Sulfur, Selenium and Tellurium Ring Clusters: Experimental and Density-Functional Theoretical Study of Polarized Optical Absorption and Raman Spectra, Light-Induced Effects and Conical Intersections

Abstract

We studied experimentally and computationally the structures and optical properties of sulfur (S), selenium (Se) and tellurium (Te) ring clusters. We encapsulated S, Se and Te into AFI, MOR, CHA and LTA zeolites via vapor adsorption or high-pressure injection from melt and studied Raman and optical absorption spectra (RS and OAS, respectively) of zeolite single crystals with incorporated S, Se and Te ring clusters. Importantly, strict orientation of the rings in zeolite crystals allowed us to study the polarization/orientation dependency of ring RS and OAS. The obtained experimental spectra are found to be in agreement with density functional theory results (DFT using the PBE0 functional and def2-TZVP basis sets) for S₈, Se₆, Se₈, Se₁₂, Te₆ and Te₈ ring molecules. The agreement is especially good for Te rings, while for S and Se rings harmonic frequency scaling factors are required. The S and Se rings display light-induced effects, which we attribute to the presence of conical intersections between their ground and excited electronic states, resulting in isomerization and subsequent fragmentation. We consider this effect using the Se₆ ring example. This phenomenon is important for understanding photostructural changes not only in chalcogen clusters but also in bulk materials such as amorphous selenium.

1. Introduction

Doubly coordinated atoms of sulfur (S), selenium (Se) and tellurium (Te) form ring or chain structures. The allotropes of elemental sulfur are well characterized and consist predominantly of ring structures. In contrast, elemental tellurium primarily exists in the form of helical chains. In this sense, elemental selenium is a borderline material in the chalcogen group since it can form both rings and chains in the solid state. Selenium has attracted considerable attention since the 19th century when its photoconductivity [1] and photovoltaic [2] effects were discovered. Scientific interest in Se peaked in the mid-20th century, driven by its applications in xerography. Nowadays, S, Se, Te and their compounds are undergoing a research renaissance due to their importance for solar cells [3], topological insulators [4], phase-change materials [5], photodetectors [6], lithium batteries [7], etc. A few years ago, Se nanoparticles were explored as potential antimicrobial agents, anticancer drugs, antioxidants and tunable light-emitting bio-markers [8]. The structure and properties of bulk Se also occupy a borderline position between molecular crystals and traditional semiconductors. Its most intriguing form is amorphous selenium (a-Se), which consists of a variety of Se species including chains and rings. This phase displays photo-induced structural changes [9], including low-temperature photomelting (photofluidity) [10].

Here, we analyze the optical properties of zeolite-confined S, Se and Te ring molecules based on polarized optical absorption and Raman spectra (OAS and RS) of zeolite single crystals containing chalcogen rings, which are examined in this and previous works. The analysis is performed by comparing experimental spectra with density functional theory results obtained using the Turbomole software package, version 7.8.1 [11]. We demonstrate good agreement between experiment and theory. Our results suggest certain structural distortions of the rings in their ground state and conical intersections of their excited states with those of related isomeric molecules. They are important for understanding photoinduced effects in a-Se and chalcogenide glasses.

2. Materials and Methods

We used four different zeolites: LTA, MOR, CHA and AFI for encapsulation of S, Se and Te into their regular pores. Zeolite structures containing ring molecules are schematically shown in Figure 1. The encapsulation was carried out using vapor adsorption with a controlled chalcogen loading density or by high-pressure injection from the melt to achieve maximum loading density. Details of the encapsulation techniques are given in Refs. [12,13,14,15,16,17]. Synthetic LTA (Na₁₂Al₁₂Si₁₂O₄₈), AFI (Al₁₂P₁₂O₄₈) as well as natural CHA (Ca_1.6Na_0.4Al_3.6Si_8.5O_21.6) and MOR (Ca₂Na₄Si₄₀Al₈O₉₆) zeolites were used in this work.

Figure 1. (a) Structures of X₆, X₈ and X₁₂ rings with X = S, Se, Te, r, R, ϕ and τ indicating nearest atom distance, next nearest atom distance, bond angle and dihedral angle, respectively; (b) X₈ and Se₁₂ rings in LTA; (c) S₈, Se₆ and Te₆ rings in MOR; (d) Se₆, Te₆ and Te₈ rings in CHA; (e) Se₆, Se₈ and Te₈ rings in AFI. Sizes are shown in pm units.

RS of zeolite single crystals with ring molecules were studied using Raman microscopes manufactured by Renishaw Co. (Wotton-under-Edge, UK), JASCO Co. (Tokyo, Japan) and Tokyo Instruments Inc. (Tokyo, Japan). The 633 nm line of the He-Ne laser as well as the 514.5 nm and 364 nm lines of the Ar⁺ ion laser were used for the RS excitation. Additional RS experiments were done with the 785 nm diode laser. Micro-objective lenses with 10×–100× magnifications and a numerical aperture of 0.2–0.95 were used for the RS excitation and collection in a back-scattering geometry. RS signals of the zeolite-confined chalcogen species were significantly stronger than those of the zeolite transparent host matrices due to resonant Raman enhancement.

OAS in the visible and near-UV spectral ranges were studied using micro-spectrophotometers with a light probe size of 2–10 μm manufactured by Carl Zeiss Co. (Jena, Germany) and CRAIC Co. (San Dimas, CA, USA). To avoid light scattering from zeolite surfaces and improve transmittance, samples were immersed into glycerol and kept between two quartz cover glasses. In most of cases, single-crystal zeolite samples were intentionally broken to pieces with few-micron or submicron thickness. This enabled reliable spectral measurements up to ~5.15 eV for samples with relatively large planar size and optical densities up to ~2.5.

RS and OAS were simulated using density functional theory (DFT) [18,19,20]. The structure and vibrational frequencies of the ring molecules were computed using the hybrid PBE0 exchange-correlation functional [20] and the resolution-of-identity approximation for the Coulomb part (RI-J) [21]. The def2-TZVP basis sets [22] together with the corresponding auxiliary basis sets [23] were employed for S, Se and Te, and small-core effective core potentials (ECPs) were used for Te [24]. RS intensities were obtained in the double harmonic approximation using analytical derivatives of static electronic polarizabilities [25] and analytical energy Hessians [26,27]. Calculations of static polarizability derivatives used the PBE0 functional and augmented def2-TZVPD basis sets [28]. Additionally, infrared (IR) spectra were computed in the double harmonic approximation using analytical dipole moment derivatives and energy Hessians [26,27]. OAS were simulated by time-dependent DFT (TDDFT) [29] using the PBE0 functional with the RI-J approximation [30] and def2-TZVPD basis sets. All calculations were performed with the Turbomole program package, version 7.8.1 [11,18]. Computed RS and OAS are presented as sums of Lorentz curves with full width at half-maximum (FWHM) of ~6 cm⁻¹ and ~0.35 eV, respectively.

The computed structural parameters (bond lengths r, bond angles ϕ and dihedral angles τ) of the chalcogen rings are shown in Supplementary Materials Table S1. Stable ring structures correspond to the energy minima whereas normal-mode-distorted structures do not. Therefore, the structural parameters of these distorted rings should be interpreted qualitatively rather than quantitatively.

3. Results and Discussion

3.1. S₈ and S₆ Rings

S₈ rings were previously obtained in the LTA large cavities [12,17,31,32,33] and in the MOR channels [34]. RS of LTA-S and MOR-S showed good agreement with the known RS of S₈ molecules in solution [35]. Here we present RS and OAS of LTA-S and MOR-S obtained using higher-quality equipment (Figure 2). DFT-computed polarized RS of a single S₈ ring is shown in Figure 2a. The resulting frequencies, IR intensities and Raman activities of the S₈ ring with D_4d symmetry are listed in Supplementary Materials Table S2.

Figure 2. Raman spectra: (a) DFT calculation for S₈ and in inset for S₆; (b) experiment for S₈ in LTA-S; (c) calculation for S₈ in LTA; (d) experiment for S₈ and S₆ in MOR-S. The axes X, Y, Z correspond to S₈, while the axes a, b, c correspond to the zeolites. Mode frequencies and symmetries are indicated.

The experimental RS of LTA-S are displayed in Figure 2b. Assuming orientation of S₈ by its four-fold axis along the LTA four-fold axis as in Figure 1b, we simulated LTA-S RS by summing the computed RS of S₈ in three possible orientations (Figure 2c). The experiment (Figure 2b) and theory (Figure 2c) are in very good agreement. In particular, the polarization dependencies of RS intensities are nearly perfectly reproduced, which confirms the assumed orientation of S₈ in LTA. The agreement between the experimental (75, 153–155, 221 cm⁻¹) and theoretical (73.4, 150, 223 cm⁻¹) bending/torsion mode frequencies is also good. However, it is not the case for the stretching modes. The DFT-computed A₁ stretching mode frequency of 499 cm⁻¹ is higher than the experimental value of 479 cm⁻¹. Scaling the computed frequency using the recommended global scaling factor of 0.9591 [36] gives 479 cm⁻¹ in excellent agreement with the experiment. Scaling vibrational frequencies by a global factor accounts for the vibrational mode anharmonicities and basis set incompleteness. The scaling factor depends on the exchange-correlation functional and the basis sets and is transferable across different chemical systems, as evidenced by the good agreement between experimental and scaled computed vibrational frequencies. Importantly, the S₈ ring symmetry in LTA is slightly distorted from the perfect D_4d, with the E₂ modes split off and the previously forbidden B₁ and E₁ modes observed (Figure 2b).

The Raman bands of the S₈ ring are also observed in the RS of MOR-S (Figure 2d). The polarization dependence of the A₁ and E₂ bending mode band intensities clearly shows that the rings are oriented with their four-fold axes aligned along the b-axis of MOR [Figure 1c]. This indicates that the S₈ rings in the MOR channels are compressed along the a-axis, whereas they remain uncompressed along the c-axis of MOR. Therefore, the E₂ bending mode splitting in MOR-S (152–158 cm⁻¹) is even larger than that in LTA-S (153–155 cm⁻¹). Interestingly, a few relatively weak bands of the S₆ rings are also observed in the RS of MOR-S. The experimental bands at ~206 cm⁻¹ and ~272 cm⁻¹ can be assigned to the theoretical 204 cm⁻¹ E_g and 270.5 cm⁻¹ A_1g bond-bending modes of the S₆ ring, respectively [(Figure 2a), see also Supplementary Materials Table S3]. The polarization dependence of these band intensities is weaker than that of the S₈ ring, indicating a less strict orientation of the S₆ rings within the MOR channel.

DFT-computed OAS of single S₈ and S₆ rings are presented in Figure 3a,b, respectively [see also Supplementary Materials Tables S4 and S5]. The insets in these figures show the ring structures in the XZ plane. An additional inset in Figure 3a illustrates the p-orbital splitting in S, Se and Te rings. The low-energy OAS in all these cases correspond to electronic transitions from the lone-pair (LP) orbitals to anti-bonding σ* states.

Figure 3. Optical absorption spectra: DFT calculation (a) for S₈ with insets showing the S₈ ring structure in the XZ plane and electronic structure with the atomic p-orbital splitting to the bonding σ, anti-bonding σ* and nearly non-disturbed lone-pair (LP) orbital states; (b) for S₆ with inset showing the S₆ structure in the XZ plane; experiment for (c) S₈ in LTA-S (E//a); and (d) for MOR-S (E//b) corresponding mainly to S₈ (E//Z) with a minor contribution of S₆.

For both S₈ and S₆ rings, in-plane polarized absorption (E//X) is stronger than the out-of-plane absorption (E//Z). Taking into account the orientations of the S₈ rings in LTA and MOR, we can conclude that OAS of LTA-S mainly corresponds to E//X absorption with a minor contribution from E//Z absorption of S₈. In contrast, OAS of MOR-S for E//b mainly corresponds to E//Z absorption of S₈ with a minor contribution from S₆ absorption. Both experimental spectra show a single absorption peak at ~4.53 eV for LTA-S (Figure 3c) and ~4.55 eV for MOR-S (E//b) (Figure 3d), respectively. These values are in reasonable agreement with the theoretical peak energies of 4.63 eV for E//X and 4.6 eV for E//Z (Figure 3a).

We should note that in the previously reported LTA-S OAS a peak position at 4.35–4.4 eV [17] was observed for samples with a higher sulfur loading density, corresponding to the significant contribution of two interacting S₈ rings per LTA large cavity. In contrast, in this work, we report the OAS of LTA-S with a low sulfur loading density, corresponding to one or zero S₈ molecule per cavity. It is likely that intermolecular interactions are responsible for the downshift of the absorption peak from 4.53 eV to 4.35–4.4 eV in the case of two S₈ rings per cavity [17].

Experimentally, S₈ ring OAS were also studied in solution [37,38]. The reported absorption band energies, 4.49 eV and 4.7 eV [37], and 4.48 eV, 4.66 eV and 5.28 eV [38], are in reasonable agreement with our DFT calculations, which yielded 4.63 eV, 4.83 eV and 5.4 eV for S₈ (E//X). Similar to S₈ in zeolites, the absorption peaks of S₈ in solution are observed at slightly lower photon energies than predicted by DFT. This discrepancy may be explained by solvent effects or by the overestimation of the electronic transition energies in DFT calculations. Furthermore, experimental OAS measurements were conducted at room temperature contrary to the DFT calculations implying T = 0 K, the S₈ ring energy gap being larger with a decrease in temperature. Another similarity of S₈ OAS in solutions with those in zeolites (Figure 3c,d) is the presence of a low-energy absorption tail extending down to ~3 eV. We attribute this S₈ absorption tail to triplet excitations in the 3.66–4.07 eV range [Supplementary Materials Table S4a].

To summarize this section, we conclude that our DFT calculations showed nearly perfect agreement with experimental Raman intensities and bending mode frequencies while they overestimated stretching mode frequencies. Applying harmonic frequency scale factors [36] to stretching mode frequencies improved the agreement. The DFT energies and oscillator strengths of the S₈ electronic transitions reasonably reproduced the experimental results. Our DFT-computed r = 205.6 pm, ϕ = 102.7° for S₆ and r = 204.7 pm, ϕ = 108.1° for S₈ [Supplementary Materials Table S1] show shorter r and nearly same ϕ compared to corresponding DFT-computed 212 pm, 103.1° and 211 pm, 109.5° [39] or 212 pm, 102.5° and 210.8 pm, 108.3° [40].

3.2. Se₆ Rings

RS and OAS of Se₆ incorporated in the pores of three different zeolites CHA, MOR and AFI (low density—LD), were experimentally studied in Ref. [41]. In some earlier works, Se₆ rings were identified in zeolites as well [34,42,43]. Se₆ ring molecules are slightly compressed in the CHA cavities possessing a nearly prolate spheroid shape with a length of ~1 nm and a cross-section of 0.67 nm × 0.67 nm. The rings are less compressed in the AFI channel with a cross-section of 0.73 nm × 0.73 nm. The D_3d symmetry of the Se₆ ring is maintained in both cases and the ring three-fold axis Z is directed along the crystal three-fold axis c. In contrast, the Se₆ ring is asymmetrically compressed in the MOR channel with a cross-section of 0.67 nm × 0.7 nm, whereas the ring three-fold axis Z is directed along the MOR b axis. The ring orientations are schematically shown in Figure 1 and the insets of Figure 4. Here, we present a more detailed optical study of Se₆ together with corresponding DFT calculations.

Figure 4. Polarized RS of Se₆: (a) DFT calculation; experimental RS at the 632.8 nm wavelength (1.96 eV) excitation: (b) CHA-Se, (c) AFI-Se(LD) and (d) MOR-Se. Insets schematically show Se₆ ring in the corresponding cavities and channels, white and black circles representing to upper and lower Se atoms, respectively. The axes X, Y, Z correspond to Se₆, while the axes a, b, c correspond to the zeolites.

Figure 4 shows the theoretical and experimental RS of Se₆ [see also Supplementary Materials Table S6]. The agreement between DFT results and the experiment is very good for the bond-bending mode frequencies and intensities. However, the discrepancy between the experiment and theory is significant for the bond-stretching mode frequencies. The experimental frequency of 273–274 cm⁻¹ of the A_1g bond-stretching mode is 12–13 cm⁻¹ lower than the computed value of 285.7 cm⁻¹, which can again be attributed to the neglect of anharmonic effects in simulations, as the scaled frequency is 274 cm⁻¹, in line with experimental data. The discrepancy between the DFT-computed stretching E_g mode frequency of 271.7 and experimentally observed band frequencies 220–221 cm⁻¹ attributed earlier to E_g [41,44] is very large. Applying the scaling factor yields 260.6 cm⁻¹, which does not fully account for the difference. Therefore, we consider the possibility to assign the observed band to the forbidden A_1u mode. This mode can be converted to the active A₁ mode under a ring distortion, which reduces its symmetry from D_3d to D₃ [see Supplementary Materials Table S1 for the structural parameters of the distortion]. The DFT-computed XX-spectrum of such a distorted ring is shown in Supplementary Materials Figure S2a and features a strong 228.8 cm⁻¹ A₁ mode band. Assuming that ~10% of Se₆ rings are distorted, we obtain the theoretical XX-spectrum shown in Supplementary Materials Figure S2b, which is in good agreement with the experimental RS.

The polarization dependencies of the intensities of both A_1g and E_g bending modes show good agreement between the experiment and DFT calculations. Both modes are highly active in the XX polarization configuration and less active in the ZZ configuration, where the E_g mode is formally forbidden by selection rules. The relatively high activity of these modes in the AFI-Se(LD) ZZ spectrum is likely associated with large amplitudes of (1) vibrations along the AFI channels and (2) librations of nearly free Se₆ molecules. Due to the ring symmetry distortion in MOR-Se, the E_g mode splits to two components at ~102 cm⁻¹ and ~108 cm⁻¹. Figure 4d suggests a C_2h symmetry for the Se₆ ring in MOR-Se. Therefore, the E_g bending mode splits to A_g and B_g modes with frequencies of 108 cm⁻¹ and 102 cm⁻¹, respectively. This splitting, with the higher A_g mode frequency and a lower B_g mode frequency, corresponds to the Se₆ ring orientation shown in Figure 4d. The actual symmetry of Se₆ in MOR-Se may be even lower, specifically, C_s, since the A_1g mode at ~134 cm⁻¹ mixes with the originally inactive A_2u mode at ~141 cm⁻¹, with both modes being converted to the A’ modes of the C_s point group.

The theoretical and experimental OAS of Se₆ are shown in Figure 5 [see also Supplementary Materials Table S7]. DFT-computed OAS (Figure 5a) shows three relatively weak bands at 3.67 eV, 4.06 eV and 4.22 eV and two strong bands at 4.6 eV and 5.1 eV polarized in the molecular plane (E//X). These absorption bands correspond to the transitions of E_u symmetry in the D_3d point group of Se₆. For the E//Z polarization, three relatively weak absorption bands of A_2u symmetry are observed. As in the case of sulfur rings, only dipole-allowed singlet electron transitions are included in the calculations.

Figure 5. Polarized optical absorption spectra of Se₆: (a) DFT calculation with inset showing OAS with forbidden transitions, (b) CHA-Se, (c) AFI-Se(LD) and (d) MOR-Se. The axes X, Y, Z correspond to Se₆, while the axes a, b, c correspond to the zeolites.

Experimentally, OAS with both E//X and E//Z polarizations are observed in CHA-Se (Figure 5b). They show rather good agreement with the DFT results. Indeed, the experimental band energies at ~3.65 eV, ~4.4 eV and ~4.63 eV nearly coincide with the computed values. The instrumental limit of ~5.15 eV does not allow the observation of the strong band expected at ~5.1 eV. Interestingly, the experimental CHA-Se OAS clearly shows a band at ~3.2 eV, which is absent in the DFT-computed OAS. We assign the experimental ~3.2 eV band to the DFT-computed forbidden Se₆ electronic transitions of E_g (3.13 eV and 3.36 eV), A_2g (3.28 eV) and A_1g (3.43 eV) symmetry, which are activated due to the inversion symmetry breaking by the antisymmetric vibrational A_1u, A_2u or E_u modes [Supplementary Materials Table S7b–g]. As a result, weak absorption bands appear in the 3.1–3.4 eV range of the Se₆ absorption spectrum. The inset in Figure 5a shows computed Se₆ OAS with (dashed lines) and without (solid lines) the contribution of activated forbidden electronic transitions. Agreement with the experiment is improved in the former case.

The anisotropy of CHA-Se OAS appears weaker than that predicted by DFT. However, it is necessary to take into account the sample-surface scattering, which increases with photon energy. OAS measurements of Se₆ in AFI-Se(LD) and MOR-Se is available only for one polarization, namely, for E//X in AFI-Se(LD) and for E//Z in MOR-Se. This limitation is associated with the existence of Se chains that strongly absorb light polarized along the AFI and MOR channels. OAS measurements for MOR-Se are not feasible for E//a//Y due to the crystal shape.

The AFI-Se(LD) OAS (Figure 5c) demonstrates good agreement with the DFT E//X spectrum. Indeed, a weak experimental band at ~3.65 eV is in good agreement with the theoretical band at ~3.67 eV, whereas a strong experimental band at ~4.65 eV is close to the ~4.6 eV theoretical value. MOR-Se OAS (Figure 5d) agrees well with the computed E//Z spectrum of Se₆ (Figure 5a). Stronger and weaker experimental bands at ~3.55 eV and ~4.5 eV can be assigned to the theoretical electronic transitions at ~3.66 eV and ~4.45 eV [Figure 5a]. The ~3.2 eV band, which is clearly observed in the CHA-Se spectrum, is likely obscured in the low-energy shoulder of the ~3.55 eV band.

To summarize this section, we state that the DFT calculations demonstrate very good agreement with the experimental Raman intensities and bending mode frequencies while they have a tendency to overestimate stretching mode frequencies. Scaling factors [36] improve the agreement. The computed energies and oscillator strengths of the electronic transitions are in satisfactory agreement with the experimental ones. We hypothesize that Se₆ undergoes antisymmetric mode distortion, which leads to better agreement of computed OAS with experiment and suggests that the experimental 220–221 cm⁻¹ Raman band corresponds to the inactive A_1u mode of the undistorted Se₆(D_3d), which becomes active for distorted Se₆(D₃). Our DFT-computed r = 233.6 pm, ϕ = 101.4° for Se₆ are in agreement with other DFT results: r = 234 pm, ϕ = 101° [45] and r = 233 pm, ϕ = 99.4° [46] and rather close to r = 232 pm [47].

3.3. Se₈ and Se₁₂ Rings

There are several zeolites suitable for accommodating Se₈ rings in their cavities, namely, LTA, AFI, CaY, SrY, RbY [15,16,32,33,48,49,50,51] and some others. However, the Se₈ rings are typically accompanied by other Se species, in particular, by Se₁₂ rings in LTA and by Se chains in AFI at high Se loading densities (AFI-Se(HD)). Using polarized RS of LTA-Se single crystals, we showed that single and double Se₈ rings can be formed in the large LTA cavities with their four-fold axes oriented along the LTA four-fold axes. Simultaneously, Se₁₂ rings can be formed in other large cavities of the same LTA crystal with their three-fold axes oriented along the LTA three-fold axes. The Se₁₂ rings were clearly identified in the RS of LTA-Se [15,16,32,33], thereby correcting earlier interpretations [52,53].

Here, we present DFT-computed RS and OAS of Se₈ and Se₁₂ rings, provide additional details on the experimental RS of LTA-Se, demonstrate the OAS of LTA-Se over a wide spectral region and extract the corresponding Se₁₂ OAS. We also present AFI-Se(HD) RS and wide-spectral-range OAS dominated by Se₈ rings (E//X). DFT-computed RS of the Se₈ ring with D_4d symmetry are shown in Figure 6a [see also Supplementary Materials Table S8]. They are very similar to those of S₈ (Figure 2a). Both A₁ modes bond-stretching at 279.3 cm⁻¹ and bond-bending at 110 cm⁻¹ are highly active in the XX polarization configuration while only the former is active in the ZZ configuration. All E₂ modes exhibit only XX and XY Raman activity due to the selection rules of the D_4d point group. Figure 6b demonstrates calculated RS of LTA-Se with Se₈ in three possible orientations with their four-fold axes along the LTA four-fold axes in accordance with our previous observations [15,16,32]. Importantly, the nearly purely XX-active 110 cm⁻¹ A₁ bond-bending mode appears to be strongly suppressed in the ab polarization configuration.

Figure 6. Raman spectra: (a) DFT calculation for Se₈; (b) calculation for Se₈ in LTA with the inset showing possible ring orientations in LTA; (c) DFT calculation for Se₁₂; (d) calculation for Se₁₂ in LTA with the inset showing possible ring orientations in LTA. Optical absorption spectra: (e) DFT calculation for Se₈; (f) DFT calculation for Se₁₂. The axes X, Y, Z correspond to Se₈ and Se₁₂, while the axes a, b, c correspond to the zeolite.

DFT-computed RS of the Se₁₂ ring with D_3d symmetry are shown in Figure 6c [see also Supplementary Materials Table S9]. Similar to the Se₈ ring, the symmetric bond-stretching mode (272.7 cm⁻¹ A_1g in this case) is active in both XX and ZZ polarization configurations. In contrast to Se₈, Se₁₂ displays two symmetric bond-bending modes: the 52.9 cm⁻¹ mode is XX-active while the 147.8 cm⁻¹ mode is ZZ-active. Figure 6d demonstrates calculated RS of LTA-Se with Se₁₂ in four possible orientations, with their three-fold axes along the LTA three-fold axes. The XX-active 52.9 cm⁻¹ A_1g bond-bending mode is suppressed in the cd polarization configuration. The computed optical energy gap for the dipole-allowed electron transitions of Se₈ ring E_G(Se₈) ~3.67 eV [(Figure 6e), see also Supplementary Materials Table S10] coincides with that for the dipole-allowed electron transitions of Se₆ [Figure 5a]. In contrast, the computed E_G(Se₁₂)~3.25 eV is noticeably reduced [(Figure 6f), see also Supplementary Materials Table S11].

Experimental RS of LTA-Se single crystals with the maximum possible Se loading density are shown in Figure 7a–d. The polarization configurations aa, ab, cc and cd are the same as those for LTA-S RS [Figure 2b]. Importantly, the RS of LTA-Se varies with the excitation wavelength. Due to the smaller energy gap of Se₁₂ compared to Se₈, the Se₁₂ Raman bands are resonantly enhanced at λ = 514.5 nm. Therefore, both Se₈ and Se₁₂ roughly equally contribute to the LTA-Se RS at λ = 785 nm (Figure 7a–d, black curves) well below the energy gap while resonantly enhanced Se₁₂ bands dominate at λ = 514.5 nm (Figure 7a–d, red curves). Indeed, the experimental LTA-Se red-curve bands at ~56 cm⁻¹, ~88–89 cm⁻¹, ~125 cm⁻¹, ~144 cm⁻¹ and ~258 cm⁻¹ can be assigned to the DFT-computed vibrational modes of Se₁₂ at 52.9 cm⁻¹ (A_1g), 89.2 cm⁻¹ (E_g), 122.2 cm⁻¹ (E_g), 147 cm⁻¹ (A_1g) and 272.7 cm⁻¹ (A_1g), respectively. The symmetric XX-active A_1g bond-bending mode band at ~56 cm⁻¹ is nearly completely suppressed in the cd- polarization configuration as expected for Se₁₂ rings oriented by their three-fold axes along the LTA three-fold axes.

Figure 7. Experimental Raman spectra of LTA-Se(8) in aa- (a), ab- (b), cc- (c) and cd- (d) configurations taken with the 785 nm (black) and 514.5 nm (red) excitation wavelengths; (e) Raman spectra of AFI-Se(HD) in cc- (black) and aa- (red) configurations excited with the 633 nm wavelength; (f) Experimental optical absorption spectra of LTA-Se(1)(black), LTA-Se(8)(red), AFI-Se(HD) E⊥c (green) and the absorption spectrum of Se₁₂ ring (blue) extracted from the spectra of LTA-Se(1) and LTA-Se(8). The axes X, Y, Z correspond to Se₈ and Se₁₂, while the axes a, b, c correspond to zeolites.

Se₈ experimental Raman bands are observed at ~78–79 cm⁻¹, ~113 cm⁻¹, ~121 cm⁻¹ and ~268 cm⁻¹ in the LTA-Se RS excited with a 785 nm wavelength [Figure 7a–d, black curves]. They are analogous to the DFT-computed ones at 74.1 cm⁻¹ (E₂), 110 cm⁻¹ (A₁), 124 cm⁻¹ (E₃) and 279.3 cm⁻¹ (A₁). The suppression of the XX-active A₁ bond-bending mode band at ~113 cm⁻¹ in the ab- polarization configuration is a clear indication of the Se₈ ring orientation with its four-fold axis along the LTA four-fold axis similar to the S₈ ring. Se₈ bands are also observed in the RS of AFI-Se(HD) (Figure 7e), which refers to AFI-Se with a high Se loading density. The bands at ~42 cm⁻¹, ~75 cm⁻¹, ~114 cm⁻¹ and ~269 cm⁻¹ are similar to the DFT-computed bands of Se₈ at 36.4 cm⁻¹ (E₂), 74.1 cm⁻¹ (E₂), 110 cm⁻¹ (A₁) and 279.3 cm⁻¹ (A₁). High activity of the XX-active modes in the aa-polarization configuration and their low-activity in the cc-configuration suggest the orientation of the four-fold axis of Se₈ along the c-axis of AFI.

Figure 7f shows the experimental OAS of LTA-Se and AFI-Se(HD). LTA-Se(1) and LTA-Se(8) correspond to Se loading densities of ~one Se atom and eight Se atoms per LTA large cavity, respectively. As we showed earlier [15], LTA-Se(8) displays a much higher Se₁₂/Se₈ concentration ratio than LTA-Se(1). Therefore, Se₁₂ OAS can be extracted using the procedure described in Ref. [15]. Here, we extend this analysis to a wider spectral range up to ~5.15 eV. DFT predicts relatively strong absorption for E//X and weaker absorption for E//Z for both Se₈ and Se₁₂ (Figure 6e,f).

Theoretical bands of Se₈ at 3.67–3.88 eV and 4.82 eV can be associated with the experimental bands of LTA-Se(1) at ~3.85 eV and ~4.85 eV (black) and with those of AFI-Se(HD) at ~3.75 eV and ~4.75 eV (green). Theoretical bands of Se₁₂ at 3.25 eV, 3.87 eV, 4.46 eV and 5.09 eV can be associated with the corresponding experimental bands at 3.0–3.3 eV, ~3.7 eV, ~4.5 eV and ~5.1 eV (blue). The doublet at 3.0–3.3 eV can result from the splitting of the 3.25 eV E_u-symmetry transition.

To summarize this section, Se₈ and Se₁₂ rings form in the LTA large cavities. The Se₈ rings are oriented with their four-fold axes along the LTA four-fold axes. The Se₁₂ rings are oriented with their three-fold axes along the LTA three-fold axes. Experimental Raman frequencies and intensities agree well with DFT-computed values for bond-bending modes of both Se₈ and Se₁₂ rings. DFT overestimates bond-stretching mode frequencies are due to neglecting anharmonic effects. Applying harmonic scaling factors [36] improves the agreement, yielding 268 cm⁻¹ for the Se₈ A₁ mode in line with experiment and 261.5 cm⁻¹ for the Se₁₂ A_1g mode close to experimental 258 cm⁻¹. Experimental OAS of Se₈ and Se₁₂ are in reasonable agreement with the DFT-computed spectra, and the energy gap of Se₁₂ is smaller than that of Se₈. Our DFT-computed structural parameters of Se₈ r = 233.6 pm, ϕ = 101.4° are close to r = 233 pm, ϕ = 100° [46] but differ from r = 236 pm, ϕ = 108.65° [54]. Our parameters of Se₁₂ r = 232.9 pm, ϕ = 105.5; 106.1° differ from the reported DFT results r = 236 pm, ϕ = 107.17–108.74° [54] and r = 237.7 pm [55]. For both Se₈ and Se₁₂ r = 231 pm was reported in Ref. [47].

3.4. Te₈ and Te₆ Rings

In contrast to sulfur and selenium, which form rather stable ring molecules, tellurium rings are very exotic clusters requiring specific conditions for their stabilization. Bulk crystalline Te and amorphous Te consist of chains. However, as we recently showed, space restriction in the LTA cavities makes the formation of Te₈ rings realistic. LTA-Te was found to be an example of a uniform regular array of Te₈ rings [56]. Te₈ rings were also found in AFI-Te with a high Te loading density [14]. Te₆ rings exhibited their signatures in the RS of MOR-Te [14,34]. In both cases, Te rings coexist with Te chains in the zeolite channels.

DFT-computed RS of Te₆ and Te₈ rings are shown in Figure 8a,b [see also Supplementary Materials Tables S12 and S13]. They are rather similar to those of S₆/Se₆ and S₈/Se₈, respectively. Symmetric bond-bending modes at 80 cm⁻¹ (Te₆ A_1g) and 65.4 cm⁻¹ (Te₈ A₁) show high Raman activity in the XX polarization configuration and low activity in the ZZ configuration. In contrast, symmetric bond-stretching modes at 192.7 cm⁻¹ (Te₆ A_1g) and 186.9 cm⁻¹ (Te₈ A₁) show comparable Raman activities in the XX and ZZ configurations. DFT-computed OAS of Te₆ and Te₈ [(Figure 8c,d), see also Supplementary Materials Tables S14 and S15] show smaller optical energy gaps compared to S₆/Se₆ and S₈/Se₈. Rather strong absorption bands are observed in the violet spectral range of Te₆ and Te₈ at energies around 3 eV. The E//X absorption dominates over the E//Z absorption for both rings.

Figure 8. DFT-computed RS of Te₆ (a) and Te₈ (b); DFT-computed OAS of Te₆ (c) and Te₈ (d).

Theoretical RS of Te₈ in LTA for the aa, cc, ab and cd polarization configurations were obtained by summing of the Raman responses of three Te₈ rings in their three possible orientations in the LTA crystal (Figure 9a). They are qualitatively similar to the theoretical RS of S₈ in LTA (Figure 2c) and Se₈ in LTA (Figure 6b). Corresponding experimental polarization dependencies of the LTA-Te bands in the Te₈ bond-bending mode region (Figure 9b) appear to be in good agreement with the theoretical ones (Figure 9a). The experimental frequency of 64 cm⁻¹ is very close to the calculated frequency 65.4 cm⁻¹ of the Te₈ A₁ bond-bending mode. The experimental 64 cm⁻¹ band is rather strong in the aa and cc polarization configurations and it is still not weak in the cd configuration while the band completely disappears in the ab configuration. This is a consequence of the two-dimensional character of the Raman tensor of this mode [Supplementary Materials Table S13] with only two strong diagonal tensor components. In contrast, the Raman tensor of the Te₈ A₁ bond-stretching mode is rather three-dimensional [Supplementary Materials Table S13]. The observed polarization dependence of the Te₈ A₁ bond-bending mode intensity is a clear indication of the orientation of the Te₈ fourfold axis along the fourfold axis of LTA.

Figure 9. Theoretical RS of Te₈ in LTA for different polarization configurations (a); experimental RS of LTA-Te at T ~77 K and λ = 633 nm (b); experimental RS of AFI-Te with high Te loading density for aa-configuration at T ~300 K and λ = 785 nm (c); experimental OAS of LTA-Te with ~three Te atoms per cavity (d).

The calculated Te₈ E₂ bond-bending mode frequency of 43.8 cm⁻¹ is in good agreement with the observed 46–50 cm⁻¹ band frequencies of LTA-Te. The splitting of the degenerate E₂ mode indicates a structural distortion of Te₈ in LTA and, therefore a reduced symmetry compared to the initial D_4d symmetry of the ring. Interestingly, the splitting of the Te₈ E₂ mode by 8.3% in LTA is very strong, in contrast to the weaker splitting by ~1.3% for the corresponding E₂ mode at 153–155 cm⁻¹ of S₈ and 78–79 cm⁻¹ of Se₈.

Bond-stretching-mode bands of Te₈ are rather broad and overlap with each other. For band sharpening, we took the RS measurement of LTA-Te at a temperature T ~77 K [Figure 9b]. Assuming structural distortion in Te₈, we can conclude that the Raman bands in the Te₈ bond-stretching-mode region at 162–163 cm⁻¹ and 171–173 cm⁻¹ likely originate from the E₃ mode and the formerly inactive B₁ mode, respectively, while the 182–183 cm⁻¹ and 186 cm⁻¹ bands correspond to the A₁ and E₂ modes of Te₈. The originally inactive E₁ bond-stretching mode may also contribute to the observed Raman bands.

Interestingly, in contrast to S₈ and Se₈, the experimental symmetric bond-stretching mode frequency of Te₈ (182–183 cm⁻¹) lies between the unscaled computed frequency of 186.7 cm⁻¹ and the scaled frequency of 179 cm⁻¹. This result may reflect the more accurate DFT prediction of bond lengths in case of Te₈. Moreover, effective core potentials (ECPs) are used to describe the inner shells of Te, which alters the basis set incompleteness and may reduce the need for frequency scaling.

Another example of Te₈ formation in zeolites is AFI-Te. As shown in Ref. [14], Te₈ bands can be observed in the AFI-Te RS recorded in the aa polarization configuration. We show such a spectrum in greater detail in Figure 9c. The dominant band at ~184 cm⁻¹ is attributed to the A₁ bond-stretching mode of Te₈. The bands at ~64 cm⁻¹ and ~80 cm⁻¹ are assigned to the A₁ and E₃ bond-bending modes, respectively. The doublet at 41–47 cm⁻¹ is attributed to the E₂ bond-bending mode.

Importantly, the experimental LTA-Te(3) OAS (Figure 9d) shows nearly perfect agreement with the computed OAS of Te₈ (Figure 8d). Similarly to the bond-stretching mode frequencies, this result may reflect the more accurate DFT prediction of bond lengths in Te₈.

As shown above, MOR channels accommodate Se helical chains and Se₆ rings. The rings are oriented with the three-fold axis along the b-axis of MOR. The actual symmetry of the Se₆ ring in the MOR channel is lower than the D_3d symmetry suggested by theory. Splitting of the E_g bond-bending mode as well as the mixture of the A_1g and A_2u bond-bending modes of Se₆ in MOR confirm its structural distortion. Figure 10a shows MOR-Te RS, which has many similarities to the MOR-Se RS. Indeed, a strong cc-active band at ~168 cm⁻¹ undoubtedly corresponds to Te helical chains. The rest of the MOR-Te bands can be attributed to Te₆. The 63 cm⁻¹ and 68 cm⁻¹ bands most likely originate from the E_g bond-bending mode of Te₆ similar to the 102–108 cm⁻¹ bands of Se₆ in the MOR-Se RS. The 83–89 cm⁻¹ doublet in the MOR-Te RS is similar to the 134–141 cm⁻¹ one in the MOR-Se RS. It can be assigned to the mixed A_1g and A_2u bond-bending modes of Te₆. The bond-bending modes of Te₆ are active in the aa- and cc- polarization configurations, while they are inactive in the bb-configuration, which proves the orientation of the rings with their three-fold axes along the b-axis of MOR. The DFT-computed frequencies of the Te₆ bond-bending modes 58.7 cm⁻¹ (E_g), 80 cm⁻¹ (A_1g) and 90.9 cm⁻¹ (A_2u) are in good agreement with the experimental values.

Figure 10. Experimental RS of MOR-Te (a) and CHA-Te (b) for different polarization configurations; experimental OAS of MOR-Te for E//b (c) and CHA-Te for E//a (black) and E//c (red) (d).

The A_1g bond-stretching mode band of Te₆ at ~196 cm⁻¹ in the MOR-Te RS is similar to the analogous band of Se₆ at ~274 cm⁻¹ in the MOR-Se RS. It is active in the aa-, bb- and cc- polarization configurations. The DFT-computed unscaled frequency 192.7 cm⁻¹ of this mode nearly coincides with the experimental value. Another bond-stretching mode band of Te₆ at ~164 cm⁻¹ is observed in the aa-spectrum of MOR-Te. The band is also active in the cc-configuration, but it is overshadowed by the strong Te chain band at ~168 cm⁻¹. The asymmetry of the ~168 cm⁻¹ band, with a low-frequency shoulder, supports this assignment. The 164 cm⁻¹ band can be attributed to the E_g or A_1u modes of Te₆. The DFT-computed frequencies of the corresponding modes are 186.7 cm⁻¹ and 168.5 cm⁻¹. The experimental polarization dependence of the 164 cm⁻¹ band intensity is in good agreement with the theoretical E_g mode, while its frequency better matches the theoretical A_1u mode.

One may assume that Te₆ rings can be formed in CHA cavities similar to Se₆ rings. Indeed, we observe several bands in the RS aa spectrum of CHA-Te (Figure 10b), which can be attributed to Te₆. The 83–91 cm⁻¹ doublet can be assigned to the mixed A_1g and A_2u bond-bending modes of Te₆. The strong 203 cm⁻¹ band most likely originates from the A_1g bond-stretching mode, while the 164 cm⁻¹ and 180 cm⁻¹ bands can be assigned to the A_1u and E_g bond-stretching modes, respectively. The high frequency of the 203 cm⁻¹ band is associated with significant compression of the ring in the CHA cavity. In contrast to the Se₆ ring in the CHA cavity, the Te₆ ring clearly demonstrates its structural distortion with its symmetry reduction. The bond-bending-mode mixing reveals this. The corresponding 83–91 cm⁻¹ doublet is inactive in the cc spectrum, indicating that the ring is oriented with its three-fold axis along the c-axis of CHA. The A_1g bond-stretching-mode band at ~203 cm⁻¹ weakens in the cc spectrum compared to the aa spectrum but remains observable. This observation is also compatible with the Te₆ ring orientation with its major axis along the c-axis of CHA.

Two distinct bands at ~45 cm⁻¹ and ~63 cm⁻¹ are observed in the cc and ca spectra of CHA-Te. Their frequencies suggest that the bands can be assigned to the E_u and E_g bond-bending modes of Te₆, respectively. However, their polarization dependencies are challenging to interpret. Theoretically, the E_g mode should be active in the aa spectrum and inactive in the cc spectrum. We assume that the structural distortion is significant. Therefore, the selection rules can be strongly affected. However, we can also consider another possibility. The CHA cavity is able to accommodate a Te₈ ring with its XY plane in the ac plane of the zeolite. In this case, the ~45 cm⁻¹ and ~63 cm⁻¹ bands may originate from the E₂ and A₁ bond-bending modes of Te₈.

OAS of MOR-Te E//b (Figure 10c) and CHA-Te (Figure 10d) display features of Te₆. The MOR-Te OAS shows three bands at ~2.7 eV, ~3.6 eV and ~4.9 eV. Theoretical calculations suggest E//Z allowed transitions at 2.91 eV, 3.2 eV, 3.54 eV and 5.14 eV. The 2.91 eV and 5.14 eV bands are clearly seen in the DFT-computed E//Z OAS of Te₆ (Figure 8c). We attribute the experimental ~2.7 eV and ~4.9 eV bands to the 2.91 eV and 5.14 eV transitions of Te₆, respectively. The 3.2 eV and 3.54 eV E//Z allowed electron transitions have lower oscillator strengths and are not seen in the theoretical spectrum. However, they may be enhanced due to structural distortions of Te₆. Therefore, we tentatively assign the observed ~3.6 eV band to the enhanced 3.54 eV transition. On the other hand, the E//X-allowed transitions at 3.72 eV can also contribute to the observed ~3.6 eV band of MOR-Te because the selection rules of Te₆ can be strongly disturbed.

CHA-Te OAS display features at ~2.45 eV, ~2.9 eV and 3.5 eV, which can be attributed to Te₆. Indeed, the ~2.45 eV band energy is in good agreement with the lowest-energy forbidden transitions of Te₆ at 2.56 eV (E_g) and 2.62 eV (A_2g). These transitions can be activated by antisymmetric ring vibrations, similar to those of Se₆ considered in the previous sections. Additionally, as mentioned above, the Te₆ ring in CHA-Te is strongly compressed, which may lead to noticeable shifts of the low-energy electron transitions. Both allowed 2.96 eV E//X and 2.91 eV E//Z transitions of Te₆ can contribute to the experimentally observed feature of CHA-Te at ~2.9 eV. The third band at ~3.5 eV, clearly observed in the E//a spectrum of CHA-Te, can be associated with the allowed 3.72 eV E//X transition.

Interestingly, the E//c absorption of CHA-Te becomes stronger than the E//a absorption at energies above 3.7 eV. One possible explanation is a strong in-plane compression of Te₆, which may enhance the E//Z absorption of the molecule. Indeed, a very much anisotropic 2D-like Te₆ ring can convert into more or less 3D-like cluster due to the compression. Another possibility is a contribution from Te₈ absorption. As mentioned above, if Te₈ exists in CHA-Te, the molecule is most likely oriented in the ac plane of CHA. Therefore, the E//X absorption of Te₈, which dominates over its E//Z absorption, likely contributes to the E//c absorption of CHA-Te.

To summarize this section, Te₈ rings are formed in the LTA large cavities. The Te₈ rings are oriented such that their four-fold axes align with the LTA four-fold axes. Experimental Raman frequencies and intensities are found to be in good agreement with DFT-computed ones for both bond-bending and bond-stretching modes of Te₈ rings. The observed splitting of the Te₈ bond-bending modes suggests the reduction of the ring D_4d symmetry in the LTA cavity. The bond-stretching modes exhibit mixing due to the reduced symmetry of the rings and the essential anharmonicity of their vibrations. The DFT-computed OAS of Te₈ shows remarkably good agreement with the experimental OAS of LTA-Te. Te₈ rings are also formed in the AFI channels, with their four-fold axes oriented along the channel. Te₆ rings are formed in MOR channels and CHA cavities. Their experimental RS and OAS show good agreement with DFT-computed ones. CHA-Te RS and OAS suggest the existence of some amount of Te₈ rings in CHA cavities. The structural parameters obtained from our DFT calculations: Te₆ r = 272 pm, ϕ = 100.5° and those of Te₈ r = 271 pm, ϕ = 105.8°. These values differ from previously reported DFT results: Te₆ r = 275 pm, ϕ = 101° and Te₈ r = 274–275 pm, ϕ = 106.3° [54]; Te₈ r = 274–275 pm, ϕ = 106.3° [57].

3.5. Interaction of the Chalcogen Rings with Light and Photostructural Effects

All chalcogen ring molecules considered above display strong absorption bands in the UV. Therefore, one can expect photo-induced effects when the molecules are irradiated with UV light. A number of studies have reported the UV-light-induced conversion of S₈ rings to sulfur chains in liquid sulfur [58,59,60]. Pulsed laser light with a wavelength of 355 nm was used in the experiment [58] and produced photo-induced polymerization of liquid sulfur. An ab initio molecular dynamics simulation suggested rapid ring opening due to a photo-induced electronic transition [59]. A more comprehensive study using a combination of time-dependent DFT and the similarity-transformed equation-of-motion coupled cluster (STEOM-CCSD) method [60] showed the importance of triplet states in the photo-induced S₈ bond breaking.

Figure 11 demonstrates photo-induced effects in the RS of several our samples, which were recorded with continuous laser excitation at a wavelength of 364 nm. Figure 11a shows the bb-spectrum of MOR-S. In addition to the S₈ and S₆ bands analogous to those observed in the bb-spectrum excited with λ = 514.5 nm [Figure 2d], one can see the bands at ~582 cm⁻¹ and ~1164 cm⁻¹. We assign the ~582 cm⁻¹ band to the S₂⁻ fundamental while the ~1164 cm⁻¹ band to its overtone. For reference, see, for example the work in [61], where S₂⁻ fundamentals in ultramarine were observed at 586–590 cm⁻¹ at room temperature. The S₂⁻ bands appear in the MOR-S RS as a result of the S₈ and S₆ ring breaking under 364 nm light irradiation.

Figure 11. Experimental RS obtained with the 364 nm wavelength excitation of MOR-S (a), LTA-S (b), AFI-Se(HD) (c) and LTA-Se (d).

Similar bands are observed in the LTA-S RS at ~583 cm⁻¹ and ~1165 cm⁻¹ [Figure 11b]. Additionally, a broad S₄²⁻ band at ~446 cm⁻¹, similar to the 454 cm⁻¹ band of S₄²⁻ [62], is observed in the LTA-S RS excited with 364 nm light. The S₈ ring-breaking mechanism is likely the same as that proposed for liquid sulfur polymerization. The difference in the final result is associated with spatial restriction and the zeolite environment, which provides extra electrons. Therefore, S₂⁻ and S₄²⁻ anions are formed in the zeolites.

We should note that the S₈ absorption at the 364 nm wavelength in both MOR-S and LTA-S is rather weak since the corresponding photon energy of 3.41 eV is well below the first allowed absorption band of S₈ or S₆ (Figure 3). The 364 nm absorption in fact corresponds to the absorption tails of S rings that arise from forbidden electronic transitions, in particular triplet excitations. In contrast, the Se₈ and Se₁₂ rings show absorption at this wavelength due to relatively strong allowed electronic transitions. These rings also display fragmentation effects under 364 nm light irradiation. The neutral Se₂ band at ~382 cm⁻¹ and its overtone at ~762 cm⁻¹ are observed in the AFI-Se(HD) aa spectrum excited with 364 nm light (Figure 11c). Similar bands at lower frequencies ~377 cm⁻¹ and ~750 cm⁻¹ are present in the RS of LTA-Se [Figure 11d]. Both ~382 cm⁻¹ and ~377 cm⁻¹ frequencies are close to the ~386 cm⁻¹ fundamental frequency of neutral Se₂ [63]. One can expect that Se₂⁻ anions rather than neutral Se₂ molecules, to be stabilized in the zeolites. However, with this assumption, we should expect the same effect as was observed in sodalite with selenium (SOD-Se) under 364 nm irradiation [63], where Se₂⁻ anions with the absorption band at ~3.4 eV [64] were photo-ionized due to perfect resonance with 364 nm light. Thus, neutral Se₂ molecules were formed. In fact, LTA-Se with 17 Se atoms per simplified unit cell case [16] is very similar to the SOD-Se case since both samples initially contain Se₂⁻ anions.

Let us consider photoinduced effects on chalcogen rings under visible light irradiation. Importantly, Se₆ interacts strongly with light at photon energies much lower than its formal electronic energy gap of ~3.2 eV since the absorption bands are rather broad and triplet excitations [Supplementary Materials Table S7a] may contribute.

Figure 12a clearly demonstrates a laser-induced heating effect on Se₆ in CHA-Se at the laser excitation wavelength of 514.5 nm, corresponding to a photon energy of ~2.41 eV. Indeed, the A_1g bond-stretching mode frequency decreases from ~272.5 cm⁻¹ to ~268.5 cm⁻¹ as the excitation laser power (P) increases from ~0.25 mW to ~1.5 mW. The heating effect causes even stronger frequency decrease of the E_g (or maybe A_1u) bond-stretching mode from ~219.5 cm⁻¹ to ~211.5 cm⁻¹ over the same increase in laser power (Figure 12b). The laser-induced heating depends on the light polarization. The heating is stronger for the E//X than for E//Z polarization (Figure 12a, black and violet curves).

Figure 12. (a) RS of CHA-Se at λ = 514.5 nm at different excitation powers (P) for aa-configuration (black, red, blue and green curves) and for cc-configuration at P ~1.5 mW (violet curve); (b) A_1g bond-stretching-mode Raman band position dependency on P; (c) CHA-Se RS at T ~77 K (black curve) and at T ~300 K at P ~0.5 mW (red curve); (d) RS of AFI-Se(LD) in the aa-configuration at λ = 633 nm at T ~77 K with P ~1 mW (black curve), P ~0.25 mW (red curve) and their difference (blue curve), dashed line showing corresponding T ~300 K spectrum for reference.

Surprisingly, the bond-bending mode frequencies slightly increase as the laser power increases up to ~0.5 mW, then slowly decrease with a further increase in power (Figure 12b). The effect may be associated with the Se₆ ring confinement in the CHA cavity, which causes bond angle contraction and an increase of the corresponding frequencies with a slight heating, when the bond lengths become larger. A similar effect is observed upon decreasing the temperature to T ~77 K [Figure 12c]. The bond-bending mode frequencies of ~103 cm⁻¹ and ~136 cm⁻¹ at T ~77 K are lower than those of ~105 cm⁻¹ and ~137 cm⁻¹ at an ambient temperature of ~300 K. (In this case, the ring temperature is slightly higher due to laser-induced heating). We also observe a non-thermal photoinduced effect in the low-temperature RS of CHA-Se, namely, the band at ~309 cm⁻¹ and its overtone at ~617 cm⁻¹ appear in the CHA-Se spectrum at T ~77 K. Most likely, the bands belong to Se₂⁻ anions. This may be associated with photoinduced fragmentation of Se₆ to three Se₂ molecules trapped in chabazite in the form of Se₂⁻ anions.

Figure 12d demonstrates a photoinduced effect with an even lower photon energy of ~1.96 eV corresponding to a 633 nm laser line. AFI-Se(LD) Raman aa-spectra were recorded at T ~77 K with excitation laser powers of ~0.25 mW (red curve) and ~1 mW (black curve). Both spectra display additional bands compared to the room-temperature spectrum, which contains nearly exclusively Se₆ bands [dashed curve, see also Figure 4c]. The additional bands are more pronounced in the spectrum recorded with the ~1 mW laser power. The differential spectrum between the normalized ~1 mW and ~0.25 mW spectra is shown as a blue curve in Figure 12d. Three characteristic bands of the Se₈ ring at frequencies of ~76, ~114 and ~269 cm⁻¹ are clearly recognized. Thus, in the relatively large space of the AFI channels, more stable Se₈ rings are formed at the expense of the less stable Se₆ rings due to photoinduced fragmentation of Se₆. We should note that prolonged illumination of AFI-Se(LD) with ~0.25 mW 633 nm light causes the same effect as the increase in the laser power.

Interestingly, we do not observe any photostructural effects for Se₈ and Se₁₂ in LTA-Se at the low-power excitations P ≤ 1 mW with the laser wavelengths of 514.5 nm or 633 nm, either at T ~300 K or T ~77 K. (We do not consider here the thermal destruction of Se₁₂ due to photoinduced heating at higher 514.5 nm laser powers [33]). One reason for this is the higher absorption of Se₆ compared to Se₈ and Se₁₂ within the 1.96–2.41 eV photon energy range. This is confirmed by the DFT-computed energy gaps of Se₆, Se₈ and Se₁₂ [Figure 13a] taking into account allowed and forbidden singlet excitations [Supplementary Materials Tables S7, S10 and S11] as well as triplet excitations [Supplementary Materials Tables S7a, S10a and S11a]. We observe that the Se₆ energy gap is smaller than those of Se₈ and Se₁₂. The computed energy gap of ~2.67 eV for Se₆ triplet excitations is rather close to the 1.96–2.41 eV photon energy range, where the photostructural effects for Se₆ are observed. Another contributing factor is the low stability of Se₆ in the excited state.

Figure 13. (a) DFT-computed energy gaps of Se rings vs. the number of Se atoms in the ring for triplet excitations (black squares), for all singlet excitations (red circles) and only allowed singlet excitations (blue triangles); (b) schematical representation of potential energy surfaces of the ground state (GS, S₀) and the lowest singlet excited state (ES, S₁) of the Se₆ ring from DFT calculations. The approximate conical intersection (CI, S₀/S₁) lies about 1.73 eV above the S₀ minimum. The horizontal axis denotes schematically the configuration coordinate for CI–S₀ relaxation. The S₀ minimum energy structure (D_3d) and the approximate CI (C_s) are annotated with their bond lengths.

Let us consider possible structural effects for Se₆ in its excited state. While our methods do not allow the calculation of relativistic effects required for accurate simulation of the intensities of triplet excitations, such as the ~2.67 eV excitation, we consider the lowest forbidden singlet transition at ~3.13 eV (Figure 13b), which can be activated via electron-vibration coupling. The important point is that the excited states of the Se₆(D_3d) are energetically very close to those of some other, less-stable forms of Se₆.

Figure 13b demonstrates a conical intersection (CI) between the potential energy surfaces of the ground state (GS, S₀) and the lowest singlet excited state (ES, S₁) of the Se₆ molecule. The DFT calculations were performed using the PBE0 functional [20] and the def2-TZVP basis set [22]. The approximate conical intersection (CI, S₀/S₁) was obtained by minimizing the S₀–S₁ energy gap. The computed energy differences do not include zero-point vibrational corrections. Se₆ with the C_s structure, corresponding to CI, is shown in Figure 13b inset.

The Se₆(C_s) structure is unstable. It can disintegrate, for example, into Se₄ + Se₂. The appearance of Se₂⁻ in CHA-Se after 514.5 nm light irradiation and an increase in amount of Se₈ in AFI-Se(LD) due to 633 nm light exposure confirm this. Importantly, we observe these effects at T ~77 K and do not observe them at T ~300 K. Most likely, relaxation of the photo-excited Se₆(D_3d) to its ground state at T ~300 K occurs via vibrations without conversion to unstable forms of Se₆. However, at T ~77 K, vibrational relaxation is not sufficiently effective. Conversion of Se₆(D_3d) into unstable forms, such as Se₆(C_s), followed by disintegration, becomes much more likely. This is why we observe formation of Se₂⁻ in irradiated CHA-Se and increase of amount of Se₈ in irradiated AFI-Se(LD) at T ~77 K.

To summarize this section, we observe a rather strong interaction of the zeolite-confined chalcogen rings with light. The interaction is very strong in case of the UV light exposure. Under the 364 nm wavelength light irradiation, S₈ and Se₈/Se₁₂ rings disintegrate producing mainly diatomic molecules, S₄²⁻ also being identified in case of LTA-S. Under normal conditions, at room temperature and with low-power visible light excitation, all chalcogen rings exhibit ordinary heating depending on their absorbance. A peculiarity of heating a molecule in the restricted space of a zeolite cavity is that the molecule bond lengths increase while bond angles decrease. Correspondingly, the molecule bond-stretching mode frequencies decrease while the bond-bending mode frequencies increase. Se₆ rings in CHA-Se clearly demonstrate this. At T ~77 K with no heating effect, the Se₆ rings disintegrate under rather low photon energy (~1.96 eV and ~2.41 eV) light irradiation. This is associated with (1) their non-zero absorption of Se₆ in this spectral range due to their triplet excitations, and (2) conversion of the stable form of Se₆(D_3d) in the excited state to unstable ones. An example of conical intersection producing Se₆(C_s) is also presented.

4. Conclusions

S, Se and Te ring clusters were examined experimentally using RS and OAS as well as theoretically using DFT. Incorporation of the rings into free spaces of zeolite single crystals (LTA, MOR, AFI, CHA) allowed us to study the polarized RS and OAS of oriented rings and compare them with the corresponding spectra computed using DFT. Firstly, we determined structural parameters of the rings [Supplementary Materials Table S1], which appeared to be close to the known experimental values for S₈ (our r = 204.7 pm, ϕ = 108.4° vs. r = 204.6 pm, ϕ = 108.2° [65]), Se₆ [our r = 233.6 pm, ϕ = 101.4° vs. r = 238 pm, ϕ = 101.1° [44] (the experimental value of 238 pm in rhombohedral crystal is slightly larger than that of individual Se₆)] and Se₈ (our r = 232.7 pm, ϕ = 106.9° vs. r = 233.4 pm, ϕ = 105.8° [66]). Regarding RS and OAS, we have found a very reasonable agreement between the experimental and theoretical spectra of S₈, Se₆, Se₈, Se₁₂, Te₆ and Te₈ rings. The agreement is nearly perfect for the bond-bending mode Raman frequencies and intensities. However, the computed bond-stretching mode frequencies of S and Se rings are overestimated compared with the experimental values because of the absence of anharmonic effects. Scaling factors [36] improve the agreement. No significant discrepancy occurs for Te rings. DFT-computed OAS of the S₈, Se₆, Se₈, Se₁₂, Te₆ and Te₈ rings generally show good agreement with experimental results. However, experimental OAS show some features with photon energies lower than those of the computed allowed singlet electron transitions. We demonstrate activation of the low-energy forbidden singlet electron transitions of Se₆ at 3.1–3.4 eV due to interaction of electrons with antisymmetric vibrational modes, the energy of the first allowed singlet transition being ~3.66 eV. Even a lower energy of ~2.67 eV is suggested by the DFT-computed triplet electron excitation of Se₆. Experimentally, no distinct Se₆ absorption band was observed; only a tail appeared in this spectral range. Photostructural effects due to the exposure of Se₆ to ~1.96 eV and ~2.41 eV light at T ~77 K are observed. Conversion of the stable form of Se₆(D_3d) in the excited state to unstable ones likely follows a complex mechanism. An example of a conical intersection producing Se₆(C_s) is considered. Importantly, at the same conditions, no such effect is observed for Se₈, which possesses a larger triplet and singlet energy gap than Se₆. Since Se₈ is a building block of a-Se [67], we can conclude that the photostructural effects in this material, induced by the 1.96–2.41 eV light, are not related to individual Se₈ rings, although rings interacting with neighboring rings or chains, and thus exhibiting a reduced energy gap, may be responsible for these effects. In contrast, individual Se₈ and S₈ rings display fragmentation due to exposure to 364 nm (3.41 eV) UV light at room temperature. This photon energy corresponds to the Se₈ singlet excitations and S₈ triplet excitations below the singlet electron transition energies. Conical intersections can be responsible for the effects.

Taking into account recent publications on intramolecular dispersion forces in large chalcogen rings [68], infrared spectra of sulfur allotropes, their fragmentation and presence in the interstellar space and atmosphere of planets [69], lone-pair-enabled polymorphism and photostructural changes in chalcogenide glasses [70], structural and optical properties of chalcogen chains and nanowires [71,72,73,74,75,76,77], etc., we consider our work as an important contribution to this rapidly developing field of science. Applications in medicine hold particular promise for novel materials like MXenes [78] and Se nanoparticles [79] due to their antibacterial properties.