Vibrational probes and determinants of the S = 0 ? S = 2 spin crossover in five-coordinate [Fe(TPP)(CN)]-

Article abstract of DOI:10.1021/ic301719v

The low-frequency vibrational characterization of the spin-crossover complex, five-coordinate cyano(tetraphenylporphyrinato)iron(II), [Fe(TPP)(CN)]^-, is reported. Nuclear resonance vibrational spectroscopy has been used to measure all low-frequ

Full text of DOI:10.1021/ic301719v

Article
pubs.acs.org/IC
Vibrational Probes and Determinants of the S = 0 ⇌ S = 2 Spin
Crossover in Five-Coordinate [Fe(TPP)(CN)]−
Jianfeng Li,*,†,‡ Qian Peng,‡ Alexander Barabanschikov,⊥ Jeffrey W. Pavlik,‡ E. Ercan Alp,§
Wolfgang Sturhahn,§ Jiyong Zhao,§ J. Timothy Sage,*,⊥ and W. Robert Scheidt*,‡
†College of Materials Science and Opto-electronic Technology, University of Chinese Academy of Sciences, 19A Yuquan Road,
Beijing, P.R. China 100049
‡Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556, United States
§Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, United States and
⊥Department of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University, 110 Forsyth Street,
Boston, Massachusetts 02115, United States
S
* Supporting Information
ABSTRACT: The low-frequency vibrational characterization of
the spin-crossover complex, five-coordinate cyano-
(tetraphenylporphyrinato)iron(II), [Fe(TPP)(CN)]−, is reported.
Nuclear resonance vibrational spectroscopy has been used to
measure all low-frequency vibrations involving iron at several
temperatures; this yields vibrational spectra of both the low- (S = 0)
and high-spin (S = 2) states. Multitemperature oriented single-
crystal measurements facilitate assignments of the vibrational
character of all modes and are consistent with the DFT-predicted
spectra. The availability of the entire iron vibrational spectrum allows for the complete correlation of the modes between the two
spin states. These data demonstrate that not only do the frequencies of the vibrations shift to lower values for the high-spin
species as would be expected owing to the weaker bonds in the high-spin state, but also the mixing of iron modes with ligand
modes changes substantially. Diagrams illustrating the changing character of the modes and their correlation are given. The
reduced iron−ligand frequencies are the primary factor in the entropic stabilization of the high-spin state responsible for the spin
crossover.
transition in such complexes are the temperature-dependent
magnetic properties and metal−ligand distances, which arise
from a change in relative occupancies of the t2g and eg
INTRODUCTION
■
We have previously reported the synthesis, multitemperature
structural, IR and Mossbauer spectroscopic, and magnetic
̈
orbitals.12 Temperature-dependent Mossbauer spectroscopy
̈
characterization of the five-coordinate complex, [K(222)][Fe-
(TPP)(CN)].1,2 In addition to the complex being the first
cyanoiron(II) porphyrinate isolated, unexpectedly the complex
is not a completely low-spin (LS) complex, rather the species is
a thermally induced S = 0 ⇋ S = 2 spin-crossover complex.1
Surprisingly, the axial ligand field of cyanide is insufficient to
yield a low-spin (LS) complex at all temperatures and a high-
spin state is seen at higher temperatures.3 The spin-crossover
transition for [K(222)][Fe(TPP)(CN)]4 is gradual, but
reversible, with no hysteresis over the 2−400 K temperature
range explored. To our knowledge, [K(222)][Fe(TPP)(CN)]
is the first spin-crossover complex reported for an iron(II)
porphyrinate, which is also unusual for having a coordination
number of five, rather than the more common value of six in
pseudo-octahedral spin-crossover species. Previously known
iron porphyrinate spin-crossover complexes are all iron(III)
species.6−11
can also be applied to iron crossover species, independent of
whether the crossover is slow or fast on the Mossbauer time
̈
scale. Spin populations as a function of temperature can be
obtained when the crossover is slow on the Mossbauer time
̈
scale (∼10−7 s).
Vibrational spectroscopy has also been used to study spin-
crossover species, typically this has been done by following a
characteristic vibration of one of the ligands. Better yet would
be to monitor metal−ligand vibrations that are most directly
responsive to changes of spin state.13 These are at relatively low
frequencies and are generally difficult to observe by conven-
tional vibrational spectroscopy such as IR and Raman, partially
due to their complex spectra in this energy region14 as well as
selection rules. An early study of the classical complex
[Fe(phen)2(NCS)2] utilized iron isotopes to assign iron−
ligand stretches;15 some of the low-frequency assignments were
There is a rich history of investigating spin-crossover
complexes, which are especially prominent for iron(II) and
iron(III) species.12 The two most studied features of the spin
Received: August 3, 2012
Published: October 19, 2012
© 2012 American Chemical Society
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a
Table 1. Measured and Calculated Structural Parameters and Vibrational Modes for [K(222)][Fe(TPP)(CN)]
b
ΔN4
Fe−CN
(Fe−N)pav
LS
HS
LS
HS
LS
HS
DFT
X-ray
0.163
0.618
1.887
2.113
2.012
2.154
100 K
0.17
400 K
0.45
100 K
400 K
100 K
400 K
1.8783(10)
2.108(3)
1.986(7)
2.089(8)
νFe−C(CN)
δFe−C−N
doming
LS
HS
LS
HS
LS
HS
DFT
461
116 K
461
336
413
116 K
413
277
108
116 K
130
90
d
290 K
290 K
290 K
c
NRVS
459/322
405/277
125/108
a
b
c
Distance values in Å, mode values in cm−1. ΔN4 is the displacement of iron from the mean plane of the four porphyrin nitrogen atoms. νFe−C(CN)
d
and doming modes are from oop measurements; δFe−C−N is from ip measurement. 290 K measurement shows both LS and HS modes.
later questioned.13 However, the low frequency vibrations of
iron complexes are conveniently studied by the synchrotron-
based method nuclear resonance vibrational spectroscopy
(NRVS),16,17 a method that is selective and sensitive only to
by crushing the crystals. The purity of all samples was confirmed by
Mossbauer measurements that showed a single quadrupole doublet at
̈
all temperatures.
Crystal Alignment and NRVS Measurements. A detailed crystal
alignment and NRVS measurement program has been developed.24
The previously described procedures were used for single-crystal
alignment on a Bruker-Nonius Kappa CCD diffractometer. Crystals of
[K(222)][Fe(TPP)((CN)] are in space group Cc with four porphyrin
molecules in the unit cell (Z = 4).1 The porphyrin planes are precisely
parallel to each other in two sets. The dihedral angle between the two
pairs of porphyrin planes is 15.9° (See Figure S1 in the Supporting
Information [SI]).25
A pseudo-porphyrin plane (mean plane bisecting the dihedral
angle) was calculated to orientate the single crystal. The Miller indices
of the pseudo-porphyrin plane were determined to be (6, 0, −12) from
the algebraic equations calculated in SHELXL26 from crystal
information. With this plane perpendicular to the X-ray beam, a 90°
rotation of the aligned crystal will give both the in-plane (ip) and out-
of-plane (oop) orientations with only minor alignment errors
(approximately 8° max).
All NRVS measurements were made at Sector 3-ID of the Advanced
Photon Source, Argonne National Laboratory. Crystal orientations
were confirmed to remain valid after the NRVS measurements.
Analysis of the NRVS data has been described previously.17,27,28
Vibrational Predictions. The first set of calculations was
performed using the Gaussian03 program package.29 The hybrid-
GGA functional B3LYP30 and the triple-ζ valence basis set without
polarization (VTZ) for iron and 6-31G* were used for the H, C, and
N atoms. Both high-spin (HS, S = 2) and low-spin (LS, S = 0) states
are calculated. The reported structures1 were used as the starting
geometry for optimization. The second set of calculations including
structure optimizations and frequency analysis has been performed on
[Fe(TPP)(CN)]− using the Gaussian09 program package.31 B3LYP
and VTZ for iron and 6-31G* for H and C atoms were used. To better
predict the anion system [Fe(TPP)(CN)]−, a basis set with diffuse
function 6-31+G* was added to the more negatively charged atoms
(the N atoms in the porphyrin and the cyanide ligand). Frequency
calculations were performed on the fully optimized structures at the
same basis level to obtain the vibrational frequencies with 57Fe isotope
set.32 Comparisons of the optimized geometry and frequencies with
the observed data are given in Table 1. The calculated frequencies are
surely no more accurate than 1 cm−1. However, we have sometimes
given another digit that is required to distinguish the mode with other
calculated modes.
Mossbauer active centers, and provides direct access to all Fe
̈
vibrations.18 Therefore, NRVS presents a unique method to
study iron spin transitions by displaying the low−frequency
vibrational displacement spectra. The method has been applied
to spin-crossover complexes.19
In this study, we apply NRVS to the spin-crossover complex
[K(222)][Fe(TPP)(CN)]. In addition to (isotropic) powder
measurements, we have also utilized oriented single-crystal
NRVS measurements at several temperatures to clarify the
vibrations and their assignments. These assignments have also
been confirmed with DFT calculations for the two spin states.
The results have allowed, for the first time, to thoroughly
correlate the changing vibrational character of the two spin
states. The large differences in character in the present case is
the result of different mixing of the iron modes with the ligand
(porphyrin) modes. Vibrational entropy calculations based on
these results confirm that the reduced iron−ligand frequencies
entropically stabilize the high-spin state and unexpectedly
suggest the possible importance of peripheral substituents.
EXPERIMENTAL SECTION
■
General Information. All reactions and manipulations were
carried out under argon using a double-manifold vacuum line,
Schlenkware, and cannula techniques. THF and hexanes were distilled
over sodium/benzophenone. Chlorobenzene was washed with
concentrated sulfuric acid and then with water until the aqueous
layer was neutral, dried with MgSO4, and distilled twice over P2O5
under argon. KCN was recrystallized and purified by a literature
procedure.20 Ethanethiol and Kryptofix 222 (Aldrich) were used as
received. The free-base porphyrin meso-tetraphenylporphyrin
(H2TPP) was prepared according to Adler et al.21 Metalation of
95% 57Fe-enriched samples was prepared by a method similar to that
of Landergren.22 [57Fe(TPP)]2O was prepared according to a modified
Fleischer preparation.23
Synthesis of [K(222)][57Fe(TPP)(CN)] (single crystal and
powder). The reaction procedures described previously were used
for the sample preparation.1 [57Fe(II)(TPP)] was prepared by
reduction of [57Fe(TPP)]2O (27.1 mg, 0.02 mmol) with ethanethiol
(0.5 mL) in benzene (8 mL) for 24 h. Vacuum evaporation of the
solvent yielded a dark-purple solid to which KCN (2.9 mg, 0.044
mmol) and Kryptofix 222 (16.6 mg, 0.044 mmol) in THF or PhCl
(∼4 mL) was added by cannula, and the mixture was stirred overnight.
X-ray quality crystals were obtained in 8 mm × 250 mm sealed glass
tubes by liquid diffusion using hexanes as nonsolvent. IR ν(C−N):
2070 (strong) and 2105 cm−1 (weak). A powder sample was prepared
Predicted Mode Composition Factors and NRVS. The
Gaussian09 output files from DFT calculation can be used to
generated predicted Mode Composition Factors with our scripts.33
e2jα for atom j and frequency α are the fraction of a mode’s total kinetic
energy contributed by atom j and is readily obtained from the atomic
displacement matrix together with the equation
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mjrj2
question. The vibrational predictions of the two calculations are
briefly compared.
We have also studied the entropy of the system on the basis
of the predicted vibrational data. We present our results on the
contributions of the vibrational entropy to the spin crossover.
ej2α
=
∑ mri2
i
where the sum over i runs over all atoms of the molecule: mi is the
atomic mass of atom i, and ri is the absolute length of the Cartesian
displacement vector for atom i. The polarized NRVS intensities are
calculated relative to an averaged porphyrin plane. The out-of-plane
atomic displacement perpendicular to the resulting porphyrin plane for
a normal mode is obtained from a projection of the atomic
displacement vector (z) of the NRVS active nuclei (here: 57Fe). The
in-plane atomic displacements are calculated from a projection of the
atomic displacement vector (x and y) on the porphyrin plane, which
can be written:
DISCUSSION
■
The low-spin to high-spin spin-crossover complex [Fe(TPP)-
(CN)]− is an unusual species on at least two counts. The first is
the presence of the cyanide ion, long considered a strong field
ligand and thus judged unlikely to be in the coordination group
of a species displaying high-spin character.3,34 The second is
that the species is a five-coordinate iron(II) species, whereas
most iron(II) species that exhibit spin-crossover behavior are
pseudo-octahedral six-coordinate complexes. The thermally
induced spin crossover has been confirmed by both magnetic
mjrj2z
∑ miri2
ej2α,out of plane
and
ej2α,in plane
=
(1a)
susceptibility measurements and by Mossbauer spectroscopy
̈
mj(rj2x + rj2y)
∑ miri2
over a range of temperatures. The interconversion of spin states
is very rapid and shows only a single quadrupole split doublet
=
(1b)
in the Mossbauer spectra.1 Thus, the interconversion is faster
̈
than the Mossbauer time scale (10−7 s). Vibrational spectros-
Finally, the directions of mode composition factors are calculated as
described above using the in-plane and the out-of-plane projection
vectors, respectively (as will be shown in a later figure). In order to
enable comparison of the directions, the coordinate systems used in
the HS and LS states of [Fe(TPP)(CN)]− are fixed along the same
iron−nitrogen bond directions (4N-in-plane) by our coordinate-
rotation script.33 Vibrational density of states (VDOS) intensities can
be simulated from the mode composition factors using the Gaussian
normal distributions function, where the full width at half height
(fwhh) is defined by the user from MATLAB, R2010a, software (fwhh
= 7.5 cm−1 is set in this Article). The x, y, and z components of iron
normal mode energy for [Fe(TPP)(CN)]− (LS) and [Fe(TPP)-
(CN)]− (HS) with eF2e ≥ 0.001 are given in Tables S1 and S2 (SI).
̈
copy, when used to investigate spin-crossover complexes,
typically follows a select band that has differing frequencies in
the two states. In this study, we have obtained the entire iron
vibrational spectrum for the low-spin complex. At higher
temperatures, the observed NRVS spectra show contributions
from both the low- and high-spin forms. Accordingly, we are
able to extract the complete spectrum for the high-spin form as
well. This observation also makes clear that the spin
interconversion rate is slow on the vibrational time scale.
The differences in the structure of the two spin states have
been obtained by multitemperature X-ray structure studies.1
The differences in structure are schematically depicted in
Figure 1 and are consistent with known spin-state correla-
tions.36
RESULTS
■
NRVS data for the spin-crossover (or spin-equilibrium)
complex [K(222)][Fe(TPP)(CN)] have been recorded at
several temperatures. The powder spectrum was measured at
∼17 K, and oriented single-crystal spectra were obtained at 116
K and between 222 and 290 K. The complex (in the solid state)
is known to be low spin at temperatures below ∼175 K. Above
this temperature, the complex undergoes a gradual transition to
a high-spin state. At 400 K, the transition is still not complete
and accordingly is halfway complete at >265 K. Thus, the
spectra measured at 17 and 116 K represent spectra from the
pure low-spin species, whereas spectra obtained at the higher
temperatures must contain contributions from both the high-
and low-spin states of the anion.
Oriented crystal spectra obtained when the porphyrin planes
are effectively perpendicular to the exciting X-ray beam reveal
all iron vibrations where the iron moves in an out-of-plane
direction. Spectra were also obtained when the porphyrin
planes were parallel to the exciting beam and in-plane motion
of iron is observed. In this case, components of both the x and y
directions are observed. No in-plane anisotropy is expected for
the four-fold symmetric [Fe(TPP)(CN)]− ion, in contrast to
[Fe(OEP)(NO)].24 The oriented single-crystal spectra provide
useful information on the direction of iron motion that
substantially aids in the spectral assignments. In addition, two
series of DFT calculations have been performed to aid in the
task of assignment. Both series of DFT calculations utilized the
B3LYP functional with the second series extended with the
additional use of diffuse functions. Diffuse functions were
included because of the negative charge on the complex in
Figure 1. Diagram illustrating the structural changes between the low-
spin and high-spin states of [Fe(TPP)(CN)]−. The high-spin
parameters are from the 400 K structure and may not reflect a
complete conversion to the high-spin system.
Vibrational Analysis. The iron vibrational spectrum of the
low-spin state of [Fe(TPP)(CN)]− is available from the NRVS
spectra collected as both a powder (17 K) and as an oriented
crystal specimen. The powder spectrum is shown in the upper
panel of Figure 2 (solid black line) and consists of six major
peaks. The powder spectrum is very well predicted by the DFT
calculation with diffuse functions as shown by the predicted
vibrational density of states (Figure 2, VDOS, filled gray
envelope). The overall quality of the predicted fits to the
powder spectrum does provide confidence in the details of the
prediction. The “standard” DFT calculation also shows good
agreement (although not quite as good) and is provided in the
Supporting Information (Figure S2) for comparison.
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Figure 2. (Upper panel) The measured VDOS for the powder sample (17 K), the single-crystal sample (in-plane, 116 K; out-of-plane, 116 K) of
[K(222)][Fe(TPP)(CN)], and predicted VDOS for the low-spin state (gray shaded, G09). (Lower panel) The predicted directional characteristics
of all modes with e2Fe > 0.001 are shown. The tick marks are the values of the predicted frequencies, but the horizontal scale is only approximately
linear in frequency to avoid overlaps. x, y, and z are illustrated in the molecular structure and defined in text.
Figure 3. The two FeCN bending modes in the x direction. The mode predicted at 413.2 cm−1 is at the left and the mode predicted at 476.4 cm−1 is
at the right (with ν50).
The available oriented crystal data are also shown in the top
panel of Figure 2 (blue line, out-of-plane; green line, in-plane)
and clearly demonstrate that several of the powder peaks are
overlapped with in-plane and out-of-plane contributions
unresolved in the powder. The lower panel of Figure 2
shows the predicted directional characteristics of each mode
with e2Fe > 0.001. As illustrated in the diagram, z is along the
heme normal, equivalent to the measured oop spectrum; x and
y directions correspond to the two ip Fe−Np vectors. This bar
graph provides details of directional contributions of the iron
motions. Predictions of the directionality are well-correlated
with the experimental orientational data. The modes can be
described in terms of the well-known porphyrin mode
classification by Abe et al.37 as adapted for [Ni(P)]38 and
[Fe(P)].39 Labels with νi denote modes with all atoms moving
in the porphyrin plane and γi denotes modes with all atoms
moving perpendicular to the porphyrin plane.
The strongest band in the powder spectrum is observed at
464 cm−1. This might be expected to solely be the Fe−CN
stretch but the oriented ip and oop measurements show that
there are substantial ip contributions to the (overlapped) peak
as well. The predicted character of the 476.4 and 476.7 cm−1 ip
peaks are the x and y components of ν50 along with some
contribution from the Fe−C−N bend. However, the
predictions and experiment show that the bend primarily
contributes to the in-plane peaks observed at 415 cm−1
(powder) or 413 cm−1 (in-plane). Thus there is significant
mixing of the Fe−C−N bend with porphyrin vibrations; the
two sets have nearly equivalent iron intensities. The predicted
character of the two distinct bending components in the x
direction is illustrated in Figure 3. There are thus three modes
with overlapped frequencies; the third mode is indeed the very
strong Fe−CN stretch. The observed peaks are at 464 cm−1
(powder, overlapped), 464 cm−1 (in-plane), and 461 cm−1
(out-of-plane). The highest resolvable peak, which has modest
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intensity, is found at 572 cm−1 (γ5, pyrrole folding) and has not
been previously seen by NRVS in porphyrins.
with the four Cm atoms moving in the opposite motion (γ7).
The peak observed at 131 cm−1 and predicted at 107.2 cm−1 is
the classical doming mode (γ9). The final peak at the very low
frequency of about 54 cm−1 and predicted at 32.6 cm−1 can be
described as the motion of all porphyrin, iron, and cyanide
atoms normal to the porphyrin plane with the peripheral
phenyls moving in the opposite direction.
Spectra measured at higher temperatures will display features
from both the high- and low-spin forms of the anion. In
principle, at high enough temperatures the spectrum of the
pure high-spin form of the anion could be obtained. However,
the highest practical temperature for the NRVS measurements
is ∼290 K, where the transition is only about 70% complete.
We have measured oriented crystal spectra at this temperature
as well as an intermediate temperature, where the transition to
high spin is about 40% complete. We thus have oriented crystal
spectra that give spectra of the low-spin state as well as two
spectra with differing amounts of the two spin states. DFT
calculations and spectral predictions were also carried out for
the high-spin state, which we believe provides an adequate
depiction of the high-spin state. The out-of-plane spectra are
simpler than those of the in-plane spectra; we consider the out-
of-plane set first.
As in other low-spin iron porphyrinate complexes, the middle
frequency range (220−360 cm−1) of the spectrum is dominated
by strong in-plane contributions. Two very strong bands are
centered at 304 and 244 cm−1; there are also modest
(overlapped) contributions from out-of-plane motion that are
unresolved in the powder. The band at 304 cm−1 exhibits in-
plane motion analogous to the ν53 modes predicted for
[Fe(Porphine)].39,40 The predicted mode in the y direction is
illustrated in Figure 4. Unexpectedly, the DFT calculations
Figure 6 presents the out-of-plane spectra at three temper-
atures. Changes in four spectral regions are readily apparent.
The stretching mode at 461 cm−1 clearly becomes less intense
while a peak at 322 cm−1 increases in intensity with increasing
temperature. In the 200 cm−1 region, the peak at 197 cm−1
increases in intensity as the temperature is increased. Finally the
peak at 130 cm−1 shifts to a peak at 108 cm−1.
The changes in spectra in the in-plane region are shown in
Figure 7. Peaks at 464, 413, 297, and 243 cm−1 all decrease in
intensity, whereas increases in intensity are observed in only
two regions, 280 and 189 cm−1. The 189 cm−1 peak also has a
clear shoulder at higher frequency.
These spectral changes clearly show that the frequencies for
the high-spin species are at lower frequency; there are also
apparent significant changes in intensity. The shift to lower
frequency in the high-spin complex is expected since the change
in spin state leads to longer and weaker bonds for the high-spin
state than those found for the low-spin state (Figure 1). Less
anticipated features were the differing vibrational pattern and
differing intensities. This appears to be the result of varying
mixing of the iron motion with porphyrin motion, a reflection
of the distinct structural features of the two states.
These features can be seen in Figure 8 where the lower
frequencies for the high-spin state and the intensity pattern
differences are clearly visible. The figure presents the predicted
vibrational density of states (VDOS, gray shaded) and the
predicted iron directional character of each mode with
Figure 4. In-plane ν53 in the y direction that is predicted at 300.1 cm−1.
predict two x in-plane modes, both with ν53 character but also
with a small amount of out-of-plane character as well (inverse
doming: γ6). It is the in-phase and out-of-phase mixing with γ6
that leads to the two predicted modes. The oriented crystal
spectra show that there is modest out-of-plane iron motion in
the region. Whether this is a separate mode or a component of
the in-plane mode cannot be determined from our
experimental data, but the predictions clearly suggest mixing.
The differences in the total predicted motion are apparent in
Figure 5. The total iron motion in these two modes is
comparable to that for the mode with y character (as would be
expected).
The band observed at 244 cm−1 is the result of the final
(strong) in-plane set of iron motions. The DFT predictions
show a set of four modes, with γ23 and ν49 character. The iron
motion is all in ν49. The four modes are illustrated in Figure S3
(SI).
The remaining observed peaks all display out-of-plane
character. The band at 210 cm−1 is predicted at 201.6 cm−1
and can be described as motion of the Fe−C−N and
porphyrinato atoms moving perpendicular to the heme plane
Figure 5. The predicted modes at 296.7 and 303.2 cm−1 showing the modest oop motion of iron.
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Figure 6. The measured VDOS for a single-crystal sample of [K(222)][Fe(TPP)(CN)] (out-of-plane) at 116, 250, and 290 K and DFT-predicted
VDOS for the low-spin state (gray shaded) and the high-spin state (red shaded). To facilitate comparisons, the predicted out-of-plane VDOS for
both spin states are shown at half height to give the approximate expected spectrum at the half conversion point.
Figure 7. The measured VDOS for single crystal sample of [K(222)][Fe(TPP)(CN)] (in-plane) at 116, 222, and 290 K and in-plane DFT predicted
VDOS for the low-spin state (gray shaded) and the high-spin state (red shaded). To facilitate comparisons, the predicted VDOS for both spin states
are shown at half height to give the expected spectrum at the half conversion point.
frequencies. Given the strong agreement between the observed
and predicted VDOS, we use the DFT-predicted spectral
features since this gives us the most useful information on the
character of the modes. The significant differences between the
spectra are the result of the mixing of the iron motion with
different porphyrin ring modes. Thus, there is not a simple one-
to-one correlation of modes in the two states. In the following
sections showing the correlations of the modes between the
two states, we use the predicted frequencies of the vibrations,
but it is to be emphasized that there is always a corresponding
observed mode. MOLEKEL depictions of the correlated LS and
HS modes are given in the SI.41
The correlation of the out-of-plane modes is fairly
straightforward as the amount of porphyrin ring mixing in
the out-of-plane modes is minimal. The predicted Fe−C−N
stretch downshifts from 460.6 to 335.9 cm−1 (Figure S4, SI);
the observed frequencies are 461 to 322 cm−1. The doming
mode downshifts from the observed value of 130 cm−1 to 108
cm−1 (Figure S5, SI); the predicted values are 107.2 and 89.8
cm−1.
porphyrin modes and iron modes. The Fe−C−N bending
modes at 413.2 and 413.4 cm−1 in the LS species are correlated
with the modes predicted at 276.6 and 277.4 cm−1. These two
HS modes are mostly Fe−C−N bending, but there is some ν53
character as well. However, these two HS modes are also
correlated with the LS modes at 476.4 and 476.7 cm−1 that are
a combination of ν50 and the Fe−CN bending mode; this
mixing is minimal in the high-spin state. Thus, porphyrin
modes mixed with Fe−C−N bending are very different in the
two spin states and the number of modes with Fe−C−N
bending character are also different. Correlations of the modes
involving the Fe−C−N bend in both the x and y directions are
shown in Figures S6 and S7 (SI). In both spin states, there is
the expected x and y degeneracy.
The correlations of the iron midfrequency modes are equally
complicated; there are two groups of LS modes to be
considered. The four LS modes between 240.3 and 244.1
cm−1 have both γ23 and ν49 character with all iron motion
arising from ν49. The LS modes centered around 300 cm−1 are
primarily ν53 with the x component also having in-phase and
out-of-phase contributions from γ6. Both the 240 and the 300
cm−1 LS groups can be correlated with the four HS modes
The correlation of the in-plane modes is more complex
owing to significant changes in the nature of mixing between
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Figure 8. Diagram illustrating the correlations of iron motion in the high- and low-spin states of [K(222)][Fe(TPP)(CN)]. The horizontal axes are
on the same linear scale, the positions of the predicted peaks are somewhat arbitrary in order to avoid overlaps.
predicted between 178.6 and 184.1 cm−1. These HS modes are
a combination of ν53 and ν49; the major contributors to the two
LS sets. This combination leads to effectively “destructive
interference” of the rotation of the pyrrole rings and the two
opposite pyrroles move in-phase with the in-plane iron motion.
Thus the porphyrin modes mixed with the iron in-plane motion
are again very different in the two spin states and the number of
Figure 9. Diagram illustrating changes in the Fe−C and C−N
modes with substantial in-plane iron character are also different.
stretches and the Fe−C−N bend between the two spin states of
The nature of the differences between the two spin states and
[Fe(TPP)CN)]−. The C−N stretches were measured previously by
IR1 and the other vibrations by NRVS.
the distinctions between the x and y directions is illustrated in
Figures S8 and S9 (SI).
Figure 8 summarizes the correlations from the above analysis
with the dashed lines connecting the HS and LS modes with
similar iron motion. The CN stretch also shows a change in the
frequency from the spin-state change; the experimental values
for the Fe−CN and C−N stretches are shown in Figure 9. The
data show that there is an inverse correlation between the
strength of the Fe−C and C−N bonds. This pattern is
reminiscent of the well-known correlation for isoelectronic
heme carbonyls.42 The change in νCN frequency is a decrease in
frequency by 35 cm−1; the calculated differences in the two
frequencies are 30 cm−1. The data is thus consistent with π-
back-bonding as a contributor to the Fe−C bonding in
[Fe(TPP)CN)]−; however, π-bonding would certainly be much
more significant for the low-spin state. The figure also shows
the effects on the Fe−C−N bending mode as the Fe−C bond
weakens and which shows the expected trend.
Vibrational Entropy. The preceding results demonstrate
that Fe−ligand vibrations are sensitive reporters of the
electronic state of [Fe(TPP)(CN)]−. These frequency changes
also help to drive the spin crossover by entropically stabilizing
the quintet state relative to the singlet, as commonly observed
for other spin-crossover materials.43−45 A simple two-state
model with temperature-independent quintet-singlet enthalpy
and entropy differences yields a good fit to the previously
published magnetic susceptibility measurements1 (Figure S11,
SI) with a crossover temperature Tc = ΔH/ΔS = 286 K and an
entropy increase ΔS = 46.6 J/mol/K for the high-spin state that
is significantly larger than the electronic contribution (ΔSel = kB
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Inorganic Chemistry
Article
ln 5 = 13.4 J/mol/K) expected from the increased spin
multiplicity alone.
The reduced Fe−ligand frequencies in the quintet state, as
detailed above (Figure 8), will contribute to an increase in the
vibrational entropy
almost completely cancels the electronic contribution. Thermal
excitation of the Fe−ligand contributions with further temper-
ature increases ultimately enhances the entropic stabilization of
the quintet state.
The relevance of these torsional frequencies to the
experimental situation is difficult to assess, in part because
calculations on an isolated molecule fail to account for
intermolecular interactions that may strongly influence the
motions of the phenyl groups on the molecular periphery.
Moreover, these vibrations do not contribute significantly to
the NRVS signal and this frequency region is also difficult to
probe with infrared or Raman spectroscopy. However, explicit
exclusion of the latter vibrations from the sums in eq 2 yields a
value ΔS = 40 J/mol/K for the entropic stabilization of the
quintet at 286 K that is closer to our experimental estimate.
Changes in the electronic state also lead to changes in the
predicted frequencies of the heme distortion modes involving
torsional motion of the bonds connecting the rigid pyrrole
rings. The observed decrease of the doming (γ9) frequency
from 130 to 108 cm−1 (see above) in the high-spin state
parallels the predicted 107−90 cm−1 decrease. In contrast, the
calculation predicts an increase of the saddling (γ19) frequency
of the porphyrin from 48 to 66 cm−1. Changes of the predicted
ruffling (γ14) frequency from 98 to 105 cm−1 and the waving
frequencies (γ26) from 137 to 131 cm−1 are less significant.
Although difficult to detect in frequency-domain IR or Raman
spectroscopy, saddling and ruffling frequencies have been
reported to contribute to the time-domain vibrational
coherences observed following femtosecond laser excita-
tion.47,48
Svib = kB
(n + 1) ln(n + 1) − n ln n
]
α α α α
̅ ̅ ̅ ̅
∑
[
(2)
α
because of the consequent increase in the vibrational
occupation numbers nα = [exp(hcν/kBT) − 1]−1. Calculation
̅
̅
of the vibrational entropy change using all DFT-computed
frequencies in eq 2 confirms a significant enhancement of the
total entropy difference as the Fe−ligand frequencies become
thermally excited with increasing temperature (red line, Figure
10). More specifically, each pair of corresponding singlet/
SUMMARY
■
We have provided a detailed comparison of vibrational changes
in the spin-crossover complex [K(222)]Fe(TPP)(CN)] as the
spin state changes. The mode character changes significantly,
owing to the strong mixing of the iron motion with porphyrin
modes. This mixing differs substantially between the two spin
states because of the large change in the force constants of
similar iron vibrations in the two electronic states. The
calculation of the vibrational entropy (the major driving force
for the spin-state change) based on the DFT predicted modes
has been examined. The calculations show that some vibrations
involving the peripheral groups of the porphyrin may, in fact,
stabilize the less favored state. This result is in keeping with the
observation that subtle molecular changes can have big effects
on the occurrence (or not) of the spin-crossover phenomenon.
Figure 10. Predicted entropy increase on crossover to the high-spin
state of [Fe(TPP)(CN)]− includes electronic and vibrational
contributions. The blue trace indicates the entropy calculated by
excluding the predicted frequencies of four torsional oscillations about
the Cm−phenyl bonds, which increase significantly in the quintet state,
while the red trace includes all vibrations. The dashed line indicates
the temperature-independent electronic contribution ΔS = kB ln 5 due
to the increased spin multiplicity in the high-spin state. The difference
between quintet and singlet vibrational entropies calculated from eq 2
using DFT-computed frequencies determines the additional vibra-
tional contribution.
quintet frequencies ν1/ν5 contributes a term that increases
̅
̅
monotonically with temperature, reaching a maximum value
ΔSmax = kB ln(ν1/ν )
(3)
̅
5̅
ASSOCIATED CONTENT
■
when the thermal excitation energy exceeds the vibrational
quantum (kBT > hcν).46 However, the ΔS = 27 J/mol/K
S
* Supporting Information
̅
Figures S1−S11 illustrating the packing of [K(222)]Fe(TPP)-
(CN)], predicted spectra, and illustration of the character of
modes in the two spin states; Tables S1 and S2 giving predicted
e2 values for iron in the low- and high-spin states. This material
is available free of charge via the Internet at http://pubs.acs.org.
entropy change calculated as the sum of electronic and
vibrational contributions at the 286 K crossover temperature
is more modest than that expected.
Examination of the vibrational calculations reveals that four
vibrational frequencies involving torsional oscillations about the
four Cm−Cphenyl bonds connecting the phenyl groups to the
porphine nucleus also contribute significantly to the predicted
vibrational entropy difference. In contrast with the Fe−ligand
frequencies, the DFT calculation predicts these torsional
frequencies to increase by approximately 40% from 27−30
cm−1 in the singlet to 38−46 cm−1 in the quintet state. Thermal
excitation of these modes, visible as a prominent minimum near
35 K in the calculated entropy difference (red line Figure 10),
AUTHOR INFORMATION
■
Corresponding Author
*jfli@ucas.ac.cn, (J.L.); jtsage@neu.edu, (J.T.S.); scheidt.1@nd.
edu, (W.R.S.).
Notes
The authors declare no competing financial interest.
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Inorganic Chemistry
Article
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Assour, J.; Korsakoff, L. J. Org. Chem. 1967, 32, 476.
ACKNOWLEDGMENTS
■
We thank Dr. Allen G. Oliver for assistance with orientations
for the single-crystal experiments. Research reported in this
publication was supported by the National Institute of General
Medical Sciences of the National Institutes of Health under
award number R01GM-038401 to W.R.S. We also thank the
NSF for support under CHE-1026369 to J.T.S. and support
from the CAS Hundred Talent Program starting grant of UCAS
to J.F.L. Use of the Advanced Photon Source, an Office of
Science User Facility operated for the U.S. Department of
Energy (DOE) Office of Science by Argonne National
Laboratory, was supported by the U.S. DOE under Contract
No. DE-AC02-06CH11357.
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