Solution structural characterization of an array of nanoscale aqueous inorganic Ga13−xInx (0 ≤ x ≤ 6) clusters by <sup>1</sup>H-NMR and QM computations
NMR spectroscopy is the go-to technique for determining the solution structures of organic, organometallic, and even macromolecular species. However, structure determination of nanoscale aqueous inorganic clusters by NMR spectroscopy remains an unexplored territory. The few hydroxobridged inorganic species well characterized by 1 H Nuclear Magnetic Resonance spectroscopy ( 1 H-NMR) do not provide enough information for signal assignment and prediction of new samples. 1 H-NMR and quantum mechanical (QM) computations were used to characterize the NMR spectra of the entire array of inorganic flat-Ga 13Àx In x (0 # x # 6) nanoscale clusters in solution. A brief review of the known signals for m 2 -OH and m 3 -OH bridges gives expected ranges for certain types of protons, but does not give enough information for exact peak assignment. Integration values and NOESY data were used to assign the peaks of several cluster species with simple 1 H-NMR spectra. Computations agree with these hydroxide signal assignments and allow for assignment of the complex spectra arising from the remaining cluster species. This work shows that 1 H-NMR spectroscopy provides a variety of information about the solution behavior of inorganic species previously thought to be inaccessible by NMR due to fast ligand and/or proton exchange in wet solvents.
Introduction<!>H-NMR spectra of hydroxo/aquo bridged coordination compounds<!>Experimental section<!>Results and discussion<!>Hydroxo ligand naming convention<!>m 3 -OH peak assignments<!>m 2 -OH peak assignments<!>View Article Online<!>Conclusion
<p>Proton Nuclear Magnetic Resonance spectroscopy ( 1 H-NMR) is an important tool heavily utilized by chemists and biochemists since its discovery in 1945. 1 Unfortunately, it is oen not a viable technique for characterizing purely inorganic clusters due to the fast exchange of protons and/or ligands in aqueous coordination clusters dissolved in wet/polar solvents. The reliable trends and generalizations in 1 H-NMR shis tabulated for numerous carbon-containing molecules do not translate to this purely inorganic world. The focus of this manuscript is to correlate the 1 H-NMR spectral shis of nanoscale aqueous clusters dissolved in wet solvents to their hydroxo ligands to substantiate cluster characterization and speciation in solution.</p><p>The 1 H-NMR spectrum of [Ga 13 (m 3 -OH) 6 (m 2 -OH) 18 (H 2 O) 24 ]-(NO 3 ) 15 (Ga 13 ) in wet d 6 -DMSO is known. 2 Due to the spectral complexity, no peaks were assigned to specic hydroxo and aquo protons in the structure at that time. Further analysis coupled with computations of the complete series of [Ga 13Àx In x (m 3 -OH) 6 (m 2 -OH) 18 (H 2 O) 24 ]-(NO 3 ) 15 clusters (1 # x # 6: Ga 12 In 1 , Ga 11 In 2 , Ga 10 In 3 , Ga 9 In 4 , Ga 8 In 5 , Ga 7 In 6 ) provides trends and clarity, allowing partial 1 H signal assignment and complete assignment of all hydroxo bridges in the "mother clusters" (i.e., clusters entirely capped with water molecules that potentially undergo exchange with coordinating solvents, Fig. 1).</p><p>1 H-NMR spectroscopy is the rst characterization technique used in modern organic, organometallic, and coordination chemistry, yet such data are only sporadically reported for aqueous inorganic clusters. We have found that under the right conditions such clusters oen exhibit rich 1 H-NMR spectra that enable characterization by 2D NMR techniques as well. 2 A bottleneck in determining solution structure by NMR spectroscopy has been the lack of tabulated data for such clusters and predictive methods for peak assignment. For instance, there is no known way for predicting where M À H 2 O or M-(m 2 -OH)-M 1 H-NMR signals should resonate like there is for organic compounds. In this manuscript we provide a literature survey of 1 H-NMR spectroscopic resonances reported for known hydroxo-and aquo-coordinated metal complexes. To the best of our knowledge, such data have not been aggregated in one location. We then use this information and complementary quantum mechanical (QM) computations to provide the complete solution structure and peak assignment for a series of clusters. The Ga 13Àx In x clusters in this work are completely inorganic. Clusters of this type are oen more difficult to isolate and challenging to characterize 13 than organic ligand-supported versions, because the ligands lower the cluster charge and can increase stability. 14 However, the lack of organic ligands makes these species attractive candidates as precursors (inks) for metal oxide lms, as the lack of organic additives that must be "burned" off during lm formation/condensation leads to fewer defects and increases density of thin lms. These clusters also serve as excellent inks/precursors due to their high solubility in aqueous and alcoholic solutions, which eliminates toxic solvents oen used in thin lm production. Minimizing the organic ligands for such applications has produced superior precursors, 13 but the lack of spectroscopic handles has limited the complete understanding of the solution behavior of these species.</p><p>Previously, single crystal X-ray diffraction (XRD) and elemental analysis were the techniques used to differentiate the seven known at-Ga 13Àx In x clusters. 15 These techniques suggest that multiple cluster species might co-crystallize during isolation (for example, Ga 10.2 In 2.8 has been isolated, which could be an 80/20 mixture of Ga 10 In 3 and Ga 11 In 2 or some other such combination). Ga 13 has been recently characterized in solution using NMR, Small Angle X-ray Scattering (SAXS), and Raman. 2,16 Although single crystal XRD can provide excellent solid-state data, it cannot answer pressing current questions. Does Ga 10 In 3 even exist or are all of the mixed clusters simply various ratios of Ga 13 and Ga 7 In 6 ? Do all of the possible isomers in the Ga 9 In 4 -Ga 11 In 2 clusters (Fig. 1) co-crystallize or are certain ones thermodynamically favored? Is there a way to determine the ratio of isomers present in a sample? Using 1 H-NMR, we have established a quick technique for characterizing samples that could address these questions and will accelerate the synthesis and identication of cluster species in solution.</p><!><p>Only a limited number of reports of completely inorganic, hydroxo bridged species have been studied via 1 H-NMR spectroscopy. However, the moderate chemical shi library of hydroxo protons identied in ligand-supported metal complexes and coordinated water allows for some comparison. The typical chemical shis of coordinated water ligands are generally downeld (Table 1). Typically hexaaquo species have proton signals in the range of 8.3 to 11.3 ppm, while water ligands on metal oligomers tend to appear slightly upeld between 6.3 and 10 ppm.</p><p>Little is known about the potential trends for these hydroxide bridges in inorganic species, although it appears that the metal atom and its coordination number are main contributors to the chemical shi of these hydroxo protons. The collected chemical shis have been tabulated and discussed for the readers benet (Tables 2-5). For diamagnetic complexes, m 2 -OH protons fall between À4.5 and 7 ppm; while m 3 -OH proton signals occur from À1.05 to 6.79 ppm (Fig. 2). The observation of these 1 H-NMR signals at lower chemical shis than that of the hexaaquo species and the free hydroxide ions is caused by the increased electron density around the proton in the bridge. 5 These are fairly large regions that are not distinguishable from one another, but can be differentiated from water ligands. By looking more closely at specic metals, coordination environments, and groups on the periodic table, rened assignments of chemical shi regions and apparent trends emerge.</p><p>Octahedral M(III) ions (M ¼ Al, Ga, Ir, Rh, and W), the most relevant for this work, tend to produce signals for m 2 -OH protons that range from 1.5-5.0 ppm, although this does not hold true for Co(III). [17][18][19][20][21] Geometries, chemical shi data, and available NMR conditions for these metal complexes are shown in Table 2. The majority of this data was referenced to TMS or residual protic peaks described in the primary papers. Solvent and temperature do not appear to signicantly affect the chemical shis. 12 The top section of Table 3 indicates some metal complexes with different oxidation states and/or non-octahedral geometries exhibit resonance for hydroxide bridges similar to the ranges observed for "trivalent octahedral" metal complexes. In addition to experimental data, computational data is occasionally found for bridging hydroxides. For instance, computed 1 H-NMR shis during the oligomerization of Be(II) species mirrors the experimental measurement of 4.3 ppm. 22,23 Like the trivalent octahedral complexes listed above, certain metals have distinct areas within the bigger region were the 1 H-NMR signals of m 2 -OH bridges appear. The data presented in the bottom section of Table 3 reveals these ranges. As previously mentioned, octahedral Co(III) complexes differ from the other trivalent octahedral complexes with signals appearing between À4.5 and 0.5 ppm. [17][18][19][20][21] Mixed valence Os(0/II) compounds tend to have bridges in the À2.8 to À0.44 ppm range. 24,25 Square planar Pd(II) and Pt(II) complexes have m 2 -OH bridges that range from À3 to 2 ppm. [26][27][28][29][30][31][32][33][34] Sn has the largest range producing signals anywhere from 1.63 to 7.33 ppm. [35][36][37][38][39] Yttrium hydroxo bridges tend to have chemical shi values downeld ranging     range. [41][42][43] The proton signal for the only example of a Cd-(m 2 -OH)-Cd bridge appeared at À2.43 ppm. 42 The typical ranges of these metal hydroxo bridges have been plotted in Fig. 3 to allow for easy comparison. Data from the literature for heterometallic complexes was also analysed because the present work focuses on heterometallic Ga/In clusters as well. Not all of the heterometallic complexes in Table 4 feature bridging hydroxides between two different metal atoms, but for completeness they were included.</p><p>The hydroxo bridges in trivalent Group 13 octahedral metal complexes are the most relevant for this report. Akitt and colleagues suggests a range of 3 to 6 ppm for Al 3+ m 2 -OH bridges. 3 However, the data listed above suggests these resonances should fall within the 2.0 to 4.8 ppm region. The heterometallic octahedral Ga-(m 2 -OH)-M (M s Ga) bridges have very similar chemical shis to the homometallic hydroxo bridges listed in Table 2. This indicates that Ga-(m 2 -OH)-Ga bridges may not easily be distinguished from Ga-(m 2 -OH)-In bridges. Fig. 4 illustrates the regions where m 2 -OH bridges and capping water ligands on the Ga 13Àx In x clusters most likely will resonate.</p><p>One trend that stood out in the general data was that hydroxide bridges shi downeld with increased coordination number of the metal. This trend is visible with metals such as Sn, Ga, and Zr (Fig. 5). These were the only metals that had data from several independent sources allowing reasonable conclusions to be made. This trend holds true for all of Group 13, not just gallium (Fig. 6). Tetrahedral gallium has a Ga-(m 2 -OH)-Ga bridge at 0.14 ppm, 50 Square pyramidal gallium and indium have peaks in the 1 to 1.5 ppm range, 51,60 and as stated above octahedral aluminium and gallium produce signals between 2 and 5 ppm.</p><p>1 H-NMR data reported for m 3 -OH protons are even scarcer. As previously stated, these signals appear from À1.05 to 6.79 ppm.</p><p>The proton chemical shis in these complexes are listed in Table 5. No examples of Group 13 metals with m 3 -OH ligands were found. The most relevant is the trivalent yttrium complex with a proton signal at 6.05 ppm. 58 Related hydroxide ligands in Th(IV) and Zn(II) compounds also resonate in this region. 56,59 Unfortunately, there are not enough examples of m 3 -OH protons to suggest any trends or regions for specic metals or coordination geometries. This brief literature survey will not only help the structural study and assignments presented herein, but we hope this serves as a useful resource for others seeking to assign aquo and bridging hydroxo ligands in inorganic clusters and related compounds. This survey highlights some of the challenges in interpreting even the most basic NMR signals. For example, when two distinct m 2 -OH signals arise in the same 1 H-NMR spectrum, it can be difficult to tell them apart. Two examples of this from above are the Al-(m 2 -OH)-Al bridges of Elders and colleagues' Keggin cluster, 7 and the hexanuclear yttrium species by Hubert-Pfalzgraf and coworkers. 57 These data can also help with identifying possibly misassigned signals. For instance, in [Al(m-OH)(hbo) 2 ] 2 (hbo: 2-(2 0hydroxphenyl)-2-benzoxazole) a peak at 11.47 ppm observed in CDCl 3 is proposed to be the bridging hydroxo ligands. 61 Is it possible that this is really a small amount of an aquo-Al(III) complex or some other aquo ligand-containing species? The data reported herein and our literature survey suggest that resonances this far downeld are typically due to aquo ligands; however, there are very few examples of NMR data reported for such species in CDCl 3 , so much remains to be learned. Similarly, are the peaks assigned to aquo ligands in the spectra of Al(III) and Ga(III) porphyrins containing Ga-(m 2 -OH)-Ga and In-(m 2 -OH)-In bridges at 1.5 and 1.56 ppm, respectively, actually the hydroxide bridges? 60 Hopefully, these tabulated data can be helpful for the future assignment of m 2 -OH and m 3 -OH bridges in related compounds and help begin to develop a reliable database of such peak assignments.   2 and 3).  2 and 3).</p><!><p>Chemicals were purchased from Sigma-Aldrich, TCI America, and STREM, and were used as received without further purication. The Ga 13Àx In x clusters were synthesized using previously published methods. 13,15,62 1 H-NMR experiments were conducted at 25 C in 5 mm tubes on a 500 MHz Varian spectrometer. Data were collected using Varian Soware, referenced to TMS, and processed using MestReNova. The DOSY experiments were performed using the gradient stimulated echo with spin-lock and convection compensation (DgsteSL_cc) pulse sequences. All Varian soware standard default settings were kept for DOSY unless otherwise stated. The diffusion delay was increased to 200 ms, the number of increments was increased to 20, and the highest gradient value was set to 25 000. The alternate gradient sign on odd scans and lock gating during gradient portions were also selected. All Varian soware standard default settings were kept for NOESY unless otherwise stated. The NOESY experiment was performed aer setting the 90 pulse-width to 13.0 ms, d scale increment to 700 ms, and the t 1 increment to 256. To acquire quality resolution, 16 scans were performed.</p><p>Quantum mechanical computations were used to predict the chemical shis of each hydroxo proton in the clusters. The geometries of all of the clusters were obtained from the crystal structures, including the counterions. The NMR chemical shis were computed using gauge-independent atomic orbital (GIAO) method in B3LYP/def2-SVP level of theory in the gas-phase, all as implemented in Gaussian03. 63 Since the position of the counterions was not perfectly symmetric, we computed the chemical shis for multiple counterion positions for each cluster structure, in order to eliminate the effects of static, individual counterion positions on the proton shis. For example, for Ga 8 In 5 , with one external gallium, we computed the chemical shis of 6 geometries of this cluster, one for each position the gallium could occupy relative to the counterion positions. Each computed shi for each type of proton was averaged across clusters of the same geometry discounting counterions, and the shis were scaled using constant factors for each type. 16 This particular method and procedure were chosen because exclusion of the counterions yielded incorrect ordering of the external and internal m 2 -OH protons, regardless of geometry of   InIn ðMÞ 2H the protons at any level of theory attempted by our hands. Initially, we fully optimized the entire cluster species, including the proton positions. However, the resulting structures deviated largely from the known symmetry of these structures as determined by NMR, yielding wildly varying values for the chemical shis of identical proton types. In addition, it is important to note that the theoretical predictions of the proton spectra appeared uncannily consistent with experimental spectra, even with accounting for all peaks. However, upon deeper examination of the experimental spectra of the clusters, we have discovered that the internal and external m 2 -OH signals were switched (see ESI †). Therefore, these were not used, and crystallographically determined positions were used instead. Bond lengths for the oxygen hydrogen bonds determined from crystallography may oen be 0.2-0.3 Å short; however, we found that experimentally consistent and useful computed shi values could still be obtained in comparison to experiments, in contrast to results from DFT geometry optimizations.</p><!><p>The mixed Ga 13Àx In x clusters each yield a unique 1 H-NMR spectrum aer one day in d 6 -DMSO solution (Fig. 7). 64 The clusters were crystallographically resolved prior to 1 H-NMR analysis to determine the stoichiometric ratio of the metal atoms. Diffusion Ordered Spectroscopy (DOSY) was used to verify the presence and integrity of clusters in solution (see ESI Fig. SI1-7 †). The hydrodynamic radius of each heterometallic cluster matches that of Ga 13 (Fig. 8), which was previously characterized using complementary techniques. 2,65 The combination of consistent hydrodynamic radii and the absence of any other proton signals (other than solvent) suggest that the spectra of the clusters consist of bridging hydroxide and/or capping water ligand signals. The distinct combinations of resonances observed in each spectrum conrm that the heterometallic clusters exist as distinct species.</p><p>Understanding the symmetry of these Ga 13Àx In x clusters is essential for analyzing and assigning the proton shis from NMR. The symmetry of each cluster dictates the number of expected signals that the cluster will have from the hydroxyl protons and aquo ligands. For example, the Ga 7 In 6 and Ga 13 clusters have identical symmetry, and therefore should only ideally yield three total signals from hydroxyl protons. Table 6 lists the symmetry of all Ga 13Àx In x clusters studied herein.</p><p>Water ligands coordinated to multimetallic Group 13 complexes are known to produce signals from 7-10 ppm. 3 The Ga 13Àx In x clusters contain signals between 2.5 and 7 ppm, which falls into the range expected for m 2 -OH and m 3 -OH bridges. The spectrum of Ga 7 In 6 is much simpler than that of the Ga 13 cluster. 2 We suspect this is due to the fact that the 1 st order rate constant of water exchange for In(III) is 100Â faster than for Ga(III) (4 Â 10 4 s À1 and 4 Â 10 2 s À1 , respectively). 66 The lack of peaks in the 7-10 ppm region indicates that the exchange rate of the outer water ligands is too fast to observe on the NMR time scale. 2 The rapid aquo ligand exchange of the In(III) ions allows us to observe only the protons associated with the central 7-atom Ga(III) core of Ga 7 In 6 leading to 3 signals (m 3 -OH, m 2 -OH ext , and m 2 -OH int ) are observable. This aquo ligand exchange process happens much slower with gallium; therefore, the symmetry within the core of Ga 13 is not retained and results in a complex spectrum containing more proton signals.</p><p>1. Ga 7 In 6 peak assignments: establishing a basis for comparison Ga 7 In 6 is a great test case to understand the more complicated clusters where gallium occupies one or more of the peripheral metal sites. The simplicity of the experimental data and the high symmetry of this cluster makes this cluster ideal for the purpose of assigning regions of the spectrum to particular types of protons, which in turn may be used to assign shis for the other clusters. This assignment was in turn used to determine an appropriate computational method for predicting the proton shis of the remaining clusters. The computations resulted in subtle differences in the positions of the signals from different types of hydroxo bridges in the clusters, in particular, the m 2 -OH region, which shows strong overlap of the two types of signals (Fig. 7). The m 3 -OH proton signals are observed between 6.5 and 7.0 ppm. The remaining m 2 -OH int and m 2 -OH ext proton signals are found between 3.5 and 5.0 ppm.</p><p>Ga 7 In 6 1 H-NMR spectra reveal 3 signals, which can be assigned to the three types of bridging hydroxides (Fig. 9). These three signals integrate to a 1 : 2 : 1 ratio, matching the number of protons on specic hydroxide bridges within the 7-atom cluster core (m 3 -OH : m 2 -OH ext : m 2 -OH int ratio ¼ 6 : 12 : 6) (Fig. 1, Table 6). This suggests that the peak at 4. . 53 As stated above, the signal furthest down-eld ($6.8 ppm) corresponds to the protons of the m 3 -OH, similar to the chemical shi of the m 3 -OH bridge in the octahedral Y 3+ complex. 58 The nal peak at 4.0 ppm represents the m 2 -OH int protons. This assignment is in agreement with M-(m 2 -OH)-M bridges reported for other Group 13 complexes. 5,[7][8][9][10] Due to the simplicity of Ga 7 In 6 , the spectra and analysis for this cluster make a good basis for determining a suitable theoretical method for computational elucidation of the m 2 -OH signals. Most importantly, computations performed without explicit counterions in the structure predict the exact opposite ordering of the internal and external m 2 -OH signals. This was so, regardless of the theoretical methods (HF, B3LYP), basis sets (6-31G* 67,68 /LANL2DZ, 69,70 def2-SVP, 71 def2-TZVP, 71 def2-QZVP, 71 etc.), or solvation methods (gas, COSMO, 72 PCM, 73 and CPCM 74 ) employed. From our observations, improvements in levels of theory are unlikely to address the discrepancy. However, when counterions are included, correct ordering is obtained, namely that the m 2 -OH ext signals are downeld from the m 2 -OH int protons (Fig. 9). These results indicate that the presence, location, and identity of the counterions is immensely important for determining even the qualitative assignments of 1 H-NMR chemical shis of aqueous metal clusters. The ordering or the m 2 -OH int and m 2 -OH ext protons is more difficult to see for the remainder of the clusters due to signicant overlap of m 2 -OH signals, and computations were diagnostic in discriminating these convoluted overlapping signals in all the clusters.</p><!><p>As gallium is substituted for indium in the exterior positions of the cluster, a greater number of proton types emerge (Fig. 6). There are 16 unique types of protons in the clusters based on idealized symmetry: 6 m 3 -OH, 6 m 2 -OH int , and 4 types of m 2 -OH ext (Table 6). The environments of these protons were determined by the identity of the nearest external metal ion and its two nearest neighbors (i.e., Ga or In). For example, proton H</p><p>InInIn is a m 3 -OH proton in a section of the cluster with an exterior indium ion directly outside (always indicated in bold) possessing two additional exterior indium atoms on either side (Fig. 10). Proton H</p><p>InInIn corresponds to the symmetry-equivalent m 2 -OH int proton bridging the same metals as proton H m 3 InInIn (Fig. 10). The m 2 -OH ext protons are described in a similar manner. Proton H</p><p>InIn corresponds to the m 2 -OH ext proton connected to an indium ion (indicated in bold) and positioned facing towards a second indium. This naming system is comprehensively represented by Table 6.</p><!><p>The peak in the 6.55-6.85 ppm region of the Ga 7 In 6 spectrum corresponds to the m 3 -OH protons. This region contains the simplest set of signals in all the mixed clusters. We suspect that this is because the m 3 -OH protons are the farthest away from, and therefore, the least affected by the bound DMSO. Each peak in this region for the 7 NMR spectra is corresponds to one of the 6 types of m 3 -OH protons (Table 7). Proximity to the indium ion causes downeld shiing in the proton signal. This is best shown in Ga 7 In 6 , which has one type of proton ðH</p><p>InInIn Þ, and exhibits the farthest downeld signal. Ga 13 also has only one type of m 3 -OH proton ðH GaInGa , respectively) in 3 : 2 : 1 ratios. This is mirrored in the NMR spectra facilitating the assignment of each proton type to a peak (Table 7). Ga 9 In 4 , Ga 10 In 3 , and Ga 11 In 2 are slightly more complicated because each has 3 possible isomers (Table 6), but each predicted m 3 -OH peak is observed. The H</p><p>InInIn type protons are shied farthest downeld, while the H</p><p>GaGaGa type protons are shied the farthest upeld, for an overall ranking from highest to lowest ppm of H</p><p>GaGaGa (Table 7). Computations support that these signals are produced by m 3 -OH protons and that the H GaGaGa protons. The calculations cannot corroborate or contradict the relative rankings within those two sets (Table 7).</p><p>In the case of clusters with multiple isomers, the peak integrations of the m 3 -OH protons in the NMRs can provide information about the ratio of each isomer present in the sample. The statistical probability of each isomer, along with the calculated % present in solution, is shown in Table 8. Similarities in the structures of Ga 9 In 4 and Ga 11 In 2 allow for comparisons. 75 The NMR data remarkably show a strong correlation to the statistical ratio of isomeric heterometallic clusters. This data indicates that no specic substitution pattern of indium in the outer shell of the clusters is kinetically favorable.</p><!><p>The m 2 -OH regions of the NMR spectra are not as easily deconvoluted. Based on the Ga 7 In 6 spectrum, the upeld peaks correspond to m 2 -OH bridges, but as more gallium atoms are introduced into the outermost shell and exchange between the coordinating water ligands and DMSO slows, symmetry is broken, and complexity increases. We now propose to assign Table 8 The isomers of Ga 9 In 4 , Ga 10 In 3 , and Ga 11 In 2 with relative m 2 -OH peak intensities predicted using the integration of m 3 -OH protons, ratio of isomers in solution based on probability, and experimental percentage of isomers present in solution calculated using the m 3 -OH proton integrations. Green: gallium. these peaks as well. As with the m 3 -OH protons, computations were used to establish the range in which the m 2 -OH protons should be found. GaIn to be assigned using NOESY (Fig. 12).</p><p>The use of these experimental results allowed for additional verication of quantum mechanical methods. The assignments based on integration values and the NOESY spectra established a basis of comparison for determining the most accurate computational method. Using the average computed NMR shis from the structures with counterions for each proton type, the computed results were compared to the experimentally determined proton shis for several basis sets, as mentioned previously. The def2-SVP basis set was found to provide the optimal combination of accuracy and computational time, as the computed proton rankings were an exact match with experimental results. Therefore, we know this computational method can be used to assign the protons in the more complicated spectra with a larger number of isomers and an increasing number of gallium centers.</p><p>4.2 Ga 9 In 4 . Ideally Ga 9 In 4 has 5 types of m 2 -OH int and all 4 types of m 2 -OH ext bridges. As previously stated, this cluster has 3 isomers which exist in a 2 : 2 : 1 ratio. This means that the protons in Ga 9 In 4 integrate to the ratios shown in Table 8. Based on these integrations, peaks have been experimentally assigned to the Ga 9 In 4 spectrum (Fig. 13). Peaks H InIn for Ga 9 In 4 ; however, an integration of 14 suggests that proton H</p><p>GaGa also appears at this chemical shi. Interestingly, the signal for proton H</p><p>GaIn seems to have split into two peaks at $4.2 ppm. This is most likely due to the slower exchange rate of the outer water ligands on gallium. Because H</p><p>GaIn is bridging an outer gallium atom this may be the rst sign of the complex spectrum we see for Ga 13 . This may also explain the small shoulder/ splitting of peak H   peaks overlap with others, the integrations are no longer solely reliable for making full assignments. Therefore, the relative values of the computed NMR shis were used alongside the known assignments from Ga 7 In 6 and Ga 8 In 5 for the most precise results. This allowed for the H GaGa . Likewise, the computed shi for the H m 2int GaInGa was compared to the signals from the other internal and external m 2 -OH protons. This analysis showed that I should have the farthest downeld shi of the internal m 2 -OH protons, but should not be higher than any of the external m 2 -OH protons. Aer determining the identity of the peaks in the Ga 9 In 4 spectrum, this method was used to further assign the peaks in the spectra of the clusters with increasing gallium content.</p><p>While these computations were successful in reproducing the relative ordering of proton signals, the present method is not sufficient to quantitatively reproduce the exact proton shis. This is because this method does not rely on quantum mechanically determined positions of the counterions with respect to the clusters. Quantitative predictions will necessitate a more rigorous method for determining the cluster-counterion complex. We suspect that the success of our method in being able to reproduce qualitative ordering of the proton peaks suggests that the counterions are loosely coordinated around the cluster and is dynamically equilibrating among the different sites in the NMR time scale. Work is continuing in this area to produce quantitative predictions from ab initio molecular dynamics simulations with explicit counterions and solvents.</p><p>4.3 Ga 10 In 3 -Ga 13 . Experimental data suggests that Ga 10 In 3 also exists as three isomers but, in a 3 : 6 : 1 ratio leading to the peak integrations listed in Table 8. Unfortunately, the complexity caused by the increasing number of exterior gallium atoms and the isomers does not allow these signals to be assigned experimentally. Similar issues arise for Ga 11 In 2 to Ga 13 . Given the complexity of the signals arising from the protons in these clusters, computations are particularly useful for peak assignment.</p><p>Computed shis were used to assign the remaining types of protons for each of these clusters (Fig. 15). Unfortunately, we are unable to compute the changes based on coordinated DMSO breaking the symmetry; therefore, only the peaks of the "mother cluster" (fully H 2 O ligated) can be assigned in these spectra. Primarily, this involved computing the position of H m 2int GaGaGa , which represents the protons in a section of the cluster with three external gallium ions next to each other. Computed results suggest that H m 2int GaGaGa should have the lowest shi of all of the internal m 2 -OH protons, which is the lowest ppm value for all of the computed signals.</p><!><p>The Ga 13 mother cluster peaks ðH GaGa Þ assigned via computations were thereaer conrmed experimentally. By plotting the 1 H-NMR spectra of Ga 13 dissolved in a variety of ratios of d 6 -DMSO and d 7 -DMF, it is clearly visible that only 3 peaks persist from 100% d 6 -DMSO to 100% d 7 -DMF (Fig. 16). The other peaks visible in the spectra are caused by "daughter clusters" substituted with either DMSO or DMF ligands at the aquo sites; therefore, the only shared species must be the mother cluster.</p><!><p>This research has led to quick and cost effective differentiation and structural characterization of the Ga 13Àx In x clusters in solution via 1 H-NMR spectrscopy. 77 We have shown that each mixed Ga 13Àx In x cluster does independently exist in solution and that there are no kinetically or enthalpically favored isomers (i.e., only the expected statistical ratios of the various isomers were observed). These isomers exist in statistical ratios determined by probability of formation. In general, this study provides a complete method for experimentally and computationally predicting proton shis for inorganic m 3 -OH and m 2 -OH signals in gallium and indium species, as well as, a literature review of hydroxide bridges for all diamagnetic metals available in the literature to the best of our knowledge. This knowledge will initiate the study of cluster dynamics in solution, allowing for better control and manipulation of precursor clusters. The solution behavior of clusters condensing into lms is a primary interest of this research; however, inorganic cluster species are not only relevant to the thin lm and electronics markets. Many small clusters, including the Ga 13Àx In 13 clusters have structures much like fragment of minerals. The reverse process, bulk material breaking down into smaller components (i.e. minerals dissolving in acid rain) is a promising environment for locating dynamic clusters. It is possible that a plethora of clusters form naturally as minerals dissolve, but we have had no way of detecting these intermediate molecules. Geoscience may be greatly affected by the use of 1 H-NMR for the observation of inorganic -OH bridges. Al 13 Keggin and calcium carbonate clusters have both been detected in nature. 78,79 It would be benecial for the geoscience community to investigate water samples from streams, caves, hot springs, geysers, and ocean vents for the presence of these observable hydroxo bridges. 1 H-NMR research on completely inorganic systems is limited, but this study shows that it can lead to a variety of information previously thought to be inaccessible. Oregon</p>