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C: Physical Processes in Nanomaterials and Nanostructures

Spectroscopic Properties of Chalcopyrite Nanoparticles Sascha Thinius, and Thomas Bredow J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11875 • Publication Date (Web): 16 Jan 2019 Downloaded from http://pubs.acs.org on January 17, 2019

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The Journal of Physical Chemistry

Spectroscopic Properties of Chalcopyrite Nanoparticles Sascha Thinius†,¶ and Thomas Bredow

∗,‡,¶

†Corresponding author ‡Principal corresponding author ¶Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, University of Bonn, Beringstr. 4, 53115 Bonn, Germany E-mail: [email protected] Phone: +49 (0)228/73-3839. Fax: +49 (0)228/73-9064

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract An approach is presented to construct stoichiometric and saturated clusters as representative models for nanoparticles based on quantum-chemical surface energy calculations. The procedure consists of three steps. In the first step the shape of the cluster is determined by applying the Wulff-Theorem based on calculated surface energies of the solid compound. Stoichiometry is recovered by adding selected atoms on the cluster surface. If particles in solution are to be modeled, solvent molecules may be added. A global optimization is then performed to allow for full reconstruction of the cluster structure. As an example we studied spectroscopic properties of chalcopyrite (CuFeS2 ) nanoparticles and compared our calculated results to experimental O-1s-XPS, IR and optical spectra.

Introduction Chalcopyrite (CuFeS2 ) is of technological interest for copper exploitation 1 holding more than two thirds of the worlds copper reserves. 2 Copper can be extracted from this mineral through pyrometallurgical or hydro-metallurgical routes. The first route is extremely energy consuming and produces masses of noxious substances. 1 The second route (called leaching process) is assumed to be more sustainable both economically and ecologically. 3 During the leaching process the surface of micro- and nanocrystalline chalcopyrite particles is oxidized in aqueous solution. Surface oxidation products, e.g. porous sulfur, di- and poly-sulfides, iron oxides, copper sulfides and many more, have been identified under different leaching conditions. These products are problematic due to passivation or negative kinetic effects followed by inhibition of the leaching process. Since the mechanisms of these processes are not yet fully understood, we see a need to investigate chalcopyrite theoretically based on first principles. Previous theoretical investigations have been performed for structural, 4–11 energetic 5,9–11 and electronic 5–9,11–14 properties of chalcopyrite bulk and surfaces. While the bare chal2


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copyrite surfaces, as discussed in references 6–8 were evaluated in our previous work, 15 the references 5,10 have a closer relation to this work. Duarte et al. 5 have investigated water adsorption on the chalcopyrite (001) surface. IR spectra and oxygen adsorption energies were computed with iron being the most stable adsorption site. It was found that the dissociative mechanism is less favorable compared to molecular adsorption. In the work of Xu et al. 10 also iron was found to be the preferred site for water adsorption on the chalcopyrite (001) surface. They found that the non-dissociative adsorption is thermodynamically more stable than the dissociative adsorption. Adsorption on copper site was found to be only slightly exothermic. As far as we know chalcopyrite clusters have not been evaluated using atomistic simulations. In order to evaluate our models and methods, we compare calculated spectroscopic properties of chalcopyrite nanoparticles to experimental references. For this purpose we developed a cluster model to represent CuFeS2 nanoparticles which is based on quantum-chemical surface energy calculations. In the cluster generation procedure we take several aspects into account in order to adequately model the real systems. These aspects are (1) cluster shape in accordance to the Wulff-theorem, (2) correct stoichiometry of the compound, (3) reconstructed, but not necessarily global minimum structures, (4) explicit inclusion of the first solvent shell, and (5) implicit solvent effects via continuum models. This procedure can in principle be applied to any solid compound. In this work we present spectroscopic properties of CuFeS2 as an example. Calculated O-1s core-level spectra, optical absorption spectra and infrared spectra are compared to available literature data in order to validate our models and methods.

3



Computational Methods Local and Global Optimization The quantum-chemical calculations were performed with the open-source program GPAW. 16,17 Based on our experience of in a previous work 15 on structural and energetic properties of chalcopyrite surfaces, we employed the revPBE 18 functional. The lattice a, c and position parameters u of chalcopyrite bulk were taken from our previous work. 15 The cluster wave function was described with atom-centered basis sets of TZP 19 quality. The atomic cores were represented by the projector-augmented wave (PAW) method using functional-specific PAW-data sets. 20 Structure optimizations were performed with a limited-memory version of the Broyden-Fletcher-Goldfarb-Shanno 21 (LBFGS) algorithm. Force convergence criteria of 0.001 eV/Å were defined. In order to correctly describe the interaction of adsorbed solvent molecules with the cluster surface, the DFT-D3BJ method of Grimme et al. 22 was employed. The effect of the bulk water solvent has been included via the continuum solvent model (CSM). 23 A global minimum search was performed for the clusters employing the minima hopping 24 (MH) algorithm as implemented in the atomic simulation environment 25 (ASE). The MH algorithm consists of a series of NVE-ensemble molecular dynamics (MD) simulations combined with local optimization steps. In this way energy barriers separating the initial structure from lower minimum structures can be overcome. Here the force convergence criterion was set to 0.01 eV/Å. The method dynamically adjusts the MD simulation temperature and the socalled energy acceptance parameter, trying to find new minimum structures in a systematic way. Starting at a temperature of 600 K, the time step was set to 1 fs for the MH runs.

Bulk Electronic Properties In order to evaluate their predictive power, we tested the accuracy of low-cost and more sophisticated procedures for calculating electronic properties of bulk chalcopyrite. Calculated 4


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electronic and optical band gaps were compared to available experimental data obtained for polycrystalline samples, powders and single crystals. 26–28 The HCTH407 GGA functional 29 which has been parameterized to provide physically meaningful electronic levels was selected as an example for a low-cost method. As an example for more sophisticated methods, the non-selfconsistent G0 W0 approach was used to calculate the electronic band gap. The wave function was calculated with HCTH407. Optical gaps were calculated by solving the Bethe-Salpeter equation based on G0 W0 quasiparticle energies (BSE@G0 W0 ), 30 by applying the random phase approximation (RPA) 31 to the HCTH407 wave function, and with linear response time-dependent DFT (lrTDDFT) 32 also based on HCTH407. While in lrTDDFT the excitation matrix is calculated via Casida‘s equation 33 expanded in Kohn-Sham single particle-hole excitations, in the RPA calculations the optical spectrum is directly obtained as the low-frequency limit of the dielectric function. For bulk calculations a Monkhorst-Pack Γ-centered 8×8×4 k-point mesh has been used. For BSE@G0 W0 and RPA calculations a converged plane-wave basis set with an energy cutoff of 800 eV was applied. In the BSE@G0 W0 calculation an active space of 16 occupied and 16 virtual orbitals was employed. lrTDDFT calculations were performed with the TZP valence basis set. The calculated band gaps are compared to the experimental values in Table 1. A comparison of the calculated and the measured optical spectrum is shown in Figure 1. Table 1: Comparison of calculated and measured chalcopyrite direct (d), indirect (i) and optical (o) band gaps in eV.

Method gap (d) gap (i) gap (o)

HCTH407 BSE@G0 W0 lrTDDFT RPA 0.59 0.95 0.29 0.83 0.87 0.50 0.58

Experiment 0.53 26 0.59 27 0.70 28

The direct and indirect quasiparticle gaps calculated with G0 W0 are increased by 0.36 and 0.54 eV, respectively, compared to the corresponding values obtained with HCTH407. The first excitation energy from the subsequent BSE calculation, 0.87 eV, is slightly above the 5



experimental values, 0.53, 26 0.59 27 and 0.70 28 obtained from IR measurements and ultraviolet photoelectron spectroscopy (UPS), respectively. The best agreement with measured optical band gaps is obtained with lrTDDFT, 0.50 eV, and RPA, 0.58 eV.

Exp. BSE@G0W0@HCTH RPA@HCTH TDDFT@HCTH

Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.0

0.5

1.0

1.5

Energy [eV]

2.0

2.5

3.0

Figure 1: Optical absorption spectra of chalcopyrite; experimental (taken from reference 34, solid black line), calculated with BSE@G0 W0 (dashed blue line), RPA (dotted red line), and lrTDDFT (dotted-dashed green line).

The experimental optical absorption spectrum 34 shown in Figure 1 consists of a small band around 1.2 eV and a broad signal near 2.2 eV. The first band is well reproduced by RPA and BSE@G0 W0 , whereas the first lrTDDFT adsorption maximum is located at 0.8 eV. For the main peak a deviation of −0.4 eV for RPA and BSE@G0 W0 and of −0.3 eV for lrTDDFT is observed. The comparison may be hampered by the fact that the calculated spectra do not include multireference effects, which are important for systems including open-

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shell transition state elements. In particular d − d transitions involving changes of the spin state can not be described by the present methods. But in general all considered theoretical methods provide a reasonable description of the optical spectrum and are therefore suited for further studies of the nanoparticles.

Core-level Spectra As a second method test, core-level spectra of bulk water were calculated and successfully compared to experiment. 35 For the spectra see figure S3 in the appendix. For the calculation of X-ray photoelectron spectra, core-hole PAW-data sets were created. Previous investigations of water spectra have shown, 36 that core-hole states with half electron occupation (Slater’s transition state method 37 ) give better spectra than empty core states. This strategy was therefore followed here.

Cluster Structure Generation Chalcopyrite nanoparticles are modeled by a cluster with diameter of a few nm generated by the procedure outline above. As mentioned in point (3), our cluster structures do not necessarily correspond to global minima. These could be in principle obtained by global optimization, e.g. by simulated annealing techniques 38,39 or by genetic algorithms. 40,41 We followed a different strategy based on the concept of surface energy minimization. The shape of microcrystals with minimal free surface energy is obtained applying the Wulff theorem. 42 We used the surface energies obtained in our previous study on chalcopyrite 15 as input data for a Wulff construction. In this way it is ensured that the cluster surface consists of welldefined facets with areas depending on their stability. Therefore our clusters are models of quasi-crystalline nanoparticles which have been found in many studies. 43 The chalcopyrite cluster (figure 2(a)) and its shape (figure 2(b)) was created with the VESTA 44 program package, which allows to build clusters of various size based on the Wulfftheorem. The number of atoms (34 formula units) was chosen as a compromise between the 7



quality of the model and computational feasibility.

(a) bulk terminated cluster

(b) cluster shape with relevant surface planes

Figure 2: (a) The Cu34 Fe34 S68 -Cluster and cluster shape (b) showing the most relevant (012), (110), (120) and (122) surfaces. Sulfur (yellow) - copper (blue) - iron (brown) According to Ref. 45 the solvation shell of a 9871 Å2 calcite surface contains about 1200 water molecules. If we scale down this number to the area of our nanoparticle (1045 Å2 ), 127 water molecules are present in the solvation shell during the typical time scale of a particle reconstruction (≈ 200-500 ps). 46,47 If we apply the collision rate of 0.33 ps−1 from Ref. 45, 66 to 165 potentially reactive collisions with the surface will occur. For this reason we decided to saturate the dangling bonds of the cluster surface with water prior to reconstruction. For the saturation the strategy depicted in Figure 3 is applied. Under-coordinated metal and sulfur atoms on the cluster surface are saturated with OH groups (figures 3(a),3(b),3(c)) and H (figures 3(d),3(e),3(f)), respectively, to complete the tetrahedral coordination as in the bulk. In total 52 water molecules were attached to the cluster surface. These are representing the 8


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inner Helmholtz layer.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 3: Saturation modes of the cluster for metal atoms (a),(b),(c) and sulfur atoms (d),(e),(f) in a fully saturated valence configuration.

In a second step we applied the MH algorithm to allow for surface reconstruction. In our previous study 15 we have shown that the MH algorithm is well suited to identify structural minima for chalcopyrite surfaces and hence it was used for this study, too.

Results and Discussion Surface reconstruction Starting from the pre-optimized structure the MH algorithm was applied to allow for surface reconstruction. Out of 374 MH-steps 241 new minima have been identified. The ten lowest-lying minima were re-optimized. The associated energy gain per CuFeS2 formula unit compared to the relaxed cluster can be found in Table 2. We found that 6 % of the stabilization energy are due to an increase of the dispersion energy. The reconstruction is not restricted to the adsorbed water molecules but also affects the outermost shell of the cluster atoms. The optimized structure is shown in figure 4(a) , whereas the most stable reconstructed structure is shown in figure 4(b).

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(a) saturated and optimized cluster

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(b) saturated and reconstructed cluster

Figure 4: (a) Cu34 Fe34 S68 H104 O52 saturated and optimized cluster and (b) Cu34 Fe34 S68 H104 O52 saturated and reconstructed cluster with lowest energy. Sulfur (yellow) - copper (blue) - iron (brown) - oxygen (red) - hydrogen (white) Table 2: Energy gain in in eV per CuFeS2 formula unit of the 10 lowest-lying minima obtained with MH.

No. ∆E

1 -0.07

2 -0.11

3 -0.08

4 -0.08

5 -0.13

6 -0.06

7 -0.11

8 -0.15

9 -0.09

10 -0.09

From the structure of the whole cluster (figure 4) it is hard to see structural changes after reconstruction. Therefore in figure 5 an image detail is given to exemplarily demonstrate the effect of reconstruction. In the optimized cluster 5(a) one can see a dangling and almost linear S – Cu – OH group. If this atom group is regarded as a defect, it is healed by reconstruction (see figure 5(b)). Further in the upper part of both pictures three new additional water molecules from the water network near the surface were attached on surface-Cu atoms instead of forming. 10


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(a)

(b)

Figure 5: (a) optimized cluster and (b) reconstructed cluster with lowest energy. Sulfur (yellow) - copper (blue) - iron (brown) - oxygen (red) - hydrogen (white) In the following the ten most stable reconstructed and re-optimized cluster structures are used for the calculation of spectroscopic properties.

XPS calculations In the literature experimental core-level spectra are available for oxygen K-shell 48–51 of leached chalcopyrite surfaces. The measured spectra do not allow for a differentiation of the oxygen environment. For a deeper analysis we performed XPS calculations for the ten most stable clusters. In Figure 6 the calculated O-1s core level spectrum of the most stable structure (8) and the spectrum obtained by superposition of the individual cluster spectra is shown in comparison to measured spectra. 48–51 The experimental spectra were recorded under different leaching conditions. In experiments exp0 (pH=0.3) and exp3 (pH=1.0) leaching was done under acidic conditions, and in experiments exp1 (pH=9.2) and exp2 (pH=10.0) the probe was leached under basic conditions. The shape of the experimental spectra significantly depends on the pH. While spectra obtained at low pH are showing mainly one peak with a smaller shoulder, spectra at high pH have two main peaks. However the peak assignment in the experimental studies is almost the same. According to the authors of Refs. 48–51, the energy range around 533 eV is due to adsorbed H2 O and sulfates, the range around 531 eV belongs to metal hydroxides and the peak or shoulder around 530 eV was assigned to metal oxides. 11



Min Min(10) exp0 exp1 exp2 exp3 Intensity

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526

528

530

532 Energy [eV]

534

536

Figure 6: Calculated O-1s XPS spectra of the lowest-energy reconstructed cluster (8) (Min: dashed black line), superposition of the ten lowest-energy reconstructed clusters (Min(10): dotted black line) and experimental spectra (exp0 48 : solid blue line, exp1 49 : solid red line, exp2 50 : solid green line, exp3 51 : solid yellow line) under different leaching conditions.

In the Cu34 Fe34 S68 H104 O52 cluster the following species exist on the cluster surface: physisorbed H2 O, H2 O bound to copper or iron atoms and OH bound to both copper and iron atoms. In addition hydrogen-bonded species can be distinguished from other adsorbates. Since formation of copper- or iron-oxides was not observed during reconstruction, the experimental peak around 530 eV is not reproduced with the calculated spectrum. To probe the effect of structural changes on the computed spectra we plotted the lowestenergy single cluster O-1s XPS spectrum (dashed line) along with the averaged spectrum obtained from the ten lowest-lying minimum structures (dotted line in figure 6). Since there

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is no noticeable difference between the minimum and the averaged spectrum, we will restrict subsequent calculations to the lowest-lying minimum structure. H2O-M HO-M

526

528

530 532 534 Energy [eV] (a)

536

526

(HO,H2O)-Cu (HO,H2O)-Fe Intensity

Intensity

H2 O H2O-HB Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


528

530 532 534 Energy [eV]

536

(b)

526

528

530 532 534 Energy [eV]

536

(c)

Figure 7: Calculated O-1s XPS spectra of the reconstructed Cu34 Fe34 S68 H104 O52 -cluster projected on the chemical environment of the oxygen atoms: (a) physisorbed H2 O with and without hydrogen bonding (HB), (b) H2 O and OH bound to metal atoms (M) and (c) H2 O and OH bound to Cu and Fe.

According to the different O-1s core-level spectra shown in figure 7, oxygen atoms can be classified depending on their chemical environment. The peak intensity is proportional to the total number of oxygen atoms belonging to a certain environment. It can be clearly distinguished between physisorbed H2 O with and without additional hydrogen-bonding (7(a)), metal-bound H2 O or OH (7(b)) and in addition OH and H2 O species bound to both Cu and Fe (7(c)). Peaks corresponding to physisorbed water appear below 532 eV. They are shifted to higher energies if hydrogen-bonds from the cluster to the water oxygen are formed. The main peak corresponding to HO – M species occurs at 531 eV, and at 532.5 eV for H2 O – M species. The second peak at 532.5 eV found for HO – M species arises from hydrogen-bonding similar to those in figure 7(a). Peaks due to Fe-bound and Cu-bound oxygen almost coincide near 532.5 eV, while the (OH, H2 O) – Cu species have slightly lower energy than those of (OH, H2 O) – Fe species. The calculated spectra agree with the experimental peak assignment for adsorbed H2 O and HO – M. 48–51 Furthermore it is possible to distinguish if hydrogen-bonding is involved or not. Differentiation between Fe- and Cu-bound oxygen seems to be a difficult task for 13



experimentalists from O-1s XPS spectra, since both spectra overlap and the distance of the

526

Intensity

peak maxima is very small (0.3 eV).

Intensity

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528

530 532 534 Energy [eV] (a)

536

526 (b)

528

530 532 534 Energy [eV]

536

(c)

Figure 8: Single-atom O-1s core-level spectra for particular chemical environments (a) for physisorbed water (upper part of (b)) and (c) for physisorbed water with hydrogen-bonding (lower part of (b)). The next-nearest neighbors sulfur(yellow) - oxygen (red) - hydrogen (white) are colored.

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(c)

526

528

530 532 534 Energy [eV] (d)

536

526

Intensity

(b)

Intensity

(a)

Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


528

530 532 534 Energy [eV]

536

(e)

526

528

530 532 534 Energy [eV]

536

(f)

Figure 9: Single O-1s fingerprint XPS spectra with well defined chemical environment (a,d) for HO – Fe, (b,e) hydrogen-bonding HO – Fe and (c,f) H2 O – Fe. The next neighbors iron (brown) - oxygen (red) - hydrogen (white) are colored.

In Figures 8 and 9 case studies of O-1s core-level spectra calculated for single oxygen atoms are shown together with their chemical environment. For clarity all other cluster atoms are displayed in gray. Figure 7(a) represents the general case of physisorbed water with next-nearest neighbor distance larger than 3 Å with and without HB. Single O-1s core-level spectra representing the general case are shown in figure 8. In Figure 8(a) most of the spectral density is located below 532 eV, while for hydrogen-bonded water (figure 8(c)) most of the intensity comes at energies above 532 eV. The different O-1s excitation energies of the various oxygen species are due to changes in the oxygen charge and to the electrostatic potential created by the environment. The net charges calculated with the Bader 52 method can be used to quantify the intra-atomic effects. In the case of hydrogen-bonding the hydrogen atom donates electron density to the oxygen 15



atom which decreases the oxygen partial charge accompanied by a positive XPS-shift. The same trend was observed for the species shown in figure 9. Within the series of HO – Fe (Figures 9(a) and 9(d)), hydrogen-bonding HO – Fe (Figures 9(b) and 9(e)) and H2 O – Fe (Figures 9(c) and 9(f)) the peaks shift to higher energies, while the partial charges increase from −0.58 over −0.71 to −0.74 electrons, respectively.

0.55 0.60 Bader partial charge [a.u.]

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0.65 0.70 0.75 0.80 0.85

530.0

530.5

531.0

531.5 532.0 Energy [eV]

532.5

533.0

Figure 10: Bader partial charges of O atoms vs. the XPS binding energy with linear regression. Each marker represents an O-1s single excitation spectrum.

The data points shown in Figure 10 were generated by calculating the Bader net charge of the oxygen atoms for the ordinate and by taking the energy of the spectrum’s area bisection for the abscissa. The error bar size is the standard deviation of residuals of data compared to the fit with an R2 coefficient of 0.78. The low R2 indicates that the intra-atomic contributions alone cannot account for the calculated core level shifts. Nevertheless there is a linear correlation between that net charges and shifts. Therefore these can be used to approximately determine the oxidation state of O atoms within a certain tolerance.

lrTDDFT calculations The optical absorption spectrum of the chalcopyrite nanoparticle (8) was calculated using the lrTDDFT technique. For the lrTDDFT spectrum an active space of 64 occupied and 64

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unoccupied bands were used, so that more than 12900 transitions were examined. Above it was shown that lrTDDFT results are in good agreement with the experimental bulk spectrum. Moreover this method is computationally more efficient than the alternatives. As can be seen from Figure 11, good agreement with experiment was also found for the nanoparticle. For the convergence of the spectra with respect to the active space size see appendix (S1).

exp 64/64

Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

1

2

3

Energy [eV]

4

5

6

Figure 11: Experimental 53 (dashed line) optical absorption spectrum of colloidal chalcopyrite nanoparticles and the calculated lrTDDFT optical absorption spectrum (solid line) of the chalcopyrite nanoparticle No. 8 from table 2. The main peak of the experimental spectrum shown in Figure 11 is located at 2.65 eV. In the calculated spectrum two peaks at 2.20 and 2.75 eV are present, the latter being the main peak. The discrepancy between the experimental and the calculated spectrum may arise either from neglecting multireference effects or from broadening effects of the measured spectrum. The projected density of states (figure S4 in the appendix) shows that Cu-3d states are predominant at the valence bands region. The conduction band region is almost 17



entirely characterized by Fe-3d states, concluding that the intermetal-d-transitions define the spectrum seen in figure 11. Since there is a small amount of S-3p and O-2p density in the valence band region, also metal-to-ligand charge transfer states might be possible. 53 At energies above 4 eV errors arise from incompleteness of the active space. Compared to the bulk lrTDDFT spectrum in figure 1 the spectrum is shifted to higher energies.

IR spectra In addition to experimental core-level and optical absorption spectra also an IR spectrum of microcrystalline chalcopyrite 54 is available in the literature. The calculated IR spectrum of the chalcopyrite cluster is shown in Figure 12.

Bulk

400

S-H

Cu-O

Fe-O

Total

200 Intensity [ (D/Å )2 amu 1]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0 H-O@Cu

400

H-O@Fe

Total

200 0 H2O

400

H2-O@Cu

H2-O@Fe

Total

200 0

0

500

1000

1500 2000 2500 Wavenumber [cm 1]

3000

3500

Figure 12: IR spectra of the reconstructed cluster projected on the chemical bonds. The calculated modes are plotted in bars. 18


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For the assignment of the peaks it was distinguished between the bulk part of the cluster and the outermost atoms. The latter include S – H, H – O@Cu, H – O@Fe, physisorbed H2 O, H2 O@Cu and H2 O@Fe binding patterns. The modes up to 1250 cm−1 are less meaningful and belong to S – Cu, S – Fe "lattice" vibrations of the bulk part and to O – Cu and O – Fe vibrations. Most of them arise from multiple atom movements and in addition libration of water molecules. The energy range of 1579 to 1669 cm−1 is populated by water bending vibrations, followed by two peaks at 1897 and 2038.5 cm−1 (see Figure 13(a)). These belong to HO – H – OH vibrations, where a water hydrogen is transferred from water to an – OH group. The next intense peak at 2569 cm−1 (see Figure 13(b)) is corresponding to pure S – H vibrations. At frequencies between 2700 to 2873 cm−1 , HO – H – S vibrations play an important role. An example is given in Figure 13(c). Signals from 2902 to 2979 cm−1 are combinations of HO – H – OH, H2 O – H – OH (see figure 13(d)) and S – H – OH vibrations. The spectrum above 3000 cm−1 is now well resolved and normal modes are a mixture of multiple atom movements. Most of the vibrations in this region correspond to symmetric (Figure 13(e)) and asymmetric (Figures 13(f) and 13(g)) stretching modes of physisorbed water molecules. Sketch 13(h) highlights the region around 3650 cm−1 . These modes are typically due to O – H vibrations.

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(a) 2038.5 cm−1

(d) 2915.1 cm−1

(b) 2568.9 cm−1

(e) 3344.8 cm−1

(g) 3516.5 cm−1

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(c) 2739.4 cm−1

(f) 3449.4 cm−1

(h) 3674.4 cm−1

Figure 13: Prominent modes with high intensity in the IR-spectrum. Arrows indicate the direction of the vibration and atoms in brackets belong to surface metal atoms. Compared to the experiment, 54 water and OH signals around 1620 cm−1 and from 3150 to 3650 cm−1 were accurately reproduced in terms of signal position and shape. Other signals between 1620 and 3150 cm−1 were not present in the experimental spectrum recorded in aqueous solution at pH=10.0. In the XPS subsection we have seen that calculated XPSspectra show better agreement with experimental spectra at low pH and therefore species with signals between 1620 and 3150 cm−1 might not be formed under high-pH conditions. In the literature 3 and references therein it is also stated that polymeric sulfur and SO4 2 – units are formed during chalcopyrite leaching, concluding that those species might not be accessible with our level of theory at reasonable simulation time scales. As with the XPS spectra, the dependence of the calculated spectrum from the cluster structure was tested.

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The summed up IR spectra of all minimum structures are provided in the appendix (S2). Comparison shows that the characteristic signals obtained for the ten cluster structures match closely. Therefore only results for the most stable structure are discussed. Duarte et al. 5 compared their calculated frequencies to experimental spectra of molecular water. They observed good agreement for water symmetric stretch (ν1 ) and bending (ν2 ) modes and a rather strong deviation for the asymmetric stretching (ν3 ) mode. If the cluster spectra are compared with the spectrum of bulk water (see appendix (S2)), the water vibrations ν1 , ν2 and ν3 were generally found at lower frequencies. This indicates weakening of the O – H bonds by the interaction with the cluster.

Conclusion Starting with chalcopyrite bulk calculations, we have shown that optical band gaps can be reproduced best with RPA and lrTDDFT methods. For the BSE@G0 W0 calculation, however, the optical gap is overestimated. The optical absorption spectra match the experimental spectrum with sufficient accuracy. Spectroscopic properties, calculated with a stoichiometric reconstructed cluster match well with experimental spectra obtained under leaching conditions. For O-1s-XPS calculations the literature peak assignment for hydroxy groups and adsorbed water could be confirmed. In addition we have shown that it is possible to distinguish hydrogen-bonded species (e.g HOH – – S) from physisorbed water. The spectrum calculated with lrTDDFT matches large parts of the experimental spectrum taken from colloidal nano-sized particles. Compared to the bulk spectrum an overall shift to higher energies is observed. The calculated vibration modes of all common binding patterns were mapped on the full spectrum. For common surface species sketches were made and their exact frequencies were given. Prominent signals from the experimental spectrum were reproduced accurately. We have shown that a reconstructed medium-sized cluster with a structure based on 21



the Wulff-construction in combination with surface saturation may be used to reproduce experimental results obtained for much larger particles.

Supporting Information Available The following files are available free of charge. • Filename: supplementary.pdf (including convergence of the lrTDDFT spectrum with respect to the active space, the convergence of the IR spectrum with respect to the number of different structures, the XPS spectrum of bulk water and the density of states for the Cu34 Fe34 S68 H104 O52 cluster) This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement The authors gratefully acknowledge the Leibniz-Rechenzentrum der Bayerischen Akademie der Wissenschaften for funding this project with ID pr92mu by providing computing time on the SuperMUC system. We also acknowledge the DAAD funding for the project entitled ’Theoretical Investigation of Chalcopyrite Surfaces’ with project ID 57060317.

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Spectroscopic Properties of Chalcopyrite ... - ACS Publications

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