New Insights in the Catalytic Activity of Cobalt Orthophosphate Co3(PO4)2 from Charge Density Analysis

Article abstract of DOI:10.1002/chem.201902303

An extensive characterization of Co₃(PO₄)₂ was performed by topological analysis according to Bader‘s Quantum Theory of Atoms in Molecules from the experimentally and theoretically determined electron density. This study sheds light on the reactivity of cobalt orthophosphate as a solid-state heterogeneous oxidative-dehydration and -dehydrogenation catalyst. Various faces of the bulk catalyst were identified as possible reactive sites given their topological properties. The charge accumulations and depletions around the two independent five- and sixfold-coordinated cobalt atoms, found in the topological analysis, are correlated to the orientation and population of the d-orbitals. It is shown that the (011) face has the best structural features for catalysis. Fivefold-coordinated ions in close proximity to advantageously oriented vacant coordination sites and electron depletions suit the oxygen lone pairs of the reactant, mainly for chemisorption. This is confirmed both from the multipole refinement as well as from density functional theory calculations. Nearby basic phosphate ions are readily available for C?H activation.

Full text of DOI:10.1002/chem.201902303

A Journal of
Accepted Article
Title: New insights in the catalytic activity of cobalt orthophosphate
Co3(PO4)2 from charge density analysis
Authors: Dietmar Stalke, Helena Keil, Matti Hellström, Claudia Stückl,
Regine Herbst-Irmer, and Jörg Behler
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To be cited as: Chem. Eur. J. 10.1002/chem.201902303
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Chemistry - A European Journal
10.1002/chem.201902303
RESEARCH ARTICLE
New insights in the catalytic activity of cobalt orthophosphate
Co
3
(PO
4
2
) from charge density analysis
[
a]
[b,c]
[a]
[a]
[b]
Helena Keil , Matti Hellström , Claudia Stückl , Regine Herbst-Irmer , Jörg Behler , Dietmar
Stalke*[
a]
Abstract: An extensive characterization of Co
3
(PO
4
)
2
was
materials development process. Electron density (ED) investiga-
tions provide an ideal tool for understanding these interactions.[
Already in 1932, Pauling[4] proposed an interrelation between the
structure of a compound and its properties:
3]
performed by topological analysis according to Bader‘s Quantum
Theory of Atoms in Molecules from the experimentally and
theoretically determined electron density. This study sheds light
on the reactivity of cobalt orthophosphate as a solid-state hete-
rogeneous oxidative dehydration and dehydrogenation catalyst.
The topological properties identified various faces of the bulk
catalyst as possible reactive sites. The charge accumulations and
depletions around the two independent five- and six-fold
coordinated cobalt atoms, found in the topological analysis, are
correlated to the orientation and population of the d orbitals. It is
shown that the (011) face has structural features best for catalysis.
Five-fold coordinated ions in close proximity to advantageously
oriented vacant coordination sites and electron depletions suit the
reactant’s oxygen-lone pairs most for chemisorption. This is
confirmed both from the multipole refinement as well as from
density functional theory calculations. Close-by basic phosphate
ions are readily available for C–H activation.
The properties of a compound depend on two main factors, the nature of the
bonds between the atoms, and the nature of the atomic arrangement. […] The
satisfactory description of the atomic arrangement in a crystal or molecule
necessitates the complete determination of the position of the atoms relative to
one another.
From the knowledge of the distances at the atomic level and
the arrangement in the solid phase many properties, both at the
molecular and macroscopic scale, can be deduced. However, the
most basic concepts such as the chemical bond and reactivity are
still vigorously discussable.
Introduction
Scheme 1. Catalytic reaction of butan-2-ol with oxygen to the products
butene and butenone.[5]
The synthesis of today’s bulk chemicals heavily relies on catalysis,
reducing energy consumption and preventing waste in atom-
economically tailored reaction sequences.[1,2] The design of ap-
propriate reagents, precisely adapted to the specific demand, is
one of the fundamental objectives in chemistry. While the exact
synthetic targets might differ, the aim is always the same:
selective replacement of individual atoms or residues within a
material to fine-tune its properties and by these means its reac-
tivity or functionality. As a major draw-back it is still not always
predictable which alterations cause the desired effects. Hence the
benchmarking of working models along established concepts is
required. The proper understanding of the structure / property
relation of a chemical system is vital for the improvement of the
Single crystal structural analyses based on the independent atom
model only provide the positions of the centroids of the atoms and
the distances between the atoms. In contrast, the multipole model
from high resolution data provides physically meaningful
properties far beyond simple geometrical considerations. In this
paper we investigate the ED in catalytically active cobalt
orthophosphate Co (PO ) (Scheme 1) derived from both, high
resolution diffraction data and density functional theory (DFT)
calculations, to get some insight in the various properties
contributing to that activity. Not only the bonding is studied but
also the ED distribution at the two different metal sites is
determined and linked to various substrates.
3
4 2
[
a]
H. Keil, Dr. A. C. Stückl, Dr. R. Herbst-Irmer, Prof. D. Stalke
Universität Göttingen
Results and Discussion
Institut für Anorganische Chemie
Tammannstraße 4, 37977 Göttingen
E-mail: dstalke@chemie.uni-goettingen.de
Cobalt orthophosphate crystallizes in the monoclinic space group
[6,7]
P2
P2
1
/n, while in earlier publications
sometimes the other setting
/c was chosen. Furthermore, a metastable phase[ of cobalt
8]
1
[
[
b]
c]
Dr. M. Hellström, Prof. J. Behler
orthophosphate is known in the non-standard setting P2
1
/b. The
Universität Göttingen
Institut für Physikalische Chemie, Theoretische Chemie
Tammannstraße 6, 37077 Göttingen
unit cell contains two formula units of Co (PO . One of the two
3
4 2
)
independent Co(II) atoms is six-fold coordinated in an
approximately ideal octahedral fashion (Figure 1a). The second is
Dr. M. Hellström
Software for Chemistry and Materials B.V.
De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
five-fold coordinated, giving
a severely distorted trigonal
bipyramidal coordination polyhedron (Figure 1b). The octahe
Supporting information for this article is given via a link at the end of
the document.
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Chemistry - A European Journal
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RESEARCH ARTICLE
Coppens[11] formalism, was employed. It enables the description
of aspherical ED by spherical harmonics, where the total density
is partitioned in a spherical core density, a spherical valence and
an aspherical deformation valence density. To describe the
aspherical density local coordinate systems are necessary. We
used DFT calculations, together with manual judgment, to
determine the pertinent local coordinate systems, because the
actual coordination polyhedra around the Co ions in Co (PO )
3 4 2
are distorted from the ideal polyhedra (for details see SI). The
definition of the local coordinate systems is found in Figure 3a and
b. The so derived ED can be investigated by a complete
topological analysis according to QTAIM,[
12]
based on the
Figure 1. Different environments of a) Co[6o] and b) Co[5by]. The coordination
polyhedron of phosphorus is colored in magenta and that of Co in bronze.
experimental diffraction data (MM-Expt) as well as the structure
factor derived from DFT calculations (MM-DFT), where the prefix
MM- is short for multipole model. In the Bader methodology the
presence of bond critical points (BCP) in the molecular graph is a
prerequisite for an interaction between two atoms. The features
at the BCP are also an indication for the bonding type and the
drally coordinated Co ion is O-corner-sharing connected to six
different phosphate ions; that inside the distorted bipyramidal
polyhedron only to four different anions (Figure 2). Three are
corner-sharing and one is edge-sharing connected to the metal.
The asymmetric unit contains only half the formula unit, hence the
octahedrally coordinated Co atom is located on a center of
symmetry and the five-fold coordinated on a general position.To
judge whether the latter polyhedron is closer to a square-
pyramidal or to a trigonal-bipyramidal structure, the τ parameter
proposed by Addison[9] was determined. It is defined as τ = (β
strength of a bond, which might correlate with the distance.[12]
A
consistent set of critical points was found for cobalt phosphate.
They obey Morse’s relation[13] 푛 − 푏 + 푟 − 푐 = 0 (where n, b, r and
c are the numbers of nuclei, bond, ring and cage critical points,
respectively).
Phosphate. Regarding the nature of the P−O bonds in
phosphate there is still a long-standing discussion about the
presence or absence of double bond character, hence also about
the presence or absence of valence expansion at the phosphorus
atom. Different theoretical calculations led to various binding
models. Molina and Sundberg et al.[14] investigated the bonding
situation of several theoretically calculated and geometry-
optimized structures by means of QTAIM. They showed that the
P−O bond in phosphane oxide is best described with a highly
polar σ bond with a considerable electrostatic contribution. The
same is valid for iminophosphoranes[15]. Durrant[16] calculated the
–
α)/60° where β is the largest and α the second largest ligand-
metal-ligand angle. For an ideal trigonal bipyramidal geometry τ
is unity and for an ideal square geometry zero. Here it adopts a τ
value of 0.67, which suggests
bipyramidal environment.
a predominately trigonal
number of valence electrons at the phosphorus atom in PS 3–
to
4
be 7.94 and at the sulfur atom in sulfate to be 4.34. He, among
many others, regarded the P–O bond in phosphate as very polar.
For potassium sulfate, the high polarity of the S-O bond was
already established in an experimental charge density
investigation[ . In this study we also show for phosphate the
bond between phosphorus and oxygen to be a highly polar
covalent bond with no double bond character.[18] The evidence for
this stems from the high ED and a positive Laplacian, the trace of
the Hessian matrix of the second derivative of the ED function, at
the BCP. As expected, for all four P−O bonds a high ED was
17]
Figure 2. An excerpt from the crystal structure of cobalt phosphate, a)
alternating layers of phosphates and cobalt atoms and b) connectivity of Co-
polyhedra. The coordination polyhedra of phosphorus are colored in magenta,
those of Co are bronze. a, b, c are lattice constants.
found at the BCP, which suggests a covalent bond (Table 1). The
values vary from 1.54 to 1.61 eÅ-3 and are in a good agreement
with the theoretical data. For the Laplacian at the BCP, positive
Detailed bond lengths and angles are provided in SI. For the sake
of simplicity, the different Co atoms will from now-on be termed
-5
values were found in the range of 2 − 5 eÅ , which are slightly
-5
higher than those from theory (0 − 3 eÅ ). Since the BCP is
[
6o]
[5by]
Co
and Co , respectively, according to Machatschki’s
located in a rampant edge of the Laplace function, even a small
variation in the position of the BCP will cause a tremendous
change in the numerical value and sometimes even a change of
sign (Table 1, Figure S4-2). The ellipticity describes the deviation
of the charge density around a bond path from an ideal cylindrical
terminology.[
10]
Figure 2a shows the single crystal structure
composed from alternating layers of phosphate tetrahedra
colored in magenta and Co polyhedra in bronze. The latter are
connected through corners and edges to their adjacent Co
polyhedra (Figure 2b).
Topological analysis. In order to model the ED more
appropriately than feasible from the independent atom model
1 2 1 2
symmetry: ε = λ /λ − 1, where λ and λ correspond to the
eigenvectors of the Hessian matrix. Not surprisingly we found for
all P−O bonds  values close to zero, corresponding to  single
bonds. Figure
(
IAM), the multipole model (MM), based on the Hansen and
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RESEARCH ARTICLE
2
Table 1. Calculated BCPs and local energy density properties for MM-Expt (bold) and MM-DFT (normal). R: bond path; ρ(rBCP) ED at BCP;  ρ(rBCP): Laplacian at
BCP; ε: ellipticity of the bond; G(rBCP): kinetic energy density at BCP; V(rBCP): potential energy density at BCP; H(rBCP): total energy density at BCP. The oxygen
atoms marked with an X are generated by the symmetry code. X1: -1+x, +y, +z; X2: -1/2+x, 1/2-y, -1/2+z; X3: -x, 1-y, 1-z; X4: 1-x, 1-y, 1-z; X5: 1/2-x, 1/2+y, 3/2-z;
3 4 2
X6: 3/2-x, -1/2+y, 3/2-z; X7: 1/2+x, 1/2-y, -1/2+z; X8: 1+x, +y, +z. A picture of Co (PO ) including these oxygen atoms can be found in the Supporting Information.
For the sake of clarity, the values shown below have been rounded. The exact values for MM-Expt and MM-DFT including the standard deviation can be found in
the Supporting Information.
2
R
[
(A-B)
R
(A-BCP)
R
(B-BCP)
ρ(rBCP
)
 ρ(rBCP
)
G(rBCP)/ρ(rBCP
)
|V|(rBCP
)
H(rBCP)/ρ(rBCP)
A - B
ε
Å]
[Å]
[Å]
[eÅ -3
0.41
0.43
0.33
0.36
0.32
0.34
]
[eÅ -5]
[E
h
/e]
/G(rBCP
1.00
1.06
1.00
1.02
0.97
1.05
)
h
[E /e]
2.0565
2.0563
2.1438
2.1437
2.1694
2.1694
1.9774
1.9772
2.2218
2.2217
2.0190
2.0189
1.9889
1.9888
2.0079
2.0080
1.5334
1.5333
1.5318
1.5317
1.5556
1.5556
1.5413
1.5414
1.0081
1.0270
1.0464
1.0662
1.0555
1.0780
0.9731
0.9850
1.0942
1.1099
0.9995
1.0094
0.9813
0.9942
0.9937
1.0033
0.6332
0.6431
0.6327
0.6423
0.6417
0.6528
0.6362
0.6466
1.0484
1.0294
1.0974
1.0776
1.1138
1.0914
1.0043
0.9922
1.1276
1.1118
1.0195
1.0095
1.0076
0.9946
1.0143
1.0047
0.9002
0.8902
0.8991
0.8894
0.9139
0.9028
0.9051
0.8948
7.48
7.32
5.66
5.66
5.26
5.17
9.94
9.60
4.39
4.31
8.43
8.23
9.64
9.36
8.98
8.75
4.82
2.59
5.04
2.85
1.93
-0.13
3.70
1.51
0.05
0.06
0.03
0.07
0.02
0.05
0.05
0.03
0.05
0.07
0.03
0.04
0.04
0.02
0.02
0.01
0.03
0.01
0.01
0.00
0.02
0.01
0.01
0.01
1.30
1.25
1.18
1.14
1.14
1.10
1.41
1.37
1.04
1.03
1.33
1.31
1.40
1.36
1.37
1.33
1.24
1.17
1.25
1.19
1.13
1.07
1.20
1.13
0.00
-0.07
0.00
Co[6o]
O2
Co[6o]
Co[6o]
Co[5by]
Co[5by]
Co[5by]
Co[5by]
CO[5by]
P1
O1_X1
O3_X5
O1
-0.03
0.00
-0.03
-0.08
-0.11
0.00
0.52
0.53
0.30
0.30
0.46
0.47
0.51
0.52
0.48
0.49
1.59
1.58
1.61
1.61
1.54
1.54
1.57
1.57
1.05
1.08
1.03
1.03
1.03
1.05
1.04
1.07
1.03
1.06
1.83
1.90
1.82
1.90
1.93
2.01
1.86
1.94
O2_X8
O3_X8
O4_X6
O4_X7
O1
-0.03
-0.07
-0.06
-0.06
-0.10
-0.06
-0.08
-1.02
-1.05
-1.02
-1.06
-1.05
-1.07
-1.03
-1.06
P1
O2
P1
O3
P1
O4
S5-1 depicts the distances of the BCP from the oxygen atom
position from theory (MM-DFT) plotted above those from the
experiment (MM-Expt).
tetrahedrally oriented VSCCs would be expected due to the sp3
hybridization.[14] However, the number of VSCCs could neither
from MM-Expt nor from MM-DFT be resolved. As expected, one
bonding VSCC is located near the P-O bond axis. The VSCCs in
the non-bonding region pointing away from that bond are fused to
a toroidal orientation. Even with full refinement of all feasible
multipole parameters from theoretical data it was impossible to
resolve them. We retained from that endeavor because it clearly
indicated overfitting.[22] Local mirror symmetry had to be taken into
account. Additionally, the multipole population at all oxygen atoms
had to be set to be the same.
In the experiment the BCP is slightly more shifted towards the
electropositive phosphorus atom, indicating a marginally higher
ionic character in experiment than in DFT. Cremer and Kraka[19]
proposed to use the total energy density H to classify bonds. For
covalent bonds the potential energy dominates, resulting in a
negative total energy compared to closed shell interactions. In
addition, as introduced by Espinosa et al.[20], the ratio of potential
to kinetic energy density |V|/G can be used to distinguish between
shared, intermediate and closed-shell interactions. For a closed-
shell interaction, the ratio |V|/G at the bond critical point is less
than unity, for a shared interaction greater than two, and for an
intermediate interaction between one and two. The ratios |V|/G for
the P−O bonds ranging from 1.82 to 1.93 [1.90-2.01] are much
more on the side of the shared interaction. If the ratio of the kinetic
energy density per electron density at the BCP is greater than
unity this is indicative for polarity in a bond.
Co-O polyhedra. Compared to the covalent P-O bonds, the
Co-O bonds show a significantly lower ED in the range of approx.
0.32 to 0.52 eÅ-3 at the BCP. The Laplacian at the BCP is
-5
significantly more positive and ranges from 4 to 10 eÅ . The ED
increase correlates with the reduction in distance. In the
theoretical data set, ρ(rBCP) is slightly larger for all Co-O bonds,
showing a larger diversity at the Co[6o]-O bonds than the Co[5by]-O
bonds. The found trend also reflects, how the shared character
increases with the decrease of the coordination number. Except
for one, all Co[5by]-O bonds are shorter and have a greater value
for ρ(rBCP) than the Co[6o]-O bonds (Figure S5-2). This is also valid
For the P−O bonds in phosphate, we found a G(rbcp)/ρ(rbcp) ratio
greater than unity (1.07 to 1.25). Maxima of the negative
Laplacian represent Valence Shell Charge Contributions (VSCC).
VSCCs in the non-bonding regions are indicative for lone pairs,
frequently providing the link to the classical Lewis model and the
VSEPR theory.[21] For the phosphate oxygen atoms four
2
for many other M–O bonds. The value for ∇ ρ(rBCP) increases with
the decreasing bond distance, which has also been observed for
other transition-metal-oxygen inter-
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RESEARCH ARTICLE
(
(
(
+3.94 e (MM-Expt) and +3.69e (MM-DFT)) and cobalt atoms
+1.98 e (MM-Expt) and 1.22 e (MM-DFT) for Co[6o] and (+1.59 e
MM-Expt) and 1.11 e (MM-DFT) for Co[5by]). Expectedly, the
positive charge from both approaches is slightly higher for the six-
than for the five-fold coordinated metal atom.
Deformation Density. The static deformation density is
based on the difference between the total ED from the MM and a
spherical reference ED from the IAM. This already provides a very
informative picture of the ED distribution around the metal atoms.
Regions of negative charge concentrations are depicted in sky
blue and those of negative charge depletion in orange (Figure 3c
and d). Interestingly, the number of six charge concentration
regions coincides in both metals, but not the number of depleted
regions. Co[6o] shows only six minima, each directed to the
negatively charged phosphate oxygen atom, already fueling the
idea of an electrostatic Co–O interaction. In contrast, Co[
shows eight regions of negative deformation density arranged at
the eight corners of a cube. Five of the vertices point to a
coordinated phosphate oxygen atom each and the remaining
three exposed minima are left uncoordinated, indicating free
coordination sites.
5by]
Laplacian. The indications of the difference between the Co
atoms found in the deformation density are echoed in the
Laplacian. Each dark blue array in Figures 4e-h represents a
VSCC (Table 2). The red regions represent the negative charge
depletions. At Co[5by] the match between the features of the
Laplacian from either the MM-Expt and the MM-DFT refinement
is very good. At Co[ , on the other hand, differences, such as the
position and number of depletions are obvious. The MM-DFT data
give eight negative charge depletion points arranged into an
approximate cube (Figure 3i), and six VSCCs roughly in the
center of the faces formed by the cube of charge depletions.
6o]
Table 2 Experimental maxima of negative charge concentrations around the Co
atoms. Listed are the values for the Laplacian, electron density and the distance
of the maximum to the atom. The corresponding values for MM-DFT are shown
in the Supporting Information.
-
5
2
-3
d
VSCC-atom
atom
Co[6o]
−∇ ρ (eÅ )
ρ (eÅ )
(Å)
1367
29.24
29.62
30.96
31.53
31.72
32.07
32.32
32.29
32.58
0.3059
0.3054
0.3028
0.3016
0.3014
0.3011
0.3009
0.3009
0.3008
1
424
737
1
Co[5by]
1793
1817
1862
1889
1890
Figure 3. a) and b) local coordinate systems for Co[6o] and Co[5by]; c) and d)
-
3
show the deformation density with the iso-surface values of ± 0.65 eÅ for
negative charge accumulation in sky blue and positive charge in orange; e) and
f) show the coordination sites; g) and h) depict the Laplacian with iso-surfaces
-
5
-5
of 240 eÅ (red) and -1250 eÅ (blue) for the experimental, i) and k) theoretical
1916
-
5
-5
data with iso-surfaces of 260 eÅ (red) and -1260 eÅ (blue).
The vertices of the charge depletion cube do not fully coincide
with the ion ligand bonds. In contrast, from the experimental
multipole refinement (Figure 3g), there are only six charge
depletions, that form an octahedron with vertices approximately
along the six ion-ligand bonds.
Density of states and d orbital population. DFT calcula-
tions found the lowest energy when all Co ions were in high-spin
configurations. Figure 4 shows the calculated electronic density
actions and non-metal-oxygen interactions.[23] Comparing the
difference between the experimental and the theoretical data set,
2
the values for ∇ ρ(rBCP) in the Co−O bond are almost identical.
The ratios |V|/G for the Co−O bonds of 0.97-1.05 [1.02-1.08 from
theory] indicate rather a closed shell interaction. A hint towards
slight shared interaction in the Co-O bond is the negative total
energy density, H (rBCP).
Bader Charges. The Bader charges (Table S4-4) show for
both, MM-Expt and MM-DFT, pronounced positive phosphorus
of states, DOS, for Co
3 4 2
(PO ) . The high-spin complexes cause the
spin-up (majority spin) and spin-down (minority spin)
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RESEARCH ARTICLE
Table 3. d orbital population as percentage of total d population on the
respective atoms.
atom
orbital
dxz
MM-Expt
MM-DFT
DFT
Co[5by]
23.4
23.9
17.8
19.1
15.7
22.2
22.9
22.3
16.5
16.1
23.3
23.6
17.7
19.2
16.2
20.6
21.0
25.5
16.3
16.7
25.2
22.8
19.0
17.2
15.7
19.9
22.2
25.3
16.2
16.4
dyz
dxy
dx
2ꢀy2
dz
2
dxz
dyz
dxy
Co[6o]
dx
2ꢀy2
dz
2
Figure 4. DFT-calculated electronic density of states (DOS) and partial DOS
3 4 2 F
(PDOS) for Co (PO ) . The Fermi level (E ) is set to 0 eV.
We explain this discrepancy as follows. Because the three dxz,
dyz, and dxy orbitals at Co[6o] are occupied by only 5 electrons in
a high-spin state, there may be several nearly degenerate
solutions to the Schrödinger equation, and the present DFT
calculations have converged to one of them. To obtain a truly
accurate electronic description of the Co[6o] ion, it might therefore
be necessary to make use of more advanced computational
methods, such as multi-reference methods. Still, even with this
limitation for Co[6o], the agreement between the DFT calculations
components of the DOS to be quite different from each other. The
spin-down DOS features well-localized Co d states near the
valence band maximum (as seen from the partial DOS projected
onto the individual Co ions, orange and brown in Figure 4), with a
one-electron dd gap calculated to be around ~2.5 eV. The dd
transition energy is largely consistent with the experimentally
measured absorption maximum for Co (PO ) at 590 nm (= 2.10
3 4 2
eV);[24] the HOMO-LUMO gap is here taken to be only a first order
approximation to the excitation energy. In contrast, the spin-up
valence band has significant contributions from both the two
inequivalent Co ions in the range from -6 to 0 eV (where the zero
and the experiment is very good for Co[5by]
.
Maximally localized Wannier functions (MLWFs). In
order to visualize real-space analogs of the electronic bands from
the periodic DFT calculations, we calculated maximally localized
Wannier functions centered on the Co atoms. The resulting
MLWFs had clear connections to the d orbital populations, as well
as the locations of the negative charge depletion regions and
VSCCs around the Co ions. Because all five spin-up d orbitals are
occupied, they form a roughly spherical ED. The two spin-down
orbitals add to the ED in particular directions, as can be seen from
a comparison between the spin-down MLWFs and the VSCCs.
F
level is set to the Fermi energy at 0 K, E ).
The d orbital populations were estimated by using the local
coordinate systems around Co[5by] and Co[6o] from the multipole
model. The DOS was projected onto the individual d orbitals, and
the populations were found by integrating the DOS up to the Fermi
level. The resulting d orbital populations are given in Table 3 as
percentage of the total d populations on the respective atoms. The
table also gives the estimated d orbital populations from multipole
refinement on the DFT-calculated structure factors (MM-DFT), as
well as from the experimentally obtained structure factors (MM-
Expt). The table shows overall satisfactory agreement between
both populations, confirming that the high-spin state for both Co
ions, found in the DFT calculations, is also what is present in the
experiment.
The relative populations follow what is expected from simple
crystal field theory: for the distorted trigonal bipyramidal complex
around Co[5by], the populations of dxz and dyz (~24 % each) are
larger than those of dxy and dx ꢀy
2
2
(~18 % each), which are larger
than the population of dz
2
(~16 %). For Co[6o], which has a
distorted octahedral coordination environment, the populations of
dxz, dyz, and dxy (20–25 % from DFT calculations, ~22 % from the
experimental data) are greater than those of dx ꢀy
(
2
2
and dz
2
Figure 5. a) Positions of the VSCCs (blue) and negative charge depletion (red)
~16 %). Although for Co[6o] there is qualitative agreement in the
[5by]
around the five-fold coordinated Co
ion as calculated from multipole
refinements from DFT. b-h) Maximally localized Wannier functions (isovalue
dxz, dyz, and dxy orbital populations between DFT, MM-DFT, and
MM-Expt, we note that the populations obtained from the two
DFT-based methods have a noticeably higher population on dxy
25 %) as compared to dxz (20 %), whilst this is not the case from
the experimental data (where the orbitals have roughly the same
fractional population of 22 %).
-
3
[5by]
±
0.2 Å ) around Co . The chosen local coordinate system is indicated and is
illustrated in more detail in Figure 3a/b. b) and c) show spin-down functions
(orange and gray), together with the VSCCs (blue octahedron), d-h represent
spin-up functions (pink and cyan), together with charge depletion regions (red
approximate cube).
(
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Chemistry - A European Journal
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RESEARCH ARTICLE
Figure 5a depicts the negative charge depletion
points (red cube) at Co[5by]. Figure 5b-c show
the spin-down MLWFs, pointing
towards the directions of the VSCCs. Figure 5d-
h show the five spin-up MLWFs centered on
Co[5by]. Interestingly, there is a clear connection
between the charge depletion points and the
orientation of the spin-up MLWFs. In particular,
the two MLWFs in Figure 5d-g, which have
shapes that are reminiscent of atomic dz
2
orbitals, have one of their lobes pointing
towards the charge depletion point along one of
the equatorial Co-O bonds, and the other lobe
pointing towards one of the charge depletion
points that do not lie along any Co-O bond. In
fact, this latter type of charge depletion points
towards a small void in the crystal. The MLWFs
for Co[6o] are provided in the Supporting
Information.
We also consider the charge depletion
regions and MLWFs around two edge-sharing
[
5by]
Co
ions, and correlate these regions to the
(PO faces.
different orientation at various Co
3
4 2
)
The two (011) and (110) faces of cobalt
orthophosphate expose nearby Co[5by] ions.
Figure 7a shows a side view of the Co
3
4 2
(PO )
(
011) face. The arrows indicate the two edge-
[
5by]
sharing Co
atoms in the bulk; at the (011)
Figure 6. Space filled view of the four most stable crystal planes of cobalt phosphate according to the
Bravais, Friedel, Donnay and Harker theory. Red: oxygen, bronze: cobalt, phosphorus is hidden inside
face (top layer), the two ions only share one
ligand in the sub-face layer. The MLWF from the O
4
tetrahedra.
Figure 5 is shown superimposed on two of the face Co[5by] ions.
The blue lobes pointing out of the face are pointing along negative
charge depletion regions. Similarly, at the (110) face (Figure 7b),
the MLWF from Figure 5d have lobes pointing out of the face,
towards negative charge depletion regions. Considering
cooperativity between two nearby Co ions as e. g. stabilizing low
using a nickel-cobalt catalyst.[27] The reduction of p-nitrophenol to
p-aminophenol can be effectively catalysed by nano-sized solid
solutions of copper/cobalt molybdate and chromium
phosphate.[28] For a detailed study of the cobalt-substituted
calcium phosphate catalyst, which catalyses oxidative
dehydration and dehydrogenation, Legrouri et al.[29] used
propane-2-ol as a benchmark substrate for characterizing acid
and basic properties of solid-state catalysts (Scheme 1, vide
supra). The maximum catalytic effect was found at a cobalt
content of 0.32, which also represents the maximum solubility of
Co in calcium phosphate. The reactivity for ethane, propane,
butan-2-ol and propanol was studied by Aaddane et al.[5] and
plausibility for the reactivity was provided.
oxidation states[ or molecular conductors of electricity , this
pictures would suggest the crystal plane (011) as clearly
catalytically more active than any other.
25]
[26]
Considering the reaction of butan-2-ol with oxygen to
butene and butenone at least one of the two reactants must be
chemisorbed at the catalyst’s surface and thus be activated. If the
butanol is adsorbed over several atoms on the surface due to its
size, the negative oxygen atom most likely coordinates via the two
oxygen lone pairs to an electronically depleted site of cobalt
atoms and the positively polarized methyl hydrogen atoms to a
nearby basic phosphate site. If we assume differences in the
heterogeneous catalytic ability of the solid-state faces in cobalt
3 4 2
Figure 7. Side views of (a) the (011) face, and (b) the (110) face, of Co (PO )
shown as ball-and-stick models. Colors: Co is brown, O is red, and P is magenta.
The arrows indicate Co atom pairs with a short distance 3.032 Å between them.
-
3
The iso-surfaces show two of the MLWFs (±0.08 Å ) from Figure 5f for the (011)
face and Figure 5d for the (110) face that have their upward-pointing lobes
pointing towards negative charge depletion regions around the respective Co
ions. Charge analysis was carried out for the bulk crystal.
phosphate we need to establish criteria to identify effective
catalytic sites.[30] Since the crystal structure of cobalt phosphate
shows two differently coordinated metal sites, the first question to
be asked is whether both Co atoms are equally active, and if not,
what causes the differences. If the plain coordination number of
the cobalt atoms is considered, the saturated Co[6o] most likely is
Considering catalytic abilities from ED. Phosphates, which
contain cobalt and other transition metals, are known to catalyse
organic reactions and are therefore in the spotlight of current
research. The oxidation of styrene, for example, was realized
not tremendously active as it lacks a vacant site for the substrate
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Chemistry - A European Journal
10.1002/chem.201902303
RESEARCH ARTICLE
to interact with. Figures 3g and 3h clearly show that there are no
free sites at Co[6o], whereas Co[5by] holds three of them. However,
it has to be kept in mind that Co-atoms exposed at the surface
inevitably render free coordination sites. Depending on how
exposed they are on the surface, the number of free coordination
sites also varies, which affects the probability of chemisorption.
However, statistically speaking, Co[5by] would still have to have
more free coordination sites than Co[6o] at the surface, because
they already have three more vacant sites in the bulk. In addition,
the present distortion of the geometry will promote catalysis.[31]
When e. g. C-C bonds are activated in a substrate by
rhodium and nickel catalysts, it is proven that this is a structurally
sensitive reaction that takes place on coordinatively unsaturated
atom pairs of the d metals on corners or edges of minute
crystallites.[ Thinking in terms of concepts of homometallic
cooperativity[ , short distances between the metal centers are
needed. In the crystal structure of cobalt phosphate, there are
such short distances between two five-fold coordinated edge-
sharing Co-ions (3.032 Å) (Figure 2b) and between a five-fold and
a six-fold Co-ion (3.145 Å). According to the Bravais, Friedel,
Donnay and Harker theory[33], Figure 7 shows the four most likely
from bulk-truncated cuts, and so based on this analysis we cannot
fully exclude the presence of additional relevant active sites and
surface facets. However, insofar as the catalyst surface structure
resembles any of the low-index surfaces, the (011) surface has
the right structural features and ED for catalytic conversion.
Conclusion
An extensive characterization of cobalt phosphate using
topological analysis and theoretical methods for experimental and
theoretical electron density distribution was performed. The P–O
bonds were identified as polar single bonds where the BCP is
considerably shifted to the phosphorus atom. The Co–O bonds
can be described as closed shell interaction. The calculated
MLWFs have a clear connection to the d orbital occupation, as
well as the position of the charge depletion centers. In the solid
2]
32]
state, the two independent cobalt atoms exhibit different numbers
[5by]
of charge depletion sites in the valence shell. Co
has, apart
from the charge depletions directed towards the negatively
charged phosphate oxygen atoms, three additional vacant
…
low-index crystal faces with Co Co cooperative sites.The layer is
chosen such that no covalent bonds are broken in the phosphate
and cobalt atoms appear on the surface. The positions of
electronically depleted areas found from the multipole refined
Laplacians are superimposed onto the surface of the cobalt atoms
as black areas. At the (011) face only Co[5by] and O atoms are
visible, where the Co atoms occur isolated or in pairs with a short
interatomic distance of 3.032 Å. The Co[5by] atoms facing each
other in pairs, each exposing three and four vacant coordination
sites. The pairs at the edges even have up to six vacant
coordination sites per Co atom. They are perfectly arranged to
serve as adsorption sites for the two oxygen lone pairs of the
butanol molecules, which then -bridges two Co atoms.
Looking at the other lattice planes from a similar point of
view, plane (110) shows similar properties to (011), but all Co-
atoms are slightly deeper embedded in the surface so that they
are much more difficult to be reached by the butanol oxygen atom.
At the (10-1) face exclusively five- and six-fold coordinated cobalt
atoms are exposed. Due to the solemnly electronically depleted
sites at this surface, the chemisorption of a molecule with both,
electron-rich and electron-poor regions like butan-2-ol is much
more difficult (Figure 7).The slightly positive -hydrogen atom H3
coordination sites. This suggests that the nucleophilic attack on
[5by]
Co
is much more likely. These depletions, congruent with the
unoccupied or partially occupied d orbitals, were analyzed on the
face of different solid-state surfaces. It has been shown that the
(
011) face is the most suitable for catalytic oxidative
dehydrogenation or dehydrogenation, showing Co[5by]…Co
[5by]
cooperativity. There are sufficient acidic and basic sites for the
chemisorption of butan-2-ol available. On this face Co[5by] ions and
phosphate ions are most accessible, therefore this surface is best
equipped to activate both, the C–H and O–H bonds. Furthermore,
the lobes of the MLWFs of both cooperative Co[5by] atoms face
each other to address both oxygen lone-pairs of the substrate.
The investigations show that the concerted but independent
experimental and theoretical determination of charge density
distribution is a valuable tool to rationalize catalytic active
materials.
Experimental Section
(
Scheme 1) would probably not find a more basic nearby
High resolution structure determination. Cobalt orthophosphate was
purchased as powder from Alfa Aesar. Since it is not soluble in any
conventional organic solvents it was crystallized from the melt. The solid
was heated to 1180 °C at air atmosphere in a chamber oven, then cooled
to 500 °C, tempered for one hour and finally cooled down to room
temperature. The crystallization approach known from the literature[7] in
slightly modified form was also tested, but did not produce better single
crystals. A violet single crystal of 45 x 90 x 100 μm in size was mounted at
room temperature on the goniometer using inert perfluorinated polyether
oil and cooled to 100 K.
High resolution X-ray diffraction data were collected on a Bruker SMART
APEX II diffractometer based on D8 three-circle goniometer system using
an Incoatec microfocus AgKα source (IμS) and Incoatec QUAZAR mirror
optics.[34] A Bruker APEX II CCD detector was used to record the diffracted
intensities at λ = 0.56086 Å. Data reduction was carried out with SAINT[35]
phosphate site to be activated. The (101) plane also displays Co-
atom pairs with short metal-metal distances but they occur
between five- and six-fold coordinated Co atom. Furthermore,
they are not so custom-fit arranged like at the (011) plane. Hence,
we conclude that the catalytically most active plane is the latter.
Finally, we note that the above arguments were made based
on the ED for the bulk crystal. In order to verify that the predicted
adsorption of, e.g., butan-2-ol onto the Co[5by] at the (011) surface
is favorable, we used DFT to calculate the adsorption energy of
butan-2-ol onto several different adsorption sites for two different
surface terminations of the (011) surface and found the predicted
adsorption site to be indeed the most favorable (see SI) as
expected, confirming that the bulk ED can be used as a tool to
qualitatively predict adsorption behavior at the surface.
Nevertheless, the surface structure of a real catalyst may deviate
(
version 8.30C) from the APEX2[36] program package in which the
integration box sizes were refined for every run using a standard procedure.
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Chemistry - A European Journal
10.1002/chem.201902303
RESEARCH ARTICLE
The data were scaled and equivalent reflections were merged with
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according to the Quantum Theory of Atoms in Molecules[12] (QTAIM) was
performed using the XDPROP and TOPXD programs included in the XD
package. Crystallographic details are provided in Table S1-1.
2
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RESEARCH ARTICLE
How to Cat: The experimental
and theoretical topological ana-
lysis of the electron density
Helena Keil, Matti Hellström,
Claudia Stückl, Regine Herbst-
Irmer, Jörg Behler, Dietmar
Stalke*
3 4 2
distribution in Co (PO ) identi-
fied the (011) face to be best
suited for catalysis. Five-fold
coordinated Co ions in close
proximity to advantageously
oriented electron depletion sites
suit the reactant’s oxygen-lone
pairs most for chemisorption
Page No. – Page No.
New insights in the catalytic
activity of cobalt
orthophosphate Co
3 4 2
(PO ) from
charge density analysis
and
heterogeneous
C–H
activation.
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