Systematic Study of Solid-State Fluorescence and Molecular Packing of Methoxy-trans-Stilbene Derivatives, Exploration of Weak Intermolecular Interactions Based on Hirshfeld Surface Analysis

In recent years, fluorescent compounds that emit efficiently in the solid state have become particularly interesting, especially those that are easily prepared and inexpensive. Hence, exploring the photophysical properties of stilbene derivatives, supported by a detailed analysis of molecular packing obtained from single-crystal X-ray diffraction data, is a relevant area of research. A complete understanding of the interactions to determine the molecular packing in the crystal lattice and their effect on the material’s physicochemical properties is essential to tune various properties effectively. In the present study, we examined a series of methoxy-trans-stilbene analogs with substitution pattern-dependent fluorescence lifetimes between 0.82 and 3.46 ns and a moderate-to-high fluorescence quantum yield of 0.07–0.69. The relationships between the solid-state fluorescence properties and the structure of studied compounds based on X-ray analysis were investigated. As a result, the QSPR model was developed using PLSR (Partial Least Squares Regression). Decomposition of the Hirshfeld surfaces (calculated based on the arrangement of molecules in the crystal lattice) revealed the various types of weak intermolecular interactions that occurred in the crystal lattice. The obtained data, in combination with global reactivity descriptors calculated using HOMO and LUMO energy values, were used as explanatory variables. The developed model was characterized by good validation metrics (RMSECAL = 0.017, RMSECV = 0.029, R2CAL = 0.989, and R2CV = 0.968) and indicated that the solid-state fluorescence quantum yield of methoxy-trans-stilbene derivatives was mainly dependent on weak intermolecular C…C contacts corresponding to π-π stacking and C…O/O…C interactions. To a lesser extent and inversely proportional, the fluorescence quantum yield was affected by the interactions of the type O…H/H…O and H…H and the electrophilicity of the molecule.


Introduction
Stilbene derivatives are considered interesting compounds that transcend various fields due to their biological [1] and photophysical properties. The skeleton of stilbene consists of two phenyl rings bonded by an ethylene bridge. The presence of unsaturated bond results in two diastereoisomeric forms, E-1,2-diphenylethylene (trans-configuration) and Z-1,2-diphenylethylene (cis-configuration), but the trans-isomer is more common and exhibits a more stable disposition [2]. Additionally, their π-conjugated structure possesses high fluorescence activity; hence they are commonly used as the core structure in synthesizing many fluorescence materials related to biomedicine, fine chemistry, and material science. According to reports, such compounds' main applications are organic Table 2. Fluorescence lifetime (τ), quantum yield (Φ PL ), and rate constants of radiative (k r ) and non-radiative decay (k nr ) of compounds MTS-1-MTS-14 in the solid-state. The fluorescence lifetime (τ) is the time the fluorophore spends in the excited state before emitting a photon and returning to the ground state. For seven methoxy-transstilbene derivatives, the analysis was performed based on the one-exponential function matching method. The remaining compounds were analyzed using a two-exponential function. For these molecules, considering the fractional amplitude contribution, the average τ was calculated ( Table 2). The compounds with the lowest τ were MTS-6 and MTS-9 (0.83 ns and 0.82 ns, respectively). In addition, MTS-6 showed one of the lowest Φ PL (0.10). On the other hand, MTS-5 is a compound with the longest τ (3.46 ns) and one of the highest Φ PL (0.64). Radiative (k r ) and non-radiative (k nr ) rate constants in Table 2 were calculated based on experimentally measured quantum yields and fluorescence lifetimes using the following equations: In the next step, the studied methoxy-trans-stilbene derivatives were quantitatively compared regarding fluorescent properties obtained from measurements and calculations. The results are presented in radar charts ( Figure 1A). Due to differences in the analyzed variables' values, a transformation was performed by dividing each observation by the highest occurring value (after transformation, values of variables ranged from 0 to 1, keeping the relative standard deviations unchanged). Figure 1 shows that although the tested compounds are very similar (the same diphenyl skeleton with an ethene bridge and one type of substituent), they differ significantly in photophysical properties. A cluster analysis was performed to identify compounds with the most similar fluorescence properties. As a clustering method, Ward's minimum variance algorithm was used. The Euclidean distance was taken as the measure of distance ( Figure 1B).
In the next step, the studied methoxy-trans-stilbene derivatives were quantitatively compared regarding fluorescent properties obtained from measurements and calculations. The results are presented in radar charts ( Figure 1A). Due to differences in the analyzed variables' values, a transformation was performed by dividing each observation by the highest occurring value (after transformation, values of variables ranged from 0 to 1, keeping the relative standard deviations unchanged). Figure 1 shows that although the tested compounds are very similar (the same diphenyl skeleton with an ethene bridge and one type of substituent), they differ significantly in photophysical properties. A cluster analysis was performed to identify compounds with the most similar fluorescence properties. As a clustering method, Ward's minimum variance algorithm was used. The Euclidean distance was taken as the measure of distance ( Figure 1B). The most homogeneous group (cluster 4) comprises MTS-1, MTS-4, and MTS-7. These compounds present high ΦPL, which small values of knr can explain. Fluorescence lifetimes in this group of compounds took average values. One of the lowest ΦPL values was measured for molecules from cluster 2 (MTS-3, MTS-6, MTS-10, and MTS-13). The fluorescence lifetimes of these trans-stilbene derivatives were comparable to those from cluster 1, but the kr values were significantly lower. Cluster 1 (MTS-9, MTS-11, MTS-12, and MTS-14) consists of molecules with short τ and higher knr, compared to compounds in clusters 3 and 4. The values of kr were varied, while the ΦPL was close to the average values. Cluster 3 is made by MTS-2, MTS-5, and MTS-8, characterized by a lower ΦPL than cluster 4 (except MTS-5) but longer τ.
Despite the high structural homogeneity, the tested compounds showed surprisingly different photophysical properties. The analysis indicates that the observed differences in studied properties cannot be easily related to the number of methoxy substituents or their positions in the diphenyl skeleton. The most homogeneous group (cluster 4) comprises MTS-1, MTS-4, and MTS-7. These compounds present high Φ PL , which small values of k nr can explain. Fluorescence lifetimes in this group of compounds took average values. One of the lowest Φ PL values was measured for molecules from cluster 2 (MTS-3, MTS-6, MTS-10, and MTS-13). The fluorescence lifetimes of these trans-stilbene derivatives were comparable to those from cluster 1, but the k r values were significantly lower. Cluster 1 (MTS-9, MTS-11, MTS-12, and MTS-14) consists of molecules with short τ and higher k nr , compared to compounds in clusters 3 and 4. The values of k r were varied, while the Φ PL was close to the average values. Cluster 3 is made by MTS-2, MTS-5, and MTS-8, characterized by a lower Φ PL than cluster 4 (except MTS-5) but longer τ.
Despite the high structural homogeneity, the tested compounds showed surprisingly different photophysical properties. The analysis indicates that the observed differences in studied properties cannot be easily related to the number of methoxy substituents or their positions in the diphenyl skeleton.

X-ray Structural Studies
Available literature data [13][14][15] indicate a possible relationship between the arrangement of molecules in the crystal lattice and their photophysical properties. X-ray crystallography was performed to understand the effects of the methoxy substitution pattern on the solid-state fluorescence properties. Crystal structures of 8 out of 14 tested transstilbene derivatives were previously published [16][17][18][19][20] and were taken from the CCDC database. For the remaining six compounds (MTS-3, MTS-8, MTS-9, MTS-10, MTS-13, and MTS-14), attempts were made to obtain high-quality single crystals suitable for X-ray structural studies. Only for MTS-3, the conducted measurements did not bring the intended results. The crystal structures of five compounds have been solved and refined. Crystallographic data, and experimental and refinement details are listed in Table 3, while bond lengths, bond angles, and torsion angles are entered into Tables S2-S16 (Supplementary file). Table S17 (Supplementary file) summarizes the characteristics of the crystal lattice of compounds taken from the database and newly researched. Perspective views of molecules MTS-8, MTS-9, MTS-10, MTS-13, and MTS-14 are shown in Figure 2. The main molecule consists of two benzene rings (with different located methoxy substituents) connected by a chain of two sp 2 -carbon atoms. All molecular structures are in trans arrangement with double C7=C8 central bond (torsion angle C1-C7-C8-C9 nearly half full angle, Tables S4, S7, S10, S13 and S16, Supplementary file). The double bond between C7 and C8 for compound MTS-10 is disordered over 2 positions with site occupancy ratio of 56%:44% for the A and B parts. In the molecular structure of MTS-14, the double bond between C7 and C8 can be indicated as the center of symmetry. The observed lengths of double bonds for MTS-8, MTS-9, MTS-13, and MTS-14 (ethene bridge, C7-C8 or C7-C7a for MTS-14) are longer (1.33 Å-1.34 Å) than the theoretical length (1.32 Å). Moreover, the lengths of bonds between the ethene bridge and benzene rings (C7-C1 and C8-C9) in compounds MTS-8, MTS-9, MTS-13, and MTS-14 are shorter (1.46-1.48 Å) than the theoretical lengths (1.51Å) indicating the formation of a weak conjugated π-electron system. The presented observations are consistent with those obtained for the other studied trans-stilbene derivatives that have been previously published [16][17][18][19][20].
For those 5 molecules, whose crystal structures are described for the first time, 2 benzene rings are in different orientations with a dihedral angle between 2 planes through the rings in the range of 0.00 • (MTS-14)-24.02 • (MTS-8) (Table S18, Supplementary file). Exploration the mutual arrangement of the benzene rings in the whole group of the studied trans-stilbene derivatives, three types of disposition can be distinguished: co-planar, slightly nonplanar, and nonplanar (twisted). Symmetrical arrangement of substituents relative to the center of the molecule (MTS-7 and MTS-14) determines the parallel arrangement of planes (dihedral angle between two planes 0.00 • ). In contrast, unsymmetrical molecules with three methoxy groups substituted on adjacent carbons (MTS-6, MTS-10, MTS-11, and MTS-13) (especially in the vicinity of the ethene bridge, MTS-11) have a nonplanar crystal structure (dihedral angle between two planes: 12  The arrangement could be categorized as slipped perpendicular head to head (MTS-1, Figure 3A), non-slipped perpendicular head to head (MTS-2 and MTS-8, Figure 3B), slipped perpendicular head to tail (MTS-4 and MTS-5, Figure 3C), slipped parallel head to head (MTS-7, MTS-9 and MTS-12, Figure 3D), slipped parallel head to tail (MTS-13, Figure 3E), herringbone head to tail (MTS-6, Figure 3F), herringbone head to head (MTS-10, Figure 3G), and herringbone head to head with inter-twisted molecule (MTS-11, The arrangement could be categorized as slipped perpendicular head to head (MTS-1, Figure 3A), non-slipped perpendicular head to head (MTS-2 and MTS-8, Figure 3B), slipped perpendicular head to tail (MTS-4 and MTS-5, Figure 3C), slipped parallel head to head (MTS-7, MTS-9 and MTS-12, Figure 3D), slipped parallel head to tail (MTS-13, Figure 3E), herringbone head to tail (MTS-6, Figure 3F), herringbone head to head (MTS-10, Figure 3G), and herringbone head to head with inter-twisted molecule (MTS-11, Figure 3H). In turn, a completely different arrangement of molecules is present for the crystal structure of MTS-14 (Figure 4), which could be described as thread and warp in the fabric. Herringbone arrangement was observed for compounds with the highest dihedral angle between planes formed by the aromatic rings. Figure 3H). In turn, a completely different arrangement of molecules is present for the crystal structure of MTS-14 (Figure 4), which could be described as thread and warp in the fabric. Herringbone arrangement was observed for compounds with the highest dihedral angle between planes formed by the aromatic rings.     Figure 3H). In turn, a completely different arrangement of molecules is present for the crystal structure of MTS-14 ( Figure 4), which could be described as thread and warp in the fabric. Herringbone arrangement was observed for compounds with the highest dihedral angle between planes formed by the aromatic rings.   Supramolecular architecture of studied compounds can be categorized into five types ( Figure 5). It can be seen that the methoxy substituent in out-of-plane arrangement favors the herringbone system. Supramolecular architecture of studied compounds can be categorized into five types ( Figure 5). It can be seen that the methoxy substituent in out-of-plane arrangement favors the herringbone system.

Supramolecular architecture
Parallel beta-sheets   Table 4 summarizes intramolecular (Intra) and intermolecular hydrogen bonds occurring in the crystal lattice of stilbene derivatives. Such interactions were not found for compounds MTS-2, MTS-5, MTS-6, and MTS-13. Among the tested compounds, the only possible type of hydrogen bonds is C-H···O. The arrangement of -OCH 3 substituents in adjacent positions or positions 2 or 6 of the phenyl ring (closest to the ethene bridge) favors the formation of intramolecular hydrogen bonds, which occur in as many as 8 out of 13 compounds tested.  The molecules MTS-6, MTS-7, MTS-8, MTS-11, and MTS-14 in their supramolecular structure are arranged in sheets lying one above the other. Consequently, staking interactions (π. . .π) occur between molecular layers, which correspond with C. . .C weak intermolecular interactions in the crystal structure of these compounds ( Figure 6) [21]. This will be further discussed in Section 2.2.2. Hirshfeld surface analysis.

Hirshfeld Surface Analysis
Based on the exact spatial structure of molecules, it is possible to identify weak intermolecular interactions. Hirshfeld surface analysis is an effective way to discern intermolecular interactions in the crystal lattice and visualize them. Different colors representing short or long contacts and color intensity indicate the relative strength of the interactions. Figure 7 shows the Hirshfeld surfaces of 13 methoxy-trans-stilbene derivatives mapped with d norm (−0.26 to 1.48 Å). Following the calculated Hirshfeld surfaces, 2D fingerprint plots were generated (Figures 7 and S3, Supplementary file). These molecular fingerprints provide qualitative and quantitative information about close intermolecular contacts ( Table 5). The most frequent type of contacts in the structure of the tested compounds corresponds to H. . .H interactions, which account for about 50% of the Hirshfeld surface. the C…H/H…C contacts. In turn, the O…H/H…O interactions form a pair of so-called spikes, the length of which is related (inversely proportional) to the distance of the atoms forming this type of contact. Analysis of the tested compounds' structural patterns ( Figure  3) and the contribution of different intermolecular interactions (Table 5) allows for noticing some relationships. In the crystal lattice of compounds with the arrangement type nonslipped perpendicular head to head (MTS-2 and MTS-8), no contacts for C…O/O…C and O…O were observed. On the other hand, for the head to tail arrangement, both slipped perpendicular (MTS-4 and MTS-5) and slipped parallel (MTS-13), favor the occurrence of C…O/O…C interactions. No O…O contacts were identified for trans-stilbene derivatives with the herringbone arrangement (MTS-6, MTS-10, and MTS-11). Furthermore, in the crystal lattice of slipped parallel head to head compounds (MTS-7, MTS-9, and MTS-12) the highest contribution of O…O interactions was observed among the tested molecules. Moreover, MTS-11 with the packing arrangement head to head with inter-twist, and MTS-14 with packing arrangement thread and warp in the fabric possess the highest contribution of C…C contacts [21].    Comparing the percentage of C. . .C interactions in the Hirshfeld surface with the motifs of the molecules' arrangement, it is worth noting that for the compounds MTS-6, MTS-7, MTS-8, MTS-11, and MTS-14, the percentage of C. . .C interactions can be distinguished (1.6-2.8%) to be larger than the others. Moreover, exactly these trans-stilbene derivatives are arranged in sheets lying one above the other, as shown in Figure 6.

MTS
Aiming to visualize the differences between the tested compounds regarding weak intermolecular interactions, the data obtained from the Hirshfeld surface decomposition were plotted on a radar chart ( Figure 8). As before, the transformation of the variables to the 0-1 range was performed. In addition, Figure 8 contains fragments of Table 2.  Pairs of compounds with similar contributions to different intermolecular interactions can be identified among the studied molecules. Compounds with a comparable contribution of various types of weak intermolecular contacts were characterized by similar photophysical properties, especially the Φ PL . Moreover, for compounds with the highest Φ PL, a much more significant contribution of C. . .O/O. . .C type of interactions was observed. On the other hand, the O. . .O contacts seem to have little influence on the fluorescent properties of the tested trans-stilbene derivatives. The analysis demonstrated a relationship between the weak intermolecular interactions occurring in the crystal lattice and the Φ PL . However, this relationship was not clear and demanded further investigation.

QSPR Model
Despite many published studies, quantitative understanding or even prediction of fluorescence properties still needs to be improved, mainly due to the mutual interplay between intramolecular and intermolecular factors affecting these properties [8].  [22]. The substantial QSPR model, with very good validation metrics, was developed for fluorescence quantum yield. Calibration models for other solid-state fluorescence parameters characterizing methoxy-trans-stilbene derivatives (fluorescence lifetime, radiative, and non-radiative rate constants) were also constructed. However, these models had unsatisfactory validation parameters. Figure    Compound MTS-6 was detected as an outlier and removed from further QSPR analysis.
The permutation test (Y randomization) confirmed the model's good quality (all three tests: Wilcoxon, Sign Test, and Rand t-test, were passed, p < 0.05). Moreover, the Williams plot ( Figure 9B) pointed out that all molecules were within the applicability domain; thus, the model was statistically acceptable.
The calibration model was built based on six variables. The values of the regression coefficients and their positive or negative impact on the predicted variable are presented in Figure 10. A linear equation could describe the relationship between the structure of methoxy-trans-stilbene derivatives and their Φ PL , also shown in Figure 10. The permutation test (Y randomization) confirmed the model's good quality (all three tests: Wilcoxon, Sign Test, and Rand t-test, were passed, p < 0.05). Moreover, the Williams plot ( Figure 9B) pointed out that all molecules were within the applicability domain; thus, the model was statistically acceptable.
The calibration model was built based on six variables. The values of the regression coefficients and their positive or negative impact on the predicted variable are presented in Figure 10. A linear equation could describe the relationship between the structure of methoxy-trans-stilbene derivatives and their ΦPL, also shown in Figure 10. Intermolecular interactions of the C…C and C…O/O…C types have the greatest and positive impact on the dependent variable (ΦPL). Although contacts of this type have a small share in all occurring interactions (ranges 0-1.8% and 0-2.8%, respectively, Figure  11), they are mainly responsible for explaining the variance of the solid-state fluorescence quantum yield of methoxy-trans-stilbene derivatives. The compounds with the largest contributions of C…C contacts (green in Figure 11) are MTS-7, MTS-11, and MTS-14. The fluorescence quantum yield of these compounds is, respectively, 0.62, 0.38, and 0.34, i.e., in the case of the last 2, it is below the average ΦPL in the entire group. This was because, in the crystal lattice of these molecules, there was a high level of H…H and O…H/H…O contacts (blue and pink colors in Figure 11), the sum of which is a component of the developed QSPR model with a negative regression coefficient (−0.486 • (O…H/H…O) + (H…H)). Apart from the compound mentioned above (MTS-7), the derivatives with the highest ΦPL were MTS-4 and MTS-5 (respectively, 0.69 and 0.64). This can be explained by the highest amounts of C…O/O…C interactions in the crystal lattice of these molecules (blue color in Figure 11); the regression coefficient of this variable is 0.859. In addition, the MTS-4 compound has one of the lowest electrophilicity values. Since the regression coefficient of electrophilicity has a negative sign (−0.492 • ω), the lower ω values give the higher ΦPL. Electrophilicity values for compounds analyzed by QSPR are shown in Figure  12.  According to [23], a lower electrophilicity value results in an easier transition of the molecule to an excited state. This rule is called the minimum electrophilicity principle (MEP). A molecule with low electrophilicity should have a high value of chemical potential and a high chemical hardness [24]. Facilitating the transition of a molecule to an excited state creates a potentially more significant chance of returning to the ground state by radiative transitions. Therefore, it can be assumed that low electrophilicity may contribute to increased fluorescence quantum yield. This hypothesis is confirmed by the QSPR model obtained in this study, where the regression coefficient for electrophilicity has a negative sign (-0.492 • ω).  Table 4). In turn, compounds MTS-13 and MTS-14 lack methoxy groups in the ortho positions and have a symmetrical arrangement of substituents along the stilbene skeleton (Figure 13), which results in high electrophilicity.  According to [23], a lower electrophilicity value results in an easier transition of the molecule to an excited state. This rule is called the minimum electrophilicity principle (MEP). A molecule with low electrophilicity should have a high value of chemical potential and a high chemical hardness [24]. Facilitating the transition of a molecule to an excited state creates a potentially more significant chance of returning to the ground state by radiative transitions. Therefore, it can be assumed that low electrophilicity may contribute to increased fluorescence quantum yield. This hypothesis is confirmed by the QSPR model obtained in this study, where the regression coefficient for electrophilicity has a negative sign (-0.492 • ω).  Table 4). In turn, compounds MTS-13 and MTS-14 lack methoxy groups in the ortho positions and have a symmetrical arrangement of substituents along the stilbene skeleton (Figure 13), which results in high electrophilicity. According to [23], a lower electrophilicity value results in an easier transition of the molecule to an excited state. This rule is called the minimum electrophilicity principle (MEP). A molecule with low electrophilicity should have a high value of chemical potential and a high chemical hardness [24]. Facilitating the transition of a molecule to an excited state creates a potentially more significant chance of returning to the ground state by radiative transitions. Therefore, it can be assumed that low electrophilicity may contribute to increased fluorescence quantum yield. This hypothesis is confirmed by the QSPR model obtained in this study, where the regression coefficient for electrophilicity has a negative sign (-0.492 • ω).  Table 4). In turn, compounds MTS-13 and MTS-14 lack methoxy groups in the ortho positions and have a symmetrical arrangement of substituents along the stilbene skeleton (Figure 13), which results in high electrophilicity. In addition, the sums of O…H/H…O and H…H interactions are the smallest for these molecules among all compounds, which has a beneficial effect on the ΦPL due to the negative regression coefficient of this component of the equation. A common feature of both compounds, and a potential explanation of the described observation, may be the presence of only two methoxy substituents in these molecules.
In quantitative structure-properties analysis, the value of the modeled variable (fluorescence quantum yield) depends on the combination of independent variables included in the model equation and their regression coefficients. Figure 14 presents stacked bars constructed with preprocessed (autoscaled) variables and regression coefficients. The subbars give the contribution of individual variables to the value of fluorescence quantum yield and, more precisely, the autoscaled value. The relationship between raw and autoscaled data is presented in Figure S4 (Supplementary file) to decode autoscaled values of fluorescence quantum yield.
The analysis of Figure 14 allows for summarizing the results of the QSPR study. Despite theoretically similar possibilities to the occurrence of C…C intermolecular contacts (number of carbon atoms in the whole group of compounds in the range of [16][17][18][19][20], the value positively influencing the ΦPL (blue bar on the right side of Y-axis, MTS-7, MTS-8, MTS-11, MTS-14) is observed only for compounds which are arranged in sheets lying one above the other (which results in π…π stacking interactions). Such interactions and hydrogen bonds are often indicated as factors that quench the fluorescence quantum yield [10,13,25]. In the group of methoxy-trans-stilbene derivatives, the average measured ΦPL of compounds with hydrogen bonds in the crystal lattice is higher (0.44) than the others (0.29). The amount and arrangement of hydrogen bonding affects the rigidity of molecules in the crystal lattice, which can improve the ΦPL by suppressing the vibrational relaxation of excitons [26]. A review of Figure 14 for the effect of C…O/O….C intermolecular interactions indicates that the presence of methoxy substituents on the adjacent carbon atoms is unfavorable for ΦPL (orange bar to the left side of the Y-axis, MTS-8, MTS-10, and MTS-11). Similar conclusions can be drawn from the study of the component of the equation calculated as the sum of the O…H/H…O and H…H contacts (grey bar on the left side of the Y-axis). In addition, this variable indicates that a low number of methoxy groups (high grey bar to the right side of the Y-axis for MTS-1 and MTS-2) is conducive to high ΦPL. Exploration of Figure 14 (high green bar on the left side of the Y-axis, MTS-14, and the right side for MTS-4 and MTS-12) together with Figure 12 demonstrates the distal arrangement of the substituents of both phenyl rings in the molecule, resulting in high In quantitative structure-properties analysis, the value of the modeled variable (fluorescence quantum yield) depends on the combination of independent variables included in the model equation and their regression coefficients. Figure 14 presents stacked bars constructed with preprocessed (autoscaled) variables and regression coefficients. The sub-bars give the contribution of individual variables to the value of fluorescence quantum yield and, more precisely, the autoscaled value. The relationship between raw and autoscaled data is presented in Figure S4 (Supplementary file) to decode autoscaled values of fluorescence quantum yield.
The analysis of Figure 14 allows for summarizing the results of the QSPR study. Despite theoretically similar possibilities to the occurrence of C. . .C intermolecular contacts (number of carbon atoms in the whole group of compounds in the range of [16][17][18][19][20], the value positively influencing the Φ PL (blue bar on the right side of y-axis, MTS-7, MTS-8, MTS-11, MTS-14) is observed only for compounds which are arranged in sheets lying one above the other (which results in π. . .π stacking interactions). Such interactions and hydrogen bonds are often indicated as factors that quench the fluorescence quantum yield [10,13,25]. In the group of methoxy-trans-stilbene derivatives, the average measured Φ PL of compounds with hydrogen bonds in the crystal lattice is higher (0.44) than the others (0.29). The amount and arrangement of hydrogen bonding affects the rigidity of molecules in the crystal lattice, which can improve the Φ PL by suppressing the vibrational relaxation of excitons [26]. A review of Figure 14

Materials and Methods
The subject of the study was 14 methoxy-trans-stilbene derivatives MTS-1-MTS-14 ( Figure 15) obtained according to the procedure described in [19,27].
The two-step synthesis started with converting the proper methoxybenzyl chloride to diethyl phosphonates via the Michaelis-Arbuzov reaction (triethyl phosphite, solventfree, 24 h, 140 °C). In the next step, obtained products were transformed in a Horner-Wadsworth-Emmons reaction with proper aromatic aldehydes (sodium methoxide, dimethylformamide, 24 h, room temperature, next 100 °C for 1.5 h, inert gas-N2) into 14 investigated trans-polymethoxystilbene derivatives. The Horner-Wadsworth-Emmons reaction is a selective way to possess trans isomers. Any traces of cis isomers during the realization of the synthetic procedure were not observed. Detailed descriptions of syntheses can be found in the Supplementary file. The structures of synthesized products MTS-1-MTS-14 were confirmed using NMR and mass spectra.

Materials and Methods
The subject of the study was 14 methoxy-trans-stilbene derivatives MTS-1-MTS-14 ( Figure 15) obtained according to the procedure described in [19,27].
The two-step synthesis started with converting the proper methoxybenzyl chloride to diethyl phosphonates via the Michaelis-Arbuzov reaction (triethyl phosphite, solvent-free, 24 h, 140 • C). In the next step, obtained products were transformed in a Horner-Wadsworth-Emmons reaction with proper aromatic aldehydes (sodium methoxide, dimethylformamide, 24 h, room temperature, next 100 • C for 1.5 h, inert gas-N 2 ) into 14 investigated transpolymethoxystilbene derivatives. The Horner-Wadsworth-Emmons reaction is a selective way to possess trans isomers. Any traces of cis isomers during the realization of the synthetic procedure were not observed. Detailed descriptions of syntheses can be found in the Supplementary file. The structures of synthesized products MTS-1-MTS-14 were confirmed using NMR and mass spectra.  Complete signal assignments for 1 H NMR and 13 C NMR for the studied trans-stilbenes, except for MTS-7 and MTS-10, are presented in previous works [19,20]. Figure 16 shows previously unassigned MTS-7 and MTS-10 signals of 1 H NMR and 13 C NMR spectra recorded in DMSO-d6. Two-dimensional NMR techniques such as 1   Complete signal assignments for 1 H NMR and 13 C NMR for the studied trans-stilbenes, except for MTS-7 and MTS-10, are presented in previous works [19,20]. Figure 16 shows previously unassigned MTS-7 and MTS-10 signals of 1 H NMR and 13 C NMR spectra recorded in DMSO-d 6 . Two-dimensional NMR techniques such as 1 H-1 H COSY (Correlation SpectroscopY), 1 H- 13

Spectroscopic Measurements
Solid-state fluorescence spectra as excitation-emission matrix (EEM) were recorded on a Shimadzu spectrofluorometer RF-5301 equipped with the solid sample holder. Measurements were conducted at excitation wavelengths 290-390 nm, and emission was recorded at 400-485 nm (the width of both slits was 1.5 nm). Based on the obtained threedimensional spectra, the wavelengths at which the absorption maximum occurs were determined. This information was used to collect classical, two-dimensional emission spectra (excitation was carried out using the wavelength at which the absorption maximum occurs). The Panorama Pro software [28] was used to measure and analyze the data.
Photoluminescence quantum yield was measured using an FLS980 spectrofluorometer (Edinburgh Instruments) equipped with an integrating sphere. The Spectralon (Labsphere, Inc., North Sutton, NH, USA) light scattering standard was used as a measurement reference. Depending on the properties of the compound, different analysis parameters were used. The wavelength of the excitation ranged from 330 to 390 nm. The beginning of the emission measurement range was between 320 and 370 nm, while its end for all compounds was 700 nm. The width of the excitation gap was 8.0 nm (except for compound MTS-7 for which it was 7.0 nm), and the emission gap was 0.1 nm (except for compounds MTS-2 and MTS-8, for which it was 0.2 nm). The step was 0.2 nm for all analyses, and the counting time was 0.3 s. Quantum yield calculations were performed using software (F980) provided by Edinburgh Instruments.
The fluorescence lifetime measurements were carried out using an FLS980 spectrofluorometer (Edinburgh Instruments) with a pulsed diode laser. A 360 nm diode laser was used as an excitation source. Depending on the sample, the emission wavelength was in the range of 395-445 nm. The excitation slit was 0.03 nm wide, while the emission slit was

Spectroscopic Measurements
Solid-state fluorescence spectra as excitation-emission matrix (EEM) were recorded on a Shimadzu spectrofluorometer RF-5301 equipped with the solid sample holder. Measurements were conducted at excitation wavelengths 290-390 nm, and emission was recorded at 400-485 nm (the width of both slits was 1.5 nm). Based on the obtained three-dimensional spectra, the wavelengths at which the absorption maximum occurs were determined. This information was used to collect classical, two-dimensional emission spectra (excitation was carried out using the wavelength at which the absorption maximum occurs). The Panorama Pro software [28] was used to measure and analyze the data.
Photoluminescence quantum yield was measured using an FLS980 spectrofluorometer (Edinburgh Instruments) equipped with an integrating sphere. The Spectralon (Labsphere, Inc., North Sutton, NH, USA) light scattering standard was used as a measurement reference. Depending on the properties of the compound, different analysis parameters were used. The wavelength of the excitation ranged from 330 to 390 nm. The beginning of the emission measurement range was between 320 and 370 nm, while its end for all compounds was 700 nm. The width of the excitation gap was 8.0 nm (except for compound MTS-7 for which it was 7.0 nm), and the emission gap was 0.1 nm (except for compounds MTS-2 and MTS-8, for which it was 0.2 nm). The step was 0.2 nm for all analyses, and the counting time was 0.3 s. Quantum yield calculations were performed using software (F980) provided by Edinburgh Instruments.
The fluorescence lifetime measurements were carried out using an FLS980 spectrofluorometer (Edinburgh Instruments) with a pulsed diode laser. A 360 nm diode laser was used as an excitation source. Depending on the sample, the emission wavelength was in the range of 395-445 nm. The excitation slit was 0.03 nm wide, while the emission slit was 0.3-2.0 nm. Fluorescence lifetime measurements were analyzed using Edinburgh Instruments software based on a one-or two-exponential fitting method without deconvolution.

Computational Methods
Semi-empirical method AM1 in a vacuum was employed to obtain the optimized geometries for studied compounds. The theoretical calculations of the molecular orbitals, HOMO and LUMO energies and, based on them, global reactivity descriptors (energy gap, ionization energy, electron affinity, hardness, softness, electronegativity, chemical potential, electrophilicity [22]) were performed in the Gaussian09 package [29] in PL-Grid infrastructure [30]. The quantitative analysis of the relationship between the crystal structure of compounds and their fluorescence properties was performed with the use of Partial Least Squares Regression (PLSR), using the PLS-Toolbox 7.5 [31] in Matlab software version R2020b [32]. Before performing the calculations, autoscaling of variables (independent and dependent variable) was performed, while their selection was based on the analysis of the VIP (variable importance in projection plot). Internal validation was performed using the "leave one out" method. Hierarchical cluster analysis was performed with STATISTICA v.13.3 software [33].

Crystallographic Data
The For the MTS-3, obtaining a single crystal of sufficient quality for X-ray structural studies was impossible.
X-ray data for compounds MTS-8, MTS-9, MTS-10, MTS-13, and MTS-14 were measured from single crystal using an XtaLAB Synergy, Dualflex diffractometer with an Hypix detector. The temperature of measurements was 100K for MTS-8 and MTS-14, 150K for MTS-9 and MTS-13, and 293K for MTS-10. In all cases, the multiscan absorption correction was performed (CrysAlisPro 1.171.41.119a (Rigaku Oxford Diffraction, 2021). All structures were solved by direct methods using SHELXT [34] and further refined on F 2 using SHELXL-2014/7 [35]. All non-hydrogen atoms were refined anisotropically. The atoms C7 and C8 for compound MTS-10 are disordered and refined with an occupancy ratio of 56%:44% for the A and B parts. The positions of hydrogen atoms were calculated from known geometry (C-H bond lengths at 0.95 and 0.98 Å for aromatic CH and methyl CH 3 atoms, respectively) and treated as riding where the isotropic thermal parameters of these hydrogen atoms were fixed as U iso (H) = 1.5U eq (C) for H atoms from a methyl group and U iso (H) = 1.2U eq (C) for all remaining atoms. PLATON [36] and MERCURY [37] were used to identify molecular geometries and hydrogen-bond patterns. Basic experimental details and crystallographic data are presented in Table 3. Further crystallographic information for the structures reported in this paper may be obtained free of charge on application to CCDC, 12 Union

Hirshfeld Surface Analysis
Crystal Explorer v. 21.3 [38] software was used to generate the Hirshfeld surfaces [39] based on the data from X-ray studies. Hydrogen atom bond lengths were normalized to standard neutron values (C−H = 1.083 Å, O−H = 0.983 Å) to ensure internal consistency, which is essential in structures' comparisons [40]. The normalized contact distance (d norm ) is based on both d e (the distance from a point on the surface to the nearest atom outside the surface) and d i (the distance from a point on the surface to the nearest atom inside the surface) and van der Waals radii of the atom, given by Equation 4, enables the identification of the regions of particular importance to intermolecular interactions [41]. The negative value of d norm (red color) or positive value of d norm (blue color) occurs when intermolecular contacts are shorter or longer than van der Waals separations.

Conclusions
In summary, the group of 14 methoxy-trans-stilbene derivatives was studied to gain insight into the quantitative structure-solid-state fluorescence properties relationship. Five molecules have been characterized by X-ray crystallography. The crystallographic data for other compounds were from CCDC. Fluorescent properties in the solid state were reported for all tested compounds. Interestingly, a slight change in the substituents pattern of compounds significantly affects their molecular packing and photophysical behavior. To determine the quantitative relationships between solid-state fluorescence quantum yield (Φ PL ) and molecular structure, a calibration model was built using the PLSR algorithm. The model's acceptable validation parameters indicate the successful application of weak intermolecular interactions, quantified using Hirshfeld surface analysis, to modeling the Φ PL suggests their predictive potential. The interpretation of the model-building variables (different types of weak contacts and electrophilicity) demonstrates a beneficial effect on the observed Φ PL of π. . .π stacking interactions, the occurrence of hydrogen bonds, and the ortho position of methoxy substituents.