The Role of Percent Volume Buried in the Characterization of Copper(I) Complexes for Lighting Purposes

The usefulness of percent volume buried (%Vbur) as a readily quantifiable property is investigated with regard to [Cu(NN)(PP)]+ complexes of interest for lighting purposes. Photoluminescence quantum yields (PLQYs) and single crystal X-ray structures of 100 reported compounds were assembled, %Vbur of the ligand systems were calculated and analyzed for correlations. We found that increased shielding of the central Cu(I) cation relying on shared contributions of both (NN) and (PP) ligand systems led to increased PLQYs. These findings are of relevance for future characterizations of Cu(I)-based complexes and their photophysical behavior in the solid-state.


Introduction
Ionic transition metal complexes (iTMCs) are widely present in chemistry for e.g., catalysis or lighting purposes. Understanding of the electronic and steric effects of ligands on the iTMCs is essential to improve rational design of iTMCs for their varied purposes. While quantifying electronic effects of ligands onto metal complexes can be performed by spectroscopic methods such as IR, [1] similar quantification of the steric impact is less straight-forward. Tolman cone-angles have been introduced for the calculation of steric parameters [2] and widely used but suffer limitations as its usefulness is greatly diminished when applied to more elaborate mono-or bi-dentate ligands. Consequently, Nolan and Cavallo introduced the percent volume buried (%V bur ) as a quantifiable parameter to describe any given ligand [3]. The %V bur describes the volume occupied by any given ligand inside a sphere with a 3.5 Å radius around the metal center and topographical steric maps [4] are created using SambVca 2.1 package [5]. Since its introduction, the %V bur parameter has proven to be useful as a descriptor of iTMCs in catalysis [6][7][8][9]. In the field of iTMC-based lighting devices, however, it has not gained attention despite its potential in structural analysis.
Heteroleptic copper(I)-based iTMCs have been employed in light-emitting electrochemical cells (LECs) and represent a promising avenue towards cost-efficient and sustainable lighting devices [10][11][12]. Consequently, understanding of the photophysical behavior of these complexes has guided their improved design for applications in LECs [13][14][15][16][17][18]. Electronic properties such as redox potentials, absorption and emission spectra are among the descriptors used in the analysis of Cu(I) complexes. Quantifiable descriptors of steric factors, however, are mostly limited to discussions regarding angles and/or bond-lengths in X-ray single crystal structures. We have recently evaluated the effect that Cu···O distances in the {Cu(POP)}

Macroscopic level
Scatter plots of the results for all 123 data points of the 100 compounds are shown in Figure 2. Careful analysis of these scatter plots suggests that, firstly, there is a small positive impact of increased %Vbur(NN) on the PLQY (Figure 2a), and, second, an optimal %Vbur(PP) seems to be located at ca 56%. An increase or decrease of %Vbur(PP) negatively impacts the PLQY (Figure 2b). Thirdly, similar to %Vbur(PP), there seems to be an optimal %Vbur(NN + PP) located at ca 92% (Figure 2c). The fourth point is that %Vbur(NN + PP) strongly depends on %Vbur(PP) while the %Vbur(NN) has little impact (Figure 2d-f).
For a more detailed analysis of the results, color-coded three-dimensional scatter plots were generated including all four variables ( Figure 3 and Figure S1-S3, Supplementary Materials). The PLQY was plotted against two %Vbur values with the remaining third %Vbur color-coded in the scatter plots. All three iterations of such plots support the dependence of large %Vbur(NN + PP) for large PLQYs as seen in Figure 2C. Furthermore, these plots reveal that the best outcome is achieved by a shared %Vbur between the NN and PP ligands. A large %Vbur(NN + PP) relying mostly on the PP ligand, on the other hand, yields low PLQYs. This shared contribution from both ligand units to the %Vbur(NN + PP) seems to be the cause for the above mentioned observation regarding a perceived optimal %Vbur(PP) at ca 56%. Most likely, a shared contribution of %Vbur(NN) and %Vbur(PP) within the [Cu(NN)(PP)] + framework is more difficult to achieve for %Vbur(PP)>60% resulting in only three data-points in that regime. At this point it should be mentioned again that the values presented here are biased by synthetic feasibility and only serve to reflect empirical trends in reported values and the usefulness of %Vbur.

Macroscopic Level
Scatter plots of the results for all 123 data points of the 100 compounds are shown in Figure 2. Careful analysis of these scatter plots suggests that, firstly, there is a small positive impact of increased %V bur (NN) on the PLQY (Figure 2a), and, second, an optimal %V bur (PP) seems to be located at ca 56%. An increase or decrease of %V bur (PP) negatively impacts the PLQY (Figure 2b). Thirdly, similar to %V bur (PP), there seems to be an optimal %V bur (NN + PP) located at ca 92% ( Figure 2c). The fourth point is that %V bur (NN + PP) strongly depends on %V bur (PP) while the %V bur (NN) has little impact (Figure 2d-f).   For a more detailed analysis of the results, color-coded three-dimensional scatter plots were generated including all four variables ( Figure 3 and Figures S1-S3, Supplementary Materials). The PLQY was plotted against two %V bur values with the remaining third %V bur color-coded in the scatter plots. All three iterations of such plots support the dependence of large %V bur (NN + PP) for large PLQYs as seen in Figure 2c. Furthermore, these plots reveal that the best outcome is achieved by a shared %V bur between the NN and PP ligands. A large %V bur (NN + PP) relying mostly on the PP ligand, on the other hand, yields low PLQYs. This shared contribution from both ligand units to the %V bur (NN + PP) seems to be the cause for the above mentioned observation regarding a perceived optimal %V bur (PP) at ca 56%. Most likely, a shared contribution of %V bur (NN) and %V bur (PP) within the [Cu(NN)(PP)] + framework is more difficult to achieve for %V bur (PP) > 60% resulting in only three data-points in that regime. At this point it should be mentioned again that the values presented here are biased by synthetic feasibility and only serve to reflect empirical trends in reported values and the usefulness of %V bur .

Case Study 1: Importance of Steric Effects
In 2018, we reported twelve copper(I) complexes with 6-alkoxy-or 6-alkylthio-substituted bpy ligands in combination with xantphos (2a-7a) or POP (2b-7b) ( Figure 4) [26]. The complexes were investigated by means of single crystal X-ray analysis, NMR spectroscopy, absorption and emission spectra, cyclic voltammetry as well as excited state lifetime measurements and density functional theory (DFT) calculations. The observed PLQY values (Table 1) were analyzed and a trend was established of increased PLQY by increased rigidity of xantphos compared to POP as well as increased steric bulk of the NN ligand in the order of bpyXMe < bpyXEt < bpyXPh (X = O, S). However, %Vbur is not included in this discussion and the explanation as such is only partially supported by the reported values (compare PLQYs of 2a and 4a or 2b and 4b). Thus, the available photophysical properties in combination with the relatively large set of substrates renders this set of compounds a suitable case study for the inclusion of %Vbur as a descriptor in the discussion of photophysical properties.

Case Study 1: Importance of Steric Effects
In 2018, we reported twelve copper(I) complexes with 6-alkoxy-or 6-alkylthio-substituted bpy ligands in combination with xantphos (2a-7a) or POP (2b-7b) ( Figure 4) [26]. The complexes were investigated by means of single crystal X-ray analysis, NMR spectroscopy, absorption and emission spectra, cyclic voltammetry as well as excited state lifetime measurements and density functional theory (DFT) calculations. The observed PLQY values (Table 1) were analyzed and a trend was established of increased PLQY by increased rigidity of xantphos compared to POP as well as increased steric bulk of the NN ligand in the order of bpyXMe < bpyXEt < bpyXPh (X = O, S). However, %V bur is not included in this discussion and the explanation as such is only partially supported by the reported values (compare PLQYs of 2a and 4a or 2b and 4b). Thus, the available photophysical properties in combination with the relatively large set of substrates renders this set of compounds a suitable case study for the inclusion of %V bur as a descriptor in the discussion of photophysical properties.  The PLQY values for the series of complexes shown in Figure 4 as well as %Vbur are summarized in Table 1 and Figure 5. An analysis of the %Vbur(NN) values shows that the intuitive assignment of increased steric bulk in the order of bpyXMe < bpyXEt < bpyXPh (× = O, S) is not reflected in the percent volume buried. Instead the following order is more appropriate based on the calculated %Vbur(NN): Overall, the %Vbur(PP) values for POP are larger than those for xantphos with the exception of compounds 7a and 7b. Moreover, %Vbur(NN + PP) seems to increase with %Vbur(NN) while the largest %Vbur(NN + PP) appears to be located at a medium %Vbur(PP) of ca. 56.5%. Visualization of all four properties in color-coded three-dimensional scatter plots reveals that the highest PLQY values are  [26] and used in case study 1. The PLQY values for the series of complexes shown in Figure 4 as well as %V bur are summarized in Table 1

Case Study 2-Investigating Electronic Effects
Tsubomura and co-workers reported a series of seven heteroleptic copper(I) complexes in 2015 with the aim of investigating oxygen-responsive luminescence in the solid state. The single crystal Xray structures of compounds 8-12 (Figure 7) were reported as well as powder PLQY values under air and under an argon atmosphere (Table 2) [31]. Given the choice of N^N and P^P ligands made by the authors, it is assumed that differences in PLQY are mostly due to electronic effects with the exception of 8 and 10. The authors rationalize the trends in the observed PLQYs through differences in the crystal packing preventing structural rearrangement and differences in the transitions based on DFT calculations. Special emphasis was placed on the presence of voids in the crystal lattices which allows for excited state quenching by atmospheric O2. While significant differences in shielding by the For PˆP = Xantphos: bpyOPh < bpyOMe ≈ bpyOEt < bpySEt ≈ bpySPh ≈ bpySMe For PˆP = POP: bpyOPh < bpyOMe ≈ bpyOEt < bpySPh ≈ bpySMe < bpySEt Overall, the %V bur (PP) values for POP are larger than those for xantphos with the exception of compounds 7a and 7b. Moreover, %V bur (NN + PP) seems to increase with %V bur (NN) while the largest %V bur (NN + PP) appears to be located at a medium %V bur (PP) of ca. 56.5%. Visualization of all four properties in color-coded three-dimensional scatter plots reveals that the highest PLQY values are reached when a high %V bur (NN + PP) is achieved by a combination of high %V bur (NN) and %V bur (PP) (Figure 6), in agreement with the interpretation of all 100 compounds (vide supra). Notably, comparing 5a or 6a to 7a shows an increased PLQY with an increased %V bur (PP) or %V bur (NN + PP) while a similar correlation is not present when comparing 5a to 6a which only differ in %V bur (NN). Consequently, the nature of the differing PLQYs when comparing 5a and 6a is not due to the steric effects of the particular ligand system. Alternative explanations may be based on crystal packing such as improved accessibility of atmospheric O 2 to the complex [20].

Case Study 2-Investigating Electronic Effects
Tsubomura and co-workers reported a series of seven heteroleptic copper(I) complexes in 2015 with the aim of investigating oxygen-responsive luminescence in the solid state. The single crystal Xray structures of compounds 8-12 ( Figure 7) were reported as well as powder PLQY values under air and under an argon atmosphere (Table 2) [31]. Given the choice of N^N and P^P ligands made by the authors, it is assumed that differences in PLQY are mostly due to electronic effects with the exception of 8 and 10. The authors rationalize the trends in the observed PLQYs through differences in the crystal packing preventing structural rearrangement and differences in the transitions based on DFT calculations. Special emphasis was placed on the presence of voids in the crystal lattices which allows for excited state quenching by atmospheric O2. While significant differences in shielding by the ligands of the central copper(I) cation are not expected, we considered that an analysis of %Vbur may provide further insight. Most importantly, %Vbur values allow for a straight-forward, quantitative comparison of steric effects if these are indeed present.
An analysis of the scatter plots in Figure 8 indicates that steric effects may participate in the decrease of PLQY in the case of 8 and 10. The remaining compounds are almost identical in the %Vbur values and any differences in PLQY may be attributed to electronic effects. On the other hand, effects due to differences in crystal packing can be excluded as changes in PLQY under air or under Ar

Case Study 2-Investigating Electronic Effects
Tsubomura and co-workers reported a series of seven heteroleptic copper(I) complexes in 2015 with the aim of investigating oxygen-responsive luminescence in the solid state. The single crystal X-ray structures of compounds 8-12 ( Figure 7) were reported as well as powder PLQY values under air and under an argon atmosphere ( Table 2) [31]. Given the choice of NˆN and PˆP ligands made by the authors, it is assumed that differences in PLQY are mostly due to electronic effects with the exception of 8 and 10. The authors rationalize the trends in the observed PLQYs through differences in the crystal packing preventing structural rearrangement and differences in the transitions based on DFT calculations. Special emphasis was placed on the presence of voids in the crystal lattices which allows for excited state quenching by atmospheric O 2 . While significant differences in shielding by the ligands of the central copper(I) cation are not expected, we considered that an analysis of %V bur may provide further insight. Most importantly, %V bur values allow for a straight-forward, quantitative comparison of steric effects if these are indeed present.      An analysis of the scatter plots in Figure 8 indicates that steric effects may participate in the decrease of PLQY in the case of 8 and 10. The remaining compounds are almost identical in the %V bur values and any differences in PLQY may be attributed to electronic effects. On the other hand, effects due to differences in crystal packing can be excluded as changes in PLQY under air or under Ar atmosphere are absent or negligible. Only complex 10 exhibits a significant increase in PLQY Molecules 2020, 25, 2647 7 of 12 upon removal of atmospheric O 2 . Structural shielding by the ligand system for compound 10 may be present but is negated by the presence of voids in the crystal packing and effective quenching of the excited state by O 2 and energy transfer occurs instead. The lack of change in the PLQYs for the remaining compounds may be explained by structural rigidity inferred by the crystal packing rather than shielding of the central copper(I) cation.

Case Study 3-Differentiating Steric from Electronic Factors
In 2016, two of us reported a series of heteroleptic [Cu(NN)(PP)] + complexes with 6-or 6,6'substituted bpy ligands in combination with POP or xantphos (13-18, Figure 9) [18]. Following investigations of the structural and photophysical properties, the complexes were tested in LECs and were also investigated using DFT calculations. While high PLQY values were obtained for complexes

Case Study 3-Differentiating Steric from Electronic Factors
In 2016, two of us reported a series of heteroleptic [Cu(NN)(PP)] + complexes with 6-or 6,6'-substituted bpy ligands in combination with POP or xantphos (13-18, Figure 9) [18]. Following investigations of the structural and photophysical properties, the complexes were tested in LECs and were also investigated using DFT calculations. While high PLQY values were obtained for complexes 13, 14, 16 and 17 (Figure 9), it was observed that replacing the Me or Et substituent with a Ph group resulted in a significantly lower PLQY (Table 3). We ascribed this sharp drop in PLQY to a lower T 1 state leading to increased feasibility of non-radiative decay pathways for 15 and 18. We note that the structural discussions in the original publication did not provide a conclusive relationship between steric effects on the observed PLQYs. While %V bur does not yield any insight into electronic effects, it does offer a concise overview of possible steric effects.
Molecules 2020, 25, x 8 of 13 13, 14, 16 and 17 (Figure 9), it was observed that replacing the Me or Et substituent with a Ph group resulted in a significantly lower PLQY (Table 3). We ascribed this sharp drop in PLQY to a lower T1 state leading to increased feasibility of non-radiative decay pathways for 15 and 18. We note that the structural discussions in the original publication did not provide a conclusive relationship between steric effects on the observed PLQYs. While %Vbur does not yield any insight into electronic effects, it does offer a concise overview of possible steric effects.
Analysis of the %Vbur values does not result in a clear correlation between the shielding of the central Cu(I) cation and PLQY values (Table 3). Graphical representation of these values further shows that the observed low PLQYs for 15 and 18 do not fit any possible correlation ( Figure 10). Lastly, color-coded three-dimensional scatter plots clearly reveal that large PLQY values are obtained by virtually any combination of %Vbur with no correlation (Figure 11) as opposed to the correlations seen in case study 1 or in the analysis of all 100 complexes. This further supports the original hypothesis of lowered PLQY values due to a lowered T1 state by virtue of the phenyl substituent.   Figure 9. Structures of complexes 13-18 from reference [18].  (Table 3). Graphical representation of these values further shows that the observed low PLQYs for 15 and 18 do not fit any possible correlation ( Figure 10). Lastly, color-coded three-dimensional scatter plots clearly reveal that large PLQY values are obtained by virtually any combination of %V bur with no correlation (Figure 11) as opposed to the correlations seen in case study 1 or in the analysis of all 100 complexes. This further supports the original hypothesis of lowered PLQY values due to a lowered T 1 state by virtue of the phenyl substituent.
structural discussions in the original publication did not provide a conclusive relationship between steric effects on the observed PLQYs. While %Vbur does not yield any insight into electronic effects, it does offer a concise overview of possible steric effects.
Analysis of the %Vbur values does not result in a clear correlation between the shielding of the central Cu(I) cation and PLQY values (Table 3). Graphical representation of these values further shows that the observed low PLQYs for 15 and 18 do not fit any possible correlation ( Figure 10). Lastly, color-coded three-dimensional scatter plots clearly reveal that large PLQY values are obtained by virtually any combination of %Vbur with no correlation (Figure 11) as opposed to the correlations seen in case study 1 or in the analysis of all 100 complexes. This further supports the original hypothesis of lowered PLQY values due to a lowered T1 state by virtue of the phenyl substituent.

Materials and Methods
The Cambridge Structural Database (CSD) [28] was searched for compounds consisting of mononuclear [Cu(NN)(PP)] + . Searches were made using CSD version 5.4.1 and ConQuest version 2.0.4 [29]. Literature sources of the results were searched for reports of appropriate PLQY values which were collected together with the CIF files (  [5]. XYZ of the crystal structures were uploaded and the Cu(I) cation was defined as the center of the sphere. The negative Z-axis was defined by the N-atoms of the diimine for %Vbur(NN) and %Vbur(NN + PP) or by the P-atoms of the bisphosphane for %Vbur(PP). The P-atoms of the bisphosphane defined the XZ-plane for %Vbur(NN) and %Vbur(NN + PP) and the N-atoms of the diimine for %Vbur(PP). All atoms, except for the diimine ligand, bisphosphane ligand or both ligands, were deleted to calculate %Vbur(NN), %Vbur(PP) and %Vbur(NN + PP), respectively. The Bondi radii were scaled by 1.17 and the sphere radius chosen as r Figure 11. 3-Dimensional scatter plot with color-coded %V bur (NN) for compounds 13-18 [18].

Materials and Methods
The Cambridge Structural Database (CSD) [28] was searched for compounds consisting of mononuclear [Cu(NN)(PP)] + . Searches were made using CSD version 5.4.1 and ConQuest version 2.0.4 [29]. Literature sources of the results were searched for reports of appropriate PLQY values which were collected together with the CIF files (Table S1 in the Supplementary Material). Topographical steric maps [4] were created using SambVca 2.1 package (https://www.molnac.unisa.it/OMtools/sambvca2.1/ index.html) [5]. XYZ of the crystal structures were uploaded and the Cu(I) cation was defined as the center of the sphere. The negative Z-axis was defined by the N-atoms of the diimine for %V bur (NN) and %V bur (NN + PP) or by the P-atoms of the bisphosphane for %V bur (PP). The P-atoms of the bisphosphane defined the XZ-plane for %V bur (NN) and %V bur (NN + PP) and the N-atoms of the diimine for %V bur (PP). All atoms, except for the diimine ligand, bisphosphane ligand or both ligands, were deleted to calculate %V bur (NN), %V bur (PP) and %V bur (NN + PP), respectively. The Bondi radii were scaled by 1.17 and the sphere radius chosen as r = 3.5 Å. Mesh spacing of 0.10 Å was used for the numerical integration and H-atoms were excluded.

Conclusions
We have demonstrated that values of %V bur represent a means of quantifying relationships between structure and PLQYs of heteroleptic [Cu(NN)(PP)] + complexes. Using the CSD as a source of structural data, we were able to analyze 100 [Cu(NN)(PP)] + complexes for which solid state PLQYs and single-crystal X-ray structures were available; this provided 123 data points. Analysis of all complexes showed that PLQY values are the highest when %V bur (NN + PP) is maximized by an increased %V bur (NN) and %V bur (PP). Three case studies underline the potential usefulness of including %V bur as an addition in the structural discussion of [Cu(NN)(PP)] + complexes as it relates to solid-state photophysical behavior. Funding: There was no external funding for this project.