Supporting Information for:
A High-Resolution XAS Study of Aqueous Cu(II) in Liquid and Frozen Solutions
Pyramidal, Polymorphic, and Non-centrosymmetric
by
Patrick Frank,1,2 Maurizio Benfatto,3 Munzarin Qayyam,1 Britt Hedman,2 and Keith O.
Hodgson1,2
1. Department of Chemistry, Stanford University, Stanford, CA 94305, USA.
2. Stanford Synchrotron Radiation Lightsource, SLAC, Stanford University, Menlo Park
CA 94025, USA.
3. Laboratori Nazionali di Frascati-INFN, P.O. Box 13, 00044 Frascati, Italy
Table of Contents
Subject
Section 1: Assessment of Photo-reduction
Figure S1.1: In liquid-phase 0.1 M Cu(ClO4)2 in 1 M HClO4
Figure S1.2: In Frozen-phase 0.1 M Cu(ClO4)2 in 1 M HClO4
Figure S1.3: Comparison of Liquid- and Frozen-phase Cu EXAFS spectra
Section 2: Pseudo-Voigt Fits to Copper K-edge XANES
Figure S2.1: Fit to Frozen Solution XANES
Table S2.1: Fitted Pseudo-Voigt Parameters for Frozen-Phase XANES
Figure S2.2: Fit to Liquid Solution XANES
Table S2.2: Fitted Pseudo-Voigt Parameters for Liquid-Phase XANES
Section 3: On the Ratio of EXAFS Amplitudes
Figure S3.1: EXAFS Amplitude Ratio, Liquid And Frozen Phases
Figure S3.2: Attenuation length of 0.1 M Cu(ClO4)2
Section 4: EXAFS Test For Axial Oxygen Scatterers In Liquid-Phase [Cu(aq)]2+
Figure S4.1: Axial Distance vs. Goodness-of-Fit F-value
Section 5: EXAFS Fits; 0.1 M Cu(ClO4)2 In Liquid Aqueous 1 M HClO4
Figure S5.1: JT-Octahedral Model
Figure S5.2: Split Axial Model
Figure S5.3: Axially Elongated Square Pyramidal Model
Section 6: EXAFS Test For Axial Oxygen Scatterers In Frozen-Phase [Cu(aq)]2+
Figure S6.1: Axial Distance vs. Goodness-of-Fit F-value
Section 7: EXAFS Fits; 0.1 M Cu(ClO4)2 In Frozen Aqueous 1 M HClO4
Figure S7.1: JT-Octahedral Model
Figure S7.2 Split Axial Model
Figure S7.3: Axially Elongated Square Pyramidal Model
Section 8: MXAN Fits; 0.1 M Cu(ClO4)2 In Liquid-Phase 1 M HClO4
Figure S8.1: JT-Octahedral, Split Axial, and Square Pyramidal Models
Table S8.1: Model-Based First Shell Fitted Metrics For [Cu(aq)]2+
Table S8.2: Alternative MXAN Fit Metrics For Liquid Phase [Cu(aq)]2+
Section 9: MXAN Fits: 0.1 M Cu(ClO4)2 In Frozen-Phase 1 M HClO4
Figure S9.1: JT-Octahedral, Split Axial, and Square Pyramidal Models
Table S9.1: Single Site Fit Metrics for Three Models
Figure S9.2: Associated Axial Perchlorate Model
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Table S9.2: Axial Perchlorate Fit Metrics
Figure S9.3: MXAN Two-Site Fit: additive vs. iterative
Addendum: Comparative study with crystalline [Cu(H2O)6](ClO4)2
References
15
15
16-30
31
1. Assessment of Photo-reduction
Photo-reduction of redox-active materials including metallo-proteins is ubiquitous in xray absorption spectroscopy, and in synchrotron x-ray crystallography.1-4 On observing
its presence, care must be taken that analyses and conclusions are not compromised.
Here, it is shown that the synchrotron x-ray induced photo-reductions of Cu(II) in liquidand frozen-phase solutions of 0.10 M Cu(ClO4)2 in 1 M HClO4 were small enough to be
neglected.
Figure S1.1: Copper K-edge XAS spectra of three successive scans of liquid-phase 0.10
M Cu(ClO4)2 in 1 M HClO4, and; (▬), the XAS spectrum of [Cu(I)(1,2dimethylimidazole)2]BF4. Inset: close-up of the immediate rising edge energy region
showing the extent of photo-reduction. The vertical line is at 8983.6 eV.
The copper K-edge XAS spectrum of Cu2O was used to model the XAS of [Cu(I)aq]+,
which is thought to also be linear 2-coordinate.5, 6 The former exhibits a low-energy
shoulder of normalized intensity 0.74, which was used to estimate the fraction of Cu(I) in
the solution sample.
The total increased intensity in the third scan, in the 8980-8985 eV range, was 0.002
normalized unit. In the XAS of three combined scans, this averages to 0.18% Cu(I). The
XANES spectra are otherwise superimposable.
2
Figure S1.2: Copper K-edge XAS spectra of two successively scans of frozen-phase (10
K) 0.10 M Cu(ClO4)2 in 1 M HClO4, and; (▬), the XAS spectrum of [Cu(I)(1,3dimethylimidazole)2]BF4. Inset: close-up of the immediate rising edge energy region
showing the extent of photo-reduction. The vertical line is at 8983.6 eV. Two scans were
taken per beam-spot.
The difference intensity maximum in the second scan was 0.0082 unit. Following from
the above, this implied average 1.1 % photo-reduction per scan. Four beam spots were
chosen on the sample, with two scans on each spot. The average Cu(I) of each two-scan
set is then 1.7% Cu(I).
Figure S1.3: Successively scanned copper K-edge EXAFS spectra of 0.10 M Cu(ClO4)2
in 1 M HClO4, in (a), liquid-phase, and; (b) frozen-phase (10 K) solution. Any effect of
Cu(I) is negligible.
3
2. Pseudo-Voigt Fits to Copper K pre-edge XAS and XANES
The copper K-edge XAS spectra were fit with pseudo-Voigts using the program
EDG_FIT within the EXAFSPAK application package. The XANES (8968-9020 eV) and
pre-edge (8960-8989 eV) energy regions were fit separately. Fits were required to match
the absorption and the second derivative of the XAS.
In general, intensities, energy positions and half-widths were allowed to float. PseudoVoigt Gaussian-Lorentzian mixing was fixed at 0.50. In fits to the full XANES, the very
low intensity of the pre-edge features led to their neglect by the fitting routine. Therefore,
these pseudo-Voigts were entered from the separate fits to the pre-edge XAS, and fixed
in position, intensity, and half-widths. Any small change in the shape of the background
intensity was accommodated by minor adjustments of the pre-edge pseudo-Voigt.
The K-edge XAS of Cu(II) frozen 1 M HClO4 solution was fit first. Following this
successful fit, the same set of pseudo-Voigts was used to fit the XAS of Cu(II) in liquid 1
M HClO4 solution.
2.1 Copper(II) in Frozen 1 M HClO4 solution.
Figure S2.1. Left panel: (▬) K-edge XAS of 0.1 M Cu(ClO4)2 in frozen (10 K) aqueous
1 M HClO4 solution; (▬) the pseudo-Voigt fit; (colored lines), the individual pseudoVoigts, and; (▬) the arctangent representing the ionization threshold. Inset: (▬) the preedge XAS; (▬) the fit; (▬) the 1s→3d transition, and; (▬) possibly a weak multiplescattering feature (see Figure S2.2). Right panel: (▬) the second derivative of the XAS,
and; (▬) the second derivative of the fit.
4
Table S2.1: Fitted Pseudo-Voigt Parameters for Frozen-Phase XANES
Feature
Energy Position (eV)
Intensitya
FWHH (eV)
Arctangent
8995.7
0.933
2.00
Pre-edge
8978.5
0.0103
1.20
Voigt 1
8985.2
0.00425
1.27
Voigt 2
8989.8
0.392
1.50
Voigt 3
8992.2
0.503
2.18
Voigt 4
8995.6
0.816
2.53
Voigt 5
8998.8
0.161
3.52
Voigt 6
9001.8
0.285
3.52
Voigt 7
9010.0
0.0630
3.52
a. Intensity is the integrated area of the pseudo-Voigt.
2.2 Copper(II) in Liquid 1 M HClO4 Solution.
Figure S2.2. Left panel: (▬) K-edge XAS of 0.1 M Cu(ClO4)2 in liquid (ambient
temperature) aqueous 1 M HClO4 solution; (▬) the pseudo-Voigt fit; (colored lines), the
individual pseudo-Voigts, and; (▬) the arctangent representing the ionization threshold.
Inset: (▬) the pre-edge XAS; (▬) the overall fit; (▬) the 1s-3d fit, and; (▬) the
background intensity. Right panel: (▬) the second derivative of the XAS, and; (▬) the
second derivative of the fit.
Figure S2.1 and Figure S2.2, especially the second derivatives, show that freezing
induces significant changes in the 8975-8995 eV energy region of XAS spectrum. The
same energy region exhibited a corresponding difference in the arrangement of the fitted
pseudo-Voigts. The array of pseudo-Voigts that successfully fit the XAS of the frozen
solution represented the first guess of the fit to the XAS of the liquid solution. Therefore,
the change in the array of pseudo-Voigts required to fit the XAS of the liquid solution
represents a real difference in the underlying structure of the respective spectra. The
5
shoulder at 8989.6 eV in the XAS of the frozen solution is only the most visible
difference.
Table S2.2: Fitted Pseudo-Voigt Parameters for Liquid-Phase XANES
Feature
Energy Position (eV)
Intensitya
FWHH (eV)
Arctangent
8995.7
0.916
2.00
Pre-edge
8978.2
0.0085
1.02
Voigt 1
8990.0
0.166
1.88
Voigt 2
8992.1
0.420
2.70
Voigt 3
8995.2
0.170
2.14
Voigt 4
8996.0
0.775
3.41
Voigt 5
9001.5
0.286
3.54
Voigt 6
9009.2
0.0740
5.77
a. Intensity is the integrated area of the pseudo-Voigt.
The small feature at 8984.9 eV in the XAS of the frozen solution, present also in the
second derivative, is completely absent from the XAS of the liquid solution. As the
electronic state of Cu(II) is largely unmodified by freezing, this small feature probably
reflects multiple scattering arising from a structural difference. See the text for further
discussion
3. Ratio of EXAFS amplitudes: structural difference or thermal disorder. From the usual
EXAFS equation, the ratio of the EXAFS amplitudes in terms of the Debye-Waller
contributions is given in condensed form by eq. S1:
 L (k )  A(k ) sin(2kR  k )e  ( 2 k L )
2 2
 F (k )  A(k ) sin(2kR  k )e
( 2 k 22F )
 e 2 k
2
( 2L 2F )
,
S1
where χL,F(k) are the photoelectron wave vector amplitudes of the EXAFS spectra, in this
case of liquid and frozen states, respectively, R is the average absorber-scatterer bond
distance, φ(k) is the phase shift, k is the photoelectron wave number, and σ2 is the mean
square thermal and static deviation in R.
The steep drop between k = 2-4 Å-1 is clearly more complex than predicted by
exponential σ2 effects alone, implying a structural cause.
6
Figure S3.1: (▬) The amplitude ratio, e 2 k ( L F ) , of the EXAFS spectra of 0.1 M Cu(II)
in 1 M HClO4 in liquid (L) and frozen (F) solution, respectively, and; (▬) the profile of
2
2
2
e 2 k ( 0.001) illustrating the expected profile, where 0.001 represents a reasonable σ2
difference value.
2
Figure S3.2 below shows the 1/e attenuation length of 0.1 M Cu(ClO4)2 in 1 M HClO4,
across the copper rising K-edge energy, in the absorbance and fluorescence geometries.
Figure S3.2: Attenuation length of 0.1 M Cu(ClO4)2 at (▬) absorption (90º) or (▬)
fluorescence (45º) geometry with respect to the x-ray beam.
7
The density of 0.1 M Cu(ClO4)2 in 1 M HClO4 was measured as 1.14±0.01 g/cc. The
density of 1 M HClO4 solvent is 1.056 g/cc,7 leaving the contribution to density of the
copper perchlorate as 0.08 g/cc. This latter value was used to calculate the 1/e attenuation
length.
Both solutions will show slight self-absorption broadening, the 45º geometry of the
frozen solution causing the greater effect. However, the liquid solution showed the
greater broadening (manuscript Figure 2), indicating that the disparity of intensities in the
EXAFS or FT spectra is not due to self-absorption.
4. EXAFS Test for axial oxygen scatterers in liquid-phase [Cu(aq)] 2+
Figure S4.1: Liquid solution EXAFS weighted goodness-of-fit F-value vs. distance for:
(a), a CuO4 fragment plus a fifth oxygen scatterer, or; (b), a CuO4O1 fragment plus a sixth
oxygen scatterer.
In the tests of Figure S4.1a, the Cu-Oeq distance was floated but remained at 1.96 Å
throughout. For Figure S4.1b, the Cu-O1ax was fixed at its prior best-fit 2.29 Å distance.
All σ2 values were floated while higher shell ΔE0 values were linked to the first shell
ΔE0, which was floated. The best-fit minima were: (a), 2.29 Å and 3.26 Å, and; (b), 2.50
Å and 3.26 Å. Geometries are based on prior knowledge.
8
5. Fits to the EXAFS of 0.1 M [Cu(ClO4)2] in liquid aqueous 1 M HClO4.
Figure S5.1: K-edge Fourier transform EXAFS spectrum of: (○), 0.1 M Cu(ClO4)2 in
liquid 1 M HClO4 solution; (▬) JT-octahedral fit;(▬) unfit residual. Inset: The fit to the
EXAFS and the unfit residual.
Figure S5.2: K-edge Fourier transform EXAFS spectrum of: (○), 0.1 M Cu(ClO4)2 in
liquid 1 M HClO4 solution; (▬) split axial fit’;(▬) unfit residual. Inset: The fit to the
EXAFS and the unfit residual.
9
Figure S5.3: K-edge Fourier transform EXAFS spectrum of: (○), 0.1 M Cu(ClO4)2 in
liquid 1 M HClO4 solution; (▬) axially elongated square pyramidal fit; (▬) unfit
residual. Inset: The fit to the EXAFS and the unfit residual.
6. EXAFS Test for axial oxygen scatterers in frozen-phase [Cu(aq)] 2+
Figure S6.1: Frozen solution EXAFS weighted goodness-of-fit F-value vs. distance for:
(a), a CuO4 fragment plus a fifth oxygen scatterer, or; (b), a CuO4O1 fragment plus a sixth
oxygen scatterer.
For the tests shown in Figure S6.1, the Cu-Oeq distance was floated but remained 1.96 Å
throughout. In (b), Cu-Oax1 was fixed at the prior best-fit distance of 2.35 Å. The best-fit
10
minima were: (a), 2.35 Å and 3.31 Å, and, (b), 2.44 Å and 3.32 Å. Geometries are based
on prior knowledge.
7. Fits to the EXAFS of 0.1 M [Cu(ClO4)2] in frozen aqueous 1 M HClO4.
Figure S7.1: K-edge Fourier transform EXAFS spectrum of: (○), 0.1 M Cu(ClO4)2 in
frozen 1 M HClO4 solution; (▬) JT-octahedral fit, (▬) unfit residual. Inset: The fit to the
EXAFS and the unfit residual.
Figure S7.2: K-edge Fourier transform EXAFS spectrum of: (○) 0.1 M Cu(ClO4)2 in
frozen 1 M HClO4 solution; (▬) split axial fit, (▬) unfit residual. Inset: The fit to the
EXAFS and the unfit residual.
11
Figure S7.3: K-edge Fourier transform EXAFS spectrum of: (○) 0.1 M Cu(ClO4)2 in
frozen 1 M HClO4 solution; (▬) axially elongated square pyramidal fit, (▬) unfit
residual. Inset: The fit to the EXAFS and the unfit residual.
8. MXAN fits to the XAS of 0.1 M Cu(ClO4)2 in liquid phase 1 M HClO4
Figure S8.1: Results from the MXAN study of the first coordination shell of [Cu(aq)]2+ in
liquid aqueous 1 M HClO4: (○) K-edge XAS spectrum, and; (▬) JT-Oh; (▬) split-axial,
and; (▬) axially elongated square pyramidal fits. Panel a: fit over the full energy range,
also showing the Rsq values and the best fit structural models. Panel b: close-up of the
rising K-edge energy region. The intensity of the K-edge shoulder near E-E0 = 2 eV
increases with axial scatterers. The split axial and JT-Oh spectra have been vertically
offset by 0.5 and 1.0 normalized units, respectively, for clarity.
12
Table S8.1: Model-Based First Shell MXAN Metrics for Liquid-Phase [Cu(aq)]2+
Model →
JT-Octahedral
Split Axial
Square Pyramidal
Structural Water↓ CN
R (Å)
CN
R (Å)
CN
R (Å)
(H2O)eq
4
1.98±0.01 4 1.95±0.01 4
1.95±0.03
(H2O)ax1
2
2.49±0.01 1 2.17±0.01 1
2.26±0.02
(H2O)ax2
--1 2.83±0.03 --Rsq
6.96
2.55
2.24
Axial-equatorial bond angles were fixed at 90º.
Table S8.2: Alternative MXAN Split Axial Metrics for Liquid Phase [Cu(aq)]2+
Model →
Split Axial #2
Split Axial #3
Structural Water↓ CN
R (Å)
CN
R (Å)
(H2O)eq
4
1.94±0.01 4
1.94±0.01
(H2O)ax1
1
2.13±0.09 1
2.06±0.03
(H2O)ax2
1
2.76±0.07 1
2.85±0.04
Second Shell H2O
8
3.6±0.3
8
3.7±0.3
92º
95º
Oax-Cu-Oeq
Rsq
1.99
2.06
Systematic plus statistical uncertainty in second shell water distance
includes positional variation. Bond angle uncertainty is ±2º.
9. MXAN fits to the XAS of 0.1 M Cu(ClO4)2 in frozen-phase 1 M HClO4
Figure S9.1: (○), K-edge XAS spectrum of frozen-phase 0.1 M Cu(ClO4)2 in aqueous 1
M HClO4. MXAN fits to the XAS spectrum: (▬) JT-Oh plus 8-water second shell; (▬)
split-axial plus 8-water second shell, and; (▬) axially elongated square pyramidal, no
second shell. Panel a: fit over the full energy range, also showing the Rsq values and the
structural models. Panel b: close-up of the rising K-edge energy region. The split axial
13
and JT-Oh spectra have been vertically offset by 0.5 and 1.0 normalized units,
respectively, for clarity.
Table S9.1: MXAN Single Site Fits for 0.1 M [Cu(ClO4)2] in Frozen 1 M HClO4
Model →
JT-Octahedral
Split Axial
Square Pyramidal
Structural Water↓ CN
R (Å)
CN
R (Å)
CN
R (Å)
(H2O)eq
4
1.94±0.02 4 1.97±0.02
4
1.93±0.02
(H2O)ax1
2
2.47±0.08 1 2.55±0.05
1
2.24±0.21
(H2O)ax2
----1 2.85±0.04 ----nd
2 Shell Waters
8
3.8±0.7
8
4.1±0.8
----Rsq
7.63
4.61
3.29
Systematic plus statistical uncertainty in the second shell water distances includes positional
variation.
Figure S9.2: (○), K-edge XAS spectrum of frozen-phase 0.1 M Cu(ClO4)2 in aqueous 1
M HClO4; (▬) MXAN fit using an axial perchlorate plus 8-water second shell structural
model. Panel a: fit over the full energy range, also showing the Rsq value and the
structural model. Panel b: close-up of the rising K-edge energy region.
14
Table S9.2: MXAN Axial Perchlorate Fit for 0.1 M [Cu(ClO4)2] in Frozen 1 M HClO4
Model →
Axial Perchlorate
Structural Shells↓
CN
R (Å)
(H2O)eq
4
1.94±0.03
(H2O)ax
1
2.37±0.01
(O3Cl-O)ax
1
3.2±0.2
nd
2 Shell Waters
8
3.4±0.6
Rsq
3.77
Systematic plus statistical uncertainty in second shell water distance includes positional
variation.
Figure S9.3: (○), K-edge XAS spectrum of frozen-phase 0.1 M Cu(ClO4)2 in aqueous 1
M HClO4; (▬) iterative 0.5 split axial and 0.5 axial perchlorate two-site fit (Figure S12
and Table S4); (▬) linear combination (LC) of the single site split axial and axial
perchlorate fits, and; (▬) the two-site fit minus LC difference. See the text for further
discussion.
15
Supporting Information Addendum
EXAFS (k = 2-13 Å ) and MXAN XAS fits for crystalline [Cu(H2O)6](ClO4)2 and 0.10 M
Cu(ClO4)2 in liquid-phase 1 M HClO4: Can the structures be distinguished?
-1
An EXAFS and MXAN analysis was carried out of strictly axially-elongated crystalline
Jahn-Teller octahedral [Cu(H2O)6](ClO4)2.8 This was compared with the XAS analyses of
liquid- and frozen-phase 0.10 M [Cu(ClO4)2] in 1 M HClO4, in order to determine
whether the solution structures are distinguishably different from the crystalline structure.
The EXAFS analyses were limited to the k = 2-13 Å-1 range throughout because the
commercial crystalline complex has a zinc impurity requiring k = 13 Å-1 truncation.
Summary of Results
1. From EXAFS amplitude ratios: the Cu(II) liquid solution state structure is different
from the [Cu(H2O)6](ClO4)2 crystalline complex in both the frozen and solution-phases.
The two liquid structures are far more similar to one another than either is to the
crystalline complex (Section 2).
2. For the crystalline complex, both axial scatterers achieve an EXAFS goodness-of-fit Fvalues minimum at a single axial ligand distance. However, for the liquid-phase
complex ion, F-value minima indicate two different axial distances (Section 3).
3. Full EXAFS analysis of the [Cu(H2O)6](ClO4)2 crystalline complex unmistakably
converged to the JT-octahedral model. The split axial or square pyramidal models were
as clearly rejected (Section 4).
4. The split axial and JT-octahedral EXAFS fits are not statistically distinguishable over
k-range 2-13 Å-1, but are so over k = 2-18 Å-1 (Section 4).
5. MXAN analysis of the Cu K-edge XAS of the solution-phase complex, constrained to
a symmetrical JT octahedral core, produced a fit definitively poorer than the fit using
the split axial core (Section 5).
A1. Comparative EXAFS
Figure A1 compares the EXAFS spectra of crystalline [Cu(H2O)6](ClO4)2, and 0.10 M
[Cu(ClO4)2] in 1 M HClO4 in liquid or frozen solution. The spike at k = 13 Å-1 in the
EXAFS of the crystalline complex shows the effect of the trace zinc impurity. All three
oscillations have nearly the same phase through k = 13 Å-1, because the EXAFS is
dominated by the four nearly invariant equatorial water ligands. The frozen solution and
the crystalline complex were measured at about the same temperature (10 K), but
nevertheless exhibit disparate amplitudes.
16
Figure A1. EXAFS spectra measured at about 10 K of crystalline [Cu(H2O)6](ClO4)2 and
of 0.10 M [Cu(ClO4)2] in 1 M HClO4 in frozen solution, or of liquid solution measured at
room temperature.
A2. EXAFS Amplitude Ratios
The mean-square fluctuation in atomic position, represented by σ2 in the EXAFS fits,
varies smoothly with temperature.9 As noted in equation S1, for a constant structure, the
amplitude ratio of EXAFS spectra measured at different temperatures should vary as
2
𝑒 −2𝑘 𝛾 , where γ=(𝜎12 − 𝜎22 ). In analogy to Figure S3.1, EXAFS amplitude ratios of the
liquid and crystalline states were tested.
Figure A2 shows the crystalline/liquid EXAFS amplitude ratio could not be fit at all
using the single exponential of equation S1. Figure A3 shows the same test of EXAFS
amplitude ratios for the frozen solution and crystalline states, which again could not be
reproduced using eqn. S1. The coefficients appearing in these fits is physically
meaningless.
These results imply that the structure of the crystalline [Cu(H2O)6](ClO4)2 complex is
dissimilar from that of aquated Cu(II) in either liquid or frozen 1 M HClO4.
17
Figure A2: EXAFS amplitude ratios: crystalline complex/solution state. Measurement
temperatures were 10 K and ambient, respectively. The amplitude ratio could not be fit
with the single exponential of equation S1. An unphysical coefficient was needed to
reproduce the steep descent. Overall, the conformance is poor.
Figure A3: EXAFS amplitude ratio of the crystalline complex/frozen solution state. The
fit again needed an unphysical coefficient to approach conformance.
Figure A4 compares the EXAFS amplitude ratio of the liquid and frozen states of 0.10 M
[Cu(ClO4)2] in 1 M HClO4. This EXAFS amplitude ratio could be much more closely
approximated with the single physically justified exponential.
18
In the context of Figure A2 and Figure A3, Figure A4 implies that the structures of 0.10
M [Cu(ClO4)2] in liquid or frozen 1 M HClO4. solution are far more similar to one
another than either is to the structure of crystalline [Cu(H2O)6](ClO4)2.
Figure A4. EXAFS amplitude ratio of 0.10 M [Cu(ClO4)2] in liquid vs. frozen 1 M
HClO4 solution.
A3. EXAFS Axial Distance Test
In these tests, the EXAFS goodness-of-fit is monitored while stepping the distance of the
axial oxygen. The first starting model was the square plane, to which one axial oxygen
was added. The axial Cu-O distance was then stepped. All other distances, all σ2 values
and the linked ΔE0 were optimized. This test determines the best-fit distance for a single
axial oxygen appended to a square planar core structure.
Following this, the best-fit square pyramid from the above test was further tested by
adding and step-wise varying the Cu-O distance of a second axial oxygen scatterer. This
tests the best-fit distance of a second axial ligand in the constant presence of the first. In
this test, the first axial ligand was kept fixed at its best-fit square pyramidal value. Other
parameters were optimized as noted above.
In a symmetrical Jahn-Teller axially elongated Oh structure, these tests should reveal two
nearly identical best fit Cu-O distances for the two isometric axial oxygen ligands. Figure
A5 shows this test carried out on the EXAFS of the crystalline [Cu(H2O)6](ClO4)2
complex.
19
Figure A5. Axial Cu-O distance tests of the EXAFS of crystalline [Cu(H2O)6](ClO4)2.
(▬), square plane plus one oxygen; (▬), square pyramid plus one oxygen. The EXAFS
k-range = 2-13 Å-1.The best-fit distances were: square plane plus oxygen, 2.31 Å; square
pyramid plus oxygen: 2.29 Å. In the crystal structure, 2×Cu-O = 2.38 Å. The minimum at
3.29 Å corresponds to the Cu-Oeq-Oeq-Cu triangular multiple scattering path, to which
Feff8 assigned a 9% relative intensity.
Figure A5 shows the expected result deriving from a true axially elongated
centrosymmetric JT-octahedral structure with two identical Cu-Oax distances.
Figure A6 shows the same experiment done using the EXAFS of Cu(II) perchlorate in
liquid 1 M HClO4.
Figure A6. Axial Cu-O distance tests of the EXAFS of liquid solution-phase 0.10 M
[Cu(ClO4)2] in 1 M HClO4 over EXAFS k-range = 2-13 Å-1. (▬), square plane plus one
oxygen; (▬), square pyramid plus one oxygen. The best-fit distances: square plane plus
oxygen, 2.28 Å; square pyramid plus oxygen: 2.39 Å.
20
The Cu-Oeq-Oeq-Cu triangular multiple scattering paths were not found by Feff8 in the
XAS of the solution model, despite the same 3-leg criterion and the same intensity cutoff
(2%).
Figure A7: Comparison of k = 2-13 Å-1 EXAFS axial Cu-O distance tests, square plane
plus one oxygen: (▬), liquid solution-phase 0.10 M [Cu(ClO4)2] in 1 M HClO4, and;
(▬), crystalline [Cu(H2O)6](ClO4)2.
Figure A8: Comparison of k = 2-13 Å-1 EXAFS axial Cu-O distance tests, square
pyramid plus one oxygen: (▬), liquid solution-phase 0.10 M [Cu(ClO4)2] in 1 M HClO4,
and; (▬) crystalline [Cu(H2O)6](ClO4)2.
21
Figure A7 compares the liquid-phase and crystalline square plane plus one oxygen
EXAFS axial test result while Figure A8 compares the homologous square pyramid plus
one oxygen result. The behaviors are disparate, in that the axial distances of the solution
complex bracket the invariant axial distances of the crystalline complex. This result puts
metrics onto the structural variance indicated by the EXAFS amplitude ratio tests.
A4. Full EXAFS Fits
A4.1 Crystalline [Cu(H2O)6](ClO4)2 EXAFS fits were carried out over the range k = 2-13
Å-1. Initially, the three basic core models, namely axially elongated square pyramid, split
axial, and JT axially elongated octahedron, were compared. These fits are shown in
Figure A9 and Figure A10.
For small to moderate shifts in initial conditions, the split axial fit quickly converged
back to the JT-octahedral axial distance. If the initial Cu-Oax2 distance was set to R ≤ 2.55
Å, the distance reverted to the fit shown in Table A1. For larger shifts in initial
conditions, 2.75 Å ≤ R ≤ 2.95 Å, the OPT routine crashed. When the initial Cu-Oax2 R ≥
3.05 Å, the axial distance refined to R = 3.29 Å (σ2 = 0.00697), i.e., the distance
representing the crystalline multiple-scattering path (F = 0.1902).
Figure A9: Basic first-shell core-model fits to the EXAFS of crystalline
[Cu(H2O)6](ClO4)2. The models used are indicated on the face of the Figure.
22
Figure A10: Fourier transforms of the EXAFS of crystalline [Cu(H2O)6](ClO4)2 and of
the core-model fits. The models used are indicated on the face of the Figure.
Table A1: Fits to the EXAFS of [Cu(H2O)6](ClO4)2 Using First-Shell Core Models
Square Pyramid
Split Axiala
JT-Octahedral
2
2
CN
R (Å)
σ
R (Å)
σ
R (Å)
σ2
4 Oeq
1.96
0.00530
1.96
0.00523
1.96
0.00524
1 Oax1
2.33
0.00498
2.32
0.00962
2.33
0.01014
1 Oax2
----2.35
0.01029 (2.33) (0.01014)
ΔE0 (eV)
-6.1982
-5.6636
-5.7289
F-value
0.2052
0.1710a
0.1710
a. The split axial fit converged to the JT-octahedral model.
These results show a clear preference for the JT-Oh model over the square pyramidal for
crystalline [Cu(H2O)6](ClO4)2, and further show the instability of the split axial model
toward the JT-octahedral fit phase-space minimum. This behavior marks a distinct
departure from the performance of fits to the liquid solution Cu(II) EXAFS.
Figure A11 shows fit to the EXAFS of crystalline [Cu(H2O)6](ClO4)2, using the full
centrosymmetric axially elongated JT-octahedral model.
23
Figure A11. (o) Fourier transform of the Cu K-edge EXAFS of crystalline
[Cu(H2O)6](ClO4)2; (▬), the fit using the JT-Oh model, and; (▬), the unfit residual.
Inset: (o), the EXAFS; (▬), the fit, and; (▬), the unfit residual.
The parameters of the full JT Octahedral fit are given in Table A2 below. The analogous
square pyramidal fit was overall a bit poorer (weighted k-value = 0.1261), but the single
axial ligand σ2 value was unphysical (R = 2.34 Å, σ2 = -0.00296), rendering the fit
unacceptable. Likewise, the split axial form of this fit produced bifurcated axial
distances, but again with negative σ2: Cu-Oax1 = 2.26 Å, σ2 = 0.01725; Cu-Oax2 = 2.36 Å,
σ2 = -0.00045; weighted F-value = 0.1249. This fit, too, proved unacceptable.
Table A2: JT-Octahedral Model Fit to the EXAFS of crystalline [Cu(H2O)6](ClO4)2
CN
R (Å)
σ2
4 Oeq
1.96
0.00543
2 Oax
2.33
0.00694
8 Heq
2.65
0.00696
8 Oeq-Heq MS
2.91
0.00359
16 Oeq-Oeq cis-triangular MS
2.98
0.01225
6 Oeq-Oeq trans-linear MS
4.14
0.00950
3 Oax-Oax trans-linear MS
4.66
0.00738
ΔE0 (eV)
-5.7693
Weighted F-value
0.1244
24
These results show that analysis of the crystalline complex EXAFS is able to distinguish
among alternative models, in favor of the JT-octahedral, even over the limited k = 2-13
Å-1 range.
A4.2 Liquid-phase [Cu(ClO4)2] in 1 M HClO4. In contrast, and as shown in the
manuscript, analysis of Fourier-filtered EXAFS over k=2-13 Å-1 is unable to distinguish
among the same alternative models for liquid solution-phase Cu(II) in 1 M HClO4.
Illustrated below (Figure A12 and Figure A13), analysis of the liquid solution EXAFS
over a range k = 2-13 Å-1, produced a slightly better weighted F-value for the split axial
model relative to the octahedral for the solution structure. This result is consistent with
the distinct preference for disparate Cu-Oax distances, as indicated in Section A3 above.
The goodness-of-fit weighted F-values were 0.1117 (JT Octahedral) and 0.1003 (split
axial), respectively. The statistical validity of the difference in two weighted F-values can
be determined using the F-criterion of Michalowicz, et al.,10 which takes into account any
difference in the number of fit degrees of freedom:
F = [12   22 ) /( 1  2 )] /(  22 / 2 )
A1
where  n2 is the Chi-squared value of fit “n”, νn = Nind – Npar is the degrees of freedom
in the fit, Nind is the number of independent data points, and Npar is the number of
adjustable parameters. The Nind in an EXAFS fit are calculated using the Stern equation,
N ind  (2  Rk  )  2 .11 In the k = 2-13 Å-1 fits, with Fourier transform R-range = 3.5
Å, Nind = 26.
To test whether the k = 2-13 Å-1 JT-octahedral (JT) and split axial (SA) fits are
2
2
statistically distinguishable,  JT
= 0.04431 and νJT = 11,  SA
= 0.03879 and νSA = 9,
and finally, the Michalowicz F = [(5.52×10-3)/2]/4.31×10-3 = 0.64.
The Michalowicz criterion is that an alternative fit is statistically distinguishable when
F>1. Over the k = 2-13 Å-1 EXAFS range, the split axial fit is thus statistically
indistinguishable from the JT octahedron. Over the manuscript k = 2-18 Å-1 range, Nind =
2
2
37,  JT
= 0.08417 and νJT = 22,  SA
= 0.07266 and νSA = 20, and the Michalowicz F =
[(1.15×10-2)/2]/(3.63×10-3) = 1.58.
25
Figure A12. (-o-), k = 2-13 Å-1 copper K-edge EXAFS of liquid solution-phase Cu(II)perchlorate in 1 M HClO4, and the fits: (▬), JT-octahedral model, and; (▬), split axial
model.
Table A3: k = 2-13 Å-1 EXAFS Metrics of the Fits to Solution-Phase Cu(II)-Perchlorate
JT-Octahedral
Split Axial
2
CN
R (Å)
σ
CN
R (Å)
σ2
4 Oeq
1.96
0.00647
4 Oeq
1.96
0.00658
2 Oax
2.29
0.01549
1 Oax1
2.24
0.00566
------1 Oax2
2.41
0.00777
8 Heq
2.55
0.01527
8 Heq
2.58
0.00926
1 Osolv1
3.25
0.00780
1 Osolv1
3.24
0.00854
1 Osolv2
3.48
0.00884
1 Osolv2
3.47
0.00904
2 Osolv3
3.75
0.00519
2 Osolv3
3.75
0.00578
1 Osolv4
3.91
0.00246
1 Osolv4
3.90
0.00324
ΔE0 (eV)
-7.5287
-7.8200
Weighted F-value
0.1117
0.1003
2
Fit Δχ
0.04431
0.03879
26
Figure A13. Fourier transforms of the EXAFS and fits for liquid solution-phase Cu(II)perchlorate in 1 M HClO4shown in Figure 12. The two fits are again indistinguishable.
A5 MXAN Fits
An MXAN fit was carried out using the JT-octahedral structure of the crystalline
complex as the input model. All the surrounding oxygens within 4.33 Å were included,
providing fourteen second shell atoms mimicking a solvation array. The distances and
angles were kept fixed, while the non-structural parameters, most importantly the
interstitial potential and the muffin-tin radii, were optimized to maximize correspondence
to the XAS spectrum of 0.10 M [Cu(ClO4)2] in 1 M HClO4.
In the fit using crystal structure coordinates, the structured continuum feature near 60 eV
(E-E0) reflects the regularity of the second shell. Likewise, the strong shoulder on the
rising K-edge, which is greatly attenuated in the experimental XAS, is a scattering feature
arising from equidistant axial water molecules.
As a further test of the JT-octahedral model, an MXAN fit was performed that allowed
the axial distances to optimize. The equatorial Cu-O distances were also refined. An
eight-water second shell was substituted for the oxygen atoms of the crystal structure.
The Cu-O distances to the second shell water molecules were also optimized.
27
Figure A14. (o) XAS of 0.1 M Cu(ClO4)2 in 1 M HClO4,and the best MXAN fit using;
(▬), the crystal structural metrics of [Cu(H2O)2](ClO4)2, and; (▬), the split axial model.
During this fit, the axial waters moved to 2.58 Å, while equatorial ligands remained near
the crystal structure values. The region near E-E0 = 60 eV improved greatly. The
octahedral fit to the XAS is shown in Figure A15, along with that of the split axial model.
In the rising K-edge XAS of the JT-Oh core model fit, the extra intensity in the shoulder
again arises from the scattering of the symmetrical axial ligands. With the split axial
model, both the rising K-edge andthe continuum features are better reproduced. The quite
disparate Rsq values definitively favor the non-centrosymmetric split axial model.
Table A4 provides the metrics of all the MXAN fits. It is interesting to note that the sums
of the axial distances in the two structurally optimized models are nearly the same. It
seems likely that the MXAN routine minimizes the error of the JT-octahedral model by
centering the two axial ligands at an intermediate position between the two scattering
paths.
28
Figure A15. (o) Copper K-edge XAS spectrum of 0.1 M Cu(ClO4)2 in 1 M HClO4, and
the MXAN fits using: (▬), the best JT-octahedral core model, Rsq = 4.20, or; (▬), the
split axial structural model, Rsq = 1.43. Both MXAN structural models included the
analogous 8-water second shell.
Table A4: MXAN Metrics JT-Octahedral and Split Axial Models
CN
4Oeq
Oax1
Oax2
Osolv
Rsq
Crystal
Structure
1.966
2.382
2.382
--3.32
JT
Octahedral
1.99±0.02
2.58±0.04
2.58±0.04
3.8±0.6
4.20
Split Axial
1.94±0.03
2.06±0.07
2.99±0.23
3.7±0.3
1.43
Figure A16 compares the second derivatives of the rising K-edges, again illustrating the
clear superiority of the split axial model.
29
Figure A16. Second derivatives of: (-o-), the rising Cu K-edge XAS of 0.1 M Cu(ClO4)2
in 1 M HClO4, and of the MXAN fits using: (▬), the fitted JT-Oh core, or; (▬), the split
axial core. Both MXAN fits include the same second shell solvation array.
These MXAN fitting experiments make clear that the axially elongated JT-octahedron
does not describe the structure of Cu(II) in water solution. The definitive result confirms
MXAN as an excellent method of obtaining structural information from XAS spectra,
especially when only a more limited range of data (k = 2-13 Å-1) is available and EXAFS
analysis alone yields ambiguous results.
Together, the MXAN and EXAFS comparative analyses of the copper K-edge XAS of
crystalline [Cu(H2O)6](ClO4)2 and liquid-phase 0.1 M Cu(ClO4)2 in 1 M HClO4 solution
show that both EXAFS and MXAN can distinguish the crystalline complex from the
solution complex.
The EXAFS amplitude ratio comparisons and the axial distance tests favor the split axial
model, despite the ambiguous goodness of fit of the full k = 2-13 Å-1 EXAFS analysis.
MXAN analysis is able to definitively resolve the split axial model from the JT
octahedral model as the preferred liquid-phase structural model.
Even over the more limited k = 2-13 Å-1 EXAFS range, both methods taken in
conjunction unambiguously argue for the split axial model and against a solution
complex ion composed of, or dominated by, a centrosymmetric axially elongated JToctahedral structure.
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S. Della Longa et al., Biophys. J. 85, 549 (2003).
30
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G. N. George et al., J. Synchr. Radiat. 19, 875 (2012).
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J. C. Gallucci, and R. E. Gerkin, Acta Cryst. C 45, 1279 (1989).
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3
31