PbS Clusters Embedded in Sodalite Zeolite Cavities of Different

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PbS Clusters Embedded in Sodalite Zeolite Cavities of Different Compositions: Unraveling the Structural Evolution and Optical Properties Using Ab Initio Calculations Lukas Grajciar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09423 • Publication Date (Web): 08 Nov 2016 Downloaded from http://pubs.acs.org on November 10, 2016

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The Journal of Physical Chemistry

PbS Clusters Embedded in Sodalite Zeolite Cavities of Different Compositions: Unraveling the Structural Evolution and Optical Properties Using Ab Initio Calculations Lukáš Grajciar* Otto-Schott-Institut für Materialforschung (OSIM), Friedrich-Schiller-Universität Jena, Löbdergraben 32, 07742 Jena, Germany

Abstract The structure and properties of the PbS quantum dots (QDs) encapsulated in the zeolite host – a system reported to exhibit extremely high nonlinear optical properties – were determined employing a combination of a robust structure prediction tool based on genetic algorithm approach and density functional calculations (DFT) including state-of-the-art two component time-dependent DFT implementation for hybrid exchange correlation functionals. Sizable changes in cluster structures and even isomer stability ordering are observed either with respect to the gas phase or as a result of the change of the sodalite zeolite composition (extra-framework cations and Si:Al ratio). Presence of very small clusters in the zeolite cavities such as monomers

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or dimers is predicted which are stabilized mostly via dispersion and to lesser extent electrostatic interaction with the host. The optical excitations of the PbS-zeolite composite are confined mostly to the QDs, i.e., the zeolite can be regarded as a confining dielectric matrix that only modulates the optically active states of the PbS QDs. These findings are corroborated by a very good agreement between calculated and experimental optical adsorption spectra, although sizable computational effort is needed as inclusion of relativistic effects (spin-orbit coupling) is essential for proper assignment of the adsorption bands.

Introduction Semiconductor nanoclusters or quantum dots (QDs) often exhibit unique chemical, electronic, optical and structural properties that can be very different from their bulk counterparts. The extreme confinement due to the proximity of boundaries stabilizes new structures and phases that otherwise cannot be obtained as bulk materials.1 Moreover, quantum confinement effects arising from the restriction of the electronic wave function to gradually smaller regions of space result in a size-dependence of electronic properties. These effects open up new possibilities for the development of advanced materials with controlled and tunable properties, making semiconductor QDs appealing for many applications, such as photocatalysis,2 sensing,3 energy storage and conversion4 and optoelectronics,5 to name only a few. However, full realization of the potential of semiconductor QDs for these applications is faced with a number of challenges including fabrication of QDs with a narrow size distribution allowing to control and fine-tune their properties, and assembly of QDs into large (even macroscopic) and well-ordered superstructures and superlattices. A common avenue to address these challenges is encapsulation of QDs in a host matrix, either periodic, for example, metal-organic frameworks6–8 and zeolites,9–


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or aperiodic one such as porous glasses or polymers.18–21 In this respect, zeolites represent a

particularly important hosts for semiconductor QDs enabling formation of extremely uniform and regular QDs assemblies with narrow size distribution up to 1.5 nm. Zeolites are very stable against environmental or temperature degradation and since there are more than 200 topologically distinct zeolite framework types22 with a large variety of pore systems a significant variability and flexibility for specific application purposes is granted as well. In addition, a possibility to readily exchange the extra-framework cations in the zeolite host presents an additional handle to tune properties16,23,24 of the encapsulated semiconductor QDs. In recent years, the lead sulfide (PbS), a narrow gap semiconductor having a large exciton Bohr radius of 18 nm and thus exhibiting strong size-dependence of its electronic properties,25 has attracted considerable interest as it was reported14,16 to show extremely high third-order nonlinear optical (3NLO) activity upon encapsulation in the zeolite host. The reported nonlinear refraction coefficients were one to two orders of magnitude higher than the highest values measured before26 for PbS QDs and at the chosen excitation energies they even surpassed the highest values ever reported for any type of QD-dielectric matrix system.27 Moreover, Kim et al. were able to systematically improve the 3NLO activity of the PbS-zeolite system by changing the PbS loading14 and/or the type of the extra-framework cation16 used for compensating the negative charge of the zeolitic framework. In fact, even before the discovery of its large 3NLO activity, the PbS-zeolite system has been a subject of numerous experimental investigations,12,28– 34

mostly aimed at revealing its optical and structural properties. Despite the obvious

experimental interest, to our best knowledge, the structural and electronic properties of PbSzeolite system have not been previously investigated computationally. The calculations so far have been limited to isolated gas-phase (PbS)n clusters, carried out either at the DFT level35–40 or


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using more approximate approaches41–43 such as semiempirical tight-binding method. We note also that computational studies for related CdS-zeolite system have been already carried out in 1990s, however, lower levels of theory such as atomic simulations parameterized using small DFT cluster calculation44,45 or Car-Parinello ab initio dynamics46 were employed. In this work, we set out to determine the structures, electronic and optical properties of small PbS clusters confined in the zeolite host with different framework compositions and various types of extra-framework cations. The lowest-lying structures of the PbS-zeolite systems were obtained using DFT calculations combined with a global structure optimization tool based on genetic algorithm (GA). To properly describe the host-guest interaction in zeolite47,48 dispersion interactions missing for standard semi-local DFT functionals49 were taken into account. Additionally, the relativistic effects characteristic for Pb-containing compounds50,51 were considered at the two-component (2c) DFT level including also the effect of spin-orbit coupling (SOC). Note that neither SOC nor dispersion effects have been considered in previous DFT investigations of the PbS clusters. Finally, the optical adsorption spectra of the PbS-zeolite systems were calculated using 2c time-dependent density functional theory (TD-DFT). The predicted spectra compared favorably to the experimental ones supporting the observations made regarding the structure of the PbS-zeolite system, the nature of the PbS-zeolite interaction or the growth pattern of the embedded PbS QDs.

Models and Methods Computational details


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To investigate the effect of zeolite environment on the structure and properties of the lead sulfite clusters we employed a cluster model representing the sodalite (SOD) cavity, as shown in Fig. 1. The SOD cavity with four different compositions are considered in order to differentiate between effects of confinement imposed by the zeolite topology and the effects of various types of extraframework cation: (i) SiSOD - a purely siliceous H-terminated SOD cluster Si24H24O36 , (ii) HSOD - a partially Al-substituted SiSOD model with hydrogen atoms acting as extra-framework cations, H4Al4Si20H24O36, and (iii) NaSOD, Na4Al4Si20H24O36, and (iv) LiSOD, Li4Al4Si20H24O36, with sodium and lithium, respectively, being the framework charge-compensating cations. The structural parameters of SiSOD cluster are taken from the experimental crystal structure of the SOD zeolite52 and are kept fixed. Geometries of the Al-substituted models are optimized using periodic boundary conditions53 with extra-framework cations located on the four six-membered rings (6-MR) (see, e.g., Fig. 4 below). The geometries of the SOD models are fixed during the GA run, only the positions of PbS QDs and cations are optimized. We also tested the effect of allowing the whole SOD framework to relax for a couple of (PbS)3 isomers embedded in SOD cages of various compositions (see Table S1 in Supporting Information). Upon relaxation the SOD cage expands leading to minor changes in (PbS)3 structures with relative energies of the isomers changing on the order of few tenths of eV. However, with one exception, the stability ordering of the isomers stayed intact and the most stable isomers for rigid SOD framework remained the most stable isomers also after the relaxation. Nevertheless, since the effect of framework relaxation is non-negligible as shown also in previous investigations54,55 we plan on relaxing the rigid framework approximation in our future studies, presumably in conjunction with the periodic boundary conditions.53,56


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Figure 1. The structure of the purely siliceous H-terminated cluster representing sodalite building unit. The semitransparent yellow sphere represents the cavity within the sodalite building unit. Atoms are shown in red (oxygen), white (hydrogen) and brown (silicon). GA algorithm To efficiently identify the most stable structures of (PbS) quantum dots (QDs) confined in the zeolite host we employed the genetic algorithms approach. The implemented GA version for clusters in confining environment follows the scheme proposed by Vilhelmsen et al.57 as well as previous studies concerning the clusters in gas-phase58 and surface-adsorbed.59,60 To start a GA calculation a random starting population is generated. The atomic positions of the candidate structures are constrained to lie inside the confining environment. To achieve this a random Monte Carlo sampling within a sphere centered inside the sodalite cavity is conducted (see yellow sphere in Fig. 1). The diameter of sphere is set to the largest cavity diameter of the cage, i.e., 5.0 Å. In addition, the atoms of the cluster are not allowed to overlap and inclusion of


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atoms detached from either the cluster or the environment is forbidden. This simplistic approach well-suited for the system in question is now being supplemented by a general approach to identify and characterize voids in porous systems introduced by Edelsbrunner et al.61 based on alpha shape theory62,63 and weighted Voronoi decomposition of the porous environment. To evolve the pool of the structures two evolutionary operators – crossover and mutation – are then used to exchange structure information between the pool members. In the crossover, first a pair of structures is chosen according to their fitness60,64 to act as parents that will produce a new structure for the next generation. After the selection of the parents, within each parent pair, random pieces are exchanged to form the new mixed structure, the child, which is subsequently optimized to the nearest local minimum. The assumption is that the child will combine the good structural features of the parents and thus will be more stable than either one. In this work we introduce modified cut-and-splice crossover operator originally proposed by Deaven et al.65 for gas-phase clusters and by Chang et al.66 for clusters on surfaces. New operator reflects the fact that the stability of confined clusters is not only a function of their structure but also of their location and orientation within the host, in particular in case of the strong interaction with the environment. Two modifications are introduced: • In case of no overlap between the parent structures the two clusters are cut by a randomly oriented plane passing through the centroids of both clusters (see Figure 2a). A union of two cluster fragments, one from each side of the plane, then constitutes the new child structure. This operator is expected to be particularly well-suited for clusters strongly interacting with the host such as the extra-framework charge compensating cations in zeolites.


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• For overlapping parent structures the overlapping region adjacent to the surface of the host is sliced by a randomly oriented plane passing through the clusters common centroid (see Figure 2b). The dividing plane being determined by the host-bound cluster fragment is a straightforward generalization of the typically used dividing plane for clusters adsorbed on the (flat) surfaces – the surface normal.

Figure 2. Schematic representation of the proposed cut-and-splice crossover operator for systems in spatial confinement: (a) no overlap and (b) overlap between the parent structures. The left panel depicts the two parent structures with their atoms depicted as blue and red disks, respectively. The resulting child structures on the right have their atoms highlighted with the atom coloring inherited from the respective parents. The randomly oriented plane is represented as the black line segment and the thin black closed curve in (b) highlights the overlapping region of the parent structures that are adjacent to the host.


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For both modifications only the cluster and cations are considered for mating operations within this study. To prevent trapping of the population in the local minima mutation is added in which random changes are introduced to a 25% of randomly chosen structures in the pool.58 The following mutations are used for the selected atoms: (i) the atomic coordinates are replaced by a randomly generated values or (ii) the atom types are swapped without perturbing the structure of the cluster. In order to ensure the diversity of the GA population, multiple occurrences of similar structures in the population is to be avoided. This is accomplished by employing a geometric measure to determine the similarity of the two configurations. From the multiple geometrical comparisons available in the literature58,60,67 (inertia tensors, radial distribution of atoms, the average of atomic distances or fingerprint functions etc.) we follow the one proposed by Vilhelmsen et al.59 based on a sorted list, Di, of all interatomic distances for each structure i. We employed standard values of the thresholds used in literature59,68 - δrel = 0.03 and dmax = 0.7 Å. We note that each run of GA included few hundreds of tested (DFT optimized) candidates (500 for dimers and at least 1000 for larger PbS clusters). DFT set-up The structures of the PbS clusters in SOD cavity were obtained from the GA algorithm described above at the density functional theory (DFT) level using the Becke-Perdew69–71 (BP86) exchange-correlation (XC) functional with polarized double-ζ valence SVP basis72 set along with the corresponding auxiliary basis73 set and small effective core potential74 (ECP) describing 60 core electrons of lead. Dispersion correction by Grimme et al.,75,76 i.e. the so-called DFT-D3 approach, was employed to account for the van der Waals interactions between PbS cluster and


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zeolite environment. The most stable structures were subsequently re-optimized using a larger polarized triple-ζ valence def2-TZVPP basis72 set using both the BP86 functional and hybrid PBE077 functional since hybrids were shown in previous studies51,78 to provide superior geometries to pure GGA functionals for similar semiconductor clusters. This is confirmed in Table 1 that shows that hybrid PBE0 functional provides PbS monomer bond length in closer agreement with experimental values. In the next step, the excitation energies and the corresponding adsorption spectra were obtained using time-dependent DFT (TD-DFT).79,80 However, TD-DFT in condensed-phase-like systems such as solvated clusters81 or liquids82 is often beset by serious contamination from spurious, low-energy charge-transfer (CT) excited states comparable in energy with the valence excitations. Besides making it difficult to identify valence transitions in spectra, e.g. due to intensity borrowing, it significantly increases the cost of calculations since much more states need to be calculated for a given excitation energy range. Unfortunately, we have observed this CT contamination also in our PbS@SOD systems (see Figures S5-S7 in Supporting Information), in particular, when using the pure GGA BP86 functional and to a smaller extent also for the PBE0 hybrid. To remove this CT contamination we employed XC functional with increased amount of Hartee-Fock exchange (HFE), namely the BHLYP83 with 50% HFE, as advocated in prior investigations.40,82,84 Table 1 also shows the effect of spin-orbit coupling (SOC) on the properties of the benchmark PbS monomer. While inclusion of SOC has a minor influence on the optimal Pb-S bond length, the binding energies and the lowest excitation energies (i.e. the optical gaps) are considerably lowered. Hence, based on the ground-state structures obtained from one-component treatment we carried out the DFT and TD-DFT calculations (stabilities, excitation energies) both with and without the SOC correction. The two-component (2c) approach employed here is based on


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quasirelativistic “valence-only” Hamiltonian, that includes the SOC effects via ECPs.50,85,86 In the 2c calculation, two basis sets optimized for the usage with 2c-ECPs74 were considered, def2SVP-2c and def2-TZVPP-2c.87 Due to the relatively large size of the systems considered and a need to include multiple transitions to obtain adsorption spectra in reasonably large energy range (at least up to 4 eV) the smaller basis set, def2-SVP-2c, was employed for calculation of excitation energies at the hybrid XC functional level. Our tests for the lowest lying excitations employing larger def2- -2c basis set show that the use of smaller basis set in general introduces errors in excitation energies smaller than 0.1 eV and only mildly effects the oscillator strengths (see Figure 12 below illustrating similar effect for 1c case). Table 1. Bond-lengths (R, in Å), binding energies (BE, in eV) and the lowest excitation energies (LEE, in eV) of PbS monomer calculated by various XC functionals using one-component (1c) and two-component (2c) treatment. R

BE

LEE

1c

2c

1c

2c

1c

2c

BP86

2.315

2.315

4.89

3.86

2.97

2.11

PBE0

2.282

2.278

4.62

4.12

3.03

2.08

BHLYP

2.275

2.272

4.14

3.35

3.01

2.05

Expt.88,89

2.287

3.43±0.12

1.81-1.83

All calculation were performed using the TURBOMOLE program package.53,90,91 The multipole accelerated resolution of identity method for Coulomb term (MARI-J)92 along with appropriate auxiliary basis sets73 was used to speed up the calculations. The TD-DFT equations were solved within the Tamm-Dancoff approximation.86,93 The computed absorption spectra


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reported in the paper are broadened by Gaussian function with a full width at half maximum equal to 0.1 eV. All the oscillator strengths shown were taken in the length representation. The non-relaxed difference densities of excitations are calculated using the PANAMA script,94 which post-processes the TD-DFT results from TURBOMOLE.

Figure 3. The lowest-energy gas-phase isomers of (PbS)n (n=1-4). Sulphur and lead are colored yellow and gray, respectively.

Results and discussion Structures and stabilities First, for the sake of reference the structures of the most stable (PbS)n clusters (n = 1-4) in the gas phase were obtained and are presented in Figure 3. The bond length of PbS monomer (at the reference SO-PBE0/TZVP level) is 2.282 Å close to the experimental88 value (2.287). The PbS


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dimer favors the bent rhombus (dihedral S-Pb-Pb-S angle of 154°) with C2v symmetry in which all Pb-S bonds are 2.539 Å long. In addition, a nearly energetically degenerate square D2h isomer (0.02 eV less stable) is also found. (PbS)3 is a bridged trigonal bipyramid (C2v) with two threecoordinated Pb/S atoms and two two-coordinated Pb/S atoms. The Pb-S bond lengths in this isomer are about 2.55 Å for the bonds involving two-coordinated atoms and approximately 2.85 Å for those between the three-coordinated atoms. The (PbS)4 cluster shows a cubic structure (Td) with the Pb-S bond length of 2.69 Å still significantly smaller than the Pb-S distance (2.96 Å) in lead sulfide crystal.95 To compare with previous computational studies35–38 we have also considered larger gas-phase PbS clusters up to n=8. We here only summarize that the same low energy isomers have been encountered.

Figure 4. The most stable (PbS)1 adsorption configurations in (a) SiSOD, (b) HSOD, (c) LiSOD and (d) NaSOD at the PBE0/TZVP level. Aluminum atoms are shown in cyan, lithium in magenta, sodium in green and H+ charge compensating cations in blue color.


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Figure 5. The most stable (PbS)2 adsorption configurations in (a) SiSOD, (b) HSOD, (c) LiSOD and (d) NaSOD at the PBE0/TZVP level.

Figure 6. The most stable (PbS)4 adsorption configurations in (a) SiSOD, (b) HSOD, (c) LiSOD and (d) NaSOD at the PBE0/TZVP level.


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Figure 7. The lowest-energy and low-lying isomers of (PbS)3 in gas-phase and embedded in SOD cages with different composition obtained at the PBE0/TZVP level. The individual isomers are color-coded – “bipyramid” (red), “book” (green), “cup” (yellow) and “prism” (blue) - with the dark colored lines on the black axes indicating the relative stabilities of the corresponding


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isomers (lighter shading behind the isomer figures) with respect to the lowest one located at 0 eV. Table 2. The average Pb-S bond-lengths (Å) of the most stable (PbS)n isomers in gas-phase and embedded in SOD cages with different composition calculated at the PBE0/TZVP level.

(PbS)n Environment 1

2

3

4

Gas-phase

2.28 2.54 2.67 2.69

SiSOD

2.28 2.51 2.60 2.61

NaSOD

2.32 2.51 2.60 2.57

LiSOD

2.30 2.53 2.56 2.55

HSOD

2.53 2.54 2.67 2.60

We now consider the case of encapsulated PbS clusters in SOD cage. The structures of the most stable isomers with n ≤ 4 are displayed in Figures 4-7. Larger clusters with n=5 were found to be instable in the SOD cage and dissociated to a smaller cluster embedded in SOD cage and gas-phase PbS monomer or dimer. We note that the effect of a number of model variables - XC functional, basis set size, cluster size, cluster termination (Si-H or Si-O-H) and inclusion of spinorbit coupling – was thoroughly tested (see Figures S1-S4 and Table S1 in Supporting Information). Although the effects are in some cases non-negligible they do not qualitatively change the outcomes of the investigation discussed below. Inclusion of environment results in changes in relative stabilities of isomers with respect to the gas-phase on the order few tenths of eV as illustrated in Figure 7 for n=3. However, for dimer and tetramer, the most stable gas-phase


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structures (rhombus and cuboid, respectively) are separated by more than an eV from the other structural isomers. Hence, the same structural isomers as for the gas phase are observed to be the most stable ones for dimer and tetramer for all the different SOD cage. This is not the case for n=3, for which there are more lower lying isomers available (although still at least 0.3 eV less stable) such as folded rectangular “book” structure or triangular “prism” (see Fig. 7). As a result, the trigonal “bipyramid” remains the most stable isomer only for the purely siliceous and Hexchanged SOD cage. For the Na-exchanged cage, the “book” isomer becomes almost degenerate with “bipyramid” with the exact ordering depending on the exchange-correlation functional used while for the LiSOD the distorted “book”-like structure is the lowest isomer separated by at least 0.3 eV from the other structural isomers independent from the XC functional. This can be partly understood as the steric effect since “bipyramid” is the most prolate of the low lying isomers and significant distortion is observed, in particular for the LiSOD. For the NaSOD frameworks the “book” isomer is also very well coordinated to the framework thanks to a swap of one Na cation during the GA run to a neighboring empty (no Na cation present) 6-MR. Following this change in distribution: (i) the “book” isomer is able to form five Na-S bonds with lengths in the range of 2.51-2.77 Å as compared to only three weaker96,97 Na-S close contacts (2.58-2.89 Å) for the “bipyramid” isomer and (ii) all Pb atoms can be positioned in the empty 6-MR simultaneously minimizing the steric hindrances and coordinating weakly with the oxygen atoms of the SOD cage. Besides the isomer reordering encapsulation introduces distortions in the PbS clusters which are quantified in Table 2 by changes in the averaged bond-length of (PbS)n. While for the monomer the average bond length increases upon embedding, this trend is inverted for larger n with the average bond lengths of the PbS tetramers being smaller by more than 0.1 Å with


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respect to gas phase pointing to a significant steric repulsion taking place for the tetramer. However, Table 2 also shows that PbS@HSOD is a specific case, in particular for n=1,3. For these n at least one of the sulphur atoms in PbS cluster forms a strong bond (1.3-1.4 Å) with the charge compensating hydrogen cation leading to a formation of the [(PbS)nH]+ moiety. In addition, some of the remaining sulfur and hydrogen atoms participate in weaker hydrogen bonds (2.0-2.1 Å). For n=2 and 4, the isomers with strong S-H bond are not, however, the most stable one – only a weaker hydrogen bonds are present for the most stable isomers. In contrast to HSOD, the structure of PbS cluster is least influenced in the purely siliceous SiSOD cage. In SiSOD, PbS clusters orient themselves towards either 6-MRs (n=2-4) or 4-R (monomer) in order to maximize the dispersion interaction with the framework and at the same time to minimize the steric repulsion. These effects are also at work for the Na/LiSOD cages, however, an additional directional electrostatic interaction with the charge compensating cations needs to be taken into account. It results in the cluster structures that need to accommodate these competing interactions. In some cases, such as the above discussed “book” trimer in NaSOD, the (PbS)3 cluster fits nicely in the cage and undergoes only minor distortion, while for other cases, such as “bipyramid” trimer in LiSOD, the original gas-phase structures are often significantly distorted, clusters form smaller number of weaker bonds with cations and dispersion interaction with the whole framework is reduced. To compare the stabilities of differently sized clusters and estimate which clusters are formed preferentially in the SOD cage we calculated the binding energy 𝐸! defined as

𝐸! =

𝐸tot 𝑛 − 𝐸SOD − 𝑛𝐸!"# , 𝑛

(1)


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where 𝐸tot 𝑛 is the total energy of the (PbS)n@XSOD (X = Si, H, Na, Li) system, 𝐸SOD is the energy of the optimized XSOD cage without the PbS adsorbed and 𝐸!"# is the energy of the PbS monomer in gas-phase. The calculated binding energies are depicted in Figure 8 for all the XSOD cages considered in the study as well as for the gas phase (PbS)n clusters. The choice of the XC functional significantly affects the binding energies of adsorbed PbS clusters. The binding energies of (PbS)n@XSOD systems at the PBE0 level are by 0.6-0.7 eV lower than for the BP86. This discrepancy between the description at the hybrid and pure GGA level is due to a greatly differing description of the PbS interaction with the framework since only negligible functional effect is seen for the stabilities of (PbS)n clusters in gas-phase (see Fig. 8a). However, this functional-dependent shift for adsorbed species is rather uniform and therefore does not change the observed trends. (see Figure S8 in Supporting Information). Figure 8a shows that energy gains from encapsulation in the framework are very large – on the order of eVs. As an example of the extent of stabilization, for the dimer in HSOD the binding energy is almost the same as for one of the most stable species in the gas-phase, the magic number cluster (PbS)4.38 And if BP86 is employed then all the adsorbed cluster with n ≤ 3 are more stable than the magic PbS tetramer. However, tetramers in Al-substituted SOD cages are much less stabilized (by tenths of eV) than smaller clusters in contrast with the gas-phase case. This suggests that the tetramer is too large for the SOD cage which is in line with the findings from the neutron powder-diffraction study by Sun et al.32 or Moller30 who rule out the formation of (PbS)4 clusters in SOD cages (the samples in the study contained both the H and Na chargecompensating cations). Therefore the tetramer is not considered in detail in further discussion.


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Figure 8. The binding energies for the most stable (PbS)n isomers in gas-phase and embedded in various SOD cages as a function of n. In (a) the energies calculated at the 1c-PBE0+D/TZVP level are shown along with a sample of results (PbS in LiSOD and in gas-phase) for BP86 functional. In (b) effect of dispersion interaction and inclusion of spin orbit coupling on the binding energies is displayed for the case of PbS clusters encapsulated in SiSOD and HSOD cages (calculated at the PBE0/TZVP level). For the adsorbed clusters the binding energies actually peak for the dimer and then decrease for larger n as the steric repulsion builds up. Out of the different frameworks considered the Hexchanged SOD is typically the most stabilizing one followed by the Na- and Li-exchanged frameworks and even the purely siliceous SiSOD binds the PbS clusters quite strongly. This


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implies that an important contribution to stabilization of PbS clusters in SOD cage is due to dispersion interactions since stabilization in purely siliceous zeolite frameworks originates mainly in dispersion interactions.48 Figure 8b confirms this expectation showing the binding energies with and without the dispersion corrections not only for the SiSOD but also for the HSOD cages. The stabilizing dispersion contributions are large ranging from 0.8 to 1 eV. Inclusion of the SO effects influences the binding energies as well, however, the effect is rather small – the clusters are about 0.1 eV less stable when SO is applied (see Fig. 8b). Table 3. The NBO charges on the (PbS)n cluster embedded in SOD cages with different composition calculated at 1c-BHLYP/TZVP level.

(PbS)n Environment 1

2

3

SiSOD

-0.05

-0.19

-0.31

NaSOD

-0.07

-0.19

-0.28

LiSOD

-0.01

-0.17

-0.24

HSODa

0.60 (0.80)

-0.11

0.56 (0.79)

a

Values in parenthesis are for the [(PbS)nH]+ species.

Electronic structures To reveal the nature of the interaction between the (PbS)n cluster and the SOD cage we first carried out the NBO analysis. Table 3 shows NBO charges on the (PbS)n clusters embedded in various frameworks and clearly captures two trends. For the SiSOD, LiSOD and NaSOD the


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(PbS)n clusters gain some (negative) charge from the framework, the total amount of the charge slightly increases with the cluster size and it is donated primarily from the oxygen atoms of the SOD cage. However, this charge is distributed across more atoms so that all the clusters can be considered to be close to neutral. A different behavior is apparent for the HSOD, in particular for n=1, 3, in which the [PbSH]+ and [(PbS)3H]+ moieties are formed, respectively. Calculated NBO charges for these moieties are close to the their formal charges (about 0.8e) and thus one can indeed consider them to represent new charge compensating cations [(PbS)nH]+. This 0.8e hole is not, however, located predominantly on the H atom. Most of it (about 0.6e) is transferred to the closest PbS unit. For trimer this results in elongation of both the respective Pb-S bond as well as of the bonds to other atoms in the trimer. Hence, it seems more appropriate to think of these moieties as composed of the PbSH+ cation coordinated to a unit smaller (PbS)n-1 cluster, i.e, (PbS)n-1(PbSH)+. This observation combined with the reports36–38 of the higher stability of even-n wrt. odd-n gas-phase clusters then also provides a rationalization for the fact that the most stable (PbS)2@HSOD isomer does not form such a charged moiety, albeit such an isomer was found and is about 0.2 eV less stable. The positive charge due to (PbS)n-1(PbSH)+ cation is compensated by a built-up in negative charge localized at the O atoms in the vicinity of the Al atom from which the H+ cation was taken. (PbS)n@HSOD structures for n=1,3 also show that Pb atom from (PbSH)+ is in close interaction with these O atoms (2.5-2.7 Å). Thus, the (PbS)n-1(PbSH)+ (or rather PbSH+ only) is in these cases effectively exchanged for the H+ cation. Next, the densities of states (DOS) for the (PbS)n@XSOD (X = Si, H, Na, Li) systems were calculated and are illustrated in Figure 9 for three selected systems ((PbS)1@SiSOD, (PbS)3@LiSOD and (PbS)3@HSOD). These DOS graphs suggest that frontier orbitals (HOMOs and LUMOs) are composed basically only from the AOs of the PbS cluster.


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Figure 9. Density of states of (a) (PbS)3@LiSOD, (b) (PbS)3@HSOD and (c) (PbS)1@SiSOD systems evaluated at 1c-BHLYP/TZVP level; colored solid curves represent different components of the total DOS (black solid line). The vertical full and dashed lines indicate the position of HOMO and LUMO levels, respectively. This shows that there is almost no orbital mixing between the PbS clusters (or (PbSH)+ cation for that matter) and the embedding environment and thus the covalent bonding with the environment


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can be largely disregarded. Hence, as previous analyses show (binding energies, NBO charges), it is rather a strong stabilization due to van der Waals forces (mostly dispersion) exerted by the SOD cavity combined with electrostatic interactions, in particular for the HSOD environment, that determines the character of the PbS-SOD interaction.

Figure 10. (a) Differences between HOMO and LUMO eigenvalues for embedded (PbS)n (n=13) clusters and gas phase cluster of the same size defined as: Hn = HOMO((PbS)n@XSOD) – HOMO((PbS)n) and Ln = LUMO((PbS)n@XSOD) – LUMO((PbS)n) where (X = Si, H, Na, Li), (b) HOMO-LUMO gaps of (PbS)n (n=1-3) clusters as a function of the embedding environment; results with and without the inclusion of SOC effects are shown. The reported values are calculated at the BHLYP/TZVP level.


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Having established the character of the PbS-SOD interaction, we now focus on a brief analysis of the bonding in the PbS cluster itself. Figure 9c shows decomposition of the PbS bands in (PbS)1@SiSOD system into s, p and d components. The bands are dominated by the p component with a minor contribution from the s-type AOs. Contributions from the Pb and S atoms to the Pb-S bonding is however disproportionate for HOMO and LUMO orbitals as illustrated in Figure 9b. For HOMOs the PbS component is constituted mostly (about 80%) from the AOs on sulphur while LUMOs are dominated by the contributions from the Pb atoms. As a result, one can expect localization of the electron upon excitation on Pb atoms, while the hole localizes predominantly on S atoms. This is in fact corroborated by the calculated difference densities for the lowest excitations for the (PbS)1@HSOD system depicted in Figure 15 below. HOMO-LUMO gap The HOMO-LUMO gaps (HLG) of (PbS)n clusters (both gas-phase and embedded) calculated at the BHLYP/TZVP level with and without the inclusion of SOC effects are shown in Figure 10b. In general the HLG value increases upon embedding for all the cluster sizes. The enlargement of the gap is most pronounced for H-SOD (between 0.3-0.7 eV) while Si-SOD influences HLG least (variation of less than 0.3 eV compared to gas-phase). The embedding also evens out the HLG values for different-sized clusters. For the gas-phase the HLG of PbS monomer is by 1.3 eV larger than for the trimer, however, upon encapsulation inside either NaSOD or LiSOD this difference is reduced to only 0.8 eV. Moreover, the inclusion of SOC correction results in a further equalization of the HLGs. The calculated SOC-corrected gap decreases for all the calculations, regardless of the cluster size or type of the environment, however, the extent of the reduction is size-dependent. It decreases by about 0.1 eV for n=2 and 3, but by as much as 0.5 eV for n=1. The SOC corrections are similar in magnitude for all the different embeddings


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considered and for the gas-phase. We note that all the observed effects (HLG increase and equalization upon embedding, HLG decrease for SOC calculations) are consistent with the trends reported for the binding energies (see Fig. 8) which confirms commonly cited51,98,99 relation between stability of a molecule and its HLG. For example, inclusion of SOC tends to decrease both the binding energies and HLGs while stabilization upon embedding is mirrored by the increase in the HLG. The variation in HLG is a consequence of the disproportionate shifts in the energies of the frontier orbitals. Figure 10a displays the magnitude of the shifts for the embedded clusters relative to their gas-phase values. The environment influences the energy levels of both HOMO and LUMO orbitals in a qualitatively similar way; for n=1 the frontier orbitals are mostly stabilized wrt. the gas-phase while a destabilization is observed for n=2 and 3. However, the extent of the (de)stabilization is different for HOMO and LUMO. HOMO levels are either more stabilized (n=1) or less destabilized (n=2 and 3) upon encapsulation than the LUMOs. As a result, the HLGs for embedded clusters increases. This can be understood as a consequence of the more diffuse character of the virtual orbitals100,101 localized on PbS atoms (see DOS analysis above) which need to be confined to a small SOD cage. In addition, the fact that the energy levels of the frontier orbitals are for n=2 and 3 destabilized relative to the gas-phase suggests an increased role of the steric repulsion already for the PbS dimer. In contrast to the environment effect, inclusion of SOC correction does not influence the energy levels of HOMO, only lowers those of LUMO (see Figure S10 in Supporting Information), making the HLGs narrower for all the PbS clusters, regardless of the environment. Similar trend due to SOC has been reported51 also for the PbSe gas-phase clusters.


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Optical properties (photoabsorption spectra) In Fig. 11, the vertical TD-DFT excitation spectra for all the systems considered in the study are presented. At least 30 excited states were computed for each system using both 1c and 2c TDDFT implementation. Since calculation of 2c spectra for such large systems becomes extremely resource-demanding a smaller SVP basis set was employed. However, Fig. 12 displaying (PbS)3@HSOD spectra illustrates that the impact of using smaller basis set is minor and rather systematic; with larger TZVP basis set all the bands are redshifted by about 0.1 eV85 with their oscillator strengths (OSs) changing by at most few tens of percent. Similarly, enlarging the size of the enclosing environment by inclusion of another layer of SiO2 around the SOD cage (see Fig. S1 in Supporting Information) has a rather small effect on the spectra, in particular for the lowest excitations. In addition, accurate description of higher lying excitations are often of less importance from the experimental point of view that is focused mostly on visible or near UV range below 4-4.5 eV (see Section Comparison with experiment below). The observation of a weak dependence of the spectra on the cage model size corroborates previous findings of a weak covalent bonding of the PbS clusters to the environment. It is clear from the spectra shown in Fig. 11 it is clear that effect of SO coupling is remarkable. First, the adsorption edge is significantly redshifted. For systems containing PbS monomer the shift is approximately 1 eV while a smaller shift of about 0.6 eV is observed for systems with dimers or trimers. Part of the shift is related to the reduction of the HLG due to SOC discussed above. In addition, SOC mixes up the singlet and triplet excitations and thus some of the “spin-forbidden” triplet excitations within 1c treatment become allowed by SOC. Since the lowest-lying triplet excitations (see Fig. 11) lie below their “spin-allowed” singlet


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Figure 11. Simulated 1c (blue lines) and 2c (red lines) TD-DFT excitation spectra of (PbS)n (n=1-3) clusters in gas-phase and embedded in various SOD cages calculated at BHLYP/SVP level. The dots show the energy of the first 1c singlet-singlet transition (blue), “spin-forbidden” 1c singlet-triplet transition (black) and 2c transition (red).


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counterparts (on average by 0.4-0.5 eV) the spectral edge is shifted further to lower energies at the 2c level. Second, the 2c spectra are more complicated than the 1c spectra. While for some systems such as (PbS)2@LiSOD or (PbS)2@SiSOD the 1c and 2c spectra can be roughly superimposed by a simple rigid shift, in most cases the corresponding 1c and 2c spectra differ not only in the peak positions (of the strongest peaks) but also in their oscillator strengths with many more peaks appearing at the 2c level as a consequence of the singlet-triplet mixing and splitting of the energy levels. Hence, it is difficult to identify corresponding transitions in 1c and 2c spectra simultaneously.

Figure 12. Simulated 1c TD-BHLYP excitation spectra of (PbS)3@HSOD system using SVP and TZVP basis set and small (Fig. 1) and large model (Fig. S1 in Supporting Information) of SOD cage. Nevertheless, to demonstrate typical character of excitations found for the PbS clusters embedded in SOD cage we carry out the analysis of both 1c and 2c spectra for the simple (PbS)1@HSOD system. In Table 4, the most important excitations/bands from (PbS)1@HSOD spectrum (Fig. 13) are described by their energies, oscillator strengths and the type and character


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of the participating frontier orbitals. The shapes of the orbitals involved are shown in Figure 14. Our tests showed (see Figure S9 in Supporting Information), that SOC has negligible effect on the shape of the frontier orbitals (spinors) in line with previous studies94,102 for organometallic complexes. Therefore, the 1c frontier orbitals are used also for the description of the excitation bands in 2c case. First four bands of the 2c spectrum, bands a-d, are composed/mixed of the same type of transitions as first two bands of the 1c spectrum, bands I-II. Next three bands in 2c spectrum between 4.08-4.55 eV, bands e-g, are due to the transitions found predominantly in 1c bands at 4.42 and 5.08 eV, bands III-IV. Note an increased mixing of different transitions for the 2c case as well as varying peak shifts for different transitions due to SOC. Regardless of the SOC correction, all the bands depicted in Fig. 13 correspond to p -> p transitions, in particular to transitions from π to π* orbitals (both have minor σ character) with the degeneracy of the π/π* orbitals lifted by the asymmetric environment. These excitations are all localized dominantly on the [PbSH]+ moiety which is clear from Figure 15 showing the (nonrelaxed) excitation difference densities for four representative bright transitions in 2c spectrum. In particular, the hole resides mainly on the S atom while electron upon excitation moves to lead which is consistent with previous report40 for pure (PbS)32 nanoparticles. Contributions to the excitations from the environment are small, mostly localized at the O atoms in the vicinity of the Al atom from which the H+ cation was taken. For other SOD cages (SiSOD, LiSOD, NaSOD) the excitation is even more localized on the (PbS)n cluster. This conclusion is not expected to change if relaxed 2c difference densities were used;80,103 at least for the 1c case the changes upon density relaxation were found to be only minor.


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Table 4. Excitation energies, maximal oscillator strengths in the individual excitation band and character of the excitation bands described in terms of the contribution from frontier molecular orbitals calculated for (PbS)1@HSOD system at BHLYP/SVP level. Both 1c and 2c calculations are considered. The corresponding spectra are shown in Figure 13.

Energy [eV]

Maximal f

Character of excitationa

Band I

3.89

0.008

HOMO -> LUMO (84%)

Band II

4.01

0.017

HOMO-1 -> LUMO (93%)

Band III

4.42

0.021

HOMO -> LUMO+1 (91%)

Band IV

5.08

0.052

HOMO-1 -> LUMO+1 (78%)

Band a

2.79-2.91

0.005

HOMO -> LUMO (68%) HOMO-1 -> LUMO (23%)

Band b

3.22

0.006

HOMO -> LUMO (72%) HOMO-1 -> LUMO (18%)

Band c

3.30-3.40

0.001

HOMO-1 -> LUMO (72%) HOMO -> LUMO (18%)

Band d

3.55

0.012

HOMO-1 -> LUMO (65%) HOMO -> LUMO (22%)

Band e

4.07-4.08

0.001

HOMO -> LUMO+1 (64%) HOMO-1 -> LUMO+1 (29%)

Band f

4.33-4.43

0.010

HOMO -> LUMO+1 (57%) HOMO-1 -> LUMO+1 (28%)

Band g

4.46-4.55

0.006

HOMO-1 -> LUMO+1 (62%) HOMO -> LUMO+1 (28%)

1c

2c

a

The character of the excitations at the 2c level is discussed in terms of the 1c orbitals rather than spinors

since relativistic effect have only small effect on the shape of the frontier orbitals (see Figure S9).


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Figure 13. Simulated 1c (blue) and 2c (red) TD-DFT excitation spectra for (PbS)1@HSOD system calculated at BHLYP/SVP level. Discrete spectra are convoluted with Gaussian function with a FMWH = 0.1 eV. The labeled bands correspond to the bands described in detail in Table 4. Contours of difference densities were drawn at 0.0005 (yellow) and -0.0005 (green) a.u., respectively. There are few general trends due to environment that are discernible in the spectra. First, there is a notable blue-shift of the adsorption edge upon embedding. The shift is smallest for SiSOD (variation of less than 0.4 eV compared to gas-phase) and largest for the HSOD cage (between 0.4-0.8 eV). This trend agrees well with the changes due to embedding reported for HLGs, albeit spectral shift is slightly larger than would be expected based only on the HLG values. Second, spectra for (PbS)n clusters in SiSOD and to some extent also for LiSOD cage are similar (number of peaks, relative peak position, oscillator strengths) to gas-phase PbS spectra, albeit blue-shifted


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Figure 14. The frontier molecular orbitals for (PbS)1@HSOD system calculated at 1cBHLYP/SVP level: (a) HOMO-1 (-8.54 eV), (b) HOMO (-8.28 eV), (c) LUMO (-1.93 eV) and (d) LUMO+1 (-1.31 eV). Contours of molecular orbitals were drawn at 0.03 (yellow) and -0.03 (green) a.u., respectively.

Figure 15. Non-relaxed difference densities for the brightest excitations in (a) band a, (b) band d, (c) band e and (d) band g of the 2c-BHLYP/SVP spectrum of (PbS)1@HSOD system (Fig. 13).


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as discussed above. Hence, at least for SiSOD the cage seems to act only as a spatial confinement representing a steep repulsion wall around the PbS cluster and if interacting then in a very isotropic fashion (dispersion) such that the PbS energy levels are quite evenly shifted. However, the resemblance to gas-phase spectrum is significantly diminished for the NaSOD and HSOD cages. This is not only due to structural changes of PbS clusters upon embedding such as formation of (PbS)n-1(PbSH)+ moieties but can be related to stronger and more specific interaction of these environments with the embedded cluster (see Fig. 8). Last, there is only a minor variation (typically a blue-shift of up to 0.3 eV) in the first peak position as the cluster grows from monomer to trimer. For the Na- and H-exchanged SOD cages the adsorption edge is basically the same (within 0.1 eV) for all the cluster sizes considered, i.e. there is a environmentinduced equalization of the adsorption edge for stronger interacting SOD cages. In contrast, however, the brightest peaks do shift considerably to lower energies as the cluster grows. This is more clearly shown in Figure S13 in Supporting Information depicting build up of the total adsorption intensity for dimer and trimer close to the adsorption edge for all the environments considered. Optical properties – comparison with experiment Finally, we compare the calculated spectra with those reported experimentally. We start with benchmarking the accuracy of our computational setup (functional, basis set, inclusion of SOC, etc.) using the experimental spectra of monomolecular PbS trapped in an argon matrix88 depicted in Figure 16. Since argon matrix is a porous environment interacting with the trapped species only via van der Waals forces104,105 (particularly repulsion and dispersion only) the pure silica SOD cage should represent such an environment quite accurately (see previous discussion). The calculated BHLYP/SVP spectrum of PbS monomer in SiSOD (also in Fig. 16) matches the


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experimental spectrum well, both in terms of peak positions and their relative intensities. The predicted peak maxima of the longest and shortest wavelength peaks at ~440 nm (2.82 eV) and ~310 nm (4 eV) are within 20 nm from the experimental values, albeit former is blue-shifted while latter red-shifted with respect to the experiment. Note that without inclusion of SOC the PbS@SiSOD spectrum, or gas-phase monomer spectrum for that matter, is composed only of a single bright peak at ~340 nm (3.65 eV) in a substantial disagreement with the multi-featured experimental spectrum. The very good performance of the BHLYP functional in this case is noteworthy. Its use has been advocated previously also for rocksalt nanoparticles (MgO, CaO, SrO etc.).40,106

Figure 16. Comparison between experimental spectrum of monomolecular PbS in argon matrix88 (black) and calculated 2c-BHLYP/SVP excitation spectra for gas-phase PbS monomer (red) and PbS monomer embedded in purely siliceous SOD cage (blue). There are available numerous experimental spectra of zeolite-encapsulated PbS clusters, mostly in zeolite faujasite14,16,28,30,31,107 but also in zeolite A12 or mordenite30 where both faujasite and zeolite A contain sodalite cages as one (but not the only) of their buildings units. However, most of reported spectra show a single very broad and feature-less adsorption band


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Figure 17. Comparison between experimental spectrum of PbS QDs in zeolite A12 (lowest panel) and calculated 2c-BHLYP/SVP excitation spectra for PbS@HSOD, PbS@NaSOD and (PbS)4@NaSOD systems (three upper panels). Discrete spectra are convoluted with Gaussian function with a FMWH = 0.1 eV. The vertical black full lines correspond to the positions of the experimental a, b, c, d and e bands.


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spanning the range of 250-600 nm (~2-5 eV). On the one hand, all the calculated spectra (at the 2c level) fall within the range of experimentally observed signal, but, on the other hand, it is difficult to gain any specific information on the size or structural details of the embedded clusters other that no large mesoscopic QDs are being formed. There is, however, a study by Calzaferri and Leiggener12 who measured excitation spectra of PbS QDs in zeolite A in low-loading regime (about 10% of maximum capacity or 1 PbS per SOD cage) at low temperature (-190°C) reporting a number of rather narrow and well distinguishable bands (see Fig. 17). The zeolite A sample used was mostly sodium exchanged but it also contained H+ as the charge-compensation cation (Na+/H+ ~ 6). With the exception of a single band, band d, all the bands can be readily matched in position and most importantly also in relative intensities with the calculated bands for the PbS@HSOD system depicted in detail in Fig. 17. The minor shifts in positions of the bands (blue-shift of long wavelength peaks and redshift of the short ones) are consistent with the benchmark calculations discussed above. The band d missing in the PbS@HSOD spectrum originates most likely from the interaction of PbS monomer with Na-exchanged part of the zeolite and/or from PbS tetramer in H-exchanged part as illustrated in Fig.17 that shows the spectrum of the both PbS@NaSOD and (PbS)4@NaSOD systems. This less prominent tetrameric signal in the experimental spectrum could originate from PbS tetramer occupying a larger pore also present in the zeolite A structure, the so-called α– cage.22 We have also considered the calculated spectra of other clusters but their fit with the experiment was less satisfactory. The presence of the monomeric PbS embedded in zeolites was suggested by the experimentalists as well and not only in low-loading regime for zeolite A12 but also for higher loadings in different zeolite (faujasite) by Moller et al.30 The neutron powderdiffraction study by Sun and Seff32 went even further and hinted that it is PbSH+ moiety, rather


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than PbS, which resides in the zeolite faujasite (with high PbS loading), although other clusters such as (Pb-S-Pb)2+ were proposed as well. Our results show that at least for the low-loading regime in zeolite A the monomeric PbS and PbSH+ species are indeed the dominant species present in the zeolite framework, however, some smaller fraction of PbS tetramers is probably also embedded in the zeolite structure. This compares well with the calculated binding energies of the PbS clusters in SOD cage (Fig. 8), which show a large stabilizing effect of the embedding environment for smaller sized cluster. The effect of increasing the PbS loading was investigated by Kim et al.107 for mixed Na- and H-exchanged faujasite zeolite. A single broad band (between ~300-550 nm) was reported for all the loadings considered with its absorption maximum progressively red-shifted from 330 to 345 and to 381 nm with increasing PbS loading from 11 to 16 and to 22% of maximum capacity (see Figure S12 in Supporting Information). The broadness of the reported band precludes unambiguous fit with the calculated spectra. However, the red-shift of the experimental absorption maximum appears to be mirrored well in the predicted spectra for monomer, dimer and trimer in either HSOD or NaSOD cage. As the cluster grows, the brightest peaks in the calculated spectra shift from ~310 to ~410 nm and from ~350 to ~390 nm for NaSOD and HSOD, respectively (see also Fig. S12 in Supporting Information). However, one should be a bit careful with overinterpreting the good fit between the experiment and prediction, as for example the calculated spectrum of the PbS tetramer in HSOD does match the first experimental band (11% of maximum PbS capacity) in Kim et al. investigation very well (see Fig. S11 in Supporting Information). The PbS tetramer is too big for the SOD cage as shown in this study and indicated in previous experimental investigations30,32, however, the faujasite structure contains a larger pore as well - a supercage – that could accommodate bigger PbS clusters. In


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addition, for even larger clusters such as pentamer or hexamer the absorption maximum redshifts with respect to the tetrameric spectrum (see their gas-phase spectra in Fig. S12) in a similar manner as for the dimer and trimer with respect to the monomeric one. Nevertheless, the claim that Kim et al. observes a growth of the PbS clusters within the faujasite, be it a growth starting from monomer, tetramer or some mixture of both, appears to be substantiated by the calculations.

Conclusion In the present paper, we investigated the structure and properties of the PbS quantum dots (QDs) encapsulated in the sodalite (SOD) cage (PbS@SOD), a building unit of a number of industrially relevant zeolites. SOD cages with four different compositions (pure silica, H-, Li- and Naexchanged) were considered in order to differentiate between effects of confinement imposed by the zeolite and the effects of various types of extra-framework cation. The structures of embedded QDs were obtained using a newly developed tool for global structure optimization of clusters in confining environments based on the genetic algorithm approach employing DFT calculations for local relaxations. For H-exchanged SOD (HSOD) inclusion of the environment lead to formation of [(PbS)nH]+ species that effectively represented new charge compensating cations. For other environments a distortion of the gas-phase QD structures was observed. This often resulted in stability reordering of the isomers with respect to gas-phase, even for the most stable ones. Moreover, these changes were dependent on the type of the extra-framework cation present in the SOD cage, e.g., the most stable structure of (PbS)3 in Na-exchanged SOD (NaSOD) is trigonal bipyramid while the trimer adopts the structure of an open rectangular “book” in Li-exchanged SOD (LiSOD).


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We found that encapsulation in the SOD cage is favorable for clusters up to trimer while tetramers or larger clusters are not expected to form within the SOD cage due to significant steric repulsion with zeolite walls. For small clusters the energy gains due to embedding are significant and are actually comparable in size with the gains due the cluster-enlargement. Hence, even very small clusters such as PbS monomers are expected to be found within the zeolitic cavities. The stabilization of the small QDs was shown to originate in a strong dispersion interaction with the SOD cavity combined with the electrostatic interactions, in particular for the HSOD environment. The covalent bonding with the environment was, however, mostly disregarded based on the analysis of the density-of-states and charge distribution within the PbS@SOD system. These findings hint at the possibility and adequacy of employing a rather small cluster models of zeolitic environment to investigate zeolite-embedded PbS QDs. Furthermore, we studied the magnitude and nature of the excitations in the PbS@SOD systems. First, on the technical note we observed a serious contamination of the low-lying transitions with spurious charge-transfer (CT) excitations at BP86 and to a smaller extent also at PBE0 level. To remove the CT contamination the exchange-correlation functional with increased amount of Hartee-Fock exchange, BHLYP, was employed with BHLYP absorption spectra comparing well with the experimental ones. Our calculations also revealed remarkable effect of the spin-orbit coupling (SOC) on the optical absorptions – the spectra with and without SOC are markedly different in terms of peak position, oscillator strength or even number of peaks with the adsorption edge redshifted by almost an eV upon inclusion of SOC. This suggests that it is essential to include the SOC in studying the electronic excitation properties of PbS clusters, either in gas-phase or as embedded species. Concentrating on the BHLYP/SOC results, we found that all the lower-lying excitations (in range of 2-5 eV) are localized dominantly on the (PbS)n


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clusters with the hole residing mainly on sulphur atoms and electron moving to lead atoms. Contributions to the excitations from environment are small even for the [(PbS)nH]+ species. We also observed that upon encapsulation the HOMO-LUMO gap as well as the adsorption edge (optical gap) increased by few tenths of eV for all the cluster sizes (n=1-3) and environments considered. For different-sized clusters in the same SOD cage, however, the optical gap stays approximately the same and as cluster grows only the brightest peaks in spectra shift to lower energies. Importantly, our findings were corroborated by a very good agreement between predicted and experimental absorption spectra. In particular, significant concentration of the monomeric PbS and PbSH+ species in zeolite A and faujasite can be confirmed, at least for low PbS loading. As the loading increases formation of the larger clusters is predicted. We conclude that a combination of robust structure prediction tool and state-of-the-art TDDFT implementation86 enable us to reliably compare with the experiment and thus better understand the structure and properties of (PbS) QDs embedded in zeolitic framework. However, sizable computation effort is needed both for the global structure determination using genetic algorithm and for the calculation of excitation spectra at the two-component level employing hybrid exchange correlation functional.

ASSOCIATED CONTENT Supporting Information. Supplemental material includes examples of (a) the effect of basis set size, DFT functional, size of the SOD model, termination of the SOD model (Si-H or Si-O-H), relaxation of the SOD


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framework and inclusion of spin-orbit coupling on the stabilities of PbS-zeolite composites, (b) the contamination of valence states by low-energy charge-transfer states at the non-hybrid DFT level, (c) the effect of SOC on the shape and energy levels of the frontier molecular orbitals, and (d) also shows the evolution of the optical absorption spectra with the increasing size of the (PbS)n clusters. AUTHOR INFORMATION Corresponding Author * [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This work was supported by the German Research Foundation (DFG grant no. GR 4546/2-1). The author is grateful to Professor M. Sierka for stimulating discussions and for support. REFERENCES (1) (2) (3) (4) (5) (6)

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PbS Clusters Embedded in Sodalite Zeolite Cavities of Different

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