Scripta Materialia 55 (2006) 811–814
www.actamat-journals.com
On similarities and differences of the electronic structure for
Cu(II)/O2 and Ag(II)/F1 infinite layer compounds
Wojciech Grochala*
Department of Chemistry, Warsaw University, Pasteur 1, 02093 Warsaw, Poland
Interdisciplinary Center for Mathematical and Computational Modeling, Warsaw University, Pawińskiego 5a, 02106 Warsaw, Poland
Received 24 June 2006; accepted 6 July 2006
This work commemorates the 120th anniversary of the discovery of elemental F2 by Moissant
We calculate and compare the band structures of a hypothetical difluoride of Ag(II) with flat [AgF2] layers and of known
CaCuO2 infinite layer compound. Electronic structure of [AgF2] is strikingly similar to that of Ca[CuO2], but there are subtle
differences as well. Calculations suggest that charge-doped [AgF2] materials show good prospects for superconductivity, provided
that delocalization of extra charge is avoided.
2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Silver; Fluorine; Copper; Oxygen; Superconductivity
Fluorides of divalent silver (Ag2+) constitute a fascinating family of materials. Divalent silver is unique to
fluorides, and so far it has not been found in other
ligand environments. Due to its enormously large electron affinity, it is capable of oxidizing ‘noble’ gas Xe,
and vigorously reacts with elemental metals including
the most electronegative Au or Pt. It has been postulated – based on a multitude of appealing qualitative
and semi-quantitative arguments – that properly doped
fluorides of Ag2+ might exhibit high-temperature superconductivity [1].
Recent experimental study of Cs2AgF4 [2] has revitalized interest in layered fluorides of Ag2+. Cs2AgF4 crystallizes orthorhombically [2], and it contains flat [AgF2]
sheets separated by two [CsF] spacers; its structure is
related to the structure of La2CuO4, parent (undoped)
compound of the first oxocuprate superconductor,
La2xBaxCuO4 [3].
Prediction of superconductivity in doped fluorides of
Ag2+ [1] and recent study of Cs2AgF4 [2] call for careful
re-examination of the electronic structure of layered
fluorides of Ag2+. In this contribution we calculate
and compare the band structures of a hypothetical
difluoride of Ag(II) with flat [AgF2] sheets and of known
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CaCuO2, an infinite layer compound [4]. Difluoride of
Ag(II) with flat [AgF2] layers is not purely a theoretical
creation; such material might indeed be obtained from
genuine binary AgF2 (with its puckered sheet structure)
by (i) intercalation of various oxidation-resistant Lewis
bases between the sheets, with their concomitant flattening, or (ii) by applying external pressure [3]. We will subsequently denote hypothetical two-dimensional (2D)
difluoride of Ag(II) simply as [AgF2].
The CASTEP code was used for all calculations [5].
Our density functional theory calculations utilized the
Perdew–Burke–Ernzerhof correlation–exchange functional, typical cut-off of 380 eV, k-point grid of
6 · 6 · 7 or 6 · 6 · 8, and ultrasoft Vanderbildt pseudopotentials. Spin polarization was not enforced. The
tetragonal P4/mmm cell with the unit cell vectors of
a = b = 3.854 Å and c = 3.200 Å [4] was adopted for
CaCuO2, as illustrated in Figure 1. For a hypothetical
infinite layer AgF2 we have used an analogous cell with
the unit cell vectors of a = b = 4.14 Å and c = 3.50 Å
(Fig. 1). Such choice guarantees reasonable values of
the intrasheet and the intersheet Ag–F separations, as
compared to the known polymorph of binary AgF2.
The calculated pressure on the cell is only 0.7 GPa
for [AgF2] (compared to 0.6 GPa for Ca[CuO2]),
ensuring the validity of this choice.
The band structures of a hypothetical infinite-layer
[AgF2] material and that of Ca[CuO2], are shown in
1359-6462/$ - see front matter 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.scriptamat.2006.07.028
812
W. Grochala / Scripta Materialia 55 (2006) 811–814
Figure 1. View of the unit cells of a hypothetical polymorph of AgF2
with flat [AgF2] sheets (left) and of the CaCuO2 infinite layer
compound (right).
Figure 2. The electron density integrated over selected
bands of interest is presented in Figure 3.
Electronic structure of a [AgF2] is quite similar to
that of Ca[CuO2] (Fig. 2), but there are some differences
as well.
Two characteristic bands with large width can easily
be distinguished in the band structure of [AgF2], one
from ca. 6.3 eV to 3.8 eV (occupied), and another
from 1.9 eV to +1.8 eV (approximately half occupied,
due to d9 electronic configuration of Ag2+). Appreciable
dispersion and integrated electron density in those bands
(Fig. 3 and ESD) clearly point to their origin from the r
combination of the d(x2–y2)Ag/p (x, y)F atomic orbitals.
The orbitals of nonmetal and transition metal must mix
in the bonding manner in the lower band, and in the
antibonding way in the associated upper band, as obtained from the usual picture of the d orbitals split in
a square planar ligand field [6].
The half-occupied r* band of [AgF2] is a direct analogue of such a band for infinite layer oxocuprates; it
Figure 3. The electron density integrated over selected bands in the
electronic structure of a hypothetical polymorph of AgF2 with flat
[AgF2] sheets (left) and of the CaCuO2 infinite layer compound (right).
(A) and (C) – bands crossing the Fermi level, (B) and (D) – bands
immediately below those shown in (A) and (C), respectively. Isosurface
of electron density was shown for density of 0.02e Å3.
is believed that the presence of this band is a prerequisite
for superconductivity in doped materials [7]. Significant
dispersion of the r and r* bands for [AgF2] indicates
appreciable mixing of the transition metal’s d and nonmetal’s p valence functions. This unusual feature makes
fluorides of Ag2+ quite similar to their oxocuprate siblings; appreciable ‘hybridization’ (as understood in solid
state physics) has been first suggested in Ref. [1] and
then confirmed by XPS measurements [8] and – indirectly – by magnetic measurements [2]. Fluoroargentates
thus join a fascinating family of ‘strongly correlated materials’, and the world of unusual phenomena,
Figure 2. Electronic band structure and electronic density of states (DOS [electrons/eV]) for a hypothetical polymorph of AgF2 with flat [AgF2]
sheets (top) and of the CaCuO2 infinite layer compound (bottom). Partial DOS from s, p and d electrons has also been shown, p contribution
originating predominantly from nonmetal (F or O), d one from transition metal (Ag or Cu).
W. Grochala / Scripta Materialia 55 (2006) 811–814
such as for example superconductivity and giant
magnetoresistance.
One notices two bands in the 4.7 eV to 2.9 eV energy window; these are p combinations of the in-plane
d(xy)Ag orbital and of appropriate p(x, y)F functions
(see ESD). The p overlap to F is poor for the majority
of transition metal cations, and bonding is polarized towards nonmetal; this allows F to attain net negative
charge. The in-plane p-bands have their in-plane p*
counterpart, at about 1.9 eV to 0.9 eV. Analogous
p- and p* bands are seen for Ca[CuO2], from 5.4 eV
to 2.8 eV and from 1.7 eV to 0.6 eV, respectively.
The uppermost p* band merits particular attention,
as it may become of importance upon hole-doping to
the d9 system; note, this band is the highest occupied
band of the ‘d8 Ag3+ site’ in the ‘localized’ bonding
picture. Subsequent hole transfer from Ag3+ to F, with
the predominant hole occurrence on F centers, might be
viable [1,9]; this might ultimately lead to the magic electronic state – in analogy to superconducting oxocuprate
materials [10].
Four other bands with varying widths fill the energy
gap between the r and r* bands; the concomitant crystal
orbitals are composed of p or p* combinations of the
out-of-plane d(xz, yz)Ag and the p(z)F orbitals (see
ESD). The last interesting band propagates from
2.4 eV to 1.3 eV; it is made up mainly from the
d(z2) orbitals of Ag. This band should have very small
dispersion for a truly 2D case; its noticeable width observed here originates mainly from the intralayer overlap via 2s orbitals of F, and from the interlayer d(z2)/
d(z2) overlap. The respective band is seen at 2.3 eV
to 0.9 eV for Ca[CuO2].
As may be seen from this comparison, the general
bonding scheme is very similar for two quasi-isoelectronic systems considered, [AgF2] and Ca[CuO2]. But,
most importantly of all, what are the differences? And
how might they influence the propensity of these systems
for charge localization/delocalization upon hole- or electron-doping? We will now attempt to answer these
questions.
First of all, the presence of Ca2+ between the [CuO2]
layers allows for more efficient through-orbital interlayer interactions as compared to [AgF2]; this leads to
more complex band structure (particularly for the pand p*-bands, which are most affected by this interaction), and to the appearance of several ‘avoided’ and
‘allowed’ interband crossing regions.
Electronic DOS of Ca[CuO2] may be divided into
three regions in the energy scale: (i) the first one, from
7.2 eV to 3.7 eV, where the pO contribution predominates [11]; (ii) the second one, from 3.7 eV to 1.8 eV,
where the dCu contribution takes over; and (iii) the third
one, from 1.8 eV to 0.0 eV, where the pO contribution is nearly equal to the dCu one [12]. Analogous
regions may also be detected in the DOS for [AgF2],
but their ordering is different: (i) the first region, from
6.8 eV to 4.0 eV, is characterized by nearly equal
contribution from the metal and nonmetal states; (ii)
the second region, from 4.0 eV to 2.5 eV, is dominated by dAg orbitals; (iii) finally, the third region, from
2.5 eV to 0.0 eV, shows the largest share of the pF
states [12].
813
We have determined the energy of the center of gravity, Eicent , for the metal (i = d) and nonmetal (i = p)
states, using the following formula:
Eicent ¼ R½ðDOSi ÞEi =RðDOSi Þ;
ð1Þ
i
where E is a particular energy for a given state i, while
DOSi is the associated value of partial DOS, and
summing goes over the (7.5 eV to +2.5 eV) energy
window.
eV,
The calculated values are: E4d;Ag
cent ¼ 2:73
2p;F
Ecent ¼ 2:65 eV, for [AgF2]. The corresponding values
2p;O
for Ca[CuO2] are: E3d;Cu
cent ¼ 2:52 eV, E cent ¼ 2:85 eV
[13]. Thus, separation of the metal and nonmetal states
is small, but different in both cases; 0.08 eV for
[AgF2], +0.33 eV for Ca[CuO2] [14].
The third important difference between [AgF2] and
Ca[CuO2] is related to the absolute values of the partial
DOS for nonmetal states. The maximum value of
DOS2p,O is about 3.2 e/[eV cell], yet that of DOS2p,F is
noticeably larger, some 4.3 e/[eV cell]. This difference
could be due to either (i) the larger contraction of the valence 2p orbital of F than of O, at a larger F–F than the
O–O separation, or/and (ii) the weaker interaction of the
valence 2p orbitals of nonmetal via d orbitals of transition metal (smaller overlap, less mixing). Most likely,
both effects are operative with comparable weights.
And what about ionicity of the Cu2+/O2 and Ag2+/
1
F bonding? Table 1 shows the results of the Mulliken
population analysis and the net atomic charges for
[AgF2] and Ca[CuO2].
Seemingly, charge distribution is very different for
[AgF2] and Ca[CuO2], as indicated by the Mulliken
charges on atoms. However, transition metals show
similar population of their valence d orbitals – there is
slightly over 0.5 hole in the d-band in each case. Populations of valence p orbitals of nonmetals differ by
0.6e; charge transfer from lone pairs (those perpendicular to the [CuO2] layers) of oxide anions to the diffuse d
(less so s) orbitals of Ca (formally unoccupied for Ca2+)
may be held responsible for this effect. Correct division
of the total electron density between O and Ca is difficult, but it should not affect too much our estimate of
the polarity of the Cu–O bonds. If one shifts the discussed 0.6e back from Ca to O atoms, virtually identical
populations of transition metal d and nonmetal p orbitals are obtained for [AgF2] and Ca[CuO2]. Thus, the
Ag2+–F1 and Cu2+–O2 bonds have pretty similar
polarity, an intermediate one between the ‘ionic’ and
‘covalent’ formulations [15].
Table 1. Population analysis of s, p and d electrons, and net atomic
charges for [AgF2] and Ca[CuO2]
System/atom
s
p
d
Total
Charge
[AgF2]
Ag
F
0.36
1.96
0.22
5.54
9.43
–
10.01
7.50
+0.99
0.50
Ca[CuO2]
Cu
O
Ca
0.54
1.85
2.05
0.76
4.95
5.99
9.45
–
0.60
10.75
6.80
8.64
+0.25
0.80
+1.36
Important populations are in italics.
814
W. Grochala / Scripta Materialia 55 (2006) 811–814
Last but not least, different strength of magnetic
interactions (not accounted for in our calculations) constitutes another important difference between [AgF2]
and Ca[CuO2]. The magnetic moment of an unpaired
d electron of Cu2+ is about 1.7 1.9 lB; the corresponding moment for Ag2+ is 2.1 2.2 lB. This comparison
shows that magnetic interactions between the adjacent transition metal atoms are supposedly larger for
[AgF2] than for Ca[CuO2], provided that they occur
with equal ease via 2p orbitals of nonmetals [16].
The similar nature of the chemical bonds and of the
band structure is a good indication for possible generation of superconductivity in the layered compounds
which contain the [AgF2] sheets. But will these similarities suffice? It remains to be seen if genuine 2D [AgF2]
materials could be obtained and charge-doped without
localization of charge carriers, and if they would exhibit
high-temperature superconductivity.
Author thanks the ICM and the Department of
Chemistry for continuing financial support of this
research. All calculations were performed at ICM supercomputers. Dr. Jacek Piechota is gratefully acknowledged for making available his license of Materials
Studio.
Electronic supplementary data (ESD) accompanies
this paper (electronic structure of related hypothetical
[AgCl2] and [AuCl2] infinite layer systems, electron density in all bands for [AgF2] and Ca[CuO2] and molecular
orbitals of AgF2
4 Þ. Supplementary data associated with
this article can be found, in the online version, at
doi:10.1016/j.scriptamat.2006.07.028.
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Another occupied band with large width shows up in the
electronic structure of [AgF2] in the same energy window as
the r band. This band can be approximately assigned to the
combination of selected p(x, y) atomic orbitals of F atoms.
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Z̆emva, Chem. Phys. Chem 4 (2003) 997.
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Correct population analysis is often very difficult for
solids, particularly when the planewave basis is used.
However, here we discuss the relative differences in the
DOS division for two compounds, rather than the
absolute division of DOS for a given compound. In our
calculations, various orbital contributions nicely sum up
to total DOS (not shown).
In fact, states at the Fermi level show small dominance of
the valence orbitals of a transition metal.
Note, CASTEP automatically sets the energy of the Fermi
level to zero.
Similar analysis for [AgCl2] (see ESD) yields the position
of 3p states of Cl way above that for 4d states of Ag. This
result indicates that Ag2+ should spontaneously introduce
holes into the Cl(3p) band, thus liberating Cl2. This is in
good agreement with chemical intuition and common
experience; recollect: binary AgCl2 could not been
prepared so far.
Population of s and p functions of transition metals is very
different for both compounds considered. An overall
(s + p) occupation is larger for Cu than for Ag by 0.7e.
Cu is forced to use its diffuse valence functions in order to
accommodate much negative charge into ½CuO2
2 sheets.
This difference between [AgF2] and Ca[CuO2] is not very
important; occupation of (s + p) states may easily be
affected by intercalation of various electron-withdrawing
or electron-donating (formally neutral) species between
the [AgF2] layers.
Indeed, McLain et al. [2] show that magnetic superexchange constant is pretty large for ferromagnetic Cs2AgF4
(3.8 to 5.0 meV, i.e. 50 K), without precedence
among related fluoride systems.