Towards Understanding the Reactivity and Optical Properties of Organosilicon Sulfide Clusters

Abstract We report the extension of the class of organotetrel sulfide clusters with further examples of the still rare silicon‐based species, synthesized from RSiCl3 with R=phenyl (Ph, I), naphthyl (Np, II), and styryl (Sty, III) with Na2S. Besides known [(PhSi)4S6] (IV), new compounds [(NpSi)4S6] (1) and [(StySi)4S6] (2) were obtained, the first two of which underwent reactions with [AuCl(PPh3)] to form ternary complexes. DFT studies of cluster dimers helped us understand the differences between the habit of {Si4S6}‐ and {Sn4S6}‐based compounds. Crystalline 1 showed a pronounced nonlinear optical response, while for intrinsically amorphous 2, the chemical damage threshold seems to inhibit a corresponding observation. Calculations within the independent particle approximation served to rationalize and compare electronic and optical excitations of [(RSi)4S6] clusters (R=Ph, Np). The calculations reproduced the measured data and allowed for the interpretation of the main spectroscopic features.


Introduction
Thec hemical and structural properties of tetrel chalcogenide clusters with organic substituents have been extensively studied in the past. [1] In particular,alarge variety of compounds has been reported for the element combinations Sn/E [1a, 2] (E = S, Se,T e) and Ge/E, [1c, 3] whereas significantly fewer compounds with Si/E-based cluster cores have been known so far. [1b, 4] Several studies investigating the reactivity and properties of tin chalcogenide clusters were undertaken, showing the possible derivatization of the organic substituents [5,2f] as well as the formation of ternary inorganic cluster cores by introducing transition metal complexes. [6] In addition to the chemical features of such clusters,t he styryl-substituted cluster [(StySn) 4 S 6 ]( Sty = 4-vinylphenyl), which was determined via DFT calculations to have aheteroadamantane-type molecular structure,was recently shown to possess an extreme nonlinear optical behavior. [7] These findings led to the investigation of further compounds of the type [(RSn) 4 S 6 ]with cyclic and/or aromatic substituents Rto understand how the substituents influence the compounds properties.Generally,itwas shown that distinct order within the solid material (crystallinity or pronounced p-stacking interactions) leads to second-harmonic generation (SHG), while ah igh degree of amorphousness results in white-light generation (WLG). [8] In this context, we intended to find out, whether the principles of Sn/E chemistry can also be applied to the Si/E elemental combination, and whether ar eplacement of Sn atoms with Si atoms leads to changes in the clustersreactivity and properties.H erein, we present the first results of these studies.
Thep reparation of corresponding silicon analogs from RSiCl 3 (R = organic substituent) and ac orresponding chalcogen source is much more challenging than the corresponding tin or germanium chemistry,a st he use of the most appropriate reactant, E(SiMe 3 ) 2 (E = S, Se,T e), logically lacks the driving force of Si À Cl bond formation. Here,aSi À Cl bond needs to be cleaved at the same time in the other reactant. So, the use of binary chalcogen salts such as A 2 E( A = alkali metal) is required, which leads to am ore complicated workup.H owever,b esides the reproduction of known [(PhSi) 4 S 6 ] (IV)weherein report on the successful synthesis of two new organosilicon sulfide compounds,[ (NpSi) 4 S 6 ]( 1)a nd [(Sty-Si) 4 S 6 ](2), their characterization and follow-up chemistry with gold complexes to form ternary complexes [{RSi(m-S)} 2 -{AuPPh 3 (m-S)} 2 ]( 3:R = Ph, 4:R = Np). We used density functional theory (DFT) methods to gain insight in structural features of the adamantane-based compounds,i np articular regarding inter-cluster interactions that contribute to the macroscopic habitus of the solid. All new compounds were investigated regarding their linear and nonlinear optical properties,w hich were additionally studied by means of quantum chemistry.T he calculations explain the preferred habitus of the compounds,and reveal the deep impact of the ligands in the optical response
While synthesizing NpSiCl 3 (II)a saprecursor for [(NpSi) 4 S 6 ](1), single crystals were obtained upon distillation, and the molecular structure (Figure 1, left) was determined via single crystal X-ray diffraction. As expected, the Si atom Abstract: We report the extension of the class of organotetrel sulfide clusters with further examples of the still rare siliconbased species,s ynthesized from RSiCl 3 with R = phenyl (Ph, I), naphthyl (Np, II), and styryl (Sty, III)w ith Na 2 S. Besides known[ (PhSi) 4 S 6 ]( IV), new compounds [(NpSi) 4 S 6 ]( 1)a nd [(StySi) 4 S 6 ](2)were obtained, the first two of which underwent reactions with [AuCl(PPh 3 )] to form ternary complexes.DFT studies of cluster dimers helped us understand the differences between the habit of {Si 4 S 6 }-and {Sn 4 S 6 }-based compounds. Crystalline 1 showed apronounced nonlinear optical response, while for intrinsically amorphous 2,t he chemical damage threshold seems to inhibit ac orresponding observation. Calculations within the independent particle approximation served to rationalizea nd compare electronic and optical excitations of [(RSi) 4 S 6 ]c lusters (R = Ph, Np). The calculations reproduced the measured data and allowed for the interpretation of the main spectroscopic features. exhibits at rigonal pyramidal coordination environment. Furthermore, p-interactions between the naphthyl substituents are observed in the unit cell, alternating between parallel-displaced p-stacking and T-shaped CH/p-interactions (Figure 1, right). Thedistance between the adjacent naphthyl rings with p-stacking is slightly larger (3.4397(18) )than the distance between the layers in graphene (3.35 ), [9] whereas the distance between the center of one of the naphthyl rings to the closest Ha tom of the next perpendicular naphthyl ring (2.9371(1) )i si nt he typical range of strong CH/p-interactions. [10] Ther eaction of II with 1.5 equivalents of Na 2 Sa ffords acrystalline,colorless solid. Upon dissolution in toluene and cooling to À25 8 8C, single crystals of [(NpSi) 4 S 6 ]·0.5 C 7 H 8 (1·0.5 C 7 H 8 )s uitable for X-ray diffraction were obtained. Themolecular structure of 1 is shown in Figure 2. 1 crystallizes in the triclinic space group P1 with two molecules per asymmetric unit. Like [(PhSi) 4 S 6 ], 1 is an adamantane-type Si/ Scluster with four organic substituents,each bound to one Si atom. Themolecule shows minor deviations from T d symmetry,d ue to slightly different angles in the inorganic core and different orientations of the organic substituents.F urthermore,t he two individuals differ greatly in the orientation of the organic substituents (see Figure 2, bottom), indicating av ery low energy barrier for rotation of the organic substituents about the SnÀCbond, which in most cases leads to intrinsic amorphousness.N otably,w hile both [(PhSn) 4 S 6 ] and [(NpSn) 4 S 6 ]a re amorphous (with the Np compound comprising ac onsiderable amount of order according to its optical response,s ee also below), [7b] the two Si analogs are crystalline.Initially,this was ascribed to the smaller radius of the Si/S core with respect to the Sn/S core only,a st he corresponding smaller volume per given number of cluster molecules causes the aromatic rings of neighboring clusters to approach more closely overall, and thus form more efficient p-stacking interactions.I nt his work, we present ar efined version of this interpretation (see below). Thereaction of StySiCl 3 (III)with 1.5 equivalents of Na 2 S should proceed similarly and lead to the formation of Scheme 1. Summary of reactions done to produce compounds IV and 1-5.  (2). [15] [(StySi) 4 S 6 ]( 2). However,o nly the crude product could be isolated upon evaporation of the solvent in form of acolorless "solid" with the consistencyo fc otton candy or honeydepending on the duration of the reaction and drying process. We attribute this to the high polymerization tendency of the styryl substituents,a nd the corresponding oligomerization/ polymerization that proceeds visibly as time goes by.Notably, this was not the case for the Sn analogs,w hich we take as af urther hint for the correlation of the nature of the T/E cluster core with the properties of the organic substituents:in the Sn/S clusters,the styryl substituents of neighboring cluster units are obviously not close enough to allow for ac hemical reaction of neighboring vinyl groups.Asaconsequence of the different situation with an underlying Si/S cluster core, 2 could neither be obtained as single crystals,n or could individual clusters be detected by means of liquid injection field desorption/ionization (LIFDI) or electrospray ionization (ESI) mass spectrometry.H owever,w ewere able to collect 29 Si NMR data of af reshly prepared sample of 2 that turned out to be sufficiently soluble.Adownfield shift of % 9ppm of the observed singlet with respect to the precursor signal is in accordance with the NMR data of other Si/S adamantanetype clusters and their corresponding organosilicon trichloride precursors reported previously,such as [(EtSi) 4 S 6 ]/EtSiCl 3 , [(PhSi) 4 S 6 ]/PhSiCl 3 ,o r[ (CH 2 =CHSi) 4 S 6 ]/CH 2 =CHSiCl 3 . [11] Another indication is given by the 1 Ha nd 13 CNMR spectra, which clearly show the signals of the styryl substituent at as ignificant downfield-shift compared to the starting compound III,w ith the ipso-a nd meta-atoms being the most affected, which indicates ar eaction at the Si atom to have taken place.Hence,the NMR data indicate the formation of acompound comprising individual adamantane-type clusters [(StySi) 4 S 6 ]. Yetw ea ssume that they start to unstoppably form oligo-/polymers shortly upon synthesis.
Further studies on the reactivity of the adamantane-like organosiliconsulfide clusters were undertaken. Thea ddition of Na 2 Sa nd [AuCl(PPh 3 )] leads to the fragmentation of the clusters and the formation of the four-membered rings [{RSi(m-S)} 2 {AuPPh 3 (m-S)} 2 ](3:R= Ph, 4:R= Np). Colorless single crystals of 3·CH 2 Cl 2 and 4 were obtained by layering the respective reaction solutions with n-hexane.Their molecular structures are shown in Figure 3. 3·CH 2 Cl 2 crystallizes in the monoclinic space group C2/c,a nd 4 crystallizes in the triclinic space group P1 ,b oth with half am olecule per asymmetric unit. Themolecules in these compounds have an inversion center in the center of an {RSi(m-S)} 2 ring, with nearly linear {Au(PPh 3 )(m-S)} substituents attached to the Si atoms.Although the structural parameters of the central unit in both compounds are quite similar, they differ significantly in the orientation of the {Au(PPh 3 )(m-S)} units:whereas they point away from the central {Si 2 S 2 }r ing in 3 with aC 1 ÀSi1À S2ÀAu1 cis arrangement, the corresponding atoms in 4 show a trans arrangement. Thus,while the interatomic distances in these compounds are similar, the Si1 À S2 À Au1a nd S2 À Au1 À P1 bond angles are different. Homologous Sn/S compounds exhibiting this structural motif as well as a cis or trans arrangement depending on the organic moiety at the tetrel atom were described previously,s howing the same trends in the TÀSÀAu and SÀAuÀPbond angles. [12] Upon fragmentation of the adamantane-type cluster and formation of 4,af urther downfield shift by 5.6 ppm was observed in the 29 Si NMR spectrum. Table 1s ummarizes the respective NMR data for compounds I-IV, 1, 2,a nd 4.N ote that NMR data of compound 3 were not obtained owing to very poor solubility of the crystals.

Quantum Chemical Investigation of Structural Features
It was experimentally shown, that [(PhSi) 4 S 6 ]( IV)a nd [(NpSi) 4 S 6 ]( 1)a re observed in ac rystalline phase,w hile [(PhSn) 4 S 6 ]a nd [(NpSn) 4 S 6 ]a re intrinsically amorphous. Nevertheless,i tw as suggested that [(NpSn) 4 S 6 ]f eatures as tructure with ah igher amount of order compared to [(PhSn) 4 S 6 ], owing to more efficient p-stacking interactions between the Np substituents as compared to the Ph substituents. [7] This assumption was based on the different nonlinear optical responses of the two compounds,w hich showed SHG (requiring phase matching) for the Np compound but not for the Ph analog,f or which WLG was reported.
To explain the general difference observed in the [(RSn) 4 S 6 ]a nd [(RSi) 4 S 6 ]c luster compounds with R = Ph, Np,o ne may consider the smaller radius of the {Si 4 S 6 }c ore with respect to the {Sn 4 S 6 }c ore to enable as tronger interaction of the neighboring clusters through more efficient pstacking interactions.T oinvestigate this hypothesis,quantum chemical calculations of the interaction in cluster dimers as am inimal model were carried out, which already provide valuable insights into the cluster interaction that can be transferred to the extended crystalline or amorphous material.  (7);Si ÀSÀSi 82.40 (9), SÀSiÀS97.60(9)-115.54 (10),S i ÀSÀAu 90.97 (7) (10), SiÀSÀ Au 103.57 (9), SÀAuÀP173.35 (7). [15]  In order to classify the flexibility of the substituents,w e initially calculated the rotation barriers of the substituents for both cluster cores.Rotation barriers of the substituent at the single cluster are hardly present (< 1kJmol À1 )for the clusters with phenyl substituents,while for the clusters with naphthyl substituents,abarrier height of 17 kJ mol À1 is obtained for the [(NpSi) 4 S 6 ]c luster and 9kJmol À1 for the [(NpSn) 4 S 6 ]c luster (see Figure 4and Figure S12). Thelarger rotation barrier for the cluster with an {Si 4 S 6 }core as compared to the cluster with an {Sn 4 S 6 }c ore can indeed be explained by the smaller core radius.T he smaller Si À Cd istance in this cluster (1.889 )i n comparison with the corresponding SnÀCd istance (2.088 ) increases the barrier by as tronger interaction between the hydrogen atom of the substituent and the sulfur atoms of the cluster.The relative positions of Sand Hatoms at the rotation barrier are visualized in Figure 5.
Furthermore,t he substituent-substituent interaction can increase the rotation barrier,b ut this is of minor importance for the considered conformers.I ns ummary,t he calculations indicate ahigh orientational flexibility for phenyl substituents on both Si/S and Sn/S clusters,asopposed to acomparatively lower freedom of orientation for naphthyl substituents.T he latter show ah igher orientational flexibility for the cluster with larger core radius (Sn/S) than for those with smaller core radius (Si/S), which is in agreement with the tendencyf or (a) higher order in compounds with R = Np than in compounds with R = Ph, and (b) higher order in {Si 4 S 6 }-based clusters than in {Sn 4 S 6 }-based clusters.
Thei nvestigation of the cluster dimer structures was performed to analyze the interaction between the molecules with different cluster cores and substituents.T he cluster dimer structures were determined by two computational approaches and their results were combined to obtain alarger number of possible conformers.T he dissociation energies of all cluster dimers are plotted against their core-core distance in Figure 6, and selected cluster dimer structures are plotted in Figure 7.
First, we discuss the obtained cluster dimers in regard of their core-core distances and geometric structures.M ost of the cluster dimers have ad istance of the two adamantane cores between 5.9 and 6.5 (orange region in Figure 6). The [(PhSi) 4 S 6 ]c luster dimers show ac ore-core distance range that is shifted to slightly smaller values than the range calculated for [(NpSi) 4 S 6 ]. Thes ame trend, but even more pronounced, is observed for the {Sn 4 S 6 }-based cluster dimers. Cluster dimers in this region of inter-cluster distances yielded stacked or alternating substituents and different orientations of the cluster cores ( Figure 7). In all of them, am inimum of two substituents of one cluster interact with at least two substituents of the other cluster.I nt he "stacked dimer" conformers,t he substituents are arranged directly towards each other. In the "alternating dimer" conformers,t he substituents of one cluster are located in av oid between the substituents of the other cluster.I nterestingly,t he "alternating dimer" structure is slightly preferred on average for clusters with phenyl substituents,while for naphthyl substituents the "stacked dimer" structure is slightly preferred. The   . Dissociation energy of cluster dimers, plotted against the corresponding core-core distance calculated at the BP86-D3/cc-pVDZ-(-PP) level of theory.Medium core-core distances are indicated by an orange background, large core-core distances by agreen background. The region of small core-cored istances is plotted in Figure S13. core-core distances between Si/S and Sn/S clusters,r espectively,d iffer only slightly for analogous cluster dimers (by % 0.15 on average). The" alternating dimers" show ah igh similarity to the arrangement of the cluster in the crystal structures,a sd emonstrated for [(PhSi) 4 S 6 ]i nF igure 8. Although similar structural units are present, the core-core distance in the crystal structure (closest core-core distances: 7.05-7.46 in IV,7.44-7.58 in 1)i smuch larger (by 0.5 to 1.0 )ascompared to the calculated cluster dimers,asinthe crystal, the interaction is shared between more than two clusters.B esides the majority of cluster dimers with ac orecore distance between 6.0 and 6.5 ,t here are af ew cluster dimers with core-core distances between 7.2 and 8.0 ,w ith apoor relative orientation of the clusters to each other (green region in Figure 6; example of astructure shown in Figure 7, top). TheS i/S cluster dimers with phenyl and naphthyl substituents listed in this green region show larger core-core distances than the corresponding crystal structures.O nt he other hand, for some of the Sn/S-based cluster dimers,w e found af usion of cluster structures (purple region in Figure S13). Since we do not consider them to be relevant for the solid-state structures of this study,wehave not considered the fused clusters further.
Second, we discuss the obtained cluster dimers depending on their dissociation energy.C onsidering each individual cluster composition, the majority of dimer clusters with corecore distances between 5.9 and 6.5 yield higher absolute dissociation energies as compared to the absolute dissociation energies of the cluster dimers with core-core distances between 7.2 and 8.0 .The difference in dissociation energies between the medium and large core-core cluster dimers is smaller for clusters with Np ligands than for those with Ph ligands.
Considering the cluster dimers with core-core distances between 5.9 and 6.5 ,t here are 2-3 regions of dissociation energies for the individual cluster compositions in Figure 6, each of which correlates with acertain number of substituents interacting with each other. Thus,t he highest dissociation energies were obtained for cluster dimers in which three substituents of one cluster interact with three substituents of the other one.T he "stacked dimer" and "alternating dimer" conformers for individual cluster compositions yield similar dissociation energies.Among the cluster dimers with highest dissociation energies,[ (NpSi) 4 S 6 ]e xhibits ad issociation energy that is by about 65 kJ mol À1 higher than that of [(PhSi) 4 S 6 ]. As imilar, but slightly smaller, difference in dissociation energies is calculated for the corresponding {Sn 4 S 6 }-based cluster dimers ( % 53 kJ mol À1 ). Obviously,t he larger Np substituents lead to astronger interaction between cluster dimers than Ph substituents.O ther than originally anticipated, the investigation of the cluster dimers did not indicate larger dispersive interaction for clusters comprising asmaller radius of the cluster core.The {Sn 4 S 6 }-based clusters have ah igher absolute dissociation energy than the {Si 4 S 6 }based cluster dimers,w hich illustrates as tronger interaction overall. To understand this result, we performed ad ecomposition analysis of the cluster dimer binding energy contributions into the substituent-substituent interaction, the substituent-core and core-core interaction (see Figure 9).
Thed ecomposition of the binding energy reveals similar substituent-substituent binding energies for cluster dimers with the same substituent. Thel arger naphthyl substituents show ah igher binding energy than the smaller phenyl substituents due to larger dispersive interactions.Incontrast, the core-core binding energy is larger for the Sn/S-based cluster dimers than for the Si/S based cluster dimers due to the larger adamantane core.T his stronger core-core interaction for the larger Sn/S-based cluster dimers leads to higher absolute values of the dissociation energies than observed for the Si/S-based analogs.F or the cluster dimers with larger core-core distances (green region in Figure 6), the same trend in dissociation energies is observed, although larger core-core distances are found here than for crystalline [(PhSi) 4 S 6 ]a nd [(NpSi) 4 S 6 ]. We therefore believe that these insights can be transferred to crystalline and amorphous cluster materials Centre:cluster dimer with medium core-core distance and alternating substituents (two views). Bottom:cluster dimer with medium corecore distance and stacked substituents (two views). with core-core distances between the medium and large corecore distance regions of Figure 6.
In conclusion, we propose that the predominance of the relatively isotropic core-core interactions in [(PhSn) 4 S 6 ] outplay the rather directional interactions involving the substituents,w hich explains why this compound shows ad istinctly lower tendency for order in the solid than the crystalline {Si 4 S 6 }-based homologue.T his trend is also visible for the clusters with Np substituents,y et for [(NpSn) 4 S 6 ]t he relatively similar strengths of core-core and substituentsubstituent interactions allow for ah igher degree of intermolecular order,w hich is in agreement with the (virtually contradicting) experimental findings:t he powder produces SHG (as as ign of phase matching) in spite of an apparently amorphous nature according to X-ray diffraction. Theresults of this study thus contribute significantly to the overall understanding of the origin of (dis)order in compounds of the type [(RT) 4 E 6 ]( T= Si, Ge,Sn; E= S, Se,T e).

Optical Properties
We explored the optical response of compounds 1-4 by optical spectroscopy.The absorption and emission spectra are summarized in Figure 10.
Clearly,t he emission and absorption data are mirrorimage-like for the solution data. Thee mission spectra of the solid phase show an additional resonance about 500 meV below the emission maximum in solution. Such features are commonly attributed to excitons or an ensemble thereof. Notably,the higher-energy emission maximum persists in the condensed matter phase for all samples.H owever, it is significantly quenched by the existence of Au/S moieties in compounds 3 and 4 in contrast to 1 and 2.T his apparently enhances the lower-energy emission channels.I np articular, for compound 4,s everal distinct emission channels are observed which are tentatively attributed to transitions involving atomic orbitals of the Au I atom.
Thec rystalline compound 1 shows ac lear nonlinear optical response.Inagreement with the observation made for IV, [7b] we observe SHG here in spite of the centrosymmetric space group,which therefore is attributed to surface effects or defects of the crystal (see Figure 11). Theother compounds,in general, do not show an onlinear response that is clearly distinguishable from luminescence effects owing to chemical transformations.H ence,w ec an neither confirm nor exclude that the adamantane-based compound 2 exhibits WLG,but its significantly higher chemical sensitivity to oxygen and humidity as compared to the heavier homologue hampers aclear statement to date (note that it is technically not possible to prevent that the samples are exposed to air for av ery short moment prior to the measurement).

Calculation of Optical Properties
We investigated the role of the substituents (phenyl vs. naphthyl) on the optical response of the molecular clusters. Thereby,wemodeled two of the synthesized clusters with the same core but different substituents,[ (PhSi) 4 S 6 ]a nd [(NpSi) 4 S 6 ]. Thes tructural relaxation of single clusters and molecular crystals performed by the plane-wave implemen- Figure 9. Decomposition of the binding energy contributionsofcluster dimers into substituent-substituent interaction, the substituent-core and core-core interactionc alculated at the BP86-D3/cc-pVDZ(-PP) level of theory.  tation of the DFT within the periodic supercell method leads to geometries of the same symmetry and in overall close agreement with the structures calculated with al ocalized basis.T he optimized geometries were employed for the calculation of the electronic and optical excitations. Figure 12 shows the relaxed geometry as well as the HOMO and LUMO states for the [(PhSi) 4 S 6 ]and [(NpSi) 4 S 6 ] clusters.T he structural differences between the cluster cores of the two molecules are limited. TheSi À Sdistance amounts to 2.15 in both clusters,while the S À Cbond length is 1.87 in [(PhSi) 4 S 6 ]a nd 1.88 in [(NpSi) 4 S 6 ]. However,t he different substituents have ad eeper impact on the molecular electronic structure.T he (degenerate) HOMO of the [(PhSi) 4 S 6 ]molecule is localized at the Sa toms in the cluster core,w hile the HOMO of the [(NpSi) 4 S 6 ]c luster is localized on the naphthyl rings.T he LUMO of both systems is similar and localized on the substituents (see Figure 12). Thus,t he DFT-calculated HOMO-LUMO gap of the two systems is rather different and amounts to 3.76 eV for [(PhSi) 4 S 6 ]a nd 2.96 eV for the [(NpSi) 4 S 6 ]c luster.Q uasiparticle effects, calculated in an approximate manner by the DSCF method as described in Ref. [13],open up the fundamental independent-particle-approximation( IPA) gap to av alue of 6.54 eV for [(PhSi) 4 S 6 ]a nd 5.09 eV for the [(NpSi) 4 S 6 ]c luster (see Figure S15 in the Supporting Information). Theenergy of the lowest excitonic excitation, describing the transition of one electron to the LUMO leaving ahole behind in the HOMO,is calculated following the procedure described in Ref. [13]. Excitonic excitations of 3.92 eV for [(PhSi) 4 S 6 ]a nd 2.89 eV for the [(NpSi) 4 S 6 ]c luster,r espectively,a re predicted. These energies are rather close to the HOMO-LUMO gap, suggesting that the quasiparticle shifts are nearly canceled out by the electron-hole attraction. Thus,a sm any-body effects due to the electron-electron and the electron-hole interaction counterbalance,t he IPA-calculated optical excitation spectra are expected to yield ar easonable description of the measured optical response,atl east for the low-energy excitations.
Thee xtinction coefficient of [(PhSi) 4 S 6 ]( blue line) and [(NpSi) 4 S 6 ]( black line) single clusters is shown in Figure 13. Thecomponents of the dielectric tensor are averaged to allow for ad irect comparison with experimental data later in the manuscript. Thegeneral shapes of the dielectric functions are rather different, although the structures of the two clusters are similar. In order to rationalize these differences and understand their origin, we analyzed the electronic transitions of the two clusters.I ndeed, spectral resonances can be directly related to electronic transitions between occupied and empty states at the IPAl evel.
Theonset of the optical absorption corresponds exactly to the DFT-calculated HOMO-LUMO transition in the case of the [(NpSi) 4 S 6 ]cluster (black line). Structures in the first peak match quite well the energy of the HOMO-LUMO + 1,2 (degenerate) and HOMO-LUMO + 3. Them ain peak at about 4eVi sm ainly due to transitions from the HOMO to ag roup of energetically close states localized at the Ca toms of the naphthyl rings.I nstead, in the case of the [(PhSi) 4 S 6 ] cluster (blue line), the onset of the optical absorption is located at much higher energies than the DFT-calculated HOMO-LUMO difference.I ndeed, the HOMO-LUMO transition probability is small, due to the different spatial localization and orbital character of the two states.W eassign the first spectral peak to transitions from the HOMO to three molecular orbitals about 4.4 eV above the HOMO and with as patial extension partially overlapping the HOMO.S ummarizing,the absorption spectra of [(PhSi) 4 S 6 ]and [(NpSi) 4 S 6 ] clusters are rather different concerning the positions and line shapes of the spectral features.T he deviations in the optical response originate from the qualitatively different and differently localized electronic states involved in the transitions resulting in the main spectral peaks of the two compounds.
Theo ptical answer of the isolated clusters represents the basis for understanding the absorption spectra of the solid material comprising the molecules.A ccording to the calculations,which started from the experimental crystal data, the  Angewandte optimized geometries show only small modifications of the geometrical parameters determined for the isolated molecules.T he largest bond length deviation is 1.4 pm, while the bond angles of the substituents are rotated by 13.28 8 with respect to the single molecules due to the presence of toluene. When the single clusters aggregate to form the crystalline material, the discrete energy levels broaden to become energy bands.T hese have been calculated in the IPAapproximation along the directions in reciprocal space shown in Figure S16, and are illustrated in Figure 14. Theelectronic band gap of the crystals is slightly smaller than the HOMO-LUMO energy differences of the corresponding molecules;h owever, the orbital characters of valence and conduction band edges closely resembles those of the HOMO and LUMO of the parent molecules (see Figure 12). As the band dispersion is rather flat and no major rearrangement is expected upon inclusion of quasiparticle effects,s elf-energy correction mainly serves to widen the band gap,a nd may be replaced by anumerically less costly scissors-shift for the calculation of the optical response.
We then proceeded with the optical characterization of the synthesized crystalline compounds.Owing to the synthesis method, the experimental crystal structure of [(NpSi) 4 S 6 ]( 1) comprises toluene molecules (0.5 C 7 H 8 per formula unit of 1, see Table S1). As illustrated in Figure S17, the extinction coefficient calculated with and without toluene does not substantially differ, demonstrating that the optical response of the molecular cluster is not affected by the presence of solvent. Thee xtinction coefficient calculated within the IPA for the [(PhSi) 4 S 6 ]( IV)d erived and [(NpSi) 4 S 6 ]( 1)d erived molecular crystals is shown in Figure 15.
Forb oth compounds,t he spectral signatures of the isolated clusters are clearly recognizable in the optical answer of the corresponding molecular crystals.T hey barely shift in energy,a nd the relative intensity compares well with that predicted for the single clusters.Itcan thus be concluded that the transitions leading to the absorption peaks of the single clusters are chiefly responsible for the major peaks in the dielectric function of the semiconducting crystals.T he main difference between molecules and crystals comprising these molecules is that the crystal absorption features are broadened with respect to the molecular peaks due to the energy dispersion of the molecular states upon aggregation. As the onset of the molecular and crystalline absorption coincides, we can exclude new intermolecular low-energy electronic transitions to occur when the clusters aggregate to form crystals.T hus,for the investigated compounds,the molecules seem to individually interact with light rather than jointly. However,t he relative orientation of the molecules in the solids (ordered vs.n on-ordered) controls the nature of the nonlinear optical response (with or without phase matching).
In order to compare the calculated spectra of the crystalline material comprising [(NpSi) 4 S 6 ]c luster (1)w ith the measured data, we accounted for many-body effects in an approximated manner by means of as cissors-shift. [14] We chose as cissor-shift of 0.7 eV,c orrecting the DFT underestimation of the experimentally measured band gap of the molecular crystals.T he corresponding results are shown by the blue line Figure 16 together with experimental results (yellow line) from Figure 10. Thec omparison with the experimental data shows that calculations at the IPAl evel with scissors-shifts already agree with the measurements.
Thecalculations fairly describe the main absorption peak, originating from transitions between the valence band edge  and bands localized at the Ca toms of the naphthyl rings, including the shoulder observed at about 4.6 eV.H owever, the intensity of the peak at about 3.5 eV corresponding to the transition from the valence band maximum to the conduction band minimum is overestimated in the calculations in comparison with the measured spectra. More refined and computationally demanding approaches accounting for quasiparticle effects in aperturbative manner and accounting for the electron-hole attraction by means of the Bethe-Salpeter equation might further improve the agreement with the experiment.
Thec alculation of the second-order polarizability tensor for the crystalline phases of [(PhSi) 4 S 6 ]( IV)a nd [(NpSi) 4 S 6 ] (1)s hows vanishing optical nonlinearities for all tensor components,a se xpected for ac entrosymmetric crystal structure.D eviations from this behavior in experiments thus arise from structural defects and amorphous regions in the samples,a sw ell as from surface-related contributions.A t least for centrosymmetric crystals,they are not inherent bulk properties.

Conclusion
We presented the synthesis of new members of the rare class of organosilicon sulfide clusters of the general formula [(RSi) 4 S 6 ]. We added new members with R = naphthyl (Np, 1) and styryl (Sty, 2), which were investigated with respect to their reactivity towards [AuCl(PPh 3 )],t heir structures,a nd their optical properties by ac ombination of comprehensive experimental and theoretical studies.T he investigations contributed to characterize and further understand the chemical behavior of such clusters,w hich showed to behave differently from the much better known germanium and tin homologues.O ur studies indicate am uch more pronounced tendency to polymerization in case of 2 than observed for its Sn homologue,and confirm the expected, much higher air and water sensitivity of the Si compounds.S econd, the observa-tion that clusters with the combination Ph/Si/S (reported previously) and Np/Si/S (1)a re crystalline,w hile the Sn homologues are amorphous was studied on the bases of cluster dimer models calculated with DFT methods.Different types of intra-cluster interactions were found, that led to different dissociation energies as af unction of the nature of the substituents,t heir relative orientation, and the core compositions {Si 4 S 6 }v ersus {Sn 4 S 6 }. Thed etailed study ultimately helped to explain the experimental findings on the basis of much stronger isotropic interactions in the {Sn 4 S 6 }-based cases in comparison with directional interactions that play amuch more notable role in the {Si 4 S 6 }-based materials.R egarding the optical properties of the new compounds and the products of their reaction with the gold complex, we could show that the emission is quenched upon fragmentation and formation of the gold compounds.M oreover, the crystalline compound 1 was proved to exhibit SHG as ac onsequence of high order that allows for phase matching;h owever, the SHG signal does not stem from the crystalline bulk but should be attributed to surface phenomena or structural defects.The behavior of 2 is clearly different, but its chemical nature inhibited as tatement regarding the compoundsn onlinear response.T he experimental findings were corroborated by static and time-dependent DFT calculations of both the molecules and the crystalline material, which are in full agreement with the measurements and therefore indicate the applicability of the used methods and models.