Charge delocalization, oxidation states and silver mobility in the mixed silver-copper oxide AgCuO 2¤

The electronic structure of AgCuO 2 , and more specifically the possible charge delocalization and its implications for the transport properties, has been the object of debate. Here the problem is faced by means of first-principles density functional theory calculations of the electron and phonon band structures as well as molecular dynamics simulations for different temperatures. It is found that both Cu and Ag exhibit non-integer oxidation states, in agreement with previous spectroscopic studies. The robust CuO 2 chains impose a relatively short contact distance to the silver atoms which are forced to partially use their d z2 orbitals to build a band. This band is partially emptied through overlap with a band of the CuO 2 chain which should be empty if copper were in a Cu 3+ oxidation state. In that way, although structural correlations could roughly be consistent with an Ag + Cu 3+ O 2 formulation, the appropriate oxidation states for the silver and copper atoms become Ag (1+ δ )+ and Cu (3- δ )+ , and as a consequence, the stoichiometric material should be metallic. The study of the electronic structure suggests that Ag atoms form relatively stable chains which can easily slide despite the linear coordination with oxygen atoms of the CuO 2 chains. Phonon dispersion calculations and molecular dynamics simulations confirm the stability of the structure although pointing out that sliding of the silver chains is an easy motion that does not lead to substantial modifications of the electronic structure around the Fermi level and thus, should not alter the good conductivity of the system. However, this sliding of the silver atoms from the equilibrium position explains the observed large thermal factors.


I. INTRODUCTION
Silver-copper mixed oxides emerged as a possible alternative for high-T c Hg-Cu superconductors because of the structural and chemical similarities between Hg 2+ and Ag + .
Even if no superconducting phase of this type has so far been reported, these mixed oxides have been shown to exhibit intriguing structural and chemical properties. The first synthesized silver-copper mixed oxide was Ag 2 Cu 2 O 3 , 1,2 which through chemical 3 or electrochemical 4 oxidation led to Ag 2 Cu 2 O 4 (or equivalently AgCuO 2 ), a solid of this family which has been the object of debate and presents unique features. AgCuO 2 was independently prepared through alternative procedures, from a Cu(NO 3 ) 2 and AgNO 3 solution after oxidation with persulfate, 5,6 or from electrochemical oxidation of the single metals or oxides. 4 Although the structural studies showed that the solid generated by the two procedures is   Figure 1a). 4, 6 Jansen and coworkers 6 noted that diamagnetic AgO contains two different Ag sites exhibiting linear and square planar coordinations. 11,12 Since such coordination environments are usually associated with the oxidation states, M + and M 3+ , the silver atoms in AgO, formally in the Ag 2+ oxidation state, can be considered as originating from a disproportionation process leading to Ag + and Ag 3+ . By analogy they proposed that the Ag and Cu sites in AgCuO 2 should be associated with Ag + and Cu 3+ . However, X-ray photoemission (XPS) studies 13 suggested that the situation could be more complex. For instance, in contrast with Ag 2 Cu 2 O 3 , where oxidation states are unambiguously Ag + and Cu 2+ , and each peak of the Ag 3d 3/2 and Ag 3d 5/2 doublet exhibits a single component with binding energies typical of Ag + , the Ag 3d lines in AgCuO 2 present a main component and a shoulder suggesting the occurrence of both Ag + and Ag 3+ . The Cu 2p region of the XPS spectra of Ag 2 Cu 2 O 3 and AgCuO 2 were however very similar suggesting the presence of Cu 2+ in both cases. Thus, the Ag + Ag 3+ Cu 2+ 2 O 4 formulation, with mixed valence for silver, and copper in a lower oxidation state, was proposed. Subsequent XPS and X-ray absorption (XAS) measurements 14 on AgCuO 2 and the Ag 2 O, AgO, CuO and NaCuO oxides as well as the Ag 2 Cu 2 O 3 precursor, suggested an even more complex electronic description for AgCuO 2 , where both metal atoms are partially oxidized and the charge is delocalized among all atoms, including oxygen. As a consequence, it was suggested that the more appropriate formulation for this oxide was Ag (1+x)+ Cu (2+y)+ O (2-z)-2 with x, y and z values varying for the compounds generated using different synthetic procedures. This formulation was interpreted as reflecting the incipient formation of a not fully occupied Ag 4d band which should be associated with a good conductivity. Several observations such as a dark black color, absence of diamagnetism and a small Pauli paramagnetism were in line with this proposal. 15 (for instance they are of 1.84 Å in NaCuO 2 where there is no ambiguity in the oxidation state). This seems to be at odds with the previous remarks suggesting an oxidation state larger than +1 for the silver atoms. In order to check the possible occurrence of some disorder and its effect on the oxidation states, neutron diffraction experiments at 1.5 K and room temperature were carried out. 17 The Rietveld refinement showed the same atomic positions described from X-ray diffraction data at both temperatures evidencing the absence of a thermally activated disorder. The Ag thermal parameters were found to be significant at room temperature and decrease in magnitude as expected under cooling without structural change.
It must be concluded that neither the structural information coming from X-ray or neutron diffraction nor the structural analysis of the first coordination shell provided by X-ray spectroscopies lead to a complete description of the oxidation states of the copper and silver atoms in AgCuO 2 . A recent report of in situ measurements of the transport properties of AgCuO 2 single crystals, 18 19 Under such circumstances it seems that a first-principles theoretical study of the stoichiometric solid could provide important clues to rationalize the electronic description of this material. Thus, in the present work we examine the situation from the viewpoint of first-principles density functional theory (DFT) calculations. We analyze in detail the band structure and phonon spectrum of stoichiometric AgCuO 2 and carry out a molecular dynamics study at different temperatures to explore the stability of the structure. New specific heat measurements and previously reported neutron diffraction data for AgCuO 2 17 usefully complement the discussion.

II. COMPUTATIONAL DETAILS AND EXPERIMENTAL MEASUREMENTS
Calculations to explore the electronic structure of AgCuO 2 have been carried out with a numeric atomic orbitals density functional theory (DFT) approach 20 implemented in the SIESTA code. 21 We tested the performance of three generalized gradient approximation The sorting plots based on the correlations between d-orbital occupation and core orbital binding energies were obtained using the ab initio CRYSTAL17 code [35][36][37] and using the B3LYP functional. 38 The all-electron atomic Gaussian basis sets used were of the 8-6-411-(41d)G and 9-7-6631(41d)G types for Cu and Ag, respectively. 39  with a step size of 0.02° and using a scanning rate of 0.16°/min. No evidence of any additional phase derived from AgCuO 2 reduction was found.

III. RESULTS and DISCUSSION
A. Crystal structure. It will be important to fully understand the electronic description of AgCuO 2 to realize that its crystal structure can be formally assembled from two different   We first tested the performance of several functional (PBE, PBEsol and WC) in coping with the main structural details of the system. Shown in Table 1 is the comparison of the experimental and calculated results for the cell constants. Both the PBEsol and WC functionals lead to results in good agreement with the experimental data, with a slight underestimation of the volume (-2%) and very similar errors for all optimized unit cell parameters, which are kept within a small range between -2% and 2%. In contrast, the PBE functional leads to a large overestimation of the volume (+8%) mostly due to a large overestimation of the a parameter.   The origin of this metallic behavior is clear-cut when looking at the lower panel of Figure   2b, which contains the calculated density of states (DOS) for AgCuO 2 as well as the contribution of the Ag orbitals. The Ag levels below the red line are mostly associated with dtype orbitals. Since the Fermi level occurs at a lower energy it is obvious that the d levels of silver are not completely full and consequently, the Ag + oxidation state does not reflect the actual electronic structure of the system. The DOS diagrams of Figure 2b also indicate that around the Fermi level the Cu and Ag orbitals participate to a similar extent and that there is also a substantial participation of oxygen levels. Note that the Fermi surface corresponds to a 3D-type conductivity. Consequently, such conductivity cannot independently arise from the silver (i.e. AgO 2 ) and CuO 2 chains, which run along the b-direction: a non-negligible interaction between the two types of chains is needed to lead to the 3D conductivity. In summary, the present results provide support for the idea that stoichiometric AgCuO 2 must exhibit a substantial electronic delocalization leading to non-integral oxidation states for both Ag and Cu atoms and that irrespective of the hypothetical presence of metallic silver at the surface, the system should be conducting. As mentioned, despite difficulties in measuring the conductivity, relatively high values have been reported for AgCuO 2 . 15 This feature has been assumed to provide proof for the non-integer oxidation states suggested by the spectroscopic studies. 14 Since the calculated Mulliken atomic populations do not seem to yield large differences in electron populations for the different oxidation states, we have used an additional indicator, the energy of a selected core level, to devise a procedure yielding reasonable differences to allow a distinction of the oxidation states of Cu and Ag. 40 The basic idea is that a higher oxidation state will lead to a lower population of the d shell of a given atom while core electrons will be more tightly bound in higher oxidation states. Plotting the d electron population vs. the binding energy of the selected core level (minus the orbital energy according to Koopman's theorem so that they should not be directly compared with experimental values) should provide a sorting plot able to separate the regions associated with different oxidation states. Since an all electron basis set is needed to calculate energy eigenvalues for core electrons we have carried out the calculations using the CRYSTAL program. Although the conclusions are practically independent of the functional used, the best results were obtained with the hybrid B3LYP functional. 38 The sorting plots developed for Ag and Cu are shown in Figures 4a and 4b, respectively. According to the B3LYP calculations the silver atoms in AgCuO 2 have a 4d orbital population of 9.904e-and the core 3d binding energy is 369.9 eV. Using the plot of Figure 4a these values clearly indicate that Ag is in an Ag + oxidation state. The Cu 3d orbital occupation in AgCuO 2 is 9.278e-and the core 2p binding energy is 928.6 eV. These values are perfectly compatible with a Cu 3+ oxidation state according to the plot of Figure 4b.
Although calculations for copper compounds do not allow a sharp distinction between the Cu 2+ /Cu 3+ oxidation states, those for silver compounds (Figure 4a) allow to definitively discard the hypothesis of an Ag 2+ oxidation state.
We are thus led to the conclusion that the Ag + Cu 3+ O 4 formulation provides the best starting point to describe the electronic situation in AgCuO 2 . This is in agreement with wellknown structural trends in Cu-based high T c superconductors 41 as well as with our discussion above, where we noted that the Cu-O distance in AgCuO 2 is similar to that in NaCuO 2 . Yet, a Cu 3+ oxidation state implies that silver is present in AgCuO 2 as Ag + , something meaning  See the text for the local axes used for labeling the orbitals.
The Ag d z2 curve is very different. Although the two maxima corresponding to the Ag-O bonding (at -5. eV) and antibonding levels (-0.6 eV) are visible, they are not that different from many of the values in-between as it was the case for the Cu d xy curve. This simply means that the Ag d z 2 orbitals contribute not only to the localized levels associated with the Ag-O bonds but also to quite delocalized states. As can be easily seen in Figure 1a, the Ag-Ag separation is imposed by the relatively rigid CuO 2 chains since the silver atoms must be coordinated by the oxygen atoms of these chains. This leads to an intrachain Ag-Ag distance of 2.80 Å which is surprisingly short for an Ag + -Ag + contact (the Ag-Ag distance in elemental silver is even larger, 2.89 Å). As a consequence, the circular ring of d z2 orbitals in adjacent Ag atoms along the b direction overlap very well and acquire dispersion leading to relatively large and spread contributions along the main peaks (i.e. the band that becomes emptied around the point E of the band structure in Figure 2a). This peculiar feature of the AgCuO 2 structure has two important consequences. First, the d z 2 orbitals are only partially used to establish the Ag-O bonds and this is why, as noted above, these bonds are considerably weaker and thus, longer than expected (2.25 Å but 2.07 Å in Ag 2 Cu 2 O 3 with a non-ambiguous Ag + ). Second, the upper part of the d z 2 contribution which occurs above the Fermi level is empty. Since this part is that associated with the d z 2 --d z 2 interactions leading to the Ag-based band and the upper part of this band is antibonding, the emptying of these levels provides a substantial stabilization to the Ag sublattice which must be considered, at least partially, as a silver chain. The situation is reminiscent of the stabilization of the Pt chains in Consequently it may be expected that the silver atoms of AgCuO 2 form silver chains which can easily slide along the b direction.
D. Silver mobility. The structural data for AgCuO 2 exhibits some unusual aspects such as weak peaks that could imply breaking of the C-centering, weak diffuse scattering lines suggesting the possible occurrence of disorder, etc. 4,13 The possibility that the presently known structure is some kind of average structure cannot be dismissed. In addition, the results of the previous section and the noted anomalous coordination of the silver atoms in the crystal structure, which in fact exhibit large thermal factors, 4,13 suggest that the silver atoms could exhibit some mobility. In order to shed some light into this question we have first calculated and analyzed the phonon structure for the optimized AgCuO 2 crystal structure.
The phonon dispersion diagram (Figure 6a) shows that this structure is indeed a stable structure (the very small negative frequencies found for wave vectors in the Γ-Y direction in the proximity of the center of the Brillouin zone can be attributed to small numerical errors).
The phonon DOS curve (Figure 6b, left) and the phonon partial DOS (Figure 6b Altogether, these data suggest that the present structure is dynamically stable and not susceptible to a major energy lowering distortion. In order to confront these results with experimental data we have measured the heat capacity and calculated the heat capacity at constant volume. The results are shown in Figure   6c. With four atoms per unit cell the heat capacity should reach a limiting value of 12R at high temperatures. The calculated curve agrees very well with the experimental data at low temperatures, up to approximately 100 K, and rises a bit less steeply for larger temperatures.
The experimental results show that no abrupt localization of a disordered structure is present, as it could be expected, at low temperatures. The differences at high temperatures are most likely due to the large anharmonic phonon modes in the AgCuO 2 structure which are not taken into account in the phonon calculation. Anharmonicity effects lead to a softening of phonon frequencies and consequently these modes will have larger contributions to the heat capacity at lower temperatures than in a model considering only harmonic vibrations.
Consequently, although according to these results the present structure is stable at low temperatures we should more carefully consider the possible influence of anharmonicity effects at higher temperatures.  At low temperatures all four power-spectra in Figure 7 have a peak structure similar to the corresponding projections of the phonon DOS curves in Figure 6b. The most interesting feature appears for Ag atoms between 400 and 450 K, where the power spectrum loses its structure indicating the lack of correlation between their velocity at a given time and sometime later, or in other words, the more or less free movement of the Ag atoms within the structure at temperatures above approximately 400 K. This is an important result which can be analyzed in more detail by calculating the Ag power spectrum for each direction of space separately. The three graphs included in Figure 8 show very clearly that the lack of correlation between the motions of Ag atoms at longer times is circumscribed to the motion along the direction of the silver chains parallel to the crystallographic b axis (y axis in our calculation).
It can thus be concluded that the motion of Ag atoms upon raising the temperature increases progressively with larger and larger vibrations around their equilibrium position until a critical temperature between 400 and 450 K is reached when the Ag chains most likely begin to freely slide in a direction parallel to the crystallographic b axis. Previously reported neutron diffraction experiments at 1.5 K and room temperature in reference 17 support these results. In these refinements the same structure reached from X-ray data refinement 4,13 is found, and additionally such structure is found both at room temperature and 1.5K, evidencing the absence of a thermally activated disorder. The Ag thermal parameters are significant at room temperature and decrease in magnitude, as expected, under cooling. Structural work at higher temperatures would be worthwhile doing in order to test the results of our study.
To have a better idea of the silver atoms displacements we carried out a series of model calculations using a 2a×2b×c supercell of the optimized structure thus containing four silver chains with two atoms per chain, where only the silver atoms were allowed to move. Since we are using the optimized structure with the CuO 2 sublattice kept frozen the calculated activation energies will be overestimated and should be taken as an upper bound. The sliding of undistorted silver chains was found to be the easier type of distortion. For instance, the sliding of a single chain in the 2a×2b×c supercell is associated with an activation energy of 0.25 eV. A dimerization within the silver chain is associated with an activation energy around three times larger. Distortions implicating lateral displacements of the silver atoms lead to large activation energies (around ten times that of the sliding motion). Since the 0.25 eV activation energy is an upper bound we conclude that sliding of the silver chains are easy motions which may occur at not too high temperatures. Calculations where more than a single chain are sliding suggest that the sliding of adjacent chains should be practically uncorrelated.
An important result is that these sliding motions do not lead to substantial modifications of the overlapping copper and silver based bands around the Fermi level and there is no opening of a gap at the Fermi level. Thus, the sliding motions should not alter the good conductivity of the system. However, this sliding back and forth of the equilibrium position should induce the observed large thermal factors along the b direction.
At this point one may wonder why the sliding motion of the silver chains is an easy process. Every silver atom is linearly coordinated to two oxygen atoms and these bonds must be partially broken during the sliding. Here we must remember that these two Ag-O bonds

IV. CONCLUDING REMARKS
The puzzling electronic structure of AgCuO 2 has been studied by means of firstprinciples DFT calculations as well as molecular dynamics simulations. These studies provide evidence that both Cu and Ag must be considered as having non-integer oxidation states thus supporting previous spectroscopic studies. The CuO 2 chains impose a relatively short Ag-Ag contact distance to the silver atoms which are forced to partially use their d z2 orbitals to build a band. This band is partially emptied through overlap with the band of the CuO 2 chain built from the Cu d xy levels, which should have been empty if the appropriate oxidation state for Cu were Cu 3+ . In that way, although structural correlations are consistent with the formulation Ag + Cu 3+ O 2 , the appropriate oxidation states for the silver and copper atoms in AgCuO 2 become Ag (1+δ)+ and Cu (3-δ)+ . The overlap of these silver and copper based bands is responsible for the absence of an energy gap at the Fermi level and consequently, the stoichiometric material should exhibit metallic behavior. The analysis of the DFT band structure also suggests that the Ag atoms in AgCuO 2 should form relatively stable chains which, despite being linearly coordinated with oxygen atoms of the CuO 2 chains, can easily slide among the CuO 2 chains. Phonon dispersion calculations and molecular dynamics simulations confirm the stability of the structure. However, they also point out that sliding of the silver chains is an easy motion keeping the band overlap around the Fermi level and thus should not alter the good conductivity of the system. Full agreement is found with the new specific heat and previous neutron diffraction data that evidences the same structure both at room and low temperature, without abrupt phase transitions. David Muñoz-Rojas for kindly providing the sample for heat capacity measurements and Dr.

ACKNOWLEDGMENTS.
Juan Rodríguez-Carvajal for his assistance during the neutron diffraction studies mentioned in the text. We also thank the Servicio General de Apoyo a la Investigación SAI, Universidad de Zaragoza.

ASSOCIATED CONTENT
Three figures with the complete analysis of the Cu 3d and Ag 4d contributions to the density of states of AgCuO 2 as well as the COHP curves for the Ag-O and Cu-O contacts, PBEsol optimized structure for AgCuO 2 , and information about the crystal structures used in generating the sorting plots in Figure 4.

Table of Contents Entry
Because of the overlap between Cu and Ag d-based bands AgCuO2 must exhibit metallic conductivity and the transition metal atoms hold non-integer oxidation states. Phonon dispersion calculations and molecular dynamics simulations confirm the stability of the structure although pointing out that sliding of the silver chains should be an easy motion.