Magnetic Transitions in Iron Porphyrin Halides by Inelastic Neutron Scattering and Ab Initio Studies of Zero-Field Splittings

Article abstract of DOI:10.1021/acs.inorgchem.5b01505

Zero-field splitting (ZFS) parameters of nondeuterated metalloporphyrins [Fe(TPP)X] (X = F, Br, I; H₂TPP = tetraphenylporphyrin) have been directly determined by inelastic neutron scattering (INS). The ZFS values are D = 4.49(9) cm^-1 for tetragonal polycrystalline [Fe(TPP)F], and D = 8.8(2) cm^-1, E = 0.1(2) cm^-1 and D = 13.4(6) cm^-1, E = 0.3(6) cm^-1 for monoclinic polycrystalline [Fe(TPP)Br] and [Fe(TPP)I], respectively. Along with our recent report of the ZFS value of D = 6.33(8) cm^-1 for tetragonal polycrystalline [Fe(TPP)Cl], these data provide a rare, complete determination of ZFS parameters in a metalloporphyrin halide series. The electronic structure of [Fe(TPP)X] (X = F, Cl, Br, I) has been studied by multireference ab initio methods: the complete active space self-consistent field (CASSCF) and the N-electron valence perturbation theory (NEVPT2) with the aim of exploring the origin of the large and positive zero-field splitting D of the ⁶A₁ ground state. D was calculated from wave functions of the electronic multiplets spanned by the d⁵ configuration of Fe(III) along with spin-orbit coupling accounted for by quasi degenerate perturbation theory. Results reproduce trends of D from inelastic neutron scattering data increasing in the order from F, Cl, Br, to I. A mapping of energy eigenvalues and eigenfunctions of the S = 3/2 excited states on ligand field theory was used to characterize the σ- and π-antibonding effects decreasing from F to I. This is in agreement with similar results deduced from ab initio calculations on CrX₆^3- complexes and also with the spectrochemical series showing a decrease of the ligand field in the same directions. A correlation is found between the increase of D and decrease of the π- and σ-antibonding energies e^λ_X (λ = σ, π) in the series from X = F to I. Analysis of this correlation using second-order perturbation theory expressions in terms of angular overlap parameters rationalizes the experimentally deduced trend. D parameters from CASSCF and NEVPT2 results have been calibrated against those from the INS data, yielding a predictive power of these approaches. Methods to improve the quantitative agreement between ab initio calculated and experimental D and spectroscopic transitions for high-spin Fe(III) complexes are proposed.

Full text of DOI:10.1021/acs.inorgchem.5b01505

Article
pubs.acs.org/IC
Magnetic Transitions in Iron Porphyrin Halides by Inelastic Neutron
Scattering and Ab Initio Studies of Zero-Field Splittings
Shelby E. Stavretis,† Mihail Atanasov,*,‡,§ Andrey A. Podlesnyak,*,∥ Seth C. Hunter,† Frank Neese,*,‡
and Zi-Ling Xue*,†
†Department of Chemistry, The University of Tennessee, Knoxville, Tennessee 37996, United States
‡Max Planck Institute for Chemical Energy Conversion, Stiftstraße 34-36, D-45470 Mulheim an der Ruhr, Germany
̈
§Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
∥Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
S
* Supporting Information
ABSTRACT: Zero-field splitting (ZFS) parameters of non-
deuterated metalloporphyrins [Fe(TPP)X] (X = F, Br, I;
H2TPP = tetraphenylporphyrin) have been directly determined
by inelastic neutron scattering (INS). The ZFS values are D =
4.49(9) cm−1 for tetragonal polycrystalline [Fe(TPP)F], and D
= 8.8(2) cm−1, E = 0.1(2) cm−1 and D = 13.4(6) cm−1, E =
0.3(6) cm−1 for monoclinic polycrystalline [Fe(TPP)Br] and
[Fe(TPP)I], respectively. Along with our recent report of the
ZFS value of D = 6.33(8) cm−1 for tetragonal polycrystalline
[Fe(TPP)Cl], these data provide a rare, complete determi-
nation of ZFS parameters in a metalloporphyrin halide series.
The electronic structure of [Fe(TPP)X] (X = F, Cl, Br, I) has been studied by multireference ab initio methods: the complete
active space self-consistent field (CASSCF) and the N-electron valence perturbation theory (NEVPT2) with the aim of exploring
6
the origin of the large and positive zero-field splitting D of the A1 ground state. D was calculated from wave functions of the
electronic multiplets spanned by the d5 configuration of Fe(III) along with spin−orbit coupling accounted for by quasi
degenerate perturbation theory. Results reproduce trends of D from inelastic neutron scattering data increasing in the order from
F, Cl, Br, to I. A mapping of energy eigenvalues and eigenfunctions of the S = 3/2 excited states on ligand field theory was used
to characterize the σ- and π-antibonding effects decreasing from F to I. This is in agreement with similar results deduced from ab
3−
initio calculations on CrX6 complexes and also with the spectrochemical series showing a decrease of the ligand field in the
same directions. A correlation is found between the increase of D and decrease of the π- and σ-antibonding energies eXλ (λ = σ, π)
in the series from X = F to I. Analysis of this correlation using second-order perturbation theory expressions in terms of angular
overlap parameters rationalizes the experimentally deduced trend. D parameters from CASSCF and NEVPT2 results have been
calibrated against those from the INS data, yielding a predictive power of these approaches. Methods to improve the quantitative
agreement between ab initio calculated and experimental D and spectroscopic transitions for high-spin Fe(III) complexes are
proposed.
⎡
⎤
INTRODUCTION
2
z
1
3
2
x
2
⎡
⎤
⎦
■
̂
̂
̂
̂
y
H = D S − S(S + 1) + E S − S
⎢
⎣
⎥
⎦
s
⎣
(1)
The chemistry of metalloporphyrins has the potential to impact
our understanding of biological and geological roles that the
naturally occurring systems play.1−3 The diverse biological
functions of heme proteins are often attributed to the varying
degree of changes in the local heme environment as shown in
Table 1.1,3 Many metalloporphyrins have unpaired electrons,
making the compounds paramagnetic. One intrinsic property in
paramagnetic compounds is the zero-field splitting (ZFS). For
compounds with spin S ≥ 1, the interaction of the electron
spins mediated by spin−orbital coupling (SOC) leads to a
splitting of the spin states of otherwise degenerate states.4−6
The spin Hamiltonian up to second-rank terms is given in eq
1:7
where D and E are the axial and rhombic ZFS parameters,
respectively, which measure the magnetic anisotropy of the
system. When the x and y directions are equivalent, E = 0.
ZFS manifests as differences among energy levels in the
absence of an external magnetic field. For d5 Fe(III) porphyrin
complexes in the current studies, the electronic ground states of
complexes with S = 5/2 are split as shown in Scheme 1. The
resulting energy spectrum exhibits peaks, 2D and 4D, that are
associated with transitions in ZFS. The rhombic ZFS, E, mixes
Received: July 6, 2015
© XXXX American Chemical Society
A
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Table 1. Comparison of D (cm−1) Values of Different Fe(III) Porphyrin Halides Determined by Different Methods
[Fe(TPP)X] by INS
including the current work
Fe(III) protoporphyrin IX dimethyl
ester halides (Chart 1) by far-IR
Fe(III) deuteroporphyrin IX
dimethyl ester halides by far-IR
X
[Fe(TPP)X] by other methods
F
4.49(9)
5.0(1)12
5.55(11)12
Cl 6.5 (far-IR),17 D = 3.2−11.9 determined by other
6.33(8)11
6.95(14)12
8.95(18)12
methods11
Br 4.9 (magnetic susceptibility),15b 9.15 (far-IR),17
8.8(2)
9.7517
14.517
11.80(23)12
16.40(15)12
12.5(5) (magnetic susceptibility)15a,16
13.5(5) (magnetic susceptibility)16
I
13.4(6)
Scheme 1. (a) Structures of Metalloporphyrins in the Current Studies; (b) d Orbital Splitting; (c) and (d) ZFS in Compounds
with S = 5/2 with D > 0, E = 0 (for D < 0, Energy Levels Will Be Inverted), and E ≠ 0, Mixing of Pure Doublet States (E ≪ D)4a
the ΔMS = 2 states. Thus, the MS = 1/2 states interact with
either MS = 5/2 or ∓3/2 states, leading to the shift of the
energy levels shown in Scheme 1d.
of ZFS parameters of several nondeuterated metalloporphyrins
[M(TPP)Cl] (M = Fe, Mn, Cr) and [Mn(TPP)] (H2TPP =
tetraphenylporphyrin).11 With the nature of how ligands affect
ZFS relatively unknown, the current study focuses on iron(III)
porphyrin halides, which are common inorganic ligands, with a
2-fold interest: (a) The first is determination of ZFS parameters
for [Fe(TPP)X] (X = F, Br, and I) by INS. Thus, along with
[Fe(TPP)Cl], a compound we recently studied,11 this is a rare
complete series of biomimetic halide compounds with the ZFS
values determined.12 (b) The second is ab initio study of the
electronic structure and magnetic anisotropy of the metal-
loporphyrins to explore the origin of the large and positive
ZFS is of fundamental importance to understanding
molecular magnetism. While ZFS parameters have been actively
studied, there is still a limited understanding on how ZFS
parameters relate to the geometric and electronic structures of
transition metals compounds, including how metal−ligand
bonding affects ZFS.4,5 Knowledge of the effects of metal−
ligand bonding on ZFS also helps design better single
molecular magnets (SMMs) as data storage and quantum
computing materials.8
ZFS, including that of metalloporphyrins, has been
investigated by several techniques, including high-field and
high-frequency electron paramagnetic resonance (HFEPR),
magnetic susceptibility measurement, nuclear magnetic reso-
6
zero-field splitting of the A1 ground state.
There have been many previous studies of the ZFS of Fe(III)
6
compounds with a A1 ground state. Solomon and co-workers
6
have investigated the origin of the A1 ground-state zero-field
splitting in axially distorted high-spin d5 [FeCl4]−.5 Brackett
and co-workers have reported D values of four Fe(III)
deuteroporphyrin IX dimethyl ester halides (Chart 1) that
were determined by far-IR (Table 1).12 Goff and co-workers
have reported correlations of axial ligand field strength and
zero-field splittings in the C-13 NMR spectra of 5- and 6-
coordinate high-spin Fe(III) porphyrin complexes.13 Ohya and
nance (NMR), far-infrared (far-IR), Mossbauer spectroscopy,
̈
magnetic circular dichroism (MCD), and inelastic neutron
scattering (INS).1,6,9,10 INS is one of the few techniques that
directly gives both the magnitude of the D parameter and often
its sign. Because of its spin, neutrons carry a magnetic moment
that makes them an excellent probe for the investigation of
magnetic structures and dynamics. There is a strong interaction
between magnetic field (magnetization density) created by the
unpaired electrons in the sample and magnetic moment of the
neutron. Incident neutrons are scattered from the magnet-
ization density of the atom. The effect of ZFS on a transition
metal ion is to partially or totally remove the (2S + 1)-fold
degeneracy of the ground-state multiplet. In the case of d5
Fe(III) compounds with ZFS in Scheme 1, the magnetization
density that interacts with the spin of neutrons is the spin
dipole moment from the 5 unpaired d electrons, as the orbital
angular momentum of the d electrons in the complexes is
quenched. The resulting energy spectrum exhibits peaks
associated with transitions from MS = 1/2 to 3/2 (2D)
and from MS = 3/2 to 5/2 (4D) in Scheme 1.
Sato conducted a comparative study of Mossbauer spectra of
̈
Chart 1
To our knowledge, few bioinorganic complexes have been
studied by INS. We recently reported the direct determination
B
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Article
three halides [Fe(TPP)X] (X = Cl, Br, I) to probe electronic
effects of substituents and axial ligands.14 In addition, D
parameters of [Fe(TPP)Br] and [Fe(TPP)I] have been
determined by magnetic susceptibility measurements (Table
1).15,16 For [Fe(TPP)Br], D = 13.0(5) cm−1 was reported
initially15a and later revised to 12.5(5) cm−1 based on reanalysis
of the data. For [Fe(TPP)I], the reported D = 13.5(5) cm−1.16
Far-IR studies by Uenoyama gave D = 9.15 cm−1 for
[Fe(TPP)Br] (Table 1).17 To our knowledge, ZFS of
[Fe(TPP)F] has not been studied.
Scheme 2. Synthesis of [Fe(TPP)X] (X = F, Br, I)
Although both [Fe(TPP)Br] and [Fe(TPP)I] molecules
have 4-fold symmetry, their crystals are in the monoclinic
system. Thus, the rhombic parameter E in eq 1 is required to
explain ZFS properties of their crystalline samples. However,
the earlier determination of ZFS parameters by magnetic
susceptibility measurements and far-IR did not determine the E
values.15,17 Several experimental measurements, such as
magnetic susceptibility and HFEPR, that allow for the
determination of the g-factor require the use of a magnetic
field, which prevents direct measurement of zero-field splitting
(ZFS).
sample by the McMaille method also yielded the same tetragonal unit
cell.23
The powder X-ray diffraction of the [Fe(TPP)Br] sample is
consistent with the simulated pattern predicted from the single-crystal
X-ray diffraction data of [Fe(TPP)Br],24 indicating that the solid
sample is in the monoclinic crystal system. It should be noted that
Skelton and White originally reported the structure in P21/c [a =
10.191(2), b = 16.121(5), c = 23.223(4) Å, β = 115.34(1)°].24a This
space group could be converted to P21/n.24b Conversion by the matrix
and software at http://www.cryst.ehu.es/cryst/celltran.html (using a
primitive P cell) yields P21/n, a = 10.191(2), b = 16.121(5), c =
20.990(4) Å, β = 90.69(1)°.
The powder X-ray diffraction of the [Fe(TPP)I] sample is
consistent with the simulated pattern predicted from the single-crystal
X-ray diffraction data of [Fe(TPP)I] [P21/n, a = 10.118(3), b =
16.352(4), c = 21.211(7) Å, β = 89.56(2)°],25 indicating that the
sample is also in the monoclinic crystal system.
Because INS peaks other than the two expected magnetic
transitions were observed for [Fe(TPP)Br] and [Fe(TPP)I] as
discussed below, elemental analyses of the two samples were
performed (Supporting Information), confirming the purity of the
samples. Attempts to obtain mass spectra of [Fe(TPP)X] (X = F, Br,
I) by MALDI/TOF (matrix assisted laser desorption ionization time-
of-flight) led to the observation of [Fe(TPP)+], indicating dissociation
of the Fe−X bonds during the mass spectroscopic process (Supporting
Information).
INS has been used to probe the magnetic properties of metal
complexes, especially excitations among low-lying energy
levels.18 For example, the low-lying energy levels of magnetic
clusters have been characterized by INS.4,18 D for single-
molecule magnets [Mn4O3X(OAc)3(dbm)3] (X = Br−, Cl−,
OAc−, and F−) have been studied by Gudel and co-workers to
̈
see how the D values change with the axial X− ligands.18b The
state-of-the-art facilities at Spallation Neutron Source (SNS) at
Oak Ridge National Laboratory (U.S.) have made it possible to
probe magnetic properties of nondeuterated metal complexes
in detail.18e We have used the cold neutron chopper
spectrometer (CNCS)19 at SNS to determine both the size
and the sign of ZFS parameters D for nondeuterated
metalloporphyrins [Fe(TPP)X] (X = F, Br, and I) as well as
the best fit E values for [Fe(TPP)X] (X = Br, I). In addition, we
have calculated the electronic structure of [Fe(TPP)X] (X = F,
6
Cl, Br, I) with a A1 ground state by multireference ab initio
INS Studies of [Fe(TPP)X] (X = F, Br, I). The INS measurements
were carried out on the CNCS, which is a direct geometry, time-of-
flight spectrometer that receives a beam from a coupled cryogenic H2
moderator.19 For energy selection, the CNCS employs four chopper
assemblies. The speeds and slit widths of the choppers can be varied,
allowing adjustments in the instrumental resolution and intensity of
the incident beam. Approximately 500 mg of each sample was loaded
into a 1/2-in.-thick aluminum tube. The three tubes, containing
[Fe(TPP)X] (X = F, Br, I) each, were placed in a sample holder. The
sample holder was mounted in a standard liquid helium cryostat with a
base temperature of T = 1.6 K. An oscillating radial collimator was
used to reduce background scattering form the tail of the cryostat.
Vanadium was used as a standard for the detector efficiency correction.
The incident neutron energy for every measurement was chosen to
cover the anticipated region of interest in both the energy E and
scattering-vector Q space.26,27 The small incident energy is especially
important to observe excitations near the elastic peak (at energy
transfer close to 0 cm−1), as the full-width-at-half-maximum (fwhm) of
the elastic peak, which is typically 1.5−2% of the incident energy,
would be narrow, giving better energy resolution.
For [Fe(TPP)F], measurements were performed at 1.6, 10, 50, and
100 K with incident neutron beam energies Ei = 24.20, 40.89, and
97.35 cm−1. For [Fe(TPP)Br] and [Fe(TPP)I], measurements were
performed at 1.6, 10, and 50 K with Ei = 24.20, 40.89, and 97.35 cm−1.
It took approximately 24 h to run the three samples at various
temperatures and incident neutron energies. Data were then reduced
and analyzed using the DAVE (Data Analysis and Visualization
Environment) program package.28
methods to explore the origin of their D values. A correlation is
found between the increase of D and the decrease of the π- and
σ-antibonding energies eXλ (λ = σ, π) in the series from X = F to
I. Analysis of this correlation using second-order perturbation
theory expressions in terms of angular overlap parameters
allows one to rationalize the experimentally deduced trends.
EXPERIMENTAL SECTION
■
Synthesis of [Fe(TPP)X] (X = F, Br, I). [Fe(TPP)X] were
prepared by following a literature method20 with modifications. Details
of our syntheses of [Fe(TPP)X] (X = F, Br, I) are given in the
Supporting Information.13,15b,20 The overall synthesis is shown in
Scheme 2.
Air-stable solid products of [Fe(TPP)X] (X = F, Br, I) were
characterized by UV−visible spectroscopy and powder X-ray
diffraction. Powder diffraction patterns were obtained on the
PANalytical Empyrean diffractometer using Cu Kα radiation (λ =
1.5418 Å) with samples of [Fe(TPP)X] (X = F, Br, I) on a zero-
background plate holder. Powder X-ray diffraction of the [Fe(TPP)F]
sample is consistent with the simulated pattern predicted from the
single-crystal X-ray diffraction data of [Fe(TPP)Cl] (Figure S2).21 We
could not use the reported single-crystal X-ray structure of
[Fe(TPP)F], as some key data are not available.22 The reported
crystal structure does, however, indicate that the solid sample is in the
tetragonal crystal system,22 as the crystal structure of [Fe(TPP)Cl].21
Indexing of our powder X-ray diffraction data from the [Fe(TPP)F]
C
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Table 2. Experimental (X-ray Diffraction, X = F, Cl, Br, I; Neutron Diffraction, X = Cl) versus DFT Structural Parameters of the
[Fe(TPP)X] (X = F, Cl, Br, I) Complex Series
F
Cl
X-ray21/neutron
Br
I
X
X-ray
DFT
DFT
X-ray24a
DFT
X-ray25
DFT
Fe−X (Å)
Fe−N (Å)
1.815
2.063
2.194/2.200
2.052/2.067
2.210
2.061
2.348
2.069
2.360
2.057
2.554
2.061
2.566
2.054
2.074
2.076
2.057
2.055
2.078
2.074
∠XFeN (deg)
102.78
100.99/101.96
102.89
104.10
103.89
103.67
103.04
102.37
102.94
103.38
103.26
101.83
101.86
For [Fe(TPP)Br] and [Fe(TPP)I], a pair of D and E values were
used to give a calculated INS spectrum, which was then compared to
the experimental INS spectrum to find the best fit. The D, E values
were determined through the use of the chi-square goodness of fit test
of the experimental and calculated INS peaks.
field spin−orbit coupling operator.41,42 Spin−orbit mixing of non-
relativistic CI eigenfunctions and splitting of the corresponding
eigenvalues are accounted for by Quasi Degenerate Perturbation
Theory (QDPT).42 In these, as well as in the correlated calculations,
triple-ζ valence quality basis sets (def2-TZVP)43,44 were used.
Ground-state ZFS parameters have been computed by diagonalizing
the state interaction SOC matrix nonperturbatively using effective
Hamiltonian theory. CASSCF and NEVPT2 energies for the lowest 17
excited states are listed in Tables S5 and S6.
Metal ligand antibonding energies have been derived using the
angular overlap model (AOM)45,46 of the ligand field with parameters
that have been obtained from a least-squares fit to 5 × 5 ligand field
matrixes resulting from the ab initio ligand field theory (AILFT)
method.47,48 Inter electronic repulsion between the 3d-electrons has
been modeled in terms of two Racah parameters B and C. AOM
calculations were carried out with the AOMX program.49
The line widths of the INS peaks lie within experimental accuracy
determined by the instrumental resolution. The effective resolution
function R(Q,E) of CNCS is nearly Gaussian in energy.19 Therefore,
the INS intensities were fit assuming Gaussian line shapes with fwhm
of the energy resolution for the CNCS spectrometer. The detailed
analyses, using the plots with smaller stepsize points, and calculations
of errors in the D values, are given in the Supporting Information.
Computational Details. Coordination Geometries. Although the
crystal structures of four [Fe(TPP)X] complexes in this study have
been reported (X = F,22 Cl,21 Br,24a and I25), only atomic coordinates
for the structures of X = Cl, Br, and I are available. In addition, the
structure of X = Cl is disordered.25 Therefore, for the sake of our
analysis, we have used DFT geometries for all four complexes.
Calculations for the available experimental structures show no major
differences (Table S7). DFT geometry optimization of all four
[Fe(TPP)X] (X = F, Cl, Br, I) complexes was done with the BP86
functional and def2-TZVP basis sets. van der Waals correction for
nonbonding interactions was included following Grimme.29,30 Because
of the participation of heavy ligands in the coordination sphere of
Fe(III), scalar relativistic corrections were included with the Douglas−
Kroll−Hess method along with appropriate basis sets.31 Structural
parameters from these computations are compared to X-ray data in
Table 2.
Electronic Multiplets and the Zero-Field Splitting Parameters D.
The d5 configuration of FeIII gives rise to one S = 5/2 ground (6
microstates) and to 24 S = 3/2 (96 microstates) and 75 S = 1/2 (150
microstates) electronically excited states. Because the SOC operator
connects only ΔS, ΔL = 0, 1 states, the spin-components of the S =
1/2 states do not couple to the S = 5/2 ground state and have been
neglected. Nonrelativistic energy levels and wave functions have been
computed using the Complete-Active-Space-Self-Consistent Field
(CASSCF) method,32 averaging over the electron densities of all
considered states and taking an active space with 5 electrons
distributed over the 5 3d-MOs [CAS(5,5)]. Dynamical (short-range)
correlation effects were accounted for by using N-electron valence
perturbation theory to second order (NEVPT2).33−37 The effect of
NEVPT2 on the energy levels is to replace the diagonal matrix
elements of the configuration interaction (CI) matrix given by
CASSCF with improved diagonal energies. Such a replacement
provides more accurate (but still approximate) energetics while
keeping the same (zeroth-order) CASSCF wave functions. CASSCF
and NEVPT2 methods have been efficiently implemented in the
program package ORCA38,39 and allow computations on real systems
(without the necessity of model truncations) with unprecedented size
(up to 100−200 atoms, 2000 contracted basis functions). From the
resulting energies of many-electron states, spin-Hamiltonian parame-
ters were computed applying a computational protocol described
elsewhere.40 To this end, SOC was taken into account using a mean-
RESULTS AND DISCUSSION
■
INS Studies. Neutron magnetic scattering cross-section
corresponds to the number of neutrons scattered per second,
due to the magnetic interaction described above, into a solid
angle dΩ with energy transfer between ℏω and ℏ(ω + dω),
divided by the flux of the incident neutrons. For unpolarized
neutrons, identical magnetic ions with localized electrons, and
spin-only scattering, the magnetic scattering cross-section is
expressed by eq 2:26,27
2
d2σ
1
2
k ⎡
⎤
= (γr0)2
gF(Q) e−2W(Q)
f
⎢
⎣
⎥
⎦
dΩ dω
ki
⎛
Q α Q ⎞
·
∑ ⎝⎜δαβ
−
β ⎟Sαβ(Q, ω)
Q2
⎠
α,β
(2)
where σ is the neutron cross section; γ is the gyromagnetic
ratio, r0 is the classical radius of an electron, g is the Lande g-
́
factor, F(Q) is the dimensionless magnetic form factor defined
as the Fourier transform of the normalized spin density
associated with magnetic ions; e−2W(Q) is the Debye−Waller
factor caused by thermal motion; Sαβ(Q,ω) is the magnetic
scattering function; (δαβ − (QαQβ)/Q2) is the polarization
factor, which implies neutrons can only couple to magnetic
moments or spin fluctuations perpendicular to Q; Q is the
scattering vector of the momentum transfer (Scheme 3)For
powder samples, only the length Q is measured; ℏω is the
energy change experienced by the sample; and ω is the angular
frequency of neutron.
In eq 2, the magnetic form factor F(Q) reveals the
distribution of spin and orbital magnetization from unpaired
electrons. It falls off with increased Q. Therefore, peaks of
magnetic origin decrease in intensity with increased Q. In
D
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a
the temperature increase. The excitation from the first excited,
Ms = 3/2 states to the second excited, Ms = 5/2 states
produced the second, 4D peak. This peak is observed at 18.05
cm−1, which is approximately twice the energy (8.99 cm−1) of
the 2D peak. The intensity of the 4D peak increases with
temperature, indicating its magnetic origin. Analyses of the
temperature dependence of experimental and calculated
intensities are given in Figures S6−S8.
INS may also give the sign of D for these S = 5/2 systems.
Because the 2D peak was observed at a low temperature before
the 4D peak, the axial D parameters of these complexes (X = F,
Br, I) are positive. If D < 0, the ground state would be Ms =
5/2 and the first peak observed at 1.6 K would be 4D
(Scheme 1c).
In addition, peaks with negative energy transfers were also
observed in INS. When the temperature was raised to 10 K, a
peak at −8.99 cm−1 appeared, indicating that the incident
neutrons gained energy from the sample in the INS process. In
other words, molecules at the 3/2 states in Scheme 1 returned
to the ground 1/2 states, transferring the energy to the
neutrons. Thus, the ZFS parameters are D = 4.49(9) cm−1 and
E = 0 cm−1. The error analysis is given in the Supporting
Information.
[Fe(TPP)Br]. The E parameter in the monoclinic crystals of
[Fe(TPP)Br] leads to a change of the energy levels in Scheme
1d. The transitions from MS = 1/2 to 3/2 and from MS =
3/2 to 5/2 (E ≪ D) are no longer 2D and 4D,
respectively.4a There is now an E component inside these
transitions that is not independent of D. Experimentally, the
energy of the 4D peak is very close to twice the energy of the
2D peak, demonstrating that this compound is close to the axial
symmetry with a small E value. (See Figure 4 to view how E
affects the energy levels of S = 5/2 compounds.) The INS
spectra of [Fe(TPP)Br] are given Figure 2. The first and
second magnetic peaks are located at 17.5 and 35.04 cm−1,
respectively. Thus, the ZSF parameters are D = 8.8(2) and E =
0.1(2) cm−1. A comparison of the temperature dependence of
experimental and calculated intensities, given in Figures S11−
S13, confirms the magnetic nature of the peaks. Other peaks
(∼11.5 and 26 cm−1) in the spectra have different line widths.
In comparison to the magnetic peaks, they are broader and not
well shaped. The differences suggest that the peaks are not due
to transitions from well-determined energy levels but rather
from phonon density of states. This argument is confirmed by
comparing how the intensities of the peaks change with
different Q ranges with low to high Q values. The peaks at 11.5
Scheme 3. Schematic of the INS Process
a
Q = ki − kf is the scattering vector of the momentum transfer, where
ki and kf refer to the wavevectors of the incoming and outgoing
neutrons, respectively.
contrast, peaks of vibrational origin increase with increased Q.
However, strong incoherent scattering from samples containing
hydrogen atoms may smear out Q dependence of the magnetic
peaks, and instrumentation constraints might limit the
accessible Q range, leading to roughly constant intensities of
the magnetic peaks throughout the observable Q range in the
samples.18b,g
Peak position in INS spectra gives a direct measurement of
the eigenvalues of the spin Hamiltonian. When there is no
external magnetic field and the compound is in the tetragonal
environment, the spin Hamiltonian is defined by a single
anisotropy parameter D and depends on the spin projection
along z. The E parameter provides a distortion that removes the
axial symmetry, and introduces anisotropy in the xy plane. For
[Fe(TPP)X], two magnetic INS peaks are observed, as
discussed below. The D and E parameters were then
determined from the spin Hamiltonian in eq 1 using INS
data, as described in the Experimental Section.
Simulated INS spectra were obtained by calculating the
energies and corresponding wave functions via exact diagonal-
ization of the spin Hamiltonian expressed in eq 1. These
calculations can be used to get the INS intensity, which is
proportional to the scattering function Sαβ(Q,ω). The
experimental and simulated INS spectra are given for
comparison.
[Fe(TPP)F]. In [Fe(TPP)F], the Fe(III) ion has a high spin
(S = 5/2) configuration, and its electronic ground state is split
into three Kramers doublets: Ms = 1/2, 3/2, and 5/2
(Scheme 1). The spacings among the three doublets are 2D
and 4D, respectively. In the INS spectra of [Fe(TPP)F], a peak
at 8.99 cm−1 was observed (Figure 1) at 1.6, 10, 50, and 100 K.
This peak corresponds to the first excitation from the Ms =
1/2 to the Ms = 3/2 states. Magnetic intensities are based
on Boltzmann statistics. Therefore, as the temperature is
increased, the 2D peak decreases in intensity, as shown in
Figure 1. In addition, the first excited states are populated with
Figure 1. (Left) INS spectra of [Fe(TPP)F] with incident neutron energy Ei = 24.20 cm−1, Q = 0.5−1.3 Å−1, and a step size of 0.024 cm−1. (Right)
Theoretical INS spectra of an S = 5/2 spin system with D = 4.49 cm−1.
E
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Figure 2. (Left) INS spectra of [Fe(TPP)Br] with Ei = 40.89 cm−1, Q = 0.48−1.8 Å−1, and a step size of 0.016 cm−1. (Right) Theoretical INS spectra
of an S = 5/2 spin system with D = 8.8 cm−1 and E = 0.1 cm−1.
Figure 3. (a) INS spectra of [Fe(TPP)I] with Ei = 40.89 cm−1, Q = 0.5−1.0 Å−1, and a step size of 0.024 cm−1. (b) INS spectra with Ei = 97.35 cm−1,
Q = 0.48−1.8 Å−1, and a step size of 0.024 cm−1. (c) Theoretical INS spectra of an S = 5/2 spin system with D = 13.4 cm−1 and E = 0.3 cm−1.
and 26 cm−1 were identified as phonons as they have the
greatest intensities at high Q as shown in Figure S14. It should
be noted that, in addition to a magnetic peak at 18.3 cm−1
(Table 1), Uenoyama also observed the 11.5 cm−1 peak, which
was not identified in the far-IR spectrum of [Fe(TPP)Br].17
[Fe(TPP)I]. Two incident energies had to be used to observe
two magnetic transitions in the INS spectra. An incident
neutron energy of Ei = 40.89 cm−1 only displayed the first
magnetic peak at 26.8 cm−1 (Figure 3a). At a higher incident
energy Ei = 97.35 cm−1, the second magnetic peak at 53.3 cm−1
appeared (Figure 3b). Analysis of the INS spectra for
[Fe(TPP)I] and the determination of ZFS parameters were
analogous to those for [Fe(TPP)Br]. The temperature
dependence of experimental and calculated intensities is
shown in Figure S17. The second magnetic peak is broad
and almost overlaps with a phonon peak, meaning this
magnetic peak is not as resolved as the first due to the
proximity of a phonon peak. Therefore, there is a larger error
associated with the use of this peak to calculate the D and E
parameters. Equation 1 gave the ZFS parameters D = 13.4(6)
cm−1 and E = 0.3(6) cm−1. As [Fe(TPP)Br], the spectra for
[Fe(TPP)I] also have additional peaks with broad line widths,
which were determined to be from phonon density states. The
presence of phonon peaks is confirmed by examining the Q
dependence of the peaks in Figures S18,S19. As expected, the
phonon peaks are more pronounced at high Q, while the
magnetic peaks stay constant or decrease in intensity.
peak positions. When the E parameter is small, there is little
mixing of the energy levels until E > 2 cm−1 as observed in
Figure 4. For example, in [Fe(TPP)I] with D = 13.4 cm−1,
changing from E = 0 to 0.3 cm−1 leads to a 0.58% increase and
0.11% decrease in the positions of the 2D and 4D peaks,
respectively.
The D values for [Fe(TPP)X] (X = F, Cl,11 Br, I) from the
INS studies are listed in Table 1. D values of [Fe(TPP)X],
determined by other methods, and Fe(III) protoporphyrin/
Figure 4. Effect of the E parameter on the energy levels of an S = 5/2
system with ZFS parameters of D = 13.4 and E = 0.3 cm−1 (in
[Fe(TPP)I]).
Both [Fe(TPP)Br] and [Fe(TPP)I] have a small E value.
This in turn translates into small variations of the 2D and 4D
F
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Figure 5. Structural view of the series of complexes as revealed by X-ray and neutron diffraction studies and DFT geometry optimizations.
deuteroporphyrin IX dimethyl ester halides are also summar-
ized there. Several methods gave D = 3.2−11.9 cm−1 for
[Fe(TPP)Cl] and 4.9−12.5(5) cm−1 for [Fe(TPP)Br]. Our
INS studies11 gave accurate values for the complexes. It is also
interesting to note that the D values for [Fe(TPP)X] are similar
to those of the corresponding Fe(III) protoporphyrin IX
dimethyl ester halides (Table 1).
Calculated Coordination Geometries. The geometries of
the first-coordination spheres of the four [Fe(TPP)X]
complexes are square pyramidal (Figure 5) with four equatorial
Fe−N and one axial Fe−X bond. Structural parameters from X-
ray data are well reproduced by the DFT geometry
optimization (Table 2). The set of Cartesian coordinates for
each DFT optimized structure is listed in the Supporting
Information.
Multiplet Energies and the Zero-Field Splitting (D).
From CASSCF and NEVPT2 calculations for [Fe(TPP)X] at
DFT-optimized geometries, we can conclude that all four
complexes are in a 6A1 ground state. Quartet (S = 3/2) excited
4
4
4
4
states originate from the G, D, F, and P states of the free
Fe(III) ion split by the C4v ligand field in the complex. Energies
of CASSCF and NEVPT2 of these terms in the energy range
below 50 000 cm−1 are included in Tables S5 and S6. From all
Figure 6. Term energies from CASSCF and NEVPT2 calculations
governing the sign and magnitude of the A1 ground state D value of
the series of [Fe(TPP)X] (X = F, Cl, Br, I) complexes; color code: red,
CASSCF; blue, NEVPT2.
6
4
4
of these, the states with the T1 cubic parentage split into E
4
6
4
and A2 terms. Their mixing with the A1 ground state via
spin−orbit coupling leads to splitting of its Ms = 5/2, 3/2,
and 1/2 sublevels, thus governing the sign and magnitude of
From eq 3, it is evident that when the energy of the E
excited state is greater than that of the 4A2 excited state (Figure
4
6) from the lowest cubic T1 term, a positive D value results,
4
while if the energy of the excited states is reversed (4E < 4A2), a
the zero-field splitting terms. From the three T1 cubic terms,
4
negative D value results. Because of the larger T1−6A1 energy
only two yield essential contributions to D. Their energies and
calculated D values are depicted in Figure 6. Second-order
perturbation theory yields the following 6A1 ground-state
expression for D:
4
separation for the second excited T1 state, the positive term
dominates and determines the positive sign of D for the entire
complex. Qualitative predictions of the positive sign of D for
such coordination geometries of Fe(III) using angular overlap
model consideration have been published.50
In Figure 6 and Table 3, we compare calculated and
experimental values of D. While the experimental trend D(F) <
D(Cl) < D(Br) < D(I) is well reproduced, computed CASSCF
values of D are about 1 order of magnitude (8−10) smaller
than the experimental values. This can be attributed to the ionic
2
⎡
⎢
⎣
⎤
⎥
⎦
ςeff
1
1
D(4T1) =
−
Δ(4A )
Δ(4E)
5
(3)
2
where ςeff is the effective SOC constant and Δ(4A2) and Δ(4E)
are the energies of the E and A2 C4v sublevels of each T1
4
4
4
term.
G
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Table 3. Metal−Ligand Bonding and Electron Repulsion Parameters for the [Fe(TPP)X] (X = F, Cl, Br, I, DFT Optimized
Structures) Series (in cm−1) from Ab Initio Ligand Field Analysis and a Best Fit of the Angular Overlap Model to the CASSCF/
NEVPT2 (CAS(5,5) Active Space) Quartet Excited-State Energies
X
F
Cl
Br
I
b
ligand field parameters
CASSCF
6260
NEVPT2 (C%)
CASSCF
4200
NEVPT2
CASSCF
3358
NEVPT2
CASSCF
2798
NEVPT2
a
eσX
7355
(15)
2625
(11)
6058
(7)
5348
(21)
1287
(8)
4501
(25)
873
4055
(31)
474
a
eπX
2340
5650
1177
5784
843
523
(3)
(−10)
6467
(8)
a
eσN
6266
(8)
5862
6372
(8)
5930
B
1145
0.88
4297
0.89
436
1032
0.83
4698
1.05
436
1127
0.87
4231
0.87
429
1023
0.82
4735
1.05
429
1122
0.86
4219
0.87
415
1022
0.82
4761
1.06
415
1114
0.85
1018
0.82
4800
1.07
392
c
(B/B0)
C
4197
0.87
c
(C/C0)
ζ
392
c
(ζ/ζo)
0.92
0.45
0.92
1.54
0.91
0.59
0.91
1.98
0.88
0.96
8.8(2)
0.88
2.60
0.83
0.83
3.45
D (calc)
1.48
D (exp, INS)
4.49(9)
6.33(8)
13.4(6)
a
b
Parameterization was done under the following simplifying assumptions: eNπs = eπNc = 0. Percentage covalence C%, defined as {[eλ(NEVPT2) −
c
eλ(CASSCF)]/eλ(NEVPT2)} × 100 (λ = σ, π), is listed in brackets. (See ref 47, p 187 for details.) Nephelauxetic ratios of the Racah parameters B,
C and the spin−orbit coupling parameter ζ in the complex with respect to the computed values B0, C0, and ζo for the free Fe(III) ion: 1301, 4844,
472 (CASSCF) and 1240, 4490, 472 cm−1 (NEVPT2), respectively.
nature of the CASSCF wave functions where metal−ligand
covalence is largely underestimated. In agreement with this
result, dynamical correlation accounted for by NEVPT2
improves the quantitative agreement with the experimental
data; now D(NEVPT2) values differ by a factor of 3−4 as
compared to the experimental ones. This will be thoroughly
discussed in a separate section below. The changes from the
CASSCF to NEVPT2 results are reflected by the drop down in
4
4
energy of the A2 and E lowest excited states by as much as
10 000 cm−1 and by about one-half this amount for the second
excited state of the same C4v symmetry. The trends in D across
the series are nicely reflected by the concerted lowering of the
transitions energies from F to I in the series. The contributions
to D from the two 4T1 states (Tables S5 and S6 in comparison
with eq 3) show that the improvement of the D parameters
upon NEVPT2 corrections is largely dominated by the lowest
Figure 7. Calibration between experimental and CASSCF/NEVPT2
calculated values of the zero-field splitting parameter D for the
[Fe(TPP)X] series; D (exp, INS) = 8.326D(CASSCF) + 0.997,
standard deviation = 0.18 cm−1; D (exp, INS) = 4.625D(NEVPT2) −
2.8255, standard deviation = 0.18 cm−1.
4
4T1 term and the lowering of the excitation energy to A2 (by
about 10 250 cm−1), which exceeds the energy lowering of the
higher, excited 4E state (by about 7800 cm−1). This is a
differential correlation effect, which increases with Fe−X
covalence increasing in the series F, Cl, Br, and I.
A calibration of the CASSCF and NEVPT2 values of D
allows one to predict the experimental D starting from the
computed ones. The latter are compared to the experimental D
values in Figure 7. A least-squares fit between the experimental
and the theoretical D values leads to the following expressions:
of square-pyramidal FeN4X with ligands at the x,y and z axes
are given by
e(b1, dx2−y2) = 3eσN
e(a1, dz2) = eσX + eσN − 4esNd − esXd + 4(esXdesNd)1/2
e(e, dxz,yz) = eπX + 2eπN⊥
D(exp , INS) = 8.326D(CASSCF) + 0.997 (cm−1)
(4)
D(exp , INS) = 4.625D(NEVPT2) − 2.8255 (cm−1)
(5)
e(b2, dxy) = 4eπN||
(6)
with a standard deviation of 0.18 cm−1 between the two data
sets.
Two sets of parameters eNσ , eσX and eπN, eXπ are introduced to
account for σ and π-antibonding, with eNπ∥ and eπN⊥ describing
iron−nitrogen in- and out-of-plane π-interactions, respectively.
The parameters eNsd and esXd account for the stabilization of the
dz2 orbital due to partial hybridization with the 4s one. The
mixing of these two orbitals is induced by the 4-fold symmetry
where both orbitals are of the a1 type. Because the N atoms of
Metal−Ligand Bonding from Angular Overlap Ligand
Field Analysis of the CASSCF and NEVPT2 Many-
Electron States and the Correlation with D. Bonding in
[Fe(TPP)X] is governed by two types of donors: the equatorial
nitrogen of the TPP and axial X ligands. Angular overlap
expressions for the energies of 3d-type MOs in the simple case
H
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Figure 8. Magneto-structural correlation between the experimental D values and the Fe−X π (left) and σ (right) antibonding energies as given by a
best fit of the angular overlap plus repulsion ligand field model to NEVPT2 eigenvalues.
the porphyrin ligand do not possess electrons for in-plane π-
bonding, eNπ∥ can be safely set to zero. Even so, one is left with
six parameters from which only three are independent in the
given point group. To achieve further realistic approximation to
reduce the number of parameters, we considered a Fe(TPP)+
complex without the X atom. For such a complex (D4h
symmetry), eq 6 is simplified to
e(b1, dx2−y2) = 3eσN
e(a1, dz2) = eσN − 4esNd
e(e, dxz,yz) = 2eπN⊥
e(b2, dxy) = 0
(7)
Figure 9. Ligand field 3d-MO energies from ab initio (NEVPT2)
calculations of the [Fe(TPP)X] series.
A best fit of eNσ , eπN⊥, and esNd and B to energy eigenvalues from
CASSCF calculations of a Fe(TPP)+ model complex resulted,
respectively, in values of 5725, 99, 1289, and 990 cm−1. These
Δ(4E) > Δ(4A2) and, according to eq 3, a positive contribution
results show that while keeping to an approximate CASSCF
wave function, eNπ⊥ can be safely neglected. We thus arrive at a
model with three parameters eNσ , eXσ, and eXπ, where esNd and eXsd
have been neglected. Parameters eNσ , eσX, eπX, B and C have been
obtained from a best fit to energies from CASSCF and
to D. Transitions to the upper 4T1 state are of the t2 → e type.
6
Therefore, when exciting from A1, they are adding energy to
the 10B + 6C term. According to Figure 9 (middle, right), a
Δ(4E) < Δ(4A2) term sequence for the upper 4T1 state leads to
a negative contribution to D. Coming from a lower lying
transition, positive contributions to D clearly dominate and
determine the overall sign of D. With eXσ and eπX decreasing
6
NEVPT2 calculations for transitions from the A1 ground into
the S = 3/2 excited states (Table 3). In this procedure, the
detailed angular geometry as given by the DFT structure
optimizations was taken into account. While the energy of the
Fe−N antibonding eNσ is almost constant between the various
members, eXσ and eXπ decrease across the series from F to I and
thus correlate with the increase of D in the same direction
(Figure 8). The bonding parameters from Table 3 have been
used to deduce the ligand field splitting pattern of the 3d-MOs
(Figure 9), which we in turn employ to rationalize D versus eπX
and eXσ correlation. According to eq 3, the value of D is
4
across the series X = F to I, both A2, the lowest excited state,
4
and E, the second excited state, become lower in energy.
However (Table S5), the changes of the energy of 4A2
4
dominate over those of E and are mainly responsible for the
observed increase in D. As shown in a comparison between the
CASSCF and NEVPT2 results in Tables S5 and S6, the effect is
enhanced when taking dynamical correlation into account.
Magnetic Anisotropy (D) and Metal−Ligand Cova-
lence in the [Fe(TPP)X] Series. Changes in covalence in 3d
complexes affect D: (1) decrease in the spin−orbit coupling
(SOC, quantified by ζ) reduces D, eq 3; and (2) reduction the
interelectronic repulsion (quantified by the Racah parameters B
and C) with respect to the free ions (nonrelativistic and
relativistic nephelauxetic effects, respectively) increases D. Ab
initio ligand field analyses clearly manifest a decrease of B and ζ
across the series (Table 3, CASSCF/NEVPT2 results),
reflecting the expected increase of metal−ligand covalence
from F to I, as shown in Figure S20. It is worth considering
these two effects on D separately.
4
4
dominated by contributions from E and A2 terms for the
lower and the upper 4T1 states. All four transitions are governed
by an increase of interelectronic repulsion when going from the
6A1 ground state (five unpaired electrons on each 3d MO) into
excited states with electronic configurations, where one orbital
becomes doubly occupied (an energy that equals roughly 10B +
4
6
6C for both T1 states). Excitations from the A1 ground state
into the lower 4E and 4A2 pair correspond to e → t2 transitions
with a gain of ligand field energy (ligand field de-excitation). As
illustrated in Figure 9 (middle left), this gain is larger for the
4
4A2 state than for the E state, leading to an energy ordering
I
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Effect of Spin−Orbit Coupling (SOC) on D. Desrochers
and co-workers studied ZFS in 4-coordinate C3v Ni(II)
complexes Tp*NiX [Tp*− = hydrotris(3,5-dimethylpyrazole)-
borate; X = Cl, Br, I] by HFEPR, reporting D = +3.93(2),
−11.43(3), −22.81(1) cm−1, for X = Cl, Br, I, respectively, for
the d8 S = 1 complexes.51 Studies by the Angular Overlap
Model (AOM)51 and wave function-based ab initio methods52
show that the final signs and magnitudes of D parameters here
are mostly determined by the metal−ligand covalency and low
symmetry in the scorpionate complexes. These 4-coordinate, d8
Ni(II) complexes are more covalent than the 5-coordinate,
high-spin d5 [Fe(TPP)X] in the current work. Theoretical
studies of [NiX4]2− (X = F, Cl, Br, I) also showed the
increasing contribution of intraligand spin−orbit coupling to
ZFS from F, Cl, Br to I in [NiX4]2−, leading to a sign reversal,
between Br and I, of the spin−orbit splitting within the t2-
orbitals of Ni2+ ions.53 Being relatively more ionic, the effect of
the intrinsic spin−orbit couplings of the heavier ligands on D in
the [Fe(TPP)X] series is not as strong as that in the Tp*NiX
or [NiX4]2− complexes. In other words, the {FeIII−X−}7 →
{FeII−X•}7 charge transfer is much higher in energy than
{NiII−X−}10 → {NiI−X•}10 so that the large SOC of I− cannot
affect D considerably. Although the N atoms (on the porphyrin
ligand) and halides X in [Fe(TPP)X] are involved in strong σ
bonding with Fe(III) (as quantified by the parameters eNσ and eσX
Figure 10. Variation of D with B for [Fe(TPP)Cl] taken as a model
example. The figure has been constructed using the AOMX program
package with model parameters set (NEVPT2) from Table 3. A C/B
ratio of 4.63 has been adapted using the same data.
6
4
6
4
electronic transitions A1 → A2 (4T1) and A1 → E (4T1)
from their ab initio values [NEVPT2: 11 135 and 20 006 (F) to
8960 and 16 089 cm−1 (I), Table S6] to the near-IR and IR
regions [explicitly: 4738/8878 (F), 3685/9035 (Cl), 2738/
7652 (Br), and 1719/6135 (I)]. Thus, these transitions are
falling in energy below the Soret (∼24 000 cm−1) and Q-bands
(16 000−20 000 cm−1)54 π−π* absorption region. This opens
an interesting perspective for their spectroscopic character-
ization.
6
in eq 6), there is no first-order spin−orbit coupling in the A1
ground state. Thus, the impact of all of these factors on the ZFS
of the [Fe(TPP)X] series is not as large as in the Ni(II)
complexes.
CONCLUDING REMARKS
Effect of the Nephelauxetic Reduction of B and C on
D. D values of axial FeIII complexes are generally under-
estimated by both CASSCF and NEVPT2 methods.
Correlation effects in the S = 5/2 ground state and S = 3/2
excited state are quite different. Dynamical correlation in the
latter states is much more pronounced and is largely
underestimated at both the CASSCF and the NEVPT2 level
of theories. This differential correlation effect results in
interelectronic repulsion parameters B and C distinctly larger
than those deduced from experiment. This leads to (a) a larger
gap between the 6A1 ground state and the 4A2/4E excited states;
and (b) small values of D according to eq 3. To quantify the
effect, we have adapted the angular overlap model with
parameters from Table 3 and studied the dependence of D on
B, while keeping the ratio C/B unchanged. A model calculation
for [Fe(TPP)Cl] as an example shows a dramatic increase of D
when lowering B (Figure 10). Such (nephelauxetic) reduction
of B is a measure of metal−ligand covalence. The rather large
values of B deduced from the multireference ab initio
calculations (1000−1100 cm−1) reflect the rather ionic
CASSCF wave functions. Because of this ionicity, the
nephelauxetic reduction of B is largely underestimated at the
ab initio level. The effect can be quantified by getting B that
reproduces D from the INS work. Adapting again the angular
overlap model with the same values of the parameters for the
complexes (Table 3, NEVPT2 set), we obtain B = 579 (F), 557
(Cl), 540 (Br), and 518 (I) cm−1. In other words, they are
twice as small as their ab initio counterparts (both CASSCF
and NEVPT2, Table 3). Taking this result with precaution (due
to the model character of the given considerations), we can
conclude that the reduction of B is largely governed by the TPP
ligand and further modified by the covalence of the Fe−X bond
increasing from F to I. Finally, the large reduction of the
parameters B deduced from the INS data implies a shift of the
■
Zero-field splittings in [Fe(TPP)X] (X = F, Br, I) have been
studied by inelastic neutron scattering, providing a rare,
complete determination of ZFS parameters in a metal-
loporphyrin halide series. Ligand field analysis of the ab initio
data shows that the relatively large D values for these complexes
are due to delocalization of the σ d-electrons on the TPP
ligand, which lowers the parameter B and reduces the energy
6
4
gap between the ground A1 ground and the A2 excited state.
The trend of the increase in D, from X = F, Cl, Br, to I, is
further correlated with the increase in the covalency of the Fe−
X bond in the same order. Ab initio multireference electronic
structure calculations and their ligand field analysis allow one to
relate the increase in the D values with the lowering of the
6
4
energy gap between the A1 ground state and the T1 lowest
excited state. This lowering is attributed to the weakening of
both the σ and the π antibonding interactions between the
Fe(III) ion and the axial halide ligand. Quantitative magneto-
structural correlations were derived between D and the angular
overlap model parameters eσ and eπ, characterizing the bonds of
iron(III) ion to the axial ligands.
Single ion magnets (SIMs) are of intense current interest.
There is a significant debate regarding the strategy for the
design and synthesis of SIMs. To rationally design SIMs, key
factors dictating the sign and magnitude of D values in metal
complexes need to be identified. The current work not only
reports ZFS parameters by inelastic neutron scattering for the
5-coordinate halide complexes, but also identifies key factors
that determine the sign and magnitude of D values in these FeIII
single ion complexes.
An important point we learn from the current study is that,
for square pyramidal 5-coordinate high-spin d5 complexes, D
may become negative if the equatorial ligand donors are weaker
than the axial one.
J
DOI: 10.1021/acs.inorgchem.5b01505
Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
(7) Because the electronic excited states are much higher in energy
than the ground state, fourth-rank terms given by fourth-order
perturbation theory are neglected here.
(8) Gatteschi, D.; Sessoli, R. Angew. Chem., Int. Ed. 2003, 42, 268.
(9) Nehrkorn, J.; Telser, J.; Holldack, K.; Stoll, S.; Schnegg, A. J. Phys.
Chem. B 2015, article ASAP; http://pubs.acs.org/doi/pdfplus/10.
1021/acs.jpcb.5b04156.
(10) (a) Applications of Physical Methods to Inorganic and Bioinorganic
Chemistry; Scott, R. A., Lukehart, C. M., Eds.; Wiley: New York, 2007;
including Larese, J. Z., pp 291−313. (b) Gatteschi, D. J. Phys. Chem. B
2000, 104, 9780. (c) Krzystek, J.; Ozarowski, A.; Telser, J. Coord.
Chem. Rev. 2006, 250, 2308.
(11) Hunter, S. C.; Podlesnyak, A. A.; Xue, Z.-L. Inorg. Chem. 2014,
53, 1955.
(12) Brackett, G. C.; Richards, P. L.; Caughey, W. S. J. Chem. Phys.
1971, 54, 4383.
(13) Goff, H. M.; Shimomura, E. T.; Phillippi, M. A. Inorg. Chem.
1983, 22, 66.
ASSOCIATED CONTENT
* Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.inorg-
chem.5b01505.
■
S
UV−visible spectra of [Fe(TPP)X] (X = F, Br, I), XRD
analyses of the samples, elemental analyses of [Fe(TPP)-
X] (X = Br, I), error analyses of the INS spectra,
experimental and calculated intensities of INS peaks, Q
dependence plots, tables of quartet excited-state energies
(in cm−1) from CASSCF and NEVPT2/CASSCF
calculations with an active space of five d-electrons
distributed of the five 3d MOs [CAS(5,5)] for
[Fe(TPP)X], and Cartesian coordinates resulting from
DFT geometry optimizations of the [Fe(TPP)X] series
(PDF)
(14) Ohya, T.; Sato, M. J. Chem. Soc., Dalton Trans. 1996, 1519.
(15) (a) Behere, D. V.; Date, S. K.; Mitra, S. Chem. Phys. Lett. 1979,
68, 544. (b) Maricondi, C.; Swift, W.; Straub, D. K. J. Am. Chem. Soc.
1969, 91, 5205.
(16) Behere, D. V.; Birdy, R.; Mitra, S. Inorg. Chem. 1981, 20, 2786.
(17) Uenoyama, H. Biochim. Biophys. Acta, Gen. Subj. 1971, 230, 479.
(18) (a) Furrer, A. Int. J. Mod. Phys. B 2010, 24, 3653. (b) Andres,
AUTHOR INFORMATION
Corresponding Authors
*E-mail: mihail.atanasov@cec.mpg.de.
*E-mail: podlesnyakaa@ornl.gov.
*E-mail: frank.neese@cec.mpg.de.
*E-mail: xue@utk.edu.
■
H.; Basler, R.; Gudel, H.-U.; Aromi, G.; Christou, G.; Buttner, H.;
̈
̈
Ruffle, B. J. Am. Chem. Soc. 2000, 122, 12469. (c) Basler, R.; Sieber, A.;
Notes
Chaboussant, G.; Gudel, H. U.; Chakov, N. E.; Soler, M.; Christou, G.;
̈
Desmedt, A.; Lechner, R. Inorg. Chem. 2005, 44, 649. (d) Kittilstved,
K. R.; Sorgho, L. A.; Amstutz, N.; Tregenna-Piggott, P. L. W.; Hauser,
A. Inorg. Chem. 2009, 48, 7750. (e) Wang, C. H.; Lumsden, M. D.;
Fishman, R. S.; Ehlers, G.; Hong, T.; Tian, W.; Cao, H.; Podlesnyak,
A.; Dunmars, C.; Schlueter, J. A.; Manson, J. L.; Christianson, A. D.
Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 064439/1.
(f) Carver, G.; Tregenna-Piggott, P. L. W.; Barra, A.-L.; Neels, A.;
Stride, J. A. Inorg. Chem. 2003, 42, 5771. (g) Dreiser, J.; Waldmann,
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
The work is supported by the U.S. National Science
Foundation (CHE-1362548 to Z.-L.X.). Acknowledgment is
also made to the Donors of the American Chemical Society
Petroleum Research Fund for partial support of this research.
Research at Oak Ridge National Laboratory’s Spallation
Neutron Source was supported by the Scientific User Facilities
Division, Office of Basic Energy Sciences, U.S. Department of
Energy. We acknowledge the technical and scientific support
from the staff at the SNS. We thank Dr. Jurek Krzystek
(National High Magnetic Field Laboratory, Florida State
University) and Prof. Joshua Telser (Roosevelt University)
for helpful discussions and for communicating HFEPR results
on the Fe(TPP)X complexes.
O.; Dobe, C.; Carver, G.; Ochsenbein, S. T.; Sieber, A.; Gudel, H. U.;
̈
van Duijn, J.; Taylor, J.; Podlesnyak, A. Phys. Rev. B: Condens. Matter
Mater. Phys. 2010, 81, 024408.
(19) Ehlers, G.; Podlesnyak, A.; Niedziela, J. L.; Iverson, E. B.; Sokol,
P. E. Rev. Sci. Instrum. 2011, 82, 085108.
(20) Alder, A. D.; Longo, F. R.; Kampas, F.; Kim, J. J. Inorg. Nucl.
Chem. 1970, 32, 2443.
(21) Hunter, S. C.; Smith, B. A.; Hoffmann, C. M.; Wang, X.; Chen,
Y.-S.; McIntyre, G. J.; Xue, Z.-L. Inorg. Chem. 2014, 53, 11552.
(22) Anzai, K.; Hatano, K.; Lee, Y. J.; Scheidt, W. R. Inorg. Chem.
1981, 20, 2337. The cif file from http://www.ccdc.cam.ac.uk on Jan.
24, 2015 does not contain atom coordinates.10.1021/ic50221a079
(23) Le Bail, A. Powder Diffr. 2004, 19, 249.
(24) (a) Skelton, B. W.; White, A. H. Aust. J. Chem. 1977, 30, 2655.
(b) For the conversion of the space group from the reported P21/c to
P21/n, see: Feast, G. C.; Haestier, J.; Page, L. W.; Robertson, J.;
Thompson, A. L.; Watkin, D. J. Acta Crystallogr., Sect. C: Cryst. Struct.
Commun. 2009, 65, o635 and the matrix and software at http://www.
cryst.ehu.es/cryst/celltran.html.10.1107/S0108270109046952
(25) Hatano, K.; Scheidt, W. R. Inorg. Chem. 1979, 18, 877.
REFERENCES
■
(1) The Porphyrin Handbook; Kadish, K. M., Smith, K. M., Guilard,
R., Eds.; Academic Press: San Diego, CA, 2000−2003.
(2) For geochemistry of porphyrins, see, for example: Callot, H. J.;
Ocampo, R. The Porphyrin Handbook; Academic Press: San Diego, CA,
2000; Vol. 1, Chapter 7, pp 349−398.
(3) (a) Hoffman, B. M. Proc. Natl. Acad. Sci. U. S. A. 2003, 100, 3575.
(b) Yang, F.; Shokhireva, T. K.; Walker, F. A. Inorg. Chem. 2011, 50,
1176. (c) Scheidt, W. R.; Barabanschikov, A.; Pavlik, J. W.; Silvernail,
N. J.; Sage, J. T. Inorg. Chem. 2010, 49, 6240. (d) de Visser, S. P.;
Valentine, J. S. V.; Humphreys, K. J. Pure Appl. Chem. 1998, 70, 855.
(e) Zhang, P.; Wang, M.; Li, X.; Qiang, C.; Hong, G.; Dong, J. F.; Sun,
L. C. Sci. China: Chem. 2012, 55, 1274.
(26) Basler, R.; Boskovic, C.; Chaboussant, G.; Gudel, H. U.; Murrie,
̈
M.; Ochsenbein, S. T.; Sieber, A. ChemPhysChem 2003, 4, 910.
(27) Furrer, A.; Mesot, J.; Strassle, T. Neutron Scattering in Condensed
̈
Matter Physics; World Scientific: NJ, 2009; p 17.
(28) Azuah, R. T.; Kneller, L. R.; Qiu, Y.; Tregenna-Piggott, P. L. W.;
Brown, C. M.; Copley, J. R. D.; Dimeo, R. M. J. Res. Natl. Inst. Stand.
Technol. 2009, 114, 341.
(4) (a) Boca, R. Coord. Chem. Rev. 2004, 248, 757. (b) Neese, F.;
Solomon, E. I. In Magnetism; Miller, J. S., Drillon, M., Eds.; Wiley-
VCH: New York, 2003; Vol. IV, pp 345−466. (c) Long, J. R. In
Chemistry of Nano-structured Materials; Yang, P., Ed.; World Scientific:
Hong Kong, 2003; pp 291−315.
(29) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys.
2010, 132, 154104.
(30) Grimme, S.; Ehrlich, S.; Goerigk, L. J. Comput. Chem. 2011, 32,
1456.
(5) Deaton, J. C.; Gebhard, M. S.; Solomon, E. I. Inorg. Chem. 1989,
28, 877.
(6) Browett, W. R.; Fucaloro, A. F.; Morgan, T. V.; Stephens, P. J. J.
(31) Pantazis, D. A.; Chen, X. Y.; Landis, C. R.; Neese, F. J. Chem.
Am. Chem. Soc. 1983, 105, 1868.
Theory Comput. 2008, 4, 908.
K
DOI: 10.1021/acs.inorgchem.5b01505
Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
(32) Malmqvist, P.-Å; Roos, B. O. Chem. Phys. Lett. 1989, 155, 189.
(33) Angeli, C.; Cimiraglia, R.; Malrieu, J.-P. Chem. Phys. Lett. 2001,
350, 297.
(34) Angeli, C.; Cimiraglia, R.; Evangelisti, S.; Leininger, T.; Malrieu,
J.-P. J. Chem. Phys. 2001, 114, 10252.
(35) Angeli, C.; Cimiraglia, R.; Malrieu, J.-P. J. Chem. Phys. 2002, 117,
9138.
(36) Borini, S.; Cestari, M.; Cimiraglia, R. J. J. Chem. Phys. 2004, 121,
4043.
(37) Angeli, C.; Bories, B.; Cavallini, A.; Cimiraglia, R. J. Chem. Phys.
2006, 124, 54108.
(38) Neese, F. WIREs Comput. Mol. Sci. 2012, 2, 73.
(39) Neese, F. with contributions from Becker, U.; Ganyushin, G.;
Hansen, A.; Izsak, R.; Liakos, D. G.; Kollmar, C.; Kossmann, S.;
Pantazis, D. A.; Petrenko, T.; Reimann, C.; Riplinger, C.; Roemelt, M.;
Sandhofer, B.; Schapiro, I.; Sivalingam, K.; Wennmohs, F.; Wezisla, B.;
̈
and contributions from our collaborators Kal
́
lay, M.; Grimme, S.;
Valeev, E. ORCA - An ab initio, DFT and Semiempirical SCF-MO
Package, Version 3.0; Mulheim a.d.R. The binaries of ORCA are
̈
available free of charge for academic users for a variety of platforms.
(40) Atanasov, M.; Ganyushin, D.; Pantazis, D. A.; Sivalingam, K.;
Neese, F. Inorg. Chem. 2011, 50, 7460.
(41) Neese, F. J. Chem. Phys. 2005, 122, 34107.
(42) Ganyushin, D.; Neese, F. J. Chem. Phys. 2006, 125, 024103.
(43) Schaefer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992, 97,
2571.
(44) Weigend, F.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2005, 7, 3297.
(45) Jørgensen, C. K.; Pappalardo, R.; Schmidtke, H.-H. J. Chem.
Phys. 1963, 39, 1422.
(46) Schaffer, C. E.; Jørgensen, C. K. Mol. Phys. 1965, 9, 401.
̈
(47) Atanasov, M.; Ganyushin, D.; Sivalingam, K.; Neese, F. Struct.
Bonding (Berlin, Ger.) 2012, 143, 149.
(48) Atanasov, M.; Zadrozny, J. M.; Long, J. R.; Neese, F. Chem. Sci.
2013, 4, 139.
(49) Adamsky, H. AOMX, a FORTRAN Program for the Calculation of
dn Terms within the Angular Overlap Model with Interelectronic Repulsion
and Spin-Orbit Coupling; Institute of Theoretical Chemistry, Heinrich-
Heine-University: Dusseldorf, 1995. This program, both executable
̈
and source code, is freely distributable by M.A. upon request.
(50) Gatteschi, D.; Sorace, L. J. Solid State Chem. 2001, 159, 253.
(51) Desrochers, P. J.; Telser, J.; Zvyagin, S. A.; Ozarowski, A.;
Krzystek, J.; Vicic, D. A. Inorg. Chem. 2006, 45, 8930.
(52) Ye, S.; Neese, F. J. Chem. Theory Comput. 2012, 8, 2344.
(53) Atanasov, M.; Rauzy, C.; Baettig, P.; Daul, C. Int. J. Quantum
Chem. 2005, 102, 119.
(54) Sun, Z.-C.; She, Y.-B.; Zhou, Y.; Song, X.-F.; Li, K. Molecules
2011, 16, 2960.
L
DOI: 10.1021/acs.inorgchem.5b01505
Inorg. Chem. XXXX, XXX, XXX−XXX