First Principle Study of Capping Energies and Electronic States in

Nov 22, 2013 - In the last years, colloidal semiconductor nanoclusters (NCs) have ..... a fundamental lighthouse when looking for ground state energy ...
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First Principle Study of Capping Energies and Electronic States in Stoichiometric and Nonstoichiometric PbSe Nanoclusters Fabio Grassi, Mario Argeri, Leonardo Marchese, and Maurizio Cossi* Dipartimento di Scienza e Innovazione Tecnologica (DISIT), Centro Interdisciplinare Nano-SiSTeMI, Università del Piemonte Orientale, via T. Michel 11, I-15100, Alessandria, Italy S Supporting Information *

ABSTRACT: A large variety of PbSe nanoclusters have been modeled at the DFT level, to study their structure, their affinity for different ligands and their electronic properties, also depending on surface passivation. The clusters are extracted from the bulk rock salt structure with cubic, prism, truncated cubic, cuboctahedral and octahedral shape and they are fully relaxed, before computing the addition energies of methylamine and formate anions in different positions, to model the process of surface passivation. Then the density of states of all the clusters is computed, to study in particular the band gap and the behavior of the so-called intragap states, which affect the photophysical properties of the nanoparticles, also acting as trap states for charge carriers. We confirm the strong relationship between nanocluster off-stoichiometry and intragap states: such states can be localized on the surface, in the bulk or delocalized over the nanoparticle, according to the source of off-stoichiometry. The ability of different ligands to eliminate the intragap states are tested and discussed, also proposing nonstandard capping molecules.

1. INTRODUCTION

localized on the NC surface, and their effect on optical properties and carrier mobility is not always so marked. IGS are strongly related to NC stoichiometry:18−21 filled or empty IGS can appear due to an excess of cations or anions, respectively (a phenomenon that has been referred to as stoichiometric doping).21 Off-stoichoimetry can result from core defects, like vacancies or lattice substitutions, or from the presence of nonstoichiometric crystallographic faces: in lead chalcogenide NCs, for instance, (111) faces are composed only by cations or anions, and they can cause a strong excess of one element. We have recently computed the DFT energy of the most common PbSe crystallographic faces, finding that Pb(111) is much more stable than the Se counterpart, though being markedly less stable than (100) and (110) faces.22 On the other hand, the organic ligands used to passivate the NC surfaces have different interaction energies with the various faces, and this can alter their relative stability: for instance, carboxylate (typically oleate) anions interact much more strongly with the polar Pb-(111) face, stabilizing it with respect to (100) and (110).22,23 A more detailed analysis shows that IGS are related to the overall charge balance, taking into account also the possibly charged ligands on the NC surface.19,21 For PbSe, as in general for IV−VI semiconductors, the charge balance condition can be expressed as20,21

In the last years, colloidal semiconductor nanoclusters (NCs) have been proposed for an impressive number of applications,1 primarily in optoelectronics (i.e., lasers,2 diodes, 3 and detectors4) and photovoltaics.5,6 Due to quantum confinement effects, indeed, the photophysical properties of such small particles can be finely tuned, to enhance light absorption and emission;7,8 moreover, high carrier multiplication effciencies have been reported in particular for lead chalcogenides9,10 (like PbSe, studied in the present work) with evident, important consequences for next-generation sensitized solar cells.11 A further impulse to colloidal NC production and use is expected to come from the recent techniques developed for the synthesis in aqueous solution.12 Understanding and exploiting these properties require the precise knowledge and control of NC electronic states, which is complicated since small variations in the stoichiometry, shape and degree of surface passivation can affect the electronic distribution critically. In particular, the so-called surface states are known to become more and more important as NC dimensions lower (and, hence, the surface-to-volume ratio increases): surface states are thought to play a key role in photoluminescence,13 multiple exciton generation,14,15 and charge transfer phenomena.16 Such states are often described as localized, contrary to the diffuse nature of low lying valence band states, with energy close or falling inside the band gap. They are sometimes referred to as trap states, to underline their expected effect on charge carriers, which is clearly crucial in optical and photovoltaic applications:17 however, as pointed out in the following, intragap states (IGS) are not necessarily © 2013 American Chemical Society

Nexc = 2 × NPb − 2 × NSe + q × NL

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Received: October 16, 2013 Revised: November 22, 2013 Published: November 22, 2013 26396

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where Nexc is the number of excess electrons in the NC, NL is the number of ligands, and q their net charge (thus, Nexc > 0 or < 0 corresponds to n- or p-doping, respectively). Reducing or eliminating IGS is an important issue to improve NC optical and photovoltaic perfomances: according to eq 1, a suitable amount of anionic ligands can compensate the effect of the lead excess often observed in small PbSe NCs.24,25 Recently, it has been argued that long alkyl chains prevent oleate to passivate completely the nonstoichiometric faces,26 proposing a hybrid approach where chloride ions fill the unpassivated portions (and then oleate is replaced by shorter, bifunctional organic linkers to facilitate the formation of homogeneous films).26−28 In a different approach, which also proved effective, the nonstoichiometric faces are passivated by alkylselenide ligands, acting as ligands with −1 charge with respect to eq 1: from a different point of view, the procedure reduces the lead excess by adding extra Se atoms, and in this case, eq 1 can be applied assigning q = +1 to the alkyl chains attached to the surface. In the present work, we have modeled at the DFT level several PbSe NCs, with a 2-fold objective: analyze the trend of addition energies of ligands on the various adsorption sites of different structures and gain a deeper knowledge about the nature of intragap states, depending on NC stoichiometry, shape, and surface passivation.

Figure 1. Geometrical shape of the studied clusters: (a) cube, (b) prism, (c) truncated cube, (d) cuboctahedron, (e) octahedron: (100) faces in red, (111) faces in blue.

atom; on the other hand, each (111) face can carry a larger amount of excess atoms. The effect of surface passivation was considered with small organic ligands, that is, methylamine, CH3NH2, and formate ion, HCOO−, to model neutral and charged capping agents widely used in actual PbSe NC synthesis, hexadecylamine and oleate ion, respectively. Some tests were also performed with model electrophilic ligands, namely, Al(CH3)3 and BCl3, and also with ethyl radical, CH3CH2•, though these kinds of molecules are not used in the common syntheses. When ionic ligands are used, a question arises about the overall NC charge: since evidence has been reported that oleate-capped NCs are almost neutral, as discussed below, we imposed zero net charge to all the NC models, except when we studied the addition energies of a single formate anion. In that case, the total charge was set to −1 to keep an even number of electrons and, thus, a closed shell configuration.

2. METHODS AND MODELS The ab initio package TURBOMOLE629 was used for NC geometry optimizations and energy levels calculation. Addition energies were computed with the Gaussian03 package,30 which was used also to produce the electronic densities for the orbital graphical representation. All the calculations have been performed at the Density Functional Theory (DFT) level, using pure (BLYP)31,32 and hybrid (B3LYP)33 GGA functionals and localized, Gaussiantype basis sets: 6-31G(d,p)34,35 for H and second row atoms, LANL2DZ for all the other elements,36−38 supplemented with a single set of polarization d functions with exponent 0.185 for Pb and 0.384 for Se. Some test calculations have also been performed at the Hartree−Fock (HF) level with the same basis sets. Recently, a growing concern has been raised about the reliability of DFT binding energies,39 and some approaches have been developed to include efficiently the dispersion contribution, which is otherwise missing or underestimated. Then we have corrected B3LYP addition energies with the procedure proposed by S. Grimme40 and implemented in Gaussian03. Counterpoise correction of the basis set superposition error (BSSE)41 was applied to the calculation of addition energies. PbSe crystallizes in the cubic rock-salt structure: we considered finite clusters cut out of the bulk lattice, with cubic, rectangular prism, truncated cubic, cuboctahedral, and octahedral shapes (see Figure 1); the geometry of all the clusters was fully relaxed. These clusters expose crystallographic faces with indices (100) or (111), the former being stoichiometric, that is, formed by an equal amount of Pb and Se atoms, while the latter is composed by just one kind of atom, so that we can have Pb- or Se-(111) faces. Depending on the number of atoms on the edges, even the cubes and the prisms with only (100) faces can be nonstoichiometric, as for instance the 3 × 3 × 3 cubes Pb14Se13 or Pb13Se14: in this case, there is always just one excess

3. RESULTS AND DISCUSSION 3.1. Optimized NCs. A number of PbSe clusters, with different size and shape and exposing (100) and (111) faces, have been modeled, optimizing their structure at the DFT(B3LYP) level: in Table 1 the studied clusters are listed along with their approximated size. Clearly the definition of the “diameter” of a nonspherical cluster is somehow arbitrary: we report two extreme values, that is, the distance between the closest opposite faces and the distance between the farthest atoms in the cluster, in both cases adding 3 Å, that is, the average Pb−Se bond distance, to roughly estimate the sum of the atomic radii. During the geometry optimizations, for all but the smallest clusters the “core” structure almost kept the initial conformation taken from bulk PbSe; (100) faces also were modified moderately, while (111) faces underwent larger reconstructions, as expected for this kind of high energy surfaces. We did not find evidence of the formation of Pb dimers, as recently reported for PbSe NC (110) faces in conditions described as n-type doping, that is, after removal of all the ligands from the face.19 As noted above, the NCs studied in this work do not exhibit (110) faces: on reconstructed (111) faces we found aggregates of Pb atoms, with diffuse orbitals shared among different atoms. The relation between these surface orbitals and trap states is discussed below. 26397

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Table 1. Atomic Composition, Average Size (See Text), and Example Picture of the Studied PbSe NCs

a

Pb28Se28 was obtained by cutting two opposite vertices from the Pb32Se32 cube and obtaining one Pb-rich and one Se-rich (111) faces, the other clusters had only one vertex cut and expose one Pb-rich (111) face. bDimensions corresponding to the parent cubes: Pb32Se32, Pb62Se63, Pb172Se171, and Pb171Se172, respectively.

3.2. NC Complete Capping. We have recently reported on the addition energies (Eadd) of different ligands on PbSe faces,22 concluding that neutral ligands, for example, methylamine, trimethylphosphine oxide, and propionic acid, bind more strongly to (100) face, while propionate ion has a much larger affinity for the more polar Pb-rich (111) face. However, those results had been obtained for single molecules on flat faces: to investigate the dependence of Eadd on the morphology of the binding site, it was computed for methylamine and formate ion on different Pb atoms located on vertices, edges, and faces of prismatic, cuboctahedral, and octahedral clusters with the results listed in Figures 2 and 3, respectively. Present results differ from the data presented in ref

Figure 3. Addition energy (eV) of formate anion on Pb atoms located in different positions: triangle, blue: (100) face; diamond, pink: (111) face; square, red: edge; circle, green: vertex. BSSE corrected by CP method.

22 also because they include an estimate of the dispersion energy, computed with the parametric method proposed in ref 40. Methylamine Eadd values are scattered between 0.4 and 1.2 eV, not showing a clear affinity for a particular Pb position, though the addition energies are in general higher on (100) faces and lower on vertices, somehow unexpectedly since on vertices Pb atoms are most undercoordinated. A vague trend is visible with respect to the number of atoms, with higher Eadd values for the larger clusters. On the other hand, formate ion Eadd are 1 order of magnitude higher, and they depend much more strongly on the cluster size and the binding site: in Figure 3, Eadd is seen to increase with the cluster size, probably due to the presence of more and more lead atoms that can delocalize the anion negative charge, as noted, for example, in ref 22. The ionic ligand has a greater affinity for (111) than for (100) faces, as already shown,22 even

Figure 2. Addition energy (eV) of methylamine on Pb atoms located in different positions: triangle, blue: (100) face; diamond, pink: (111) face; square, red: edge; circle, green: vertex. Filled symbols: cubic and prismatic NCs; open symbols: octahedral and cuboctahedral NCs. BSSE corrected by CP method. 26398

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if the highest addition energies are computed for vertex and edge atoms, in contrast with the results of MA. Cooperative effects were also studied, by increasing the number of methylamine molecules on cubic and prismatic clusters PbnSen, n = 4, 6, 8, 9, 10, until all the surface Pb atoms were capped: the results are presented in Figure 4.

Figure 5. HOMO−LUMO energy gap (eV) of PbSe clusters (cubes and prisms) computed at different theory level for singlet and triplet states (see text). Triangles, blue: Hartree−Fock; circles, green: B3LYP; squares, red: BLYP. Open symbols: singlet states; filled symbols: triplet states.

In a recent paper,42 a strong correlation was found between the HOMO−LUMO gap, and the singlet−triplet transition energy of a set of organic conjugated molecules using BLYP and B3LYP functionals, with medium to large size basis sets. The same comparison was performed also for the abovementioned PbSe NCs (pictures shown in the Supporting Information): BLYP confirms to be the most reliable method in the singlet state (HF being severely wrong and B3LYP somehow intermediate), while with all the methods the excitation energies correlate well with the HOMO−LUMO gap computed in the triplet state. On this basis, we decided to compute the DOS for all the systems in the singlet ground state at the BLYP level (though at the geometries optimized with B3LYP). The DOS for some PbSe NCs exposing (100) faces only (cubes and prisms) are shown in Figures 6 and 7: in the former case, the NCs are stoichiometric (i.e., they contain the same number of Pb and Se atoms); in the latter there is one excess atom, which is the only form of off-stoichiometry possible in clusters exposing (100) faces. In Figure 8 the DOS for NCs exposing one or more (111) faces are reported: in this case, the off-stoichiometry can be much more pronounced. Stoichiometric NCs present clear band gaps without IGS, narrowing as the particle size increases, as expected; on the other hand, one intragap state appears in nonstoichiometric cubes and prisms, filled in Pb-rich and empty in Se-rich clusters, while NCs with (111) faces have a larger number of IGS. In general, these calculations confirm that the number of IGS is half the excess atoms in nonstoichiometric (and ligand-free) particles.18,20,43,44 However, the IGS look quite different depending on the NC structure: as shown in Figure 9a,b, in NCs exposing (100) faces, only the IGS are delocalized over the entire cluster, while they are strongly localized on the (111) faces, when present. To get more insights on this point, we also obtained a nonstoichiometric cluster by removing one Se atom from Pb108Se108 core, as a model of off-stoichiometry related to crystalline defects rather than morphology: in this case (see Figure 9c), the IGS is core-localized. Though all IGS are

Figure 4. Average addition energy (eV) of methylamine on Pb atoms at different degree of surface coverage. Diamond, light blue: Pb4Se4; down triangle, pink: Pb6Se6; up triangle, blue: Pb8Se8; circle, green: Pb9Se9; square, red: Pb10Se10.

As expected, Eadd decreases as the number of ligands grows, due to lateral interactions which are clearly underestimated by this small molecule, with respect to the bulky ligands commonly used in syntheses. 3.3. PbSe Electronic Structure. As noted in the Introduction, the density of states (DOS) and, in particular, the orbital energies around the band gap are very important parameters for tuning NC performance in optoelectronics and photovoltaics. Strictly, the concepts of band gap and DOS are referred to periodic systems, like bulk crystals: for finite size clusters, one should speak more precisely of HOMO−LUMO gap and orbital energies, though for nanoparticles, most authors use the former expressions; in the following, we will use band gap and HOMO−LUMO gap as synonyms. A preliminary step concerns the choice of the computational level, because the variational principle, a fundamental lighthouse when looking for ground state energy and, to a certain extent, occupied orbital energies, cannot guarantee a reliable calculation of HOMO−LUMO or band gaps. To select the suitable approach, we computed the HOMO−LUMO energy gap for all the cubic and prismatic NCs listed in Table 1 at HF and DFT level, using pure (BLYP) and hybrid (B3LYP) density functionals, and compared it to the energy difference between the two singly occupied orbitals in the first triplet state. In the triplet state, both frontier orbitals are occupied and are variationally optimized: this is clearly an approximation, because the electronic structure is likely to change in the two states, and the triplet gap is slightly underestimated, but it can indicate what method provides the best LUMO orbital also in the singlet state. The results of such a comparison are illustrated in Figure 5, and they show that DFT with the pure BLYP functional has the best correlation between singlet and triplet HOMO−LUMO gaps. 26399

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Figure 6. Density of states for different stoichoimetric clusters exposing (100) faces (cubes and prisms). Occupied orbitals: red; empty (virtual) orbitals: green; to improve the readability, orbitals are represented as Gaussian functions of unitary height (arbitrary units) and 0.003 eV width.

Figure 7. Density of states for different nonstoichiometric clusters exposing (100) faces (cubes and prisms). Occupied orbitals: red; empty (virtual) orbitals: green; orbitals are represented as Gaussian functions of unitary height (arbitrary units) and 0.003 eV width. HOMO (H) and LUMO (L) orbitals are indicated by arrows.

sometimes referred to as “surface states”, this definition is correct only in the case depicted in Figure 9a: localized surface orbitals are likely to catalyze electron−hole recombination or act as trap states for mobile carriers, but it remains to understand whether delocalized or core-localized orbitals, though with midgap energy, have the same effects on charge carriers. Another useful insight about IGS nature is provided by Pb28Se28 NC, obtained by cutting two opposite vertices from Pb32Se32 so that one Pb-rich face and one Se-rich (111) face are formed. Though each (111) face alone causes the appearance of IGS, when they are both present the band gap is clear (DOS shown in the Supporting Information): the stoichiometry rule holds even when the expected IGS should be localized far apart on different faces. The presence of IGS has to be accounted for when discussing NC band gaps (or HOMO−LUMO gaps, as one prefers): using the formal definition, that is, the energy difference between the highest occupied and the lowest unoccupied orbitals, one would obtain the trend shown in Figure 10a with respect to the cluster size. Clearly stoichiometric and nonstoichiometric NCs exhibit different behavior due to the presence of IGS in the latter ones: however, if IGS are not considered in the definition of the band gap, the much smoother trend shown in Figure 10b is obtained. Note that the bulk crystalline PbSe band gap is quite small, around 0.27 eV, but it is expected to grow steeply in nanoparticles, due to the very high Bohr radius:45 recent measures of the size-dependent optical properties of PbSe NCs deposited on GaAs provided

band gaps as high as 1.01 eV for the smallest clusters (average diameter 7.1 nm).46 This is consistent with the trend shown in Figure 3b, considering that the largest clusters in our case are about 3.5 nm wide. In actual syntheses, colloidal NCs are always passivated to stop the particle growth and prevent aggregation: several organic ligands are used, the most common for PbSe being trioctylphosphine oxide (TOPO), hexadecylamine, and oleic acid. The protonation state of oleic acid is not clearly discussed in many papers, but some recent works pointed out that this ligand is bound to surface Pb atoms as oleate anions,47−49 likely in a bidentate arrangement. It is noteworthy that the total charge of colloidal NCs is near-zero (ranging from −1 to +2 au)23,50 charge even when they are capped by oleate ions: in this case, the negative charge has to be compensated by excess Pb2+ ions, and the surface layer can be thought as formed by lead oleate. The effect of surface passivation on IGS is clearly of great interest: we investigated it by attaching different model ligands on the (111) faces of Pb59Se56 (truncated cube) and Pb38Se19 (octahedron) and comparing the DOS to that of the bare clusters. Some of the results are illustrated in Figure 11, and the main findings are discussed in the following. Neutral ligands, as methylamine, do not remove IGS from the band gap, though the orbital energies are sligthly shifted. On the other hand, IGS disappear in NCs capped by formate ions (HCOO−): two ligands are needed to empty a single IGS, so that Pb59Se56FA2 keeps two out of the three IGS of the bare cluster, and Pb59Se56FA6 has a clear band gap, while in 26400

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Figure 8. Density of states for different clusters exposing (100) and (111) faces (truncated cubes, cuboctahedra and octahedra). Occupied orbitals: red; empty (virtual) orbitals: green; orbitals are represented as Gaussian functions of unitary height (arbitrary units) and 0.003 eV width. Intragap states (IGS) are evidenced.

Figure 10. Band gap (eV) of PbSe NCs as a function of the number of cluster atoms: (a) considering all the orbitals (IGS included); (b) not considering IGS (i.e., the n orbitals at highest energy, n being the number of NC excess atoms). Squares, black: stoichiometric clusters; filled circles, red: nonstoichiometric clusters. Figure 9. Isodensity surfaces (threshold 0.02 Å−3) for IGS in nonstoichiometric PbSe clusters: (a) first IGS in Pb59Se56, localized on the (111) face; (b) delocalized IGS in Pb63Se62; (c) core-localized IGS in Pb108Se107, obtained by removing one core Se atom from Pb108Se108.

completely passivated the (111) surfaces would likely be capped more than the others. Analogously, we verified that the delocalized IGS in nonstoichiometric cubes or prisms are removed by adsorbing on any face two FA anions and setting the charge to zero. On the other hand, the charge balance condition also implies that new IGS can originate due to an excessive number of ionic ligands (precisely, if NL > 2 × (NPb − NSe), NL being the number of monovalent negative ligands). Indeed, we verified that the DOS for Pb59Se56 cluster capped by 8 FA ions (6 bound to the (111) face, as in the example above, and two more bound to other faces, see structure in the Supporting Information) presents an empty IGS in the band gap; analogously, attaching two FA ions to one of the (100) faces of the stoichiometric Pb32Se32 cluster (and setting the total charge to zero) gives rise to an IGS in the originally clear band gap (figures in the Supporting Information). Removing all the IGS from a nonstoichiometric cluster through ionic ligands, then, reveals a difficult task in practice, unless a selective passivation of (111) faces only is perfomed (possibly capping

Pb38Se19FA16 the IGS decrease from 19 to 11 (Figure 11). Note that in these calculations the FA capped NCs are globally neutral, according to the experimental evidence recalled above: if the ligand ionic charge is maintained, for example, in [Pb59Se56FA2]2−, the IGS appear again. Then the ligand effect on IGS is not due to an orbital energy shift, but to the oxidation of the excess lead atoms, as implicit in the charge balance condition mentioned in the Introduction. This is confirmed by other calculations, in which two FA ions were attached to one of the (100) faces of Pb59Se56 NC (setting the total charge to zero also in this case) causing the removal of one IGS, while the addition of six FA ions on (100) faces of the same NC provided a clean band gap. However, this model is quite unrealistic since the affinity of carboxylate anions is much larger for (111) than for (100) faces22 and, even in NC, not 26401

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face effectively removes the IGS because it reduces the nonstoichiometry (DOS not shown): on the other hand, thiols loosely attach to Pb-rich (111) faces without affecting the IGS, while thiolates have the same effect as carboxylate ions, provided the overall NC charge is set to zero, as discussed above.

4. CONCLUSIONS Several PbSe nanoclusters, with different shapes and diameters ranging from 0.73 to 3.54 nm, were modeled at the DFT level with BLYP and B3LYP functionals. Two small organic molecules (methylamine and formate ion) were used to simulate the larger ligands used to cap the nanoparticles: the affinity of such molecules for the different binding sites (face, edge, or vertex) was computed, finding significant differences between neutral and charged ligands. Cooperative effects were also estimated for MA, simulating the complete passivation of the NC surface. The density of states (DOS) for all the clusters was computed with the BLYP functional, which was found to provide the most reliable orbital energies, by comparison with triplet state calculations. A strict correlation was found between NC off-stoichiometry and intragap states (IGS), whose nature varies notably for different NC shapes. In fact, IGS are localized on (111) surfaces and delocalized over the whole particle for NC with (100) faces only, while bulk-localized IGS appear around the crystal defects obtained removing one atom inside the cluster. Neutral ligands, used to passivate NC surfaces, do not remove IGS: however, filled IGS disappear from NC capped with negatively charged ligands, once the total charge of the particle is set to zero. 2n ligands are required to remove n intragap orbitals, because the charge of two negative ions is compensated by extracting the electrons from one IGS: adding more ionic ligands gives rise to new, empty IGS, so that it seems difficult to obtain a nonstoichiometric cluster with a clear band gap by simply passivating the surface. Electrophilic ligands like Al(CH3)3 are not able to extract IGS electrons, though they bind to PbSe faces: on the other hand, a clear band gap is obtained by attaching a suitable number of alkyl radicals to the excess Pb atoms on the (111) faces. These ligands, actually not used in common syntheses, establish covalent bonds with intragap orbitals, forming a layer of alkyl-lead: also, in this case, two ligands are needed to eliminate one IGS.

Figure 11. Density of states for clusters exposing (111) faces capped by different ligands: bare Pb59Se56, Pb59Se56 with one methylamine (MA), Pb59Se56 with six formate ions (FA, HCOO−; note that the capped cluster is neutral), Pb59Se56 with two ethyl radicals (Et), and Pb38Se19 with 16 formate ions (neutral cluster). Occupied orbitals: red; empty (virtual) orbitals: green; orbitals are represented as Gaussian functions of unitary height (arbitrary units) and 0.003 eV width.

the other faces with neutral ligands with a larger affinity), but to our knowledge, there are no examples of this procedure in the experimental literature. We also wondered if IGS could be removed by electrophilic ligands, possibly able to bind to high-energy filled orbitals: however, the addition of BCl3 and Al(CH3)3 to Pb59Se56 (111) face had no effects on the three IGS (DOS shown in the Supporting Information). The analysis of ligand orbital energies actually shows that in BCl3 and Al(CH3)3 the lowest empty orbitals, responsible for the electrophilic effect, lie 1.6 and 3.0 eV above the highest Pb59Se56 IGS, respectively, too far to establish a suitable coordinate bond. Another approach was attempted by adsorbing alkyl radicals, which are expected to form covalent bonds with the localized IGS: in fact, ethyl radicals (Et) were easily attached to lead atoms on the Pb59Se56 (111) face, actually removing the IGS from the DOS (two Et are needed to eliminate a doubly occupied orbital, Figure 11). This result shows that localized IGS are able to form covalent bonds, thus, lowering their energy enough to get the bandgap clean, but it remains unclear whether it would be possible (or advisable) to use alkyl-lead in actual NC syntheses to get passivated faces. On the other hand, alkyl-selenide compounds were actually used to substitute the oleate ligands on Pb-rich NC, observing a decrease of shortterm oxidation processes, and a change of the photophysical behavior, due to the restored stoichiometry of the PbSe NC.18 Indeed, as expected, the addition of Se or S atoms to the (111)

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ASSOCIATED CONTENT

S Supporting Information *

Comparison of HOMO−LUMO gaps for clusters of different size, computed at HF, BLYP, and B3LYP levels in the singlet and triplet ground states; density of states (DOS) of Pb32Se32 and Pb28Se28 clusters; optimized structure of Pb59Se56 cluster capped by eight formate ions (FA); DOS of Pb59Se56 and Pb32Se32 clusters, bare and capped by FA; and DOS of Pb59Se56, bare and capped by electrophilic ligands. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 26402

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ACKNOWLEDGMENTS This work was funded by EU in the framework of the Seventh Programme, “Future Emerging Technologies”, through the Project GLOBASOL (“Global solar spectrum harvesting through highly efficient photovoltaic and thermoelectric integrated cells”).

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