EPR Spectroscopic Characterization of a Jahn-Teller Distorted (C3v→Cs) Four-Coordinate Chromium(V) Oxo Species

Article abstract of DOI:10.1002/ijch.201600036

Metal-oxo coordination compounds have garnered significant interest over the years. The reactivity of the metal-oxo bond is governed by the geometry, charge, spin state, and identity of the other ligands. In this report, we characterize a distorted C_3v-symmetric Cr^V-oxo complex that has unique magnetic properties, compared with all other known chromyl species. Continuous wave and pulse electron paramagnetic resonance were used to measure the molecular g-values and ⁵³Cr and ¹⁷O hyperfine interactions. Analysis of density functional theory results and the g and hyperfine tensors, in the context of a crystallographically observed Jahn-Teller distortion, suggests an electronic structure that results from the mixing of two sets of doubly degenerate orbital states. This mixing is only made possible by the approximate three-fold symmetry of the ligand set.

Full text of DOI:10.1002/ijch.201600036

Full Paper
DOI: 10.1002/ijch.201600036
EPR Spectroscopic Characterization of a Jahn-Teller
Distorted (C3v!Cs) Four-Coordinate Chromium(V) Oxo
Species
Troy A. Stich,[a] Derek M. Gagnon,[a] Bryce L. Anderson,[b] Daniel G. Nocera,[b] and R. David Britt*[a]
Abstract: Metal-oxo coordination compounds have garnered
significant interest over the years. The reactivity of the
metal-oxo bond is governed by the geometry, charge, spin
state, and identity of the other ligands. In this report, we
characterize a distorted C3v-symmetric CrV-oxo complex that
has unique magnetic properties, compared with all other
known chromyl species. Continuous wave and pulse elec-
tron paramagnetic resonance were used to measure the mo-
lecular g-values and 53Cr and 17O hyperfine interactions.
Analysis of density functional theory results and the g and
hyperfine tensors, in the context of a crystallographically ob-
served Jahn-Teller distortion, suggests an electronic struc-
ture that results from the mixing of two sets of doubly de-
generate orbital states. This mixing is only made possible by
the approximate three-fold symmetry of the ligand set.
Keywords: Chromium · density functional calculations · EPR spectroscopy · Jahn-Teller distortion
1 Introduction
Transition metal complexes with terminal oxygen ligands
have been, and remain, an exciting medium with which to
explore the nuances of ligand field theory.[1–5] In particu-
lar, the reactivity of the metal-O unit has been shown to
be tuned by the nature of the other ligands filling out the
coordination sphere, the coordination geometry, and the
oxidation state and spin state of the metal ion.[6–10] High-
valent metal-oxo species are implicated as being involved
in many energetically demanding chemical processes, in-
cluding the oxidation of water. The magnetic properties
determined using various spectroscopies, including elec-
tron paramagnetic resonance (EPR), have been crucial in
deciphering the electronic structures of such metal-oxos
and allow predictions to be made concerning their reac-
tivity. We previously prepared the first trigonal d1 CrV-
oxo species (Scheme 1)[11] that was shown to have EPR
properties unique from all known tetragonal CrV-O com-
plexes, namely a very large g-shift for gj j and gj j < g?.
These unusual EPR properties are attributed to the com-
bination of two effects: 1) the presence of only four li-
gands leads (at least in part) to a reduction in crystal field
splitting that allows for the flipping of the g-tensor aniso-
tropy; and 2) the three-fold symmetry of the ligand set
allows two orbital doublets (Scheme 2) to mix, leading to
a Jahn-Teller distortion that is observed crystallographi-
cally.
[a] T. A. Stich, D. M. Gagnon, R. D. Britt
Department of Chemistry
University of California
One Shields Avenue
Davis
CA 95616
USA
e-mail: dbritt@ucdavis.edu
[b] B. L. Anderson, D. G. Nocera
Department of Chemistry and Chemical Biology
Harvard University
12 Oxford Street
Cambridge
MA 02138
USA
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/ijch.201600036.
Scheme 1.
Isr. J. Chem. 2016, 56, 864 –871
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to fit into an Oxford 935CF cryostat. Temperatures were
maintained using an Oxford Instruments ITC503 temper-
ature and gas flow controller. Four-pulse (p/2-t-p/2-T-p-
T-t-p/2-t-echo) electron spin-echo envelope modulation
(ESEEM) and hyperfine sublevel correlation (HYS-
CORE, p/2-t-p/2-T1-p-T2-p/2-t-echo) spectroscopies were
employed to detect nuclear spin-flip transition frequen-
cies for the hyperfine-coupled 17O nucleus. Spectral simu-
lations were performed using the Easyspin 5.0 tool-
box[14,15] within the MatLab software suite (The Math-
works Inc., Natick, MA).
Scheme 2.
2.3 Computational Methods
All calculations were carried out using the ORCA quan-
tum chemistry program.[16] The hybrid-functional PBE0
was used in conjunction with unrestricted Kohn-Sham/
Hartree-Fock.[17] The basis set IGLO-II was used for all
carbon and hydrogen atoms, IGLO-III for oxygen atoms,
and cc-pCVTZ for chromium.[18,19] The conductor-like
screening model (COSMO) was used to model the dielec-
tric effects from the solvent toluene.[20] The integration
grid was expanded around the chromium and oxygen
atoms to increase the accuracy of the calculation. EPR
properties were calculated using the EPRNMR module
in ORCA. The resolution of the identity, chain of spheres
approximation (RIJCOSX) was employed.[21] A typical
input file is included in the supporting information.
2 Methods
2.1 Sample Preparation
Solutions of natural abundance [CrV(ditox)3(O)] (ditoxꢀ
tBu2(Me)COÀ) were prepared in toluene, as described
previously.[11] The 17O-enriched isotopologue
of
[CrV(ditox)3(O)] was made by reacting CrIII(ditox)3 with
17O-labeled iodosobenzene (50% enriched) that had been
prepared using literature procedures.[12] The degree of iso-
tope incorporation was determined by mass spectrometry
of the oxidation product of the reaction of
[CrV(ditox)3(O)] with PPh3 (NMR of the starting PPh3 re-
agent indicated that 5% of it was already oxidized to
OPPh3). The isotope pattern for natural abundance
OPPh3 has two significant peaks: one at 279 m/z with rel-
ative intensity 1.0, assigned to the H+-adduct; and one at
280 m/z with relative intensity 0.195, assigned to the m+
3 Results and Discussion
1 H+-adduct.
The
reaction
of
17O-labeled
The
low-temperature
CW
EPR
spectrum
of
[CrV(ditox)3(O)] with PPh3 yielded a mass spectrum for
OPPh3 with relative intensities of 75.03 and 38.64 for the
279 and 280 m/z peaks, respectively. This intensity pattern
corresponds to an 17O-labeling efficiency of 25.2%. This
value was used in simulations of the EPR spectrum of la-
beled [CrV(ditox)3(O)].
[CrV(ditox)3(O)] (Figure 1, top trace) exhibits a slightly
rhombic g-tensor ([g1, g2, g3]=[1.9825, 1.9727, 1.9317]).
The parallel turning point in the spectrum centered at
g3 =1.9317 (348.8 mT) is flanked by two clear, low-inten-
sity features at 346.7 mT and 354.3 mT, which would coin-
cide with the second and fourth lines of a hyperfine split-
ting due to an ꢁ100 MHz hyperfine interaction (HFI)
with the 53Cr (I=3/2, 9.51% abundant) nucleus. A
shoulder appears on the low-field side of the g1 resonance
(g=1.9822, 339.9 mT) that suggests A1(53Cr)ꢁ25 MHz.
Alternatively, this shoulder feature could be explained by
a 60 MHz A(53Cr) along g2, though this assignment yields
an overall less good simulation. The best-fit 53Cr HFI is
found to be [A1, A2, A3]=[24(1), 20(10), 103(1)] MHz.
The [CrV(ditox)3(O)] species is rather unstable[11] and
decomposes to a variety of species, some paramagnetic
(see Figure S2). For example, in the spectrum of
[CrV(ditox)3(O)] shown in Figure 1, a series of derivative-
shaped resonances at 330.1, 332.4, 334.7, and 336.9 mT
can be seen. These same features appear much more in-
tensely in the spectrum of another preparation of
[CrV(ditox)3(O)] that was allowed to sit for an extended
period at room-temperature before being frozen (Fig-
2.2 EPR Spectroscopy
The X-band (9.43 GHz) continuous-wave (CW) EPR
spectra were recorded on a Bruker (Billerica, MA) Bio-
spin EleXsys E500 spectrometer equipped with a super-
high Q resonator (ER4122SHQE). Cryogenic tempera-
tures were achieved and controlled using an ESR900
liquid helium cryostat in conjunction with a temperature
controller (Oxford Instruments ITC503) and gas flow
controller. CW EPR data were collected under slow-pas-
sage, non-saturating conditions at a temperature of 80 K.
The spectrometer settings were as follows: modulation
amplitude=0.2 mT, and modulation frequency=100 kHz;
conversion time=88 ms. Pulse Q-band studies (ca.
34 GHz) were performed using a Bruker E-580 EleXsys
spectrometer using a laboratory-built probe[13] modified
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dipolar part of the 53Cr HFI, i.e., Adip. ꢁ[À25, À25,
+50] MHz where Adip. ꢀ1Pd[+2/7, +2/7, À4/7] for
a ground-state [dxy]1 electronic configuration, and 1 corre-
sponds to the population of unpaired spins in the d-orbi-
tal that describes that ground state, nearly 1.0 in this case.
Preparation of [CrV(ditox)3(O)] using 17O-labeled iodo-
sobenzene led to incorporation of the magnetic oxygen
nucleus (I=5/2) at the terminal oxido position (25.2%
enrichment). The features of the corresponding CW EPR
spectrum (Figure 1, bottom trace) are modestly broad-
ened, compared with the natural abundance isotopologue.
The best-fit simulations indicate that [A1, A2, A3](17O) is
roughly [13, 13, <10] MHz. Due to the incomplete en-
richment, it is difficult to determine these parameters
more precisely solely on the basis of the CW EPR spec-
tra. However, by performing four-pulse electron spin-
echo envelope modulation (ESEEM) in resonance with
g3, features were apparent only in the spectrum of the la-
beled compound (cf. top and bottom traces in Figure 2).
The traces shown in Figure 2 result from the summation
of 32 cross-term averaged ESEEM spectra acquired
under identical conditions save for the value of t, which
was incremented by 8 ns from 200 ns to 456 ns (individual
Figure 1. CW EPR spectra of [CrV(ditox)3(O)] prepared with natural
abundance benzyl iodide (top, blue) and with 17O-enriched benzyl
iodide (bottom, red) with the product enriched to a level of 25%.
Simulations obtained using parameters given in the text are
shown just below each experimental trace. Insets reveal features
around g1 and g3 that result from 53Cr hyperfine interaction (I=3/2,
9.51% natural abundance). Spectrometer settings: microwave fre-
quency=9.4 GHz; temperature=80 K; modulation frequency=
100 kHz; modulation amplitude=0.2 mT; and conversion time=
88 ms.
ure S2, green trace). Other EPR signals also develop
after a time (Figure S2, red trace), but neither set of sig-
nals overlaps with the 53Cr hyperfine features discussed
above.
The room-temperature EPR spectrum of the CrV-O
complex (published previously)[11] possesses a single de-
rivative-shaped line centered at g=1.975. This value
nearly satisfies the relation (giso)2 =1/3”((g1)2 +(g2)2 +
(g3)2). This small discrepancy could be a manifestation of
how, at room temperature, different conformers on the
ground-state adiabatic potential energy surface are ther-
mally accessible (vide infra). The room-temperature EPR
resonance is flanked by two members of the hyperfine
splitting pattern, resulting from an isotropic HFI with the
53Cr nucleus (aiso(53Cr)=46(3) MHz). This value for
aiso(53Cr) arises from Fermi contact (FC) and corresponds
to only 0.06 unpaired electrons at the nucleus (using aFC
=
À748.2 MHz).[22] The total 53Cr HFI is a combination of
isotropic, dipolar, and indirect dipolar contributions. The
indirect dipolar contribution is proportional to the magni-
tude of the corresponding g-shifts and can be calculated
using the anisotropic hyperfine parameter Pd(53Cr)=
À103.0 MHz (specifically, Pd[Dgx, Dgy, Dgz]).[22] The indi-
rect dipolar contribution is found to be small, relative to
the total HFI, whether invoking a dx2Ày2 (Aind.dip. =[+2,
+2, +8] MHz) or dxz (Aind.dip. =[+8, +2, +2] MHz)
ground-state description. Therefore, solely subtracting off
the isotropic element should give a good estimate of the
Figure 2. A) Sum-over-t four-pulse ESEEM spectra of 17O-labeled
(red trace) and natural abundance (blue trace) [CrV(ditox)3(O)].
Spectrometer settings: temperature=25 K; field=1270 mT; fre-
quency=34.307 GHz; dT=12 ns; and t=200 ns incremented by
8 ns up to 456 ns. B) HYSCORE spectrum of [CrV(ditox)3(17O)]. Spec-
trometer settings: temperature=25 K; field=1270 mT; frequen-
cy=34.307 GHz; dT=12 ns; and t=200 ns.
Isr. J. Chem. 2016, 56, 864 –871
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ESEEM spectra are presented in Figures S1 and S2). This
methodology largely removes any t-dependence of the
spectrum and has been shown previously to be adept at
revealing the magnetic parameters, and in some cases, the
electric quadrupole for hyperfine-coupled 17O nuclei.[23]
The red trace in Figure 2 possesses broad peaks centered
at 6.3, 8.7, and 10.0 MHz, as well as a broad multiplet
centered at ꢁ15 MHz, which is assigned to the sum com-
bination band (us =ua +ub) of the 6.3 and 8.7 MHz peaks.
The hyperfine sublevel correlation (HYSCORE) spec-
trum acquired at 1270 mT shows that the peaks at 6.3 and
8.7 MHz are correlated and are approximately centered
at the 17O Larmor frequency; thus, these features are as-
signed to the set of five 17O NMR transitions within each
of the spin-up (ua) and spin-down (ub) electron spin mani-
folds. Simulation of these correlated peaks requires that
the effective 17O HFI is at g3 ꢁ2.5 MHz. The splitting
(Dus) between the peaks of the combination band at
15 MHz varies between 0.2 and 0.3 MHz and is related to
the magnitude of the nuclear quadrupole interaction
(NQI), the shifting of the nuclear spin levels in response
to an electric field gradient across the nucleus. Using the
relationship e2Qq/hꢁ(40/12)Dus, the component of the
NQI tensor (e2Qq/h) that is probed when in resonance
with g3 is estimated to be 0.8(Æ0.2) MHz. The us peak is
not observed in ESEEM/HYSCORE data collected in
resonance with g1 and g2, precluding a more precise esti-
mation of the NQI along these vectors.
The crystal structure of the d1 CrV-O complex
(Scheme 1) reveals that the pseudo-C3v geometry distorts
significantly to Cs symmetry, as one of the alkoxide OÀ
CrÀO bond angles increases to 114.58 from an ideal value
of 109.58 for a tetrahedral complex (notably, however,
a tetrahedral complex would not have the principal axis
along the metal-oxo bond), while the isovalent d0 V(V)-O
complex maintains C3v symmetry (avg. ROÀV(V)ÀO=
109.68).[11] This symmetry breaking likely results from
a Jahn-Teller induced geometric distortion owing to the
2E nature of the ground state (Scheme 2 and vide infra).
DFT geometry-optimization of the [CrV(ditox)3O] struc-
ture preserved this distorted geometry (Table S3 in Ref.
[11]) and predicted a [dxz]1 ground-state description. Pop-
ulation of a CrÀO p* dxz-based orbital qualitatively ex-
plains the long CrÀO bond (1.649 Š) and low CrÀO
stretching frequency (946 cmÀ1).
Several pseudo-C4-symmetric d1 systems have been
characterized and shown to have a [dxy]1 electron configu-
ration in the ground state. Accordingly, these systems ex-
hibit axially symmetric g-tensors, and when the metal
HFI is evident, the largest magnitude element of the hy-
perfine tensor coincides with gj j, implying that gj j is
along the molecular z-axis (Table 1). Notably, all tetrago-
Table 1. Magnetic parameters for Cr(V)-containing and other relevant complexes.
Species
g
A (MHz)
uM-X (cmÀ1
)
Ref.
[VIVOCl5]2À
1.9847, 1.9847, 1.9450
1.9813, 1.9801, 1.9331
1.989, 1.989, 1.964
1.968, 1.942, 1.803
1.9825, 1.9727, 1.9317
1.9784, 1.9700, 1.9473
1.9878, 1.9792, 1.9551
S=1
51V [191, 191, 519]
51V [213, 217, 546]
51V [162, 162, 477]
51V [890, 918, 753]
53Cr [24, 20, 103]
53Cr [À65, À21, 31]
53Cr [À53, À31, 41]
[36]
[36]
[37]
[38]
[VIVO(H2O)5]2+
[VIVO(tpp)][j]
VIVO2/in SiBEA zeolite
[CrV(ditox)3(O)]
PBE0-DFT[a]
946
870
[11] and this work
PBE0-DFT[b]
[CrIV(ditox)3(O)]À
[CrVOCl4]À
[11]
[39]
[39,40]
[41,42]
[43]
[44]
[44]
[45]
[46]
[47,48]
[30,49]
[50]
[26]
[36]
[51]
[23]
[52,53]
[54]
2.006, 1.979, 1.979
2.008, 1.977, 1.977
1.987, 1.975, 1.975
n/d
[CrVOCl5]2À
53Cr [108, 30, 30]
53Cr [108, 21, 21]
Aiso 53Cr =53
53Cr [45, 45, 118]
n/d
[CrVOL]À[c]
994
988
996
967
[tBuOCO]CrVO(THF)
[CrVN(NCCH3)cyclam][d]
[CrVN(N3)cyclam][e]
[CrVNCl4]À
g
iso =1.9770
1.997, 1.997, 1.965
iso =1.983
g
1.993, 1.993, 1.948
1.992, 1.992, 1.956
1.9945, 1.9945, 1.9583
2.30, 1.98, 1.98
53Cr [62, 62, n/d]
53Cr [62, 62, 123]
53Cr [63, 63, 112]
[CrVNL][f]
[CrVN(oep)][g]
1017[h]
798
FeVNL[i]
[FeVO(TAML)]À
[FeVO(TMC)(NCCH3)]2+
[MoVOCl5]2À
1.99, 1.97, 1.74
57Fe [À49, À2, À16]
57Fe [À47, À17, 0]
95Mo [224, 98, 98]
95Mo [163, 75, 34]
95Mo [157, 66, 66]
95Mo [133, 55, 57]
95Mo [40, 111, 155]
2.053, 2.010, 1.971
1.9632, 1.9400, 1.9400
1.9871, 1.9636, 1.9529
2.020, 1.982, 1.982
2.025, 1.955, 1.949
1.9988, 1.9885, 1.9722
MoV SO high pH
[MoVO(SPh)4]À
MoV XO “very rapid” intermediate
MoV DMSOR intermediate
[a] DFT performed on model based on crystal structure coordinates. [b] DFT performed on pared-down geometry-optimized model from Ref.
[11] (coordinates are listed in Table S3 of Ref. [11]). [c] L=trans-bis-(2-ethyl-2-hydroxybutanoato). [d] trans-[Cr(N)-(cyclam)(NCCH3)]2+. [e]
trans-[Cr(N)-(cyclam)(N3)]2+
.
[f] L=N,N’-bis(pyridine-2-carbonyl)-o-phenylenediamido. [g] oep=octylethylporphryin. [h] value for
CrV(O)tetraphenylporhpryin. [i] L=phenyltris(3-tert-butylimidazol-2-ylidene) borato. [j] tpp=tetraphenylporphyrin.
Isr. J. Chem. 2016, 56, 864 –871
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nal CrV-O complexes studied previously exhibit g-aniso-
tropy, in which gj j > g?; for [CrV(ditox)3(O)], the oppo-
site is true, signaling a change in the electronic-structure
description upon going from tetragonal to trigonal sym-
metry.
2lk2?
Exy=x2Ày2 À Exz
5
6
g? ꢁ ge À
g? ꢁ ge À
! Ez2 ꢂ Exz
8lk2?
Exy=x2Ày2=z2 À Exz
À
Á
! Ez2 ꢃ Exy Ex2Ày2
Curiously, this same flipping of the order of gj j and g?
is also found when comparing the oxidos with nitridos of
a series of tetragonal CrV complexes (cf. Table 1). This
behavior was attributed to the stronger covalency (via p-
Previous DFT results for [CrV(ditox)3(O)] suggested
a ground state description of [dxz/yz]1, in agreement with
the calculations reported in this work.[11] If g3 is assigned
to gj j, having the largest part of the 53Cr HFI along the gz
axis is inconsistent with a 3dxz ground-state description
for the unpaired electron (with z aligned along the metal-
oxo bond), as we would expect amaximum(53Cr) to then be
along gy, perpendicular to the plane of the lobes of the dxz
orbital. Single-point DFT calculations using either the
crystal structure coordinates or a fully geometry-opti-
mized model predict that the largest element of a very
rhombic 53Cr hyperfine tensor (Table 1) will be along
a vector that bisects two of the CrÀO alkoxide bonds, in
the plane of those three atoms, and pointing toward the
CrÀO alkoxide with the expanded ROÀCr(V)ÀO angle
(Euler angles for the computed 17O HFI are [À32, 54,
À51]8 relative to the g-tensor using the z-y’-z“conven-
tion). In other words, the DFT-predicted vector for
amaximum(53Cr) lies in the plane of the CrÀO p* MO, not
perpendicular to it, and not along the metal-oxo bond
vector.
bonding) of the CrÀN bond, leading to a large destabili-
[24]
zation of the degenerate orbital set dxz/yz
.
The dx2Ày2 or-
bital is at the same time stabilized by deformation of the
equatorial plane. According to the ligand field equations
used to predict g-shifts from d$d electronic transition en-
ergies (1) and (2) of a [dxy]1 ion,[25] gj j can be less than g?
if the xy!xz/yz transition energy is more than one-fourth
the energy of the xy!x2Ày2 transition.
8lk2
Ex2Ày2 À Exy
1
gjj ge À
2lk2?
Exy=yz À Exy
2
g? ge À
Satisfying this condition in the case of [CrV(ditox)3(O)]
is made easier by the reduction in crystal-field splitting by
there being only four ligands. In trigonal symmetry, one
expects that the dxz and dyz ligand-field excited states will
be nearly degenerate (this degeneracy is also expected in
the tetragonal complexes), leading to the nearly axial g-
tensor (2). For trigonal complexes the dxy and dx2Ày2 states
should also be degenerate (Scheme 2). This latter case of
near-degeneracy is responsible for the large gj j shift seen
here, consistent with a [dxy]1 ground-state electron config-
uration (1).[1]
Furthermore, the experimentally-determined 17O HFI
(ꢁ[13, 13, 2.5] MHz) is found to be smaller than the com-
puted HFI values and much smaller than if a pure CrÀO
p* molecular orbital was populated with an unpaired
electron
(cf.
the
strong
17O
HFI
in
[FeVO(TMC)(NCCH3)]2+, Table 2).[26] The estimate for
aiso(17O)ꢁ9.5 MHz corresponds to merely 0.0018 un-
paired electrons at the nucleus[27] (using aFC
=
If, however, we consider the possibility of a [dxz]1 elec-
tronic configuration as implied by the DFT results, the
ligand field Equations (3) and (4) for calculating gj j and
g? are slightly more complicated by the spin-orbit cou-
pling of the dxz with the dz2 orbital wavefunctions. In the
limit that dz2 mixing is negligible, gj j can be less than g?
when the energy of the dxz!dyz transition is less than the
energy of the dxz!dxy/x2Ày2 transition (Eq. 5). In the limit
that dz2 is degenerate with dxy and dx2Ày2, gj j can be less
than g? if the dxz!dyz transition energy is less than one-
fourth of the dxz!dz2/xy/z2Ày2 transition energy (Eq. 6).
Therefore, with nearly degenerate dxz and dyz orbitals as
noted above, a [dxz/yz]1 electronic configuration can also
result in the observed gj j <g?.
À5263 MHz). Subtracting aiso from the estimated 17O hy-
perfine tensor leaves the hyperfine anisotropy, Aaniso ꢁ[Æ
Æ
3.5, Æ3.5, 7.0] MHz (we do not know the sign of the 17O
hyperfine interaction), is a composed of local (Tloc) and
nonlocal contributions (Tnonloc), which are both axially
symmetric and traceless tensors that are not necessarily
coaxial with one another.[28] The nonlocal component
(Tnonloc =[+2a, Àa, Àa]) is simply the through space
dipole-dipole interaction between the unpaired electron
on the chromium ion and the 17O nucleus that are sepa-
rated by r=1.649 Š, and is computed using the relation
a=1Crgebegnbn/r3. The above analysis of the 53Cr HFI led
to a value for 1Cr ꢁ1.0; therefore, we compute a=
À2.4 MHz. Subtracting Tnonloc from Aaniso gives either
[À1.1, À1.1, +2.2] MHz or [+5.9, +5.9, À11.8] MHz for
Tloc, depending on the sign of the measured 17O HFI. Tloc
results from spin density in the oxygen-centered p-orbi-
tals. Using the tabulated hyperfine value for an electron
in an oxygen 2p-orbital Pp =À421.0 MHz,[22] and the an-
gular factors for a p-orbital (À2/5, À2/5, +4/5), we find
2lk2k
Exy À Exz
3
gk ge À
2lk2?
6lk2?
4
g? ge À
À
Exy=x2Ày2 À Exz Ez2 À Exz
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Table 2. Magnetic parameters for axial ligand of relevant compounds.
Species
axial ligand
17O
A (MHz)
e2Qq/h (MHz)
h
Ref.
[CrV(ditox)3(O)]
PBE0-DFT[a]
13, 13, 3.5
0.8 (0.2)
+3.03
À2.33
3.24
n/d
this work
0.7, À30.4, 35.5
8.2, 26.4, À32.2
10.4, 9.5, 3.6
9.11, 6.84, 0.71
25, 128, 20
0.39
0.99
0.02
n/d
PBE0-DFT[b]
[CrVN(oep)]
14N
14N
17O
17O
17O
17O
[47]
[30]
[26]
[26]
[55, 56]
[23]
FeVNL
[FeVO(TMC)(NCCH3)]2+
B3LYP-DFT
À1.0, À70.8, 75.5
MoV SO high pH
[MoVO(SPh)4]À
2.4, 1, À3.4
1.6
1.45
0.9
0
8.1, 4.9, 4.9
[a] DFT performed on model based on crystal structure coordinates. [b] DFT performed on pared-down geometry-optimized model[11] (coordi-
nates are listed in Table S3 of Ref. [11]).
that Tloc corresponds to either 0.007 or 0.035 unpaired
electrons in an O 2p orbital, which is very small in either
case. So, both the 53Cr and 17O HFI appear to be inconsis-
tent with a pure dxz, CrÀO p* ground-state description.
Analysis of the spin-down lowest unoccupied MO
(LUMO) begins to point to a possible explanation of this
incongruity. The LUMO consists of 10% O px,y character
and 40% Cr dxz,yz character (ea, Scheme 2), consistent
with the CrÀO [p*]1 ground-state description. However,
DFT also predicts that this LUMO contains 30% Cr
dx2Ày2,xy character (eb, Scheme 2) indicating that there is
a propensity for the two doubly-degenerate orbital sets in
C3v symmetry to mix.
This mixing is expected given the geometry of the
[CrV(ditox)3(O)] complex. McGarvey and Telser provided
a quantitative analysis of how “doming”or displacement
(D) of the central metal ion from the plane formed by the
metal-bonding atoms of the three equatorial ligands
changes the relative energies of the two doubly degener-
ate orbital states.[29] This analysis was performed for the
cases of d4 and d6 electron configurations. In [Cr(V)(di-
tox)3(O)], the average value of Dꢁ21.18 is expected to
have the eb and ea orbital sets close in energy to one an-
other, leading to significant unquenched orbital angular
momentum in the ground state, and hence, the large g-
shift of gj j. However, a 2E ground state, by virtue of
having one electron (or hole) in two degenerate orbitals
is susceptible to Jahn-Teller effects.
two configurations and the spin-orbit induced angular
momentum (l). The value for l=klfree-ion, where lfree-ion
=
380 cmÀ1 for a Cr(V) ion,[34] and k is the covalency reduc-
tion parameter representing loss of chromium character
in the electronic-structure description of the ground state
due to bonding with ligand atoms. The g-values can thus
be written as functions of q and k. For the [e]1 electron
configuration exhibited by the Cr(V)-O complex, gj j =
2(1Àkcos(2q)) and g? =2sin(2q). To match the experi-
mental values of gj j =1.9317 and g? =1.9776, k=0.23 and
r=6.625. Following the procedures detailed in Ref. [30],
b2
2
the covalency parameter is defined as k
a2 À k0,
where a2 is the contribution of the ea orbital set and b2 is
2
the contribution of the eb orbital set to the E ground
state (given the condition a2 +b2 =1). If k0 assumes a typi-
cal value of 0.9, then the value of b2 ꢁ0.5, indicating an
approximately equal contribution of [ea]1 and [eb]1 config-
urations to the ground-state description. This degree of
configuration mixing is already reflected, somewhat, in
the composition of the singly occupied orbital predicted
by single determinant DFT methods, as detailed above.
This mixed MO description allows for dxz/yz orbital char-
acter, which is consistent with both the longer CrÀO
bond observed by X-ray crystallography and the low CrÀ
O stretching frequency observed in IR spectroscopy.
There has been great success of late in predicting the
magnetic properties of electron-configurationally mixed
metal complexes using complete active space self-consis-
tent field (CASSCF) calculations.[30,33,35] The single deter-
minant DFT results reported here do a fair job of predict-
ing the g-values of the Cr(V)-O complex (Table 1). How-
ever, the predictions of the 53Cr and 17O HFI would likely
be improved using CASSCF methods.
A similar result was seen in the DFT-predicted ground
state of a Cs symmetric low-spin d3 Fe(V)-nitride.[30] The
mixing of the ea and eb orbital sets is a Jahn-Teller (JT)
effect allowed by the C3v-parent symmetry of the mole-
cule.[31] For this, and other low-spin d3 trigonal com-
plexes,[32,33] it was shown that the combination of the
Jahn-Teller distortion and the spin-orbit coupling (SOC)
interaction were responsible for the shifting of g-values
away from the free electron value (ge =2.0023). For the
4 Conclusion
2
two E configurations depicted in Scheme 2, the JT-SOC
Similar to other (pseudo)trigonally symmetric metal com-
plexes with an odd number of electrons in an e-orbital
set, the present Cr(V)-O complex experiences a Jahn-
Teller distortion that is evident in the X-ray crystal struc-
effect on the g-tensor can be parametrized using a ficti-
tious angle 2q,[32] where tan 2 ꢀ r 2lV. r represents the
ratio between the JT-vibronic induced mixing (V) of the
Isr. J. Chem. 2016, 56, 864 –871
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Acknowledgements
The spectroscopic work was supported by National Sci-
ence Foundation under the NSF Center CHE-1305124 (to
R.D.B). The synthetic work was supported by NSF CHE-
1464232 (to D.G.N.). The EPR spectroscopy was per-
formed using spectrometers at the CalEPR facility
funded by the National Institutes of Health (S10-
RR021075) and the NSF (CHE-1048671).
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Received: April 22, 2016
Published online: August 8, 2016
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871