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Journal of the Korean Physical Society, Vol. 55, No. 3, September 2009, pp. 1243∼1249
Electronic and Optical Properties of Noble Metal Oxides M2O
(M = Cu, Ag and Au): First-principles Study
Fei Pei, Song Wu, Gang Wang, Ming Xu, Song-You Wang∗and Liang-Yao Chen
The Key Laboratory of Advanced Photonic Materials and Devices,
Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China
School of Physics and Engineering, Zhengzhou University, Zhengzhou 450052, China
(Received 25 August 2008)
In this work, ﬁrst-principles calculations for the structural, electronic, and optical properties of
noble metal oxides M2O (M = Cu, Ag, Au) with the cuprite structure are performed by using a
plane wave pseudopotential method in the framework of density functional theory (DFT) and the
generalized gradient approximation (GGA). The structural, electronic, and optical properties are
investigated and discussed. For Cu2O and Ag2O, good agreement was achieved between calculated
and experimental results. Within the same framework, Au2O is predicted to be a semiconductor.
In comparison with the copper and the silver oxides, the gold oxide has less ionic bonding between
Au and O, and the intra-atomic hybridization is expected to be more evident as the depletion of
the Au 5dshell appears to be more profound than it is for the Cu 3dand the Ag 4dshells.
PACS numbers: 71.15.Mb, 71.20.-b, 78.20.-e
Keywords: Noble metal oxide, First-principles calculation, Electronic, Optical properties
Cuprous oxide, Cu2O, is a p-type semiconductor with
potential applications in solar energy conversion and
catalysis [1, 2]. One of the attractive features of Cu2O
is that it has the cuprite structure with a space group
3m, as shown in Fig. 1. Each copper atom bonds to
two oxygen atoms in an unusual linear fashion. This
type of bonding is also present in copper-oxide high-
temperature superconductors. Cu2O is, thus, exten-
sively regarded and has been studied as a meaningful
benchmark material for exploring the origin of high-
temperature superconductivity discovered in oxygen-
doped cuprate materials . The interaction between
Cu+and O2−based on a simple closed-shell model is
inadequate; thus, a more complex bonding mechanism
has been proposed and adopted [4,5]. The intra-atomic
hybridization of Cu 3dwith the Cu 4sor 4pstates is
regarded as crucial for explaining the low coordination
number and the stability of the crystal structure.
Isostructural Ag2O has also been widely studied for
its important roles in fast-ion-conducting glasses of the
type AgI-Ag2O-B2O3, AgI-Ag2O-V2O3, and AgI-Ag2O-
P2O5[6,7]. Knowledge of the bonding between silver and
oxygen is helpful for understanding the micro structure
of glass and the mechanism of ionic conduction .
Recently, a binary system like oxygen-gold has at-
tracted renewed interest because of its possible role as
an intermediary in the preparation and the operation
of supported gold nanoparticle catalysts for heteroge-
neous oxidation reactions [9–14]. Gold oxide (Au2O3)
can be synthesized under hydrothermal conditions with
Fig. 1. Ball and stick model of noble metal oxides, M2O,
with a cuprite structure. The dark and the light balls rep-
resent the noble metal atoms and the oxygen atoms, respec-
-1244- Journal of the Korean Physical Society, Vol. 55, No. 3, September 2009
pressures up to several 1000 atm, as those reported in an
extended X-ray-absorption ﬁne-structure study . A
recent experimental study has proposed that with ther-
mal treatment, heating to around 450 K, Au2O3decom-
poses in a process in which Au2O is a possible interme-
diary . To our knowledge, studies on Au2O with a
cuprite structure have been limited so far. Concerning
the remarkably diﬀerent reactivity of gold compared to
copper and silver [16–18], as well as the modern impor-
tant application of gold chemistry , a study of the
properties of Au2O, which might add to the understand-
ing of gold-based catalysts for heterogeneous oxidation
reactions, is of interest.
In this work, we present ﬁrst-principles calculations
for noble metal oxides M2O (M = Cu, Ag and Au) with
the cuprite structure. The structural, electronic, and
optical properties are investigated and discussed. For
Cu2O and Ag2O, good agreement between our results
and experimental ones has been achieved to show the
validity of our calculations. Within the same framework,
Au2O is predicted to be a semiconductor. In comparison
with copper and silver oxides, the Au-O bonding is less
ionic, and the intra-atomic hybridization is expected to
be more evident in Au2O as the depletion of the Au 5d
shell appears more profound than those of the Cu 3dand
the Ag 4dshells.
II. COMPUTATION METHOD
The plane-wave-based density functional theory
(DFT) calculations are performed using the CASTEP
[20,21] code with the core orbitals replaced by ultrasoft
pesudopotentials . The generalized gradient approxi-
mation (GGA) function of Perdew, Burke, and Ernzerhof
 (PBE) is used for the exchange correlation potential.
The energy cutoﬀ is chosen as 400.0 eV. The Monkhorst-
Pack k-point sampling is set as 8 ×8×8. The initial ge-
ometry conﬁgurations are optimized by using the Broy-
den, Fletcher, Goldfarb, and Shannon minimizer .
The properties of M2O, including the electronic band
structures, density of states, diﬀerence electron density,
and optical properties, are calculated for the correspond-
ing optimized crystal structures. All of parameters are
tested for convergence in the calculation. The diﬀerence
electron density is deﬁned as the diﬀerence between the
crystalline charge density and the superposition of the
n∆(r) = n(r)−nM(r)−nO(r),(1)
where n(r) is the total electron density of the optimized
bulk M2O system, and nM(r) and nO(r) are, respec-
tively, the electron densities of the metal and the oxygen
atoms held at the same positions those in the bulk M2O.
The dielectric function of the material is a complex
symmetric second-order tensor that describes the linear
response of an electronic system to an applied external
electric ﬁeld. The imaginary part of the dielectric tensor
is directly related to the electronic band structure of a
solid, so it can be computed from knowledge of the elec-
tronic structure. The density functional calculation is
well known to tend to underestimate the band gap. To
take this into account, one can use a scissors-operator
(or self-energy operator) approximation  to correct
for the limitation of the density functional calculations
of the dielectric function. This approach has been widely
and successfully used to calculate the linear and the non-
linear optical properties for many bulk semiconductors
[26–29]. In most cases, the use of the rigid-scissors ap-
proximation will shift the unoccupied states, resulting in
a calculated value in agreement with experimental ones
to within a few percent.
The optical properties of the solid materials can be de-
scribed by means of the complex dielectric function ε(ω).
The contributions to the complex dielectric function ε(ω)
mainly come from the intraband and the interband tran-
sitions. The contribution from intraband transitions is
signiﬁcant for metallic materials. The interband tran-
sitions can be divided into direct and indirect transi-
tions. The direct transitions play an important role in
the process of optical response, whereas indirect transi-
tions make a small contribution as scattering of phonons
is involved. Therefore, the intraband transitions and in-
direct interband transitions are neglected in our calcula-
In the limit of linear optics in the visible-to-ultraviolet
region, the imaginary part of the dielectric function,
ε2(ω), represents the optical absorption in the crystal,
which can be calculated from the momentum matrix ele-
ments between the occupied and unoccupied wave func-
tions, and the real part, ε1(ω), is evaluated from the
imaginary part, ε2(ω), by the Kramers-Kr¨onig transfor-
mation. A Lorentzian broadening of 0.15 eV is used.
III. RESULTS AND DISCUSSION
1. Crystal Structure
Results of the geometrical optimization of M2O are
listed in Table 1, along with the experimental data and
other theoretical values. The calculated lattice constant
for Cu2O is in good agreement with the experimental
result . For Ag2O, the calculated value ais larger by
1.48% with respect to the experimentally measured one
. The lattice constant for Au2O is 4.82 ˚
A, which is
consistent with previous calculations (4.80 ˚
A , 4.81
A ) reported using GGA-PAW method. The lattice
constant for Au2O is only negligibly larger than that for
Ag2O, which can be attributed to the comparable atomic
radii of Ag and Au.
The isotropic variation of the volume of the cubic unit
cell employed in the determination of the lattice param-
eter can be used to evaluate the bulk modulus. The
Electronic and Optical Properties of Noble Metal Oxides M2O··· – Fei Pei et al. -1245-
Table 1. Calculated lattice constants and bulk moduli for Cu2O, Ag2O, and Au2O. Available experimental data and other
calculation results are listed for comparison.
A) Bulk modulus (GPa)
This work Expt.  Theor. [3,31] This work Expt. 
Cu2O 4.27 4.27 4.31 118 112
Ag2O 4.81 4.74 4.83 74
Au2O 4.82 4.80, 4.81 97
Fig. 2. Band structures for (a) Cu2O, (b) Ag2O, and (c)
Au2O. The dashed lines are shown as Fermi levels.
calculated bulk modulus for Cu2O is 118 GPa, which is
overestimated by about 5.4% compared to the experi-
mental value of 112 GPa . For Ag2O and Au2O, the
bulk moduli are 74 and 97 GPa, respectively. The lower
bulk modulus for Ag2O is related to the more ionic na-
ture of the Ag-O bond with respect to the Au-O bond.
The bond characteristic for M2O will be discussed in de-
tail in the following sections.
2. Electronic Structure
A. Band structures
The optical properties are related to the band struc-
ture and to the probabilities of interband optical transi-
tions. Therefore, it is of interest to analyze the electronic
structure in detail. The band structures for M2O are pre-
sented in Fig. 2. As shown in Figs. 2(a) and (b), Cu2O
and Ag2O are found to be semiconductors with direct
band gaps at the Γ point. The calculated band gaps for
Cu2O and Ag2O are 0.65 eV and 0.08 eV, respectively,
which are smaller than the experimental values (2.17 eV
for Cu2O , 1.30 eV for Ag2O ). This discrepancy
is due to an underestimate of the DFT, which consid-
ers only excited states in the calculation. For Au2O, the
calculation shows that the band gap opening at the Γ
Fig. 3. Total densities of states for (a) Cu2O, (b) Ag2O,
and (c) Au2O. An angle-integrated photoemission spectrum
 measured for Cu2O is also plotted for comparison.
point is close to zero, resulting in no overlap between the
highest valence band and the lowest conduction band.
Therefore, one can accept that Au2O may actually have
a semiconductor band structure with a larger gap due to
the well-known trend of the DFT to underestimate the
gap value. Previous DFT-GGA and GGA+U calcula-
tions  have suggested that Au2O is metallic as the
valence and the conduction bands are found to cross at
the zone center, but this overlap is only marginal and
may possibly be removed by correction of the conduc-
tion band level. Additionally, a notable band gap of 0.83
eV for Au2O has been identiﬁed in the calculation using
the screened-exchange local density approximation (SX-
LDA) approach . Further experimental studies are
required to give a clear picture of the electronic struc-
ture of Au2O.
B. Density of states
The calculated total density of states (TDOS) and par-
tial density of states (PDOS) for M2O are plotted in
Figs. 3 and 4, respectively. The vertical line indicates
-1246- Journal of the Korean Physical Society, Vol. 55, No. 3, September 2009
Fig. 4. Partial densities of states for (a) Cu2O, (b) Ag2O, and (c) Au2O.
the Fermi level. The O 2sstates (not shown in Figs.
3 and 4) are well localized at –19.5, –17.8, and –19.2
eV in Cu2O, Ag2O, and Au2O, respectively. The va-
lence band of M2O is clearly split into two regions. The
lower region mostly likely has the O 2pfeatures whereas
the upper one is dominated by M ndstates (n= 3, 4,
5 for Cu, Ag, and Au, respectively). There are some
hybridized M dstates with M sand O 2pstates near
the Fermi level, with no practical contribution from M p
states that have a dominant weight in the bottom of the
conduction band. It is noteworthy that M s,pstates ex-
hibit non-vanishing distributions within the valence band
to have an intra-atomic hybridization of M dstates with
Ms,pstates. This hybridization has been extensively
recognized in other studies on Cu2O. A similar situation
is observed in Ag2O and Au2O, as well.
The calculated width of the valence band for Cu2O is
about 8 eV, which is in agreement with the experimental
data of 8 eV from ultraviolet photoelectron spectroscopy
. The structure of the valence band is also well re-
produced in this calculation, as shown in Fig. 3(a). The
angle-resolved photoemission spectrum  is presented
for comparison. The plot has been displaced by about
0.6 eV to make the valence band maximum align with
the theoretical value. There is a good representation of
the features labeled A, B, C, and F in the calculated
density of states, as seen in Fig. 3(a). Features A and
B are shown to mainly have the characteristic of oxygen
atoms. In the upper region, the most prominent feature,
feature D, corresponds to the Cu 3dmaximum. While
the photoemission spectrum gives a large displacement
between features D and F (about 1.8 eV), this displace-
ment has been underestimated by approximately 0.5 eV
in this work. The discrepancy can be attributed to the
incomplete description of localized dorbitals in the GGA
calculation. Feature E is not visible in our calculation.
Table 2. Mulliken population analysis.
Cu 0.57 0.45 9.65 0.33
Ag 0.58 0.33 9.74 0.35
Au 0.83 0.29 9.57 0.30
However, this feature is weak in the quoted experimen-
tal spectrum and was not detected in some other angle-
resolved photoemission spectrum studies, reported by
Bruneval et al. .
For Ag2O, the width of the valence band is equal to 7
eV. The Ag 4dstates have an intensity peak at –3.2 eV
(at –4.0 eV according to the XPS data ). In the lower
region, the two O 2pmaxima are found at –6.0 and –4.6
eV, respectively. In the upper part, the contribution of
O 2pstates is larger than that found in Cu2O.
The calculated valence band structure for Au2O has a
width of 8 eV. The PDOS plots in Fig. 4(c) are consistent
with the results reported in a previous study .
C. Diﬀerence electron density
According to the calculated diﬀerence electron density
distributions for M2O as shown in Fig. 5, there is an
increase in the electron density at the O sites whereas a
complex redistribution of the electron charge around the
M sites has happened. The Mulliken population analysis
presented in Table 2 gives values of +0.33, +0.35, and
+0.30 for the eﬀective charges of Cu, Ag, and Au, re-
spectively, indicating the ionic feature of the M-O bond.
Au-O is less ionic than Cu-O and Ag-O due to that Au
has a much larger electronegativity (2.54) than Cu (1.90)
Electronic and Optical Properties of Noble Metal Oxides M2O··· – Fei Pei et al. -1247-
Fig. 5. Diﬀerence electron densities in the (110) plane calculated for (a) Cu2O, (b) Ag2O, and (c) Au2O. Positive values
representing an increase in the electron density are shown as full, negative values represent a depletion of the electron density are
shown as dashed lines, and zero is shown as dotted lines. The contour lines are presented with a constant step of 6.5×10−5e/cell.
and Ag (1.93). However, it should be noted that the
bonding between M and O might have some covalence,
resulting in M-O bond length being smaller than the sum
of the ionic radii of M+and O2−ions. The depletion of
electrons around the M sites, with the characteristics of
dorbitals, suggests that some d-orbital holes may have
been introduced on the metal ion. Positive values of the
diﬀerence electron density at the M sites can be regarded
as evidence of s−dand p−dintra-atomic hybridiza-
tions. An experimental study on Cu2O has conﬁrmed
that about 0.22 electrons per atom are removed from Cu
zstates , while our calculation give a comparable
value of 0.35. The numbers of delectrons missing from
Ag and Au are 0.26 and 0.43, respectively. The intra-
atomic hybridization is expected to be more evident in
Au2O as the depletion of the Au 5dshell appears to
be more profound than it is in the Cu 3dand the Ag
4dshells. However, the number of M d-orbital holes is
much smaller than the charge occupying the nominally
empty M sand porbitals, implying that the ionization
is incomplete, with some electrons normally expected to
be transferred to O now occupying M sand pstates.
3. Optical Prop erties
The optical properties of M2O have been analyzed ac-
cording to the calculated dielectric functions. The scissor
operators are used to rigidly shift the conduction bands
by 1.52 eV and 1.22 eV for Cu2O and Ag2O, respectively,
according to the diﬀerence between the experimental and
the calculated band gaps. The scissor operator is not
used for Au2O because the experimental band gap value
is lacking. The real and the imaginary parts of the di-
electric functions calculated for M2O are shown in Fig.
6. The imaginary curve for Cu2O indicates that there
is negligible optical absorption in the low-energy region
up to 3 eV. Two remarkable features are identiﬁed at
4.52 and 5.46 eV. These two peaks are observed at 3.58
and 4.34 eV in the experimental data  and are as-
signed to band-to-band transitions. The peak positions
in our calculations are about 1 eV blue-shifted with re-
spect to the experimental data. However, the separation
between the two peaks is 0.94 eV, which is close to the
Fig. 6. Calculated dielectric functions for (a) Cu2O, (b)
Ag2O, and (c) Au2O.
experimental value of 0.76 eV. The excitonic eﬀects ob-
served at 2.54 and 2.69 eV in the experiments are not
found in our calculations. The calculated static dielec-
tric constant ε0for Cu2O is about 6.7, which is slightly
smaller than the experimental value of 7.5 . This un-
derestimate is reasonable due to the intraband and the
phonon contribution, which has not been eﬀectively con-
sidered in the calculation. The refractive index nand the
extinction coeﬃcient kcan be derived from the dielectric
function. For Cu2O, the refractive index nhas a value
of 2.8 at 600 nm and decreases to 2.6 as the wavelength
approaches infrared (1500 nm), close to the experimen-
tal values of 2.5 ∼2.4 in this range . The value of
extinction coeﬃcient kwithin the visible light region is
For Ag2O, the optical absorption is also weak in the
energy region below 3.5 eV. Similarly, the imaginary part
presents a two-peak structure located at 4.58 and 5.57
eV, respectively. According to an experimental study
-1248- Journal of the Korean Physical Society, Vol. 55, No. 3, September 2009
, the refractive index for Ag2O is about 2.4 in the
400-to-800-nm wavelength region, as compared to the
values of 2.4 ∼2.8 given in this work. The extinction
coeﬃcient kis also negligible in the visible range.
We tentatively present the dielectric function for Au2O
because the electronic structure of Au2O has not been
veriﬁed by the experiment result, which will be funda-
mentally important to calculate the optical properties
with higher accuracy. Although the calculated gap value
is negligible, strong optical absorption seems to happen
in the region of photon energies above 2 eV. There are
two notable features, one located at 2.97 and the other
at 3.91 eV.
In this work, ﬁrst-principles calculations for noble
metal oxides M2O (M = Cu, Ag, Au) with the cuprite
structure are performed by using a plane-wave pseudopo-
tential method in the framework of DFT and the GGA.
The atomic, electronic, and optical properties of M2O
are investigated. The structural parameters for Cu2O
and Ag2O are in good agreement with experimental re-
sults. The lattice constant for Au2O is identical with
that for Ag2O. The direct band gap structures for Cu2O
and Ag2O obtained from the calculation are consistent
with the experimental results. Au2O is expected to have
a band structure similar to that of a semiconductor with
a small gap at the Γ point, but the actual gap value may
be larger than the calculated one if the typical tendency
of DFT to underestimate values is considered. Electron
charge transfer illustrates the ionic feature of the M-O
bonding. The Au-O bond is less ionic than the Cu-O and
Ag-O bonds. The calculated diﬀerence electron densities
suggest d-orbital holes with some complex intra-atomic
hybridization between M dand M s,pstates, especially
for Au2O which has a charge depletion of the Au 5dshell
that appears to be more profound than those of the Cu
3dand the Ag 4dshells.
This work was partially supported by National Basic
Research Program of China (No. 2010CB933700) and
the STCSM project of China (Grant No. 07TC14058).
The computation was performed at the National High
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