePc,
lated separation between just MJ = 9/2 and MJ = 7/2 is 476
cm−1. Additional calculations performed on a truncated
however, is in ligand field strength, with the two molecules
calculated to exhibit total d-orbital splittings of 6000 and
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release)
3

165,000 cm–1, (23) respectively. Focusing on the orbitals that coordination axes such that the Co–C direction is along the z-
give rise to the non-Aufbau states, the dx2−y2,dxy and dxz,dyz or- axis, the electron density of the cobalt valence shell is distrib-
2
bital pairs are separated by 2900 cm−1 in 1, whereas for FePc uted in the following manner: 42.8% is in the dx -y2, dxy orbit-
the dxz,dyz orbital pair and dz2 orbital are separated by 19,000 als, 41.2% is in the dxz, dyz orbitals, and 16.0% is in the dz2
cm−1 (23). Our calculations show that interelectron repulsion orbital. Furthermore, the same distribution of electrons in
in 1 easily overwhelms the ligand field stabilization energy the cobalt 3d-orbitals was obtained regardless of the manner
associated with the Aufbau configuration, destabilizing the in which the naphthalene disorder was treated.
4Σ−(4P) state by 12,000 cm−1 relative to the 4Φ state. No similar
calculations appear to have been reported for FePc, but it is
clear that it would be impossible to observe a pure non-Auf-
bau ground state as long as the ligand field stabilization en-
ergy is of the same magnitude as interelectron repulsion.
Once the ligand field requirement for a non-Aufbau ground
state is met, it is also possible to observe maximal orbital an-
gular momentum. The maximal orbital angular momentum
Variable-field far-infrared spectroscopy
We sought to confirm experimentally the magnitude of
the separation between the ground and first excited magnetic
states in 1 using variable-field far-IR spectroscopy (25, 26).
Although such energy separations are more commonly deter-
mined by fitting low-temperature magnetization data or
high-temperature magnetic relaxation data, these ap-
proaches give values that are sensitive to fitting procedures
and provide only an indirect measure of the representative
ground to excited state energy separation. Additionally, given
the calculated energy splitting of 476 cm−1 for the lowest MJ
states, dc susceptibility measurements would provide limited
information on the position of excited states, as the Boltz-
mann population of the ground state doublet is still 90% at
300 K. Thus, not only is spectroscopy a more direct measure-
ment, but in this case, it is also necessary to gain information
on the excited states. Transmission spectra in the 30 to 600
cm−1 energy range were collected at a temperature of 4.2 K
under applied fields ranging from 0 to 11 T (Fig. 3A). Alt-
hough absorption bands associated with magnetic dipole
transitions are usually significantly weaker than those of
electronic dipole transitions, a pronounced field dependence
is immediately evident in the data upon dividing the applied
field spectra by the zero-field spectrum (Fig. 3B). The only
peak visible in this energy range is at 450 cm−1 and is attribut-
able to the transition from MJ = 9/2 to 7/2 in good agreement
with the calculated separation of 476 cm–1. A steadily increas-
ing blueshift of the IR absorption maximum is observed with
increasing applied fields (fig. S5) and is in good agreement
with a simulation of the spectral envelope magnetic dipole
MJ = 9/2 to 7/2 transitions (fig. S6). In addition to the
blueshift there is a concomitant decrease in absorption inten-
sity and peak broadening with increasing field, giving rise to
the derivative shape observed in Fig. 3B.
2
of L = 3 for transition metals requires degenerate dx -y2, dxy
and dxz, dyz orbital pairs, and thus the molecule should also
be linear to avoid Jahn-Teller distortions.
The ligand-field analysis elucidates another challenge in
isolating a dialkyl cobalt complex, namely the ligand field sta-
bilization energy suggests that metal-ligand bond formation
provides only a minor stabilizing effect of 4.8 kcal/mol (1700
cm−1). This result is perhaps intuitively understood by consid-
ering that the formal Co–C bond order is approximately one
half, because the dxz, dyz orbitals have slight π-antibonding
character and are destabilized primarily by electrostatic in-
teractions. It is not until we consider transmetallic dispersion
and electrostatic (CH∙∙∙π) forces that 1 appears to be stable.
Charge density determination
The molecular charge density (CD) of 1 was obtained from
multipolar refinement of single crystal x-ray diffraction data
measured at 20 K using synchrotron radiation. A small
amount of disorder (~6%) is present in the structure due to
flipping of the naphthalene groups (also involving the O and
Si atoms); however, a detailed description of this disorder
was possible and allowed us to extract quantitative infor-
mation pertinent to the magnetic properties (see methods for
a detailed description of the experimental procedure).
The experimental temperature of 20 K is low enough that
the CD primarily represents the electronic properties of the
relativistic ground state. We used an atom-centered multi-
pole formalism to describe the CD, and thus a complete set
of spherical harmonic functions for each atom was used to
quantify the deviations from a spherical density distribution.
The use of this formalism enables estimation of 3d-orbital
populations on the central cobalt atom, under the assump-
tion that the density around the metal originates solely from
the atom itself (i.e., that no significant covalent bonding oc-
curs). The parameterized CD also enables an analysis in the
framework of quantum theory of atoms in molecules
(QTAIM) (24) and estimates of atomic charges and the
strength of chemical bonding. Defining the local
Magnetic properties
Variable-temperature dc magnetic susceptibility data for
1 are shown in Fig. 4A. The gradual decrease in the product
of the molar magnetic susceptibility and temperature (χMT)
with decreasing temperature is indicative of magnetic anisot-
ropy, while the strong field dependence at low temperature
arises from an increased Zeeman splitting at higher fields.
The room temperature χMT value of 4.89 cm3 K mol−1 is con-
sistent with a well-isolated MJ = 9/2 ground state (the theoret-
ical χMT value for an isotropic J = 9/2 ion is 5.47 cm3 K mol−1),
and reduced magnetization plots (Fig. 4B) show a saturation
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release)
4

magnetization of 3.00 μB. The simulated χMT and reduced Using the value of U = 450 cm−1 obtained from far-IR spec-
magnetization data from ab initio calculations (solid lines, troscopy, however, we determined an upper bound for τ0 of
Fig. 4) are in close agreement with the experimental data, fur- 1.79 × 10−9 s, which is a reasonable value for a single-molecule
ther corroborating the well-isolated MJ = 9/2 ground state.
magnet (5).
The low temperature relaxation dynamics of 1 and 3 were
Ac susceptometry was employed to probe magnetic relax-
ation in the 10−4 to 101 s (104 to 10−1 Hz) range. By fitting the also probed using dc relaxation and magnetization experi-
in-phase (χ′) and out-of-phase (χ″) susceptibility (figs. S8 to ments (Fig. 5B). The tunneling and direct relaxation terms
S11) to a generalized Debye model, we obtained relaxation introduced above were used in fits of the variable-field relax-
times for 1, as shown in the Arrhenius plot in Fig. 5A. The ation data and are discussed in detail in the Methods section.
temperature dependence of magnetic relaxation time (τ) in The relaxation times extracted at 1.8 K and zero applied field
are 16.4 0.7 and 48.2 4.7 s for 1 and 3, respectively, and
these values slow to 221 and 660 s at 1.8 K under a 1500 Oe
applied field. These relaxation times suggest that magnetic
hysteresis should be apparent in variable-field magnetization
data, and indeed 1 and 3 show waist-restricted hysteresis
loops between 0.7 T up to 5 K. A sudden decline in the mag-
netization as the field approaches zero can be ascribed to
rapid relaxation induced by tunneling of the magnetization
(Fig. 5, C and D), and this decline results in small values of
the remnant magnetization for 1 (0.08 μB) and 3 (0.28 μB) at
1.8 K that diminish to near zero at higher temperatures. De-
spite the relatively fast relaxation at zero field, 1 has a coer-
cive field, Hc, of 180 Oe at 1.8 K, as measured with a field
sweep rate of 32 Oe/s. Under the same conditions, the mag-
netically dilute sample, 3, exhibits Hc = 600 Oe.
molecules exhibiting slow magnetic relaxation is typically de-
scribed by the expression
A
τ −1
=
+ BH 4T + CT n +τ −1exp −U k T , (1)
1
(
)
0
B
1+ A2 H 2
where the four terms represent quantum tunneling, di-
rect, Raman, and Orbach relaxation processes, respectively
(27–29). However, we were unable to fit the relaxation data
for 1 to the total sum of these processes. An alternative model
for through-barrier relaxation has recently been proposed,
wherein specific phonon modes may facilitate relaxation
through direct doublet transitions (30, 31). Building on the
results of Lunghi and co-workers, we derived the expression




Vα2
(
)
2
∆
2
2n +1
α
α
−1
0
τ −1 =τ −1
+
+τ exp −U k T
, (2)
(
)
∑
tunnel
B
α







∆ + ω
(
)
α
α
Outlook




These results have clear implications toward technologies
that require a large magnetic anisotropy. For a magnetic bit
to retain its magnetization for information storage, the mag-
netic anisotropy energy must be significantly greater than the
thermal energy. For the cobalt adatom on MgO, the separa-
tion between the ground (MJ = 9/2) and first excited (MJ =
7/2) states was determined to be 468 cm−1, and it was sug-
gested that this value was near a physical limit for magnetic
anisotropy for 3d transition metals. This limit can be quanti-
fied using the phenomenological spin-orbit coupling Hamil-
tonian, HSOC = λL∙S = (ζ/2S)Σi lisi, where λ is the effective spin-
orbit coupling constant, ζ is the atomic spin-orbit coupling
constant, and L = Σili and S = Σisi are the operators for the
orbital and spin-angular momenta, respectively (the index i
sums over individual electrons). In systems with a doubly de-
generate ground state, the energies of the MJ states (where
MJ = MS + ML) are given by E(MJ) = (ζ/2S)ML∙MS; the separa-
tion between lowest and highest MJ states is equal to Lζ, and
the separation between adjacent states is (L/2S)ζ. Thus, the
actual limit for the energy separation between ground and
first excited state would be found in a system with L = 3 and
S = 1. However, in order to maximize relaxation times, it is
advantageous to employ half-integer spin systems, as the
crystal field cannot couple the two components of the lowest
doublet and the tunneling relaxation pathway is therefore
suppressed (33). The maximal total angular momentum for a
where the first term represents quantum tunneling and
the last term represents Orbach relaxation. The second term
represents relaxation through the α-th phonon mode, V rep-
resents spin-phonon coupling, Δ is the phonon linewidth, n
is the phonon occupation number, and ω is the phonon fre-
quency. Both Δ and n are dependent on both temperature and
ω. Values for U and ω are taken from the variable-field, far-IR
data, while τtunnel, V, and τ0 are fit parameters (see eq. S1 to
S4 for details). From this equation we were able to obtain
reasonable fits (σEST = 0.17 and 0.21 for 1 and 3, respectively)
to the relaxation data in Fig. 5A.
To further examine the effect of any tunneling relaxation
process, we collected data under a 3000 Oe field. The lack of
a temperature-independent region at low temperature under
zero and applied field indicates that molecular quantum tun-
neling is not a dominant relaxation pathway above 4 K; how-
ever, the observed increase in relaxation times upon
application of a dc field (Fig. 5A) demonstrates that it is a
contributing factor. To some extent, the tunneling relaxation
rate can be slowed through magnetic dilution (32), and in-
deed measurements of a magnetically dilute sample prepared
with a 1:49 ratio of cobalt to zinc (3) exhibits lower relaxation
rates than 1 under zero field. The lack of a linear temperature
dependence at the highest temperatures indicates that two-
phonon Orbach relaxation (involving excitation to and relax-
ation from a real excited state) is not yet dominant at 70 K.
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release)
5

transition metal with half-integer spin is J = 9/2, exhibited by out using standard air-free Schlenk line and glove box tech-
both the cobalt adatom and compound 1. The magnetic MJ niques under an argon atmosphere. Reagents were purchased
states of 1 span a substantial calculated energy range of 1469 from commercial vendors. Anhydrous CoBr2 and ZnBr2 were
cm−1, and the separation between the ground (MJ = 9/2) and used as received, while 1-naphthol was sublimed and triethyl-
first excited (MJ = 7/2) states alone is 450 cm−1. Within a rig- amine (NEt3) was dried over KOH and distilled prior to use.
orously linear manifold, it may be possible to further increase HC(SiMe2Cl)3 (17), MeK (43) were prepared according to lit-
the magnetic anisotropy by changing the nature of the Co–L erature procedures. Solvents were dried using a commercial
bond and by increasing the spin-orbit coupling constant. solvent purification system designed by JC Meyer Solvent
However, at present the barrier of Ueff = 450 cm−1 determined Systems. Elemental analysis was performed at the Microana-
here for 1 is the largest measured to date for any transition lytical Laboratory of the University of California, Berkeley.
metal single-molecule magnet, with the second largest being NMR spectra were collected on a 500 MHz Bruker spectrom-
Ueff = 413 cm−1 from the aforementioned (sIPr)CoNDmp com- eter; chemical shifts are reported in ppm referenced to resid-
plex (15). Given the similarity between the cobalt adatom and ual protiated solvent.
1, it is indeed possible that this value is near the physical
Synthesis of HC(SiMe2OPh)3 and HC(SiMe2OC10H7)3
limit. Our calculations for the Co adatom on MgO indicate
A 100 mL Schlenk flask containing a stir bar was charged
4
that the Φ(4F) ground state is also well isolated in this sys- with a THF solution (50 mL) of HC(SiMe2Cl)3 (3.73 g, 12.7
tem, suggesting that spin-orbit coupling is also the dominant mmol) and NEt3 (1.80 mL, 38.1 mmol). A separate 50 mL
factor determining the energies of the MJ states here (table Schlenk flask was charged with a THF solution (25 mL) of 1-
S13). Although information storage will certainly require naphthol (5.58 g, 38.7 mmol). The 1-naphthol solution was
longer zero-field relaxation times than observed here, we note added to the reaction flask over the course of several minutes
that magnetic relaxation times can be significantly affected with stirring, and a white precipitate immediately formed
by the molecular environment, as has been observed for upon addition. The reaction was stirred at room temperature
Tb(Pc)2 molecules in bulk solids (34) and on a variety of sur- for 3 hours, after which air-free techniques were no longer
faces (35–40). A comparison of the relaxation times of the co- required. Water (20 mL) was added to the reaction flask and
balt adatom on MgO and those of compound 1 indicates such the organic layer was collected. The water was extracted with
an environmental effect is indeed at play. Both cobalt centers 3×20 mL Et2O, and the combined organic layers were dried
have similar electronic structures, yet the relaxation time for with MgSO4. The ether solvent was removed under reduced
the adatom at 0.6 K is on the order of 10−4 s, whereas a much pressure, leaving a colorless residue. The residue was washed
longer relaxation time on the order of 101 s is observed for 1 with MeOH (50 mL) and the resulting white solid,
at 1.8 K.
HC(SiMe2OC10H7)3 (5.15 g, 66%), was collected by filtration.
Beyond the implications for molecular magnetism, an in- Anal. calcd for C37H40O3Si3: C, 72.03; H, 6.54. Found: C, 72.04;
triguing potential use of the linear L–CoII–L moiety is in the H, 6.75. 1H NMR (500 MHz, THF-d8): δ 8.33 (3 H, d), 7.83 (3
pursuit of lanthanide-free bulk magnets. Generally speaking, H, d), 7.47 (3 H, d), 7.40 (6 H, m), 7.32 (3 H, t), 7.03 (3 H, d),
orbital angular momentum and spin-orbit coupling tie the 1.39 (1 H, s), 0.63 (18 H, s) ppm. 13C NMR (500 MHz, THF-d8):
magnetic moment to lattice (41). In bulk magnetism, orbital δ 151.8, 136.0, 128.9, 128.3, 126.7, 126.4, 125.7, 123.4, 122.0,
angular momentum is responsible for magnetocrystalline an- 114.4, 13.1, 2.9, 2.8 ppm.
isotropy, the main determinant of magnetic coercivity, which
The same method was used to synthesize HC(SiMe2OPh)3,
is why the strongest magnets, such as Nd2Fe14B and SmCo5, which has been reported previously using a different syn-
feature lanthanide ions with unquenched orbital angular mo- thetic method (44). The identity of HC(SiMe2OPh)3 was con-
mentum. Our results show how linearly coordinated transi- firmed by 1H NMR spectroscopy.
tion metal ions could provide a similar effect. For example,
the extended solid Li2(Li1-xFex)N features linear iron(I) cen-
Synthesis of (CH3OCH2CH2OCH3)2KC(SiMe2OPh)3
Solid MeK (0.11 g, 1.9 mmol) was slowly added to a stirring
ters similar to those in [Fe(C(SiMe3)3)2]−, and in high concen- solution of 1 (0.91 g, 1.9 mmol) dissolved in Et2O (10 mL) and
tration (x = 0.28) this material displays an extremely large dimethoxyethane (3 mL); bubbles evolved during the course
coercivity (Hc = 11.6 T at 2 K) (42). The magnetic anisotropy of addition. The reaction was then allowed to stir for 3 hours,
of compound 1 is nearly twice as large as in [Fe(C(SiMe3)3)2]– during which time a white microcrystalline solid precipitated
, and incorporation of the L–CoII–L moiety in an extended from solution. The solid was collected by filtration and dried
solid could therefore in principle lead to permanent magnets under vacuum (0.65 g, 0.95 mmol, 49%). Anal. Calcd for
1
with an even greater coercivity.
KC33H53O7Si3: C, 57.85; H, 7.80. Found: C, 57.83; H, 7.60. H
Methods
General considerations
NMR (500 MHz, THF-d8): δ 7.15 (6 H, t), 6.91 (6 H, d), 6.83
(3 H, t), 3.42 (8 H, s), 3.26 (12 H, s), 0.24 (18 H, s) ppm. C
13
Unless otherwise noted, all manipulations were carried
NMR (500 MHz, THF-d8): δ 158.3, 129.7, 122.2, 121.0, 72.7,
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release)
6

58.9, 16.8, 15.7, 5.2 ppm.
mmol) dissolved in THF (2 mL) was added to a solution of
KC(SiMe2OC10H7)3 (206 mg, 0.314 mmol) dissolved in THF (8
Synthesis of KC(SiMe2OC10H7)3
HC(SiMe2OC10H7)3 (0.967 g, 1.57 mmol) was dissolved in mL), and the mixture was stirred at room temperature for 12
THF (15 mL). Freshly prepared MeK (0.0850 g, 1.57 mmol) hours. The reaction mixture was subsequently filtered
was added as a solid to the stirring reaction mixture; bubbles through diatomaceous earth and the THF solvent was re-
evolved from the mixture over the course of an hour. After 3 moved under reduced pressure, leaving a white solid. The col-
hours, the reaction mixture was filtered through diatoma- orless solid was stirred in hexanes (20 mL) and filtered to give
ceous earth and solvent was removed under reduced pres- a pale-yellow solution, from which colorless crystals of 1 (36.7
sure, leaving a sticky colorless residue. Hexane was added to mg, 9%) suitable for x-ray diffraction grew over the course of
precipitate a white solid, KC(SiMe2OC10H7)3 (1.20 g, 76%), 1 day. Anal. calcd for ZnC74H78O6Si6: C, 68.51; H, 6.06. Found:
which was collected by filtration. Anal. calcd for KC37H39O3Si3: C, 68.14; H, 5.92.
C, 67.84; H, 6.00. Found: C, 67.59; H, 6.31. 1H NMR (500 MHz,
Synthesis of Co0.02Zn0.98(C(SiMe2OC10H7)3)2 (3)
THF-d8): δ 8.42 (3 H, d), 7.71 (3 H, d), 7.49 (3 H, d), 7.28 (12
Initially, CoBr2(THF) was prepared by dissolving CoBr2
H, m), 0.38 (18 H, s) ppm. 13C NMR (500 MHz, THF-d8): δ (6.2 mg, 0.028 mmol) in THF (5 mL) and then removing the
solvent under reduced pressure. A suspension of CoBr2(THF)
(0.028 mmol) and ZnBr2 (57.4 mg, 25.5 mmol) was prepared
in Et2O (4 mL), and this suspension was added to a stirring
solution of KC(SiMe2OC10H7)3 (371 mg, 0.567 mmol) dissolved
in Et2O (6 mL). The mixture was stirred for 1 hour at room
temperature and then filtered through diatomaceous earth.
A light pink powder was collected from the reaction mixture
and the resulting light green Et2O filtrate was put in a 20 mL
vial. Crystallization tubes were added to the vial to increase
the amount of crystallization surfaces and Et2O was added to
fill the vial. Light pink crystals of 3 (63.9 mg, 9%) suitable for
x-ray diffraction grew over the course of 4 days. Successful
dilution was confirmed by determination of a unit cell con-
sistent with pure 1 and 2, and the metal composition was de-
termined from comparison of molar magnetization data for
the pure and diluted samples.
154.8, 135.9, 129.7, 127.7, 126.9, 125.6, 124.4, 124.2, 118.7, 114.5,
16.2, 5.9, 5.8 ppm.
Synthesis of Co(C(SiMe2OPh)3)2
Solid CoCl2 (18.2 mg, 0.140 mmol) was added to a stirring
THF solution (10 mL) of (CH3OCH2CH2OCH3)2KC(SiMe2OPh)3
(200. mg, 0.290 mmol) at room temperature and then the
mixture was stirred for 2 hours at 60°C. The solvent was re-
moved in vacuo and the resulting blue-green solid was dis-
solved in hexanes. The hexanes solution was stirred at 60°C
for 1 hour to form a yellow-green solution. The hexanes solu-
tion was filtered through diatomaceous earth and was con-
centrated in vacuo. Red-brown crystals of Co(C(SiMe2OPh)3)2
(0.044 g, 39%) suitable for x-ray diffraction grew in 2 hours
at −30°C. Anal. Calcd. for CoC50H66Si6O6: C, 60.63; H, 6.72.
Found: C, 60.98; H, 6.84.
Synthesis of Co(C(SiMe2OC10H7)3)2 (1)
Single crystal x-ray diffraction
Solid CoBr2 (41.6 mg, 0.190 mmol) was added to a stirring
THF (8 mL) solution of KC(SiMe2OC10H7)3 (249 mg, 0.380
mmol) at room temperature. The reaction mixture was
stirred for 4 hours at 60°C, after which time the solution had
turned green. The reaction mixture was filtered through dia-
tomaceous earth and solvent was removed under reduced
pressure, leaving a green solid. The green solid was dissolved
in hexanes (20 mL) and filtered to give an emerald green so-
In an argon filled glovebox, crystals of Co(C(SiMe2OPh)3,
1, 2, and 3 were coated in Paratone-N oil in individual vials,
which were then sealed and remained sealed until immedi-
ately prior to mounting. Crystals were mounted on Kaptan
loops and cooled under a stream of N2. Data were collected
using a Bruker QUAZAR diffractometer equipped with a
Bruker MICROSTAR X-Ray source of Mo Kα radiation (λ =
lution, from which brown-red crystals of 1 (17.8 mg, 7%) suit- 0.71073 Å), and an APEX-II detector. Raw data were inte-
able for x-ray diffraction grew over the course of 3 days. grated and corrected for Lorentz and polarization effects us-
Compound 1 is insoluble in all common organic solvents ex- ing Bruker Apex3 v. 2016.5. Absorption corrections were
cept THF, in which it forms a green solution. Anal. calcd for applied using SADABS (45). The space group was determined
CoC74H78O6Si6: C, 68.85; H, 6.09. Found: C, 68.36; H, 6.03.
by examination of systematic absences, E-statistics, and suc-
Cooling the green hexanes solution appears to favor pre- cessive refinement of the structure. The crystal structure was
cipitation of the THF solvate, Co(C(SiMe2OC10H7)3)2(THF). solved with ShelXT (46) and further refined with ShelXL (47)
Green crystals not suitable for single crystal x-ray diffraction operated in the Olex2 software (48). The crystal did not show
were grown from the green hexanes solution over 1 day at any significant decay during data collection. Thermal param-
−30°C, collected by filtration and thoroughly dried in vacuo. eters were refined anisotropically for all non-hydrogen at-
Anal calcd for CoC78H86O7Si6: C, 68.74; H, 6.36. Found: C, oms. Hydrogen atoms were placed in ideal positions and
68.66; H, 6.52.
refined using a riding model for all structures. A checkcif re-
Synthesis of Zn(C(SiMe2OC10H7)3)2 (2)
port for 1 gave rise to a B level alert regarding the ratio of
At room temperature, a solution of ZnBr2 (35.1 mg, 0.155 maximum/minimum residual density. The maximum
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release)
7

residual density for 1 lies in the napthyl ring. In the case of molecules in the crystal. Data from 4 to 10 K were fit with two
the low temperature synchrotron data used for charge den- relaxation processes. Once the minor relaxation process
sity modeling, disorder in the naphthyl ring was successfully moved out of frequency range of the magnetometer (0.1-1488
modeled. For the data collected at 100 K used for the genera- Hz), a one process fit was sufficient. The two fitting proce-
tion of the cifs for 1 and 2, we were unable to fully model this dures gave only modestly different τ values for the 4 and 5 K
disorder, however it is likely that the same disorder is respon- data. The data for 3 and the applied field data for 1 were fit
sible for the relatively large residual density.
sufficiently well with one process. Data collected using the
UV-visible-NIR diffuse reflectance
PPMS instrument (50-70 K, 100-10,000 Hz) gave some nega-
UV-visible-NIR diffuse reflectance spectra were collected tive values for χ′ at high frequency. Presumably this result is
using a CARY 5000 spectrophotometer interfaced with Var-
ian Win UV software. The samples were prepared in a glove-
box and held in a Praying Mantis air-free diffuse reflectance
cell. Powdered BaCO3 was used as a non-absorbing matrix.
The spectra were collected in F(R) vs wavenumber, where
F(R) is the Kubelka-Munk conversion F(R) = (1 – R)2/2R and
R is reflectance.
due to the fact that the PPMS sample consisted of less mate-
rial (6.9 mg 1, 29.0 mg eicosane) and, especially at high tem-
peratures, exhibited a smaller paramagnetic response relative
to the diamagnetic response. The negative values did not af-
fect extraction of relaxation times, however. The method for
fitting the relaxation data from 4 to 70 K is given in detail in
the ESI.
Magnetometry
Dc relaxation measurements were implemented using the
hysteresis mode of the MPMS magnetometer, using small
magnetizing fields such that the time to set the field was in
the 10-30 s range; measurements were made every ~4 s. We
found that the relaxation times had a small dependence on
the magnetizing field for 1 and a larger dependence for 3 (Ta-
ble S19-20); the times reported in the main text are averages
of those times. The relaxation times were determined using a
All magnetic measurements were carried out using a
Quantum Design MPMS-XL SQUID Magnetometer, with the
exception of the high frequency ac magnetic susceptibility
data. High frequency data (up to 10,000 Hz) was collected at
the Quantum Design facility in San Diego, CA, using a 9T
PPMS instrument equipped with the ACMSII measurement
option to probe the ac moment at frequencies above 1000 Hz.
For the measurements using the MPMS instrument, polycrys-
talline samples of 1 (32.1 mg) and 3 (49.7 mg) were loaded
into quartz tubes (5 mm i.d., 7 mm o.d.) with a raised quartz
platform. Solid eicosane was then added on top of the sam-
ples (32.0 and y 61.2, respectively) to prevent crystallite
torqueing and provide good thermal contact between the
sample and the cryogenic bath. The tubes were fitted with
Teflon sealable adapters, evacuated using a glovebox vacuum
pump, and sealed under static vacuum using an H2/O2 flame.
Following flame sealing, the solid eicosane was melted in a
water bath held at 40°C. When not in the magnetometer, the
sealed samples were stored at −30°C. Dc magnetic suscepti-
bility data was collected for each sample from 2 to 300 K un-
der dc fields ranging from 0 to 7 T. Ac magnetic susceptibility
data collected using the MPMS instrument was obtained us-
ing a 6 Oe switching field; data from the PPMS instrument
was collected using a 10 Oe switching field. All data were cor-
rected for diamagnetic contributions of the eicosane and the
individual samples using Pascal’s constants (49).
stretched exponential of the form Mt = M0 exp[−(t /τ )n ]
,
where M0 is the magnetization of the first data point meas-
ured, once the field was set, and n is a free variable (51).
Dc magnetization experiments were implemented by ap-
plying a field to a sample at zero magnetization and measur-
ing the magnetization until it became constant. Relaxation
times
were
determined
using
the
equation
Mt = Msat − (Msat − M0 )exp[−(t /τ )n ] , where Msat is the satura-
tion magnetization, M0 is the magnetization of the first data
point measured once the field was set, and n is a free variable.
Magnetization times for 1 and 3 for each field are given in
tables S20 and S21; the main text reports the average of these
values (16.4 and 48.2 s, respectively) and their standard devi-
ations (0.7 and 4.7, respectively).
Variable field, FIR spectroscopy
Far-infrared spectra were recorded on a Bruker IFS 66v/s
FTIR spectrometer with a globar source and a composite bo-
lometer detector element located inside an 11 T magnet di-
rectly below the sample. Approximately 5 mg of 1 was diluted
in eicosane (1:10 ratio) and pressed in the shape of a 5 mm
pellet. The sample was prepared and measured under inert
atmosphere. The sample was cooled to 4.2 K and irradiated
with FIR light. Transmission spectra were recorded both in
absence and in the presence of a magnetic field (0-11 T).
Charge density modeling
The ac susceptibility data was fit using a generalized De-
bye model, which accounts for relaxation time (τ), attempt
time (τ0), isothermal susceptibility (χT), adiabatic susceptibil-
ity (χS), and the presence of a distribution of relaxation times
(α) (50). Data for 1 collected under zero applied field and be-
low 7 K exhibited high frequency shoulders in χ″, and fits to
the data yielded very large α values, suggesting a second,
faster relaxation process might be operating at low tempera-
tures. This second process may be related to the disordered
Crystals of 1 are rather air-sensitive, and thus all crystal
manipulation was carried out inside of a glove box under an
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release)
8

Ar atmosphere. A triangularly-shaped single crystal with a as resulting from a mirror symmetry in the plane defined by
maximum dimension of 0.10 mm was selected, and it was C(1) (bonded to Co) and partially by Si(1) and O(1). This plane
mounted using cryo-protecting oil on a pre-centered glass fi- also very nearly includes C(2) (carbon bonded to O(1)). The
ber and then rapidly inserted into a cold He stream with a occupation of the disordered parts is 4.8%, and including this
temperature of 20 K, to minimize any risk of air exposure and disorder in the model leads to a significant improvement of
subsequent crystal decay.
the refinement.
The crystal was mounted on the goniometer of beamline
Despite the significant disorder (one of the consequences
BL02B1 at the SPring8 synchrotron in Japan. The X-ray en- of which is that some atoms in the structure are nearly over-
ergy was fixed to 40 keV, corresponding to a wavelength of lapping, we decided to attempt multipole-based charge den-
0.30988 Å. We have previously experienced significant crystal sity modeling. The independent-atom model (IAM) structure
decay due to radiation damage, and this high energy was cho- from ShelX was exported to the program XD, which is based
sen in an attempt to avoid this detrimental effect. As shown on the Hansen-Coppens multipole formalism. Herein, we
in fig. S17, the frame scale factor, which accurately captures kept the extent of disorder fixed on the values obtained from
any crystal decay (as well as other systematic effects, such as ShelX, and furthermore used isotropic thermal parameters
beam intensity fluctuations), is scattered relatively close to for the disordered atoms. We did not apply multipole param-
1.0, and importantly does not drop off systematically, indicat- eters to the disordered atoms, which were kept spherical.
ing that there is no significant crystal decay.
Given the nearly whole-molecule disorder, it is imperative to
The data was collected on a Fuji IP system using 36 ω- be extremely careful during the refinement procedure. Thus,
scans with a width of 5°, and an overlap of 0.5°, for a total of we used constraints to avoid overfitting, which otherwise is a
180° with a scan speed of 1 min/degree. Given the high sym- possibility in such a disordered system. The use of isotropic
metry of the compound, this protocol provided a complete and spherical disordered atoms helps with this as well.
data set with sufficient redundancy. The diffraction data
The final multipole model consists of hexadecapoles on Co
ceased to be significant already at sin(θ)/λ = 0.9 Å−1. As we and octopoles on all other non-H atoms (except the disor-
explain below, there is significant dynamic disorder in the dered atoms), while H-atoms were refined using one common
crystal structure, which likely results in the lack of high angle monopole and bond-directed dipole. The model was reached
data.
after several refinements, in which the level of multipoles was
The diffraction data were integrated using dedicated increased by one for each step. Both neutral and ionic scat-
Rigaku software RAPID AUTO v2.41, which only integrates tering factors were tested for Co. In the final model, a neutral
the intensity of reflections estimated to be fully present on scattering factor was used.
one frame, i.e., having been rotated fully through the Ewald
In the final refinement, the largest residuals were, as ex-
sphere during one of the 5° rotations. This estimation obvi- pected, near the Si and the Co atoms. The largest residuals
ously depends on the mosaicity of the crystal and the desired were positive (the largest is around 1.2 eÅ−3
and is close to the
Co), and significantly larger than the most negative residual
density peaks, which were around −0.55 eÅ−3. Such large dis-
crepancy between the positive and negative residuals may in-
dicate that the disorder was not fully accounted for. The Co
atom sits on a special position in the space group with a mul-
tiplicity of 6, and it is possible that the high residual density
at this position is also a result of this high symmetry. The
residual near Co does not indicate that the atom sits off-cen-
tered. However, it may be related to the disorder and perhaps
it does not sit in a harmonic potential. We tried to refine an-
harmonic thermal parameters, but this refinement had no ef-
fect on the residual density.
The residual density distribution, interpreted using the
fractal dimensionality plots as first presented by Henn and
Meindl (fig. S19) (52), shows a somewhat distorted parabola,
with a slight tendency to increase more toward the positive
residuals. However, this increase is much smaller than ex-
pected from the significant residuals near Co and Si, and sug-
gests that despite the disorder, the multipole model may be
quantitatively useful.
box size for integration. We experimented with these values
in order to optimize the integration results, and those pre-
sented herein used mosaicity of 0.7° and a box size of 13×13
pixels. The raw images were scaled to accommodate the dif-
ferent sensitivities of the photomultiplier tubes, an effect
which was uncovered in the summer of 2018.
The integration and subsequent scaling in RAPID AUTO
provided a total of 43260 reflections, which were then aver-
aged using the point group symmetry –3. This averaged data
was reduced to 9008 unique reflections with an average re-
dundancy of 4.8 and a completeness of 99.5%, using the pro-
gram SORTAV. During refinement, it was noticed that ratio
of F(obs) to F(calc) varied systematically, and thus we decided
to include ten resolution-dependent scale factors that helped
to alleviate this problem, as shown in fig. S19.
These data were used to solve the crystal structure using
SHELXT within the Olex2 interface. The structure solution
was found to contain a minor, but clearly visible, disordered
component, and the disorder is solely in the naphthalene
moiety (see fig. S18). The disorder is perhaps best explained
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release)
9

iron(II) alkyl halide complex. Organometallics 33, 1917–1920 (2014).
doi:10.1021/om500180u
It is important to note that Co sits on a −3 crystallographic
position and therefore only four multipole parameters are
symmetry-allowed. The most important parameter in this re-
spect is the quadrupole along the z-axis. However, in the least
squares refinement, this parameter correlates strongly with
the thermal parameters, including U33, which represents the
atomic vibration along the same z-direction. To avoid this
correlation, we separated the refinement of multipole param-
eters from the refinement of atomic positions and vibrations.
We first attempted a high angle refinement of the atomic vi-
brations and positions, but the resulting refinement of mul-
tipole parameters led to unphysical values, for instance
atomic charges derived from monopole values of more than
+2, and κ-parameters deviating by more than 20% from
unity. Instead, we chose to use the full data set to inde-
pendently refine the atomic positions and vibrations of all at-
oms, subsequently fixing these values and refining the
multipole parameters until convergence. This approach rep-
resented the final model, from which we extracted the d-or-
bital population ratios. In the final model, the charge on Co
was determined to be +1.3.
11. P. P. Power, Stable two-coordinate, open-shell (d1-d9) transition metal complexes.
Chem. Rev. 112, 3482–3507 (2012). doi:10.1021/cr2004647 Medline
12. T. Viefhaus, W. Schwarz, K. Hübler, K. Locke, J. Weidlein, Das unterschiedliche
Reaktionsverhalten von basefreiem Tris(trimethylsilyl)methyl-Lithium gegenüber
den Trihalogeniden der Erdmetalle und des Eisens. Z. Anorg. Allg. Chem. 627, 715
(2001). doi:10.1002/1521-3749(200104)627:4<715:AID-ZAAC715>3.0.CO;2-0
13. N. H. Buttrus, C. Eaborn, P. B. Hitchcock, J. D. Smith, A. C. Sullivan, Preparation
and crystal structure of
a
two-coordinate manganese compound,
bis[(tris(trimethyl)silylmethyl)]manganese. J. Chem. Soc. Chem. Commun. 1985,
1380–1381 (1985). doi:10.1039/c39850001380
14. C.-Y. Lin, J. C. Fettinger, N. F. Chilton, A. Formanuik, F. Grandjean, G. J. Long, P. P.
Power, Salts of the two-coordinate homoleptic manganese(I) dialkyl anion
[Mn{C(SiMe3)3}2]− with quenched orbital magnetism. Chem. Commun. 51, 13275–
13278 (2015). doi:10.1039/C5CC05166E Medline
15. X.-N. Yao, J.-Z. Du, Y.-Q. Zhang, X.-B. Leng, M.-W. Yang, S.-D. Jiang, Z.-X. Wang, Z.-
W. Ouyang, L. Deng, B.-W. Wang, S. Gao, Two-coordinate Co(II) imido complexes
as outstanding single-molecule magnets. J. Am. Chem. Soc. 139, 373–380 (2017).
doi:10.1021/jacs.6b11043 Medline
16. P. E. Kazin, M. A. Zykin, L. A. Trusov, A. A. Eliseev, O. V. Magdysyuk, R. E. Dinnebier,
R. K. Kremer, C. Felser, M. Jansen, A Co-based single-molecule magnet confined
in a barium phosphate apatite matrix with a high energy barrier for magnetization
relaxation. Chem. Commun. 53, 5416–5419 (2017). doi:10.1039/C7CC02453C
Medline
17. H. Li, A. J. A. Aquino, D. B. Cordes, F. Hung-Low, W. L. Hase, C. Krempner, A
zwitterionic carbanion frustrated by boranes—dihydrogen cleavage with weak
Lewis acids via an “inverse” frustrated Lewis pair approach. J. Am. Chem. Soc.
135, 16066–16069 (2013). doi:10.1021/ja409330h Medline
REFERENCES AND NOTES
1. I. G. Rau, S. Baumann, S. Rusponi, F. Donati, S. Stepanow, L. Gragnaniello, J. Dreiser,
C. Piamonteze, F. Nolting, S. Gangopadhyay, O. R. Albertini, R. M. Macfarlane, C.
P. Lutz, B. A. Jones, P. Gambardella, A. J. Heinrich, H. Brune, Reaching the
magnetic anisotropy limit of a 3d metal atom. Science 344, 988–992 (2014).
doi:10.1126/science.1252841 Medline
18. S. S. Al-Juaid, C. Eaborn, A. Habtemariam, P. B. Hitchcock, J. D. Smith, K.
Tavakkoli, A. D. Webb, The preparation and crystal structures of the compounds
(Ph2MeSi)3CMCl (M = Zn, Cd, or Hg). J. Organomet. Chem. 462, 45–55 (1993).
doi:10.1016/0022-328X(93)83340-2
2. W. M. Reiff, A. M. LaPointe, E. H. Witten, Virtual free ion magnetism and the absence
of Jahn-Teller distortion in a linear two-coordinate complex of high-spin iron(II). J.
Am. Chem. Soc. 126, 10206–10207 (2004). doi:10.1021/ja030632w Medline
3. J. M. Zadrozny, M. Atanasov, A. M. Bryan, C.-Y. Lin, B. D. Rekken, P. P. Power, F.
Neese, J. R. Long, Slow magnetization dynamics in a series of two-coordinate
iron(ii) complexes. Chem. Sci. 4, 125–138 (2013). doi:10.1039/C2SC20801F
4. J. M. Zadrozny, D. J. Xiao, M. Atanasov, G. J. Long, F. Grandjean, F. Neese, J. R. Long,
Magnetic blocking in a linear iron(I) complex. Nat. Chem. 5, 577–581 (2013).
doi:10.1038/nchem.1630 Medline
5. D. Gatteschi, R. Sessoli, J. Villain, Molecular Nanomagnets (Oxford Univ. Press,
2006).
6. J. M. Zadrozny, D. J. Xiao, J. R. Long, M. Atanasov, F. Neese, F. Grandjean, G. J. Long,
Mössbauer spectroscopy as a probe of magnetization dynamics in the linear
iron(I) and iron(II) complexes [Fe(C(SiMe3)3)2]1−/0. Inorg. Chem. 52, 13123–13131
(2013). doi:10.1021/ic402013n Medline
7. M. Atanasov, J. M. Zadrozny, J. R. Long, F. Neese, A theoretical analysis of chemical
bonding, vibronic coupling, and magnetic anisotropy in linear iron(II) complexes
with single-molecule magnet behavior. Chem. Sci. 4, 139–156 (2013).
doi:10.1039/C2SC21394J
8. The term “spin-reversal barrier” is somewhat ambiguous in the single-molecule
magnet literature. In the systems described here we define it as the separation
between ground and first excited MJ (or MS) states. Thus, “over-barrier” relaxation
refers to excitation from MJ = +J to MJ = +(J – 1) states followed by relaxation to
19. S. S. Al-Juaid, C. Eaborn, S. El-Hamruni, A. Farook, P. B. Hitchcock, M. Hopman, J.
D. Smith, W. Clegg, K. Izod, P. O’Shaughnessy, Tris(triorganosilyl)methyl
derivatives of potassium and lithium bearing dimethylamino or methoxy
substituents at silicon. Crystal structures of KC(SiMe3)2(SiMe2NMe2),
KC(SiMe2NMe2)3 and [LiC(SiMe3)(SiMe2OMe)2]2. J. Chem. Soc. Dalton Trans.
1999, 3267–3273 (1999). doi:10.1039/a904043i
20. M. Westerhausen, B. Rademacher, W. Poll, Trimethylsilyl-substituierte Derivate
des Dimethylzinks—Synthese, spektroskopische Charakterisierung und Struktur.
J. Organomet. Chem. 421, 175–188 (1991). doi:10.1016/0022-328X(91)86402-C
21. M. Nishio, The CH/π hydrogen bond in chemistry. Conformation, supramolecules,
optical resolution and interactions involving carbohydrates. Phys. Chem. Chem.
Phys. 13, 13873–13900 (2011). doi:10.1039/c1cp20404a Medline
22. C.-Y. Lin, J.-D. Guo, J. C. Fettinger, S. Nagase, F. Grandjean, G. J. Long, N. F.
Chilton, P. P. Power, Dispersion force stabilized two-coordinate transition metal–
amido complexes of the −N(SiMe3)Dipp (Dipp = C6H3-2,6-Pri2) ligand: Structural,
spectroscopic, magnetic, and computational studies. Inorg. Chem. 52, 13584–
13593 (2013). doi:10.1021/ic402105m
23. A. J. Wallace, B. E. Williamson, D. L. Crittenden, CASSCF-based explicit ligand field
models clarify the ground state electronic structures of transition metal
phthalocyanines (MPc; M = Mn, Fe, Co, Ni, Cu, Zn). Can. J. Chem. 94, 1163–1168
(2016). doi:10.1139/cjc-2016-0264
24. R. F. W. Bader, Atoms in Molecules: A Quantum Theory (Clarendon Press, 1990).
25. R. Marx, F. Moro, M. Dörfel, L. Ungur, M. Waters, S. D. Jiang, M. Orlita, J. Taylor, W.
Frey, L. F. Chibotaru, J. van Slageren, Spectroscopic determination of crystal field
splittings in lanthanide double deckers. Chem. Sci. 5, 3287–3293 (2014).
doi:10.1039/c4sc00751d
the MJ
= –J state (an Orbach mechanism). “Through-barrier” relaxation
mechanisms are any that allow the system to go from MJ = +J to MJ = –J without
excitation to the MJ = +(J – 1) state.
9. M. Atanasov, D. Aravena, E. Suturina, E. Bill, D. Maganas, F. Neese, First principles
approach to the electronic structure, magnetic anisotropy and spin relaxation in
mononuclear 3d-transition metal single molecule magnets. Coord. Chem. Rev.
289–290, 177–214 (2015). doi:10.1016/j.ccr.2014.10.015
10. P. Zhao, Z. Brown, J. C. Fettinger, F. Grandjean, G. J. Long, P. P. Power, Synthesis
and structural characterization of a dimeric cobalt(I) homoleptic alkyl and an
26. Y. Rechkemmer, F. D. Breitgoff, M. van der Meer, M. Atanasov, M. Hakl, M. Orlita,
P. Neugebauer, F. Neese, B. Sarkar, J. van Slageren, A four-coordinate cobalt(II)
single-ion magnet with coercivity and a very high energy barrier. Nat. Commun. 7,
10467 (2016). doi:10.1038/ncomms10467 Medline
27. D. Gatteschi, R. Sessoli, Quantum tunneling of magnetization and related
phenomena in molecular materials. Angew. Chem. Int. Ed. 42, 268–297 (2003).
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release) 10

doi:10.1002/anie.200390099 Medline
28. K. N. Shrivastava, Theory of spin-lattice relaxation. Phys. Status Solidi B 117, 437–
458 (1983). doi:10.1002/pssb.2221170202
47. G. M. Sheldrick, Crystal structure refinement with SHELXL. Acta Crystallogr. C 71,
3–8 (2015). doi:10.1107/S0108767307043930 Medline
48. O. V. Dolomanov, L. J. Bourhis, R. J. Gildea, J. A. K. Howard, H. Puschmann, OLEX2:
29. R. Orbach, Spin-lattice relaxation in rare-earth salts. Proc. R. Soc. London Ser. A
264, 458 (1961).
30. A. Lunghi, F. Totti, R. Sessoli, S. Sanvito, The role of anharmonic phonons in under-
barrier spin relaxation of single molecule magnets. Nat. Commun. 8, 14620
(2017). doi:10.1038/ncomms14620 Medline
31. A. Lunghi, F. Totti, S. Sanvito, R. Sessoli, Intra-molecular origin of the spin-phonon
coupling in slow-relaxing molecular magnets. Chem. Sci. 8, 6051–6059 (2017).
doi:10.1039/C7SC02832F Medline
32. S.-D. Jiang, B.-W. Wang, G. Su, Z.-M. Wang, S. Gao, A mononuclear dysprosium
complex featuring single-molecule-magnet behavior. Angew. Chem. Int. Ed. 49,
7448–7451 (2010). doi:10.1002/anie.201004027 Medline
A complete structure solution, refinement and analysis program. J. Appl.
Crystallogr. 42, 339–341 (2009). doi:10.1107/S0021889808042726
49. G. A. Bain, J. F. Berry, Diamagnetic corrections and Pascal’s constants. J. Chem.
Educ. 85, 532 (2008). doi:10.1021/ed085p532
50. K. S. Cole, R. H. Cole, Dispersion and absorption in dielectrics I. Alternating current
characteristics. J. Chem. Phys. 9, 341–351 (1941). doi:10.1063/1.1750906
51. C. Sangregorio, T. Ohm, C. Paulsen, R. Sessoli, D. Gatteschi, Quantum tunneling of
the magnetization in an iron cluster nanomagnet. Phys. Rev. Lett. 78, 4645–4648
(1997). doi:10.1103/PhysRevLett.78.4645
52. K. Meindl, J. Henn, Foundations of residual-density analysis. Acta Crystallogr. A
64, 404–418 (2008). doi:10.1107/S0108767308006879
33. H. A. Kramers, A general theory of paramagnetic rotation in crystals. Proc. R. Acad.
Sci. Amsterdam 33, 959 (1930).
53. P.-Å. Malmqvist, B. O. Roos, The CASSCF state interaction method. Chem. Phys.
Lett. 155, 189–194 (1989). doi:10.1016/0009-2614(89)85347-3
34. M. Gonidec, E. S. Davies, J. McMaster, D. B. Amabilino, J. Veciana, Probing the
magnetic properties of three interconvertible redox states of a single-molecule
magnet with magnetic circular dichroism spectroscopy. J. Am. Chem. Soc. 132,
1756–1757 (2010). doi:10.1021/ja9095895 Medline
35. L. Margheriti, D. Chiappe, M. Mannini, P.-E. Car, P. Sainctavit, M.-A. Arrio, F. B. de
Mongeot, J. C. Cezar, F. M. Piras, A. Magnani, E. Otero, A. Caneschi, R. Sessoli, X-
ray detected magnetic hysteresis of thermally evaporated terbium double-decker
54. K. Wolinski, P. Pulay, Generalized Möller–Plesset perturbation theory: Second
order results for two‐configuration, open‐shell excited singlet, and doublet wave
functions. J. Chem. Phys. 90, 3647–3659 (1989). doi:10.1063/1.456696
55. K. Andersson, P. A. Malmqvist, B. O. Roos, A. J. Sadlej, K. Wolinski, Second‐order
perturbation theory with a CASSCF reference function. J. Phys. Chem. 94, 5483–
5488 (1990). doi:10.1021/j100377a012
56. K. Andersson, P. Å. Malmqvist, B. O. Roos, Second‐order perturbation theory with
a complete active space self‐consistent field reference function. J. Chem. Phys.
96, 1218–1226 (1992). doi:10.1063/1.462209
oriented
films.
Adv.
Mater.
22,
5488–5493
(2010).
doi:10.1002/adma.201003275 Medline
36. M. Gonidec, R. Biagi, V. Corradini, F. Moro, V. De Renzi, U. del Pennino, D. Summa, 57. B. O. Roos, P.-A. Malmqvist, Relativistic quantum chemistry: The
L. Muccioli, C. Zannoni, D. B. Amabilino, J. Veciana, Surface supramolecular
organization of a terbium(III) double-decker complex on graphite and its single
molecule magnet behavior. J. Am. Chem. Soc. 133, 6603–6612 (2011).
doi:10.1021/ja109296c Medline
multiconfigurational approach. Phys. Chem. Chem. Phys. 6, 2919 (2004).
doi:10.1039/b401472n
58. B. Roos, M. Fülscher, P.-Å. Malmqvist, M. Merchán, L. Serrano-Andrés,
“Theoretical studies of the electronic spectra of organic molecules,” in Quantum
Mechanical Electronic Structure Calculations with Chemical Accuracy, S. Langhoff,
Ed. (Springer Netherlands, 1995), pp. 357–438.
59. C. Angeli, R. Cimiraglia, S. Evangelisti, T. Leininger, J.-P. Malrieu, Introduction of
n-electron valence states for multireference perturbation theory. J. Chem. Phys.
114, 10252–10264 (2001). doi:10.1063/1.1361246
60. C. Angeli, R. Cimiraglia, J.-P. Malrieu, N-electron valence state perturbation
theory: A fast implementation of the strongly contracted variant. Chem. Phys.
Lett. 350, 297–305 (2001). doi:10.1016/S0009-2614(01)01303-3
61. C. Angeli, R. Cimiraglia, J.-P. Malrieu, N-electron valence state perturbation theory:
A spinless formulation and an efficient implementation of the strongly contracted
and of the partially contracted variants. J. Chem. Phys. 117, 9138–9153 (2002).
doi:10.1063/1.1515317
37. D. Klar, A. Candini, L. Joly, S. Klyatskaya, B. Krumme, P. Ohresser, J.-P. Kappler,
M. Ruben, H. Wende, Hysteretic behaviour in a vacuum deposited submonolayer
of single ion magnets. Dalton Trans. 43, 10686–10689 (2014).
doi:10.1039/C4DT01005A Medline
38. M. Mannini, F. Bertani, C. Tudisco, L. Malavolti, L. Poggini, K. Misztal, D. Menozzi,
A. Motta, E. Otero, P. Ohresser, P. Sainctavit, G. G. Condorelli, E. Dalcanale, R.
Sessoli, Magnetic behaviour of TbPc2 single-molecule magnets chemically grafted
on silicon surface. Nat. Commun. 5, 4582 (2014). doi:10.1038/ncomms5582
Medline
39. J. Dreiser, C. Wäckerlin, M. E. Ali, C. Piamonteze, F. Donati, A. Singha, K. S.
Pedersen, S. Rusponi, J. Bendix, P. M. Oppeneer, T. A. Jung, H. Brune, Exchange
interaction of strongly anisotropic tripodal erbium single-ion magnets with
metallic surfaces. ACS Nano 8, 4662–4671 (2014). doi:10.1021/nn500409u
Medline
40. C. Wäckerlin, F. Donati, A. Singha, R. Baltic, S. Rusponi, K. Diller, F. Patthey, M.
Pivetta, Y. Lan, S. Klyatskaya, M. Ruben, H. Brune, J. Dreiser, Giant hysteresis of
single-molecule magnets adsorbed on a nonmagnetic insulator. Adv. Mater. 28,
5195–5199 (2016). doi:10.1002/adma.201506305 Medline
62. C. Angeli, B. Bories, A. Cavallini, R. Cimiraglia, Third-order multireference
perturbation theory: The n-electron valence state perturbation-theory approach.
J. Chem. Phys. 124, 054108 (2006). doi:10.1063/1.2148946 Medline
63. F. Neese, The ORCA program system. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2,
73–78 (2012). doi:10.1002/wcms.81
64. Max Planck Institute for Chemical Energy Conversion, ORCA, an ab initio, DFT and
semiempirical SCF-MO package, version 4.0; https://orcaforum.cec.mpg.de/.
41. M. Getzlaff, Fundamentals of Magnetism (Springer-Verlag, 2008).
42. A. Jesche, R. W. McCallum, S. Thimmaiah, J. L. Jacobs, V. Taufour, A. Kreyssig, R. 65. F. Neese, Efficient and accurate approximations to the molecular spin-orbit
S. Houk, S. L. Bud’ko, P. C. Canfield, Giant magnetic anisotropy and tunnelling of
the magnetization in Li2(Li1–xFex)N. Nat. Commun. 5, 3333 (2014).
doi:10.1038/ncomms4333 Medline
coupling operator and their use in molecular g-tensor calculations. J. Chem. Phys.
122, 034107 (2005). doi:10.1063/1.1829047 Medline
66. D. Ganyushin, F. Neese, First-principles calculations of zero-field splitting
parameters. J. Chem. Phys. 125, 24103 (2006). doi:10.1063/1.2213976 Medline
67. M. Atanasov, D. Ganyushin, K. Sivalingam, F. Neese, A modern first-principles view
on ligand field theory through the eyes of correlated multireference
wavefunctions. Struct. Bond. 143, 149–220 (2012). doi:10.1007/430_2011_57
68. S. K. Singh, J. Eng, M. Atanasov, F. Neese, Covalency and chemical bonding in
transition metal complexes: An ab initio based ligand field perspective. Coord.
Chem. Rev. 344, 2–25 (2017). doi:10.1016/j.ccr.2017.03.018
43. C. J. Schaverien, A. G. Orpen, Chemistry of (octaethylporphyrinato)lutetium and -
yttrium complexes: Synthesis and reactivity of (OEP)MX derivatives and the
selective activation of O2 by (OEP)Y(.mu.-Me)2AlMe2. Inorg. Chem. 30, 4968–
4978 (1991). doi:10.1021/ic00026a023
44. K. D. Safa, S. Tofangdarzadeh, H. H. Ayenadeh, Reactions of
tris(dimethylsilyl)methane and polymers containing Si–H groups with various
hydroxy compounds under aerobic and mild conditions. Heteroatom Chem. 19,
365–376 (2008). doi:10.1002/hc.20440
69. J. R. Burdett, Molecular Shapes: Theoretical Models of Inorganic Stereochemistry
(Wiley, 1980).
45. G. M. Sheldrick, SADABS, version 2.03 (Bruker Analytical X-Ray Systems, 2000).
46. G. M. Sheldrick, SHELXT
determination. Acta
–
integrated space-group and crystal-structure
ACKNOWLEDGMENTS
Crystallogr. 71, 3–8 (2015).
A
doi:10.1107/S2053273314026370 Medline
We thank K. R. Meihaus for editorial assistance. Funding: This work was funded by
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release) 11

NSF grant CHE-1464841 (P.C.B., J.R.L.), Max-Planck Gesellschaft (M.A., F.N.),
DNRF93 and Danscatt (E.D.-M., J.O.), and DFG SL104/5-1 (M.P., J.V.S.). Author
contributions: Synthesis, magnetic characterization, and analysis were
performed by P.C.B. and J.R.L. Ab initio calculations and analysis were
performed by M.A. and F.N. Applied-field FIR spectra were collected and
analyzed by M.P., I.C., M.O., and J.V.S. Charge density data collection and
modeling were performed by E.D.-M. and J.O. Competing interests: The authors
have no competing interests to claim. Data and materials availability:
Crystallographic data for 1, 2, and Co(C(SiMe2OPh)3)2 are freely available from
the Cambridge Crystallographic Data Centre under CCDC numbers 1872361,
1872361, and 1872363, respectively. The supplementary materials include
details on the fitting of magnetic relaxation data, as well as computational
methods.
SUPPLEMENTARY MATERIALS
www.sciencemag.org/cgi/content/full/science.aat7319/DC1
Materials and Methods
Figs. S1 to S19
Tables S1 to S22
References (53–69)
28 March 2018; resubmitted 2 August 2018
Accepted 1 November 2018
Published online 15 November 2018
10.1126/science.aat7319
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release) 12

Fig. 1. Synthesis and structure of linear Co and Zn dialkyl
complexes. (A) General synthetic scheme for ligands of the type
HC(SiMe2OR)3 and synthesis of compounds 1 and 2. (B) Molecular
structure of Co(C(SiMe2ONaph)3)2 (1). Purple, gray, turquoise, red, and
yellow spheres represent Co, C, Si, O, and H atoms, respectively. Most
hydrogen atoms have been omitted for clarity. Hydrogen atoms are
shown on three carbons to illustrate the location of the CH-π
interactions. (C) Molecular structure of Co(C(SiMe2ONaph)3)2 viewed
along the molecular z-axis.
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release) 13

Fig. 2. Electronic structure analysis. (A) Energy diagram depicting
the energy and electron occupations of the 3d-orbitals based on
ligand field analysis of ab initio calculations. (B) Electronic structure
of (i) a free Co(II) ion, (ii) Co(C(SiMe2ONaph)3)2 (1) considering only
ligand field interactions, (iii) Co(C(SiMe2ONaph)3)2 considering both
ligand field interactions and interelectron repulsion, and (iv) the
splitting of the ground 4Φ state of Co(C(SiMe2ONaph)3)2 due to spin
orbit coupling according to ab initio calculations. Term symbols are
9
for C∞v symmetry. The splitting between the ground MJ = /2 and
maximal excited MJ = 3/2 states is 1469 cm−1.
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release) 14

Fig. 3. Variable-field, far-IR
spectroscopy. (A) Absolute
transmission spectra for
1
collected at 4.2 K under applied
fields ranging from 0 to 11 T.
Phonon energies used in Eq. 2 to
describe magnetic relaxation are
marked with arrows. (B) Plots of
applied field spectra divided by
the zero-field spectrum. The peak
at 450 cm−1 corresponds to the
transition from MJ = 9/2 to MJ = 7/2.
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release) 15

Fig. 4. Magnetic susceptibility
and reduced magnetization
analysis.
(A)
Variable-
temperature molar magnetic
susceptibility times temperature
(χMT) for 1 collected under dc
fields of 0.1, 1, and 7 T; solid lines
are simulated data from ab initio
calculations.
(B)
Reduced
magnetization data for 1 collected
at temperatures from 2 to 15 K
under dc fields of 1, 4, and 7 T;
solid lines are simulated data
from ab initio calculations.
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release) 16

Fig. 5. Magnetic relaxation dynamics. (A) Arrhenius plot showing the
natural log of relaxation time, τ, versus inverse temperature for 1 in the
absence of an applied dc field (black circles), 1 under a 3000 Oe dc field (red
circles), and 3 in the absence of an applied dc field (blue circles). Relaxation
times are determined from fits of ac susceptibility measurements over the
temperature range of 4 to 70 K. The purple and green lines represent fits of
the relaxation data for 1 under 0 and 3000 Oe, respectively. (B) Dc
relaxation and magnetization times for 1 (green circles) and 3 (purple
circles). The solid lines are from fits describing relaxation via tunneling and
direct relaxation processes as described in the text and Methods. (C)
Variable-field magnetization data for 1 collected at temperatures ranging
from 1.8 to 5 K at a field sweep rate of 32 Oe/s. (D) Variable-field
magnetization data for 3 collected at temperatures ranging from 1.8 to 5 K
at a field sweep rate of 32 Oe/s.
First release: 15 November 2018
www.sciencemag.org
(Page numbers not final at time of first release) 17

A linear cobalt(II) complex with maximal orbital angular momentum from a non-Aufbau ground
state
Philip C. Bunting, Mihail Atanasov, Emil Damgaard-Møller, Mauro Perfetti, Iris Crassee, Milan Orlita, Jacob Overgaard, Joris van
Slageren, Frank Neese and Jeffrey R. Long
published online November 15, 2018
ARTICLE TOOLS
http://science.sciencemag.org/content/early/2018/11/14/science.aat7319
SUPPLEMENTARY
MATERIALS
http://science.sciencemag.org/content/suppl/2018/11/14/science.aat7319.DC1
REFERENCES
This article cites 61 articles, 2 of which you can access for free
http://science.sciencemag.org/content/early/2018/11/14/science.aat7319#BIBL
PERMISSIONS
http://www.sciencemag.org/help/reprints-and-permissions
Use of this article is subject to the Terms of Service
Science (print ISSN 0036-8075; online ISSN 1095-9203) is published by the American Association for the Advancement of
Science, 1200 New York Avenue NW, Washington, DC 20005. 2017 © The Authors, some rights reserved; exclusive licensee
American Association for the Advancement of Science. No claim to original U.S. Government Works. The title Science is a
registered trademark of AAAS.