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The chemistry of donor-acceptor cyclopropanes (DACs) is a rapidly developing field in modern organic synthesis. These stressed small carbocycles provide an attractive basis for the synthesis of acyclic as well as five-, six-, and seven-membered compounds. . Many organic reactions are known for DACs . Three main types of reactions of DACs in which donor and acceptor substituents are located vicinal can be distinguished (Scheme 1) . Ring-opening reactions involve the transformation of DAC by electrophilic and nucleophilic reagents in the presence of various Lewis acids (Scheme 1, ). This type of reaction can be used to produce 1,3-bifunctionalized compounds with an open chain, and it is widely used in the synthesis of biologically active molecules . DACs are often regarded as synthons for 1,3zwitterionic intermediates, which undergo cycloaddition and annulation reactions (Schemes 1, (2) and ( )). Indeed, the capacity of DACs to engage in cycloadditions provides access to a diverse range of carbocyclic and heterocyclic structures. . The rearrangement of DACs leads to the formation of unsaturated five-membered heterocycles, thus providing a metalfree approach to connected heterocyclic structures (Schemes 1, (2) and ( )). This paper focuses on the [3+2]-cycloaddition reaction of DACs with aldehydes, which provides a wide range of cyclic compounds depending on the Lewis acid used.
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It is known that the reaction of DACs with aldehydes under the action of anhydrous GaCl 3 is an interesting method for the formation of substituted indenes and polycyclic lactones . Recently we have discovered a novel TaCl 5 -mediated transformation of DACs in the presence of two equivalents of aromatic aldehydes, which yields tetrahydronaphthalene derivatives (Scheme 2) . However, the range of substrates studied was quite limited. In this study, we report preliminary results on the study of the influence of factors of substituents in the ester group of DAC and aromatic aldehyde on the reaction outcome.
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It was found that the reaction of dimethyl 2-(4chlorophenyl)cyclopropane-1,1-dicarboxylate 1a with 2 equiv. 4chlorobenzaldehyde and 2 equiv. TaCl 5 in 1,2-dichloroethane solution at 23 °C for 24 h leads to the selective formation of trichloro-substituted 4-phenyl-3,4-dihydronaphthalene-2,2(1H)dicarboxylate 2a in 89% yield (Scheme 3). The transformation of DAC 1b, which has an ethyl substituent in the ester group, occurs equally effectively under the action of 4-bromobenzaldehyde. Thus, the presence of a chlorine atom in the para position in the phenyl substituent of 2-(4-chlorophenyl)cyclopropane-1,1-dicarboxylate does not prevent the reaction of DAC with a halogenated aromatic aldehyde. The use of diethyl 2-(4-chlorophenyl)cyclopropane-1,1dicarboxylate also does not prevent the conversion of DAC under the action of aromatic aldehyde and TaCl 5 . The results obtained indicate a wide range of possibilities for the application of the TaCl 5mediated reaction between 2-phenylcyclopropane-1,1dicarboxylate and aromatic aldehydes in the synthesis of functionalized tetrahydronaphthalenes.
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Indium nitride (InN) is a semiconducting material with a narrow bad gap of 0.7 eV and a high electron mobility and velocity, giving it potential uses in, for example, infra-red photovoltaics and high frequency transistors. Conventional chemical vapor deposition (CVD) of InN, using the common precursors trimethyl indium (TMI, In(CH3)3) and ammonia (NH3), is limited by the low thermal stability of the material, which decomposes into metallic indium and nitrogen gas already at 500 °C. By utilizing low temperature atomic layer deposition (ALD) as a time-resolved alternative to CVD the low thermal stability could be circumvented as depositions could occur below the decomposition temperature.
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Precursors with chelating ligands forming N-In bonds have also been used successfully to deposit InN with NH3 plasma. However, a thermal ALD process has not been shown experimentally. This is in contrast to the other group 13-N semiconductors AlN and GaN which both has been grown using thermal NH3 and trimethyl aluminum (TMA, Al(CH3)3) and trimethyl gallium (TMG, Ga(CH3) 3) 13,14 respectively. Since plasma ALD of InN gives films with TMI, and since the plasma discharge is not activated when TMI is exposed to the NHx covered InN surface, it is reasonable to assume that the limitation to a thermal ALD process for InN is found in the interaction between NH3 and the -In(CH3)x covered InN surface. Although it is thermodynamically favorable for NH3 to decompose into N2 and H2 at the temperatures in the ALD processes, the decomposition is limited by very slow kinetics at these temperatures, making NH3 stable during the residence time in ALD. The majority of the NH3 molecules are therefore expected to arrive to the surface intact in thermal ALD, contrasting plasma ALD processes where the plasma decompose the NH3 molecules into more reactive species. Ab initio calculations on NH3 adsorption have been reported earlier on GaN by Krukowski and co-authors. I their work they have shown that upon adsorbing onto a bare GaN surface, NH3 can form a variety of different NHx surface species located at different adsorption sites. By thermodynamic analysis they derived the stability of these species and investigated the prevalence at different partial pressures of NH3 and H2. Using a similar approach, we investigated the stability of different NHx surface species on AlN, GaN and InN. Here we also found that there exists different stable configurations of NHx with similar structures on all three materials. In these studies, NH3 is modeled to adsorb on a bare surface allowing it to easily reach an adsorption site. However, after thermal adsorption of trimethyl metal precursors the adsorption sites would be blocked by methyl groups, kinetically hindering initial adsorption.
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The lack of a thermal ALD process for InN, which is known for AlN and GaN, indicates a reaction path for adsorption of intact NH3 on AlN and GaN, that is not accessible on InN. In this study we use quantum chemical modeling of NH3 adsorption on methylterminated GaN and InN. By comparison of adsorption energies and barriers we find that there exists a possible adsorption path of NH3 on GaN, while the similar path on InN would be orders of magnitude slower. We argue that this huge difference in reaction time would explain why adsorption of NH3 is severely limited on InN and thus that a fully thermal, low temperature ALD process of InN with TMI and NH3 would be very challenging.
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First principle density functional theory (DFT) was used to investigate the adsorption of NH3 during the 2 nd step of the thermal ALD cycle using the Vienna Ab initio Simulation Package (VASP) , with optimizers extended by the VTST package. The General Gradient Approximation (GGA) functional PBE together with the 3 rd version of Grimme's dispersion correction was used with a planar wave basis set with cut-off energy of 700 eV and Projector augmented wave (PAW) potentials. The valence electron configuration used for the different elements were 1s 1 for H, 2s 2 2p 2 for C, 2s 2 2p 3 for N, 3d 10 4s 2 4p 1 for Ga and 4d 10 5s 2 5p 1 for In. The electronic convergence was set to 10 -6 eV for geometry optimization and 10 -8 eV for phonon calculations. All structures were optimized until the forces on all atoms were less than 10 -2 eV Å -1 . For surface structures, the positions of atoms at the lower five layers were kept fixed after optimization of the initial structure. Transition State (TS) structures were found by the Nudged Elastic Band (NEB) method as implemented in VTST. After structural optimization, harmonic phonon calculations were preformed using finite displacements.
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The thermodynamic potentials for surface species were calculated using only vibrational contribution to the partition function, while for gaseous species translational and rotational contributions was included as well. Thermochemical calculations were performed at STP (298.15 K, 1 atm) and at 500 -800 K, i.e., temperatures of interest for ALD of GaN and InN.
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The investigated adsorption pathway for GaN (Fig. in the supplementary material ) and InN (Fig. ) follow a very similar path, starting from the methyl terminated surface previously found as the final product after a self-limited adsorption cycle of TMG/TMI. This surface has a methyl group on top of each surface metal atom, with a bond length of 1.97 Å for GaN and 2.18 Å for InN, pointing almost perpendicular to the surface. 1c and S1c), physiosorbed CH4 above the NH2 substituted surface (D) (Figs. and), and the NH2 substituted surface with CH4(g) (E) (Figs. and). The energies of the adsorption paths on GaN and InN are given in Tables I and II, respectively, and graphically in Fig. . Table . Energy (in kJ mol -1 ) for NH3 chemisorption pathway on GaN. All energies are relative to the methyl terminated surface and gaseous NH3 (A). When NH3 is introduced to the surface, it is sterically blocked from forming a bond to the Ga/In surface atoms by the methyl groups. This causes the NH3 molecule to form a very week physisorption, with the surface at a large distance (2.9 Å above the methyl groups). The distance is much larger than the expected distance for a covalent bond and the low adsorption energy indicates only non-covalent interactions between NH3 and the surface. NH3 is therefore expected to be able to quickly diffuse over the surface as well as easily desorb.
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As the metal atoms are protected by the methyl groups, ligand exchange of CH3 to NH2 cannot occur directly. Instead, a methyl group must desorb from the surface, leaving a vacancy onto which NH3 can adsorb, in a SN1 like mechanism. While adsorbing, a H atom can be transferred from the NH3 to the released methyl group allowing it to be released as methane leaving NH2 to adsorb onto the vacant site.
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The energy profiles, Fig. , shows that the adsorption path for NH3 follow a similar path with a net lowering of the free energy after ligand NH2 substitution, indicating that the adsorption process is thermodynamically favorable on both surfaces, and that both Ga and In prefers to bond with NH2 compared to CH3. At ALD temperatures, 500-700 K, the net free energy is almost independent of changes in temperature, due to only a small change entropy during the adsorption. However, for adsorption on InN, the energies are shifted upwards compared to on GaN, showing that the process is less favorable on InN. The energies are shifted higher when the initial carbon-metal bond is broken, suggesting that the methyl termination is more strongly bound to InN compared to GaN and that the preference to bind with NH2 instead of CH3 is much lower for In.
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The difference in the free energy of the barrier is even more pronounced than the difference in net free energy. As the main contribution to the energy of the barrier is the desorption of a CH3 group from the surface, this is also a clear indicator that InN binds CH3 harder compared to GaN. The difference in the barrier is between 86-108 kJ mol -1 at ALD temperature. Comparing rate constants of adsorption obtained from these barriers by transition state theory, Table , indicates that the chemisorption of NH3 is many orders of magnitudes slower on InN compared to GaN, with the ration of rate constant for adsorption on InN divided by the constant for adsorption on GaN ranging from 1.0 × 10 -9 at 500 K to 9.2 × 10 -8 at 800 K. Furthermore, the rate constant for adsorption on InN at 800 K is of the same magnitude as the rate constant for adsorption on GaN at STP, which is much lower than the temperatures used in thermal GaN ALD. For an ALD process of InN with thermal NH3 to work in a similar time frame as for GaN, either the temperature of the process must be increased, which is hindered by the thermal instability, or the NH3 pressure must be increased significantly, well outside the possible working pressures for ALD.
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Overcoming this limitation towards a thermal ALD of InN would require other precursor alternatives to the TMI and NH3 combination, e.g. an indium precursor that would leave a more reactive surface where NH3 could adsorb or a nitrogen precursor the would be reactive towards the methyl-terminated surface left by the TMI half-cycle.
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In this study, we have compared NH3 adsorption on GaN and InN using a DFT approach. The adsorption path is very similar for both surfaces, involving a SN1 like mechanism, in which a methyl group must desorb from the surface initially, allowing the NH3 to adsorb onto the vacant site. The pathway is less energetically favorable for
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Computing accurate reaction enthalpies represents for large molecules represents a significant challenge to computational chemistry. Sengupta and Raghavachari 1 recently demonstrated that their connectivity-based hierarchy (CBH) protocol 2 can be used to compute reaction enthalpies that, on average, are within 1-2 kcal/mol of G4 theory 3 , using density functional theory and triple-zeta basis sets (DFT/TZV). While encouraging, the computational cost of the DFT/TZV calculations are still too high to be routinely applied to large biomolecular systems. Here we test the accuracy of the CBH approach using computationally more efficient methods such as DFT/DZV, minimal basis set Hartree-Fock, tight-binding DFT, and neglectof-diatomic-differential-overlap (NDDO)-based semi-empirical methods, using the Sengupta and Raghavachari 1 data set. As part of the work we have completely automated the CBH approach so that it only requires a SMILES string representation of the molecule, which is easily generated using chemical drawing programs such as ChemDraw.
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The paper is organized as follows. We first present the computational methodology including a brief description of the CBH approach. Next we discuss the accuracy of the predicted reaction enthalpies as compared to G4 reference values for the 25 reactions used by Sengupta and Raghavachari and perform an error analysis of outliers by comparing heats of formation of the CBH fragments to G4 values. Finally we summarize our conclusions and discuss their potential implications for parameterization of semi-empirical methods. shows the mean unsigned error (MUE) relative to G4 reaction enthalpies for the parent reaction (Dev-0) and the CBH-1 (Dev-1) and the CBH-2 (Dev-2) correction schemes. In addition the maximum absolute error for the CBH-2 scheme is also listed. As observed in the Sengupta and Raghavachari 1 study CBH-1 correction scheme provides only a modest improvement in accuracy and for many of the semi-empirical methods the error actually increases. We will return the source of the error-increase in the next subsection, but for now we will focus on the accuracy of the CBH-2 results.
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The MUE of PBEh-3c, which is a dispersion-corrected hybrid DFT/double-zeta valence method, is 1.9 kcal/mol which is very similar to the 1.3-2.1 kcal/mol MUE values obtained by Sengupta and Raghavachari 1 for dispersion-corrected DFT functionals using the much larger 6-311++G(3df,2p) basis set and B3LYP/6-311+G(d,p) geometries and frequencies. This is consistent with Sengupta and Raghavachari 1 's observation that the Dev-2 error is fairly insensitive to basis set size. Similarly, the MUE of HF-3c, which is a dispersion-corrected HF/minimal basis set method is 2.4 kcal/mol, which is only 0.3 kcal/mol higher than the value obtained by Sengupta and Raghavachari 1 using HF/6-311++G(3df,2p)//B3LYP/6-311+G(d,p). The MUE is computed without reaction 19, which is a clear outlier and will be discussed in detail in the next subsection. For comparison, the STO-3G MUE is 3.0 kcal/mol, so empirical corrections (most likely dispersion) contribute to accuracy of the HF-3c method.
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GFN-xTB and DFTB-D3 are the most accurate semi-empirical methods with MUEs of 3.9 and 3.7 kcal/mol, followed by DFTB (4.5 kcal/mol) and PM3 (4.8 kcal/mol) -with both pairs of methods being statistically identical (Table ). The good performance of GFN-xTB and DFTB-D3 is especially remarkable because they are not specifically parameterized against any reaction energies. Comparison of the MUEs for DFTB-D3 and DFTB shows that dispersion corrections lead to noticeably more accurate reaction enthalpies for DFTB, consistent with previous findings. The remaining NDDO-based methods have statistically identical accuracy, with MUEs in the range 5.2 to 5.9 kcal/mol, with the exception of PM6-D3H+, which has en MUE of 6.5 kcal/mol. The MUEs for PM6, PM6-DH+, PM6-D3, PM6-D3H4X, and PM7 are computed without reaction 23, which is a clear outlier and will be discussed in detail in the next subsection. Furthermore, Reactions 16 and 22 are omitted for OM2 because it is not parameterised for fluorine. We note that PM6-D3H+ has an Dev-2 error of 15.0 kcal/mol and is therefore not considered an outlier. So while the MUE for PM6-D3H+ is higher than for the other PM6-based methods it does not lead to any outliers using the Dev-2 method. For the semi-empirical methods there is little correlation between the MUE for parent reaction and the CBH-2-corrected values. Similarly, with an MUE of 6.8 kcal/mol OM2 performs reasonably well for the parent reactions, but worst with CBH-2.
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We start by considering the PM6 result for the first reaction (R1), where the PM6 error is -0.3 kcal/mol for the parent reaction and the CBH-1 correction is -12.7 kcal/mol. PM6 error is quite low for the parent reaction so, ideally, the CBH-1 correction should be close to zero, but is in fact quite large in magnitude. In order to understand the source of this error we reformulate the (∆CBH-n(G4) -∆CBH-n(LL)) correction in terms of errors in heats of formation (HOF, ∆H
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The errors in the HOFs for PM6 (and all other methods) relative to G4 are listed in Table , and show that the error in the HOFs relative to G4 are CH 4 : -5. In contrast, the PBEh-3c error for the parent reaction is 9.0 kcal/mol, which decreases to -4.5 kcal/mol with the CBH-1 correction. The error in the HOFs relative to G4 are CH 4 : 8.5, CH 2 --CH 2 : 6.0, and CH 3 CH 3 : 14.9 kcal/mol. So the CBH-1 correction is 4(14.9) -2(6.0) -4(8.5) = 13.6 kcal/mol, which when subtracted from 9.9 lowers the error in reaction energy to -4.5 kcal/mol. Clearly the errors in HOFs are much larger than for PM6, yet most of the error cancels. The reason is that the magnitude of the HOF error tends to scale with the number and types of bonds in the molecule for ab initio methods. For example, the HOF-error of CH 2 --CHCH 3 is 13.7 kcal/mol, which is approximately the sum of the HOF-errors of CH 3 CH 3 and CH 2 --CH 2 , minus the error for CH 4 : 14.9 + 6.0 -8.5 = 12.4 kcal/mol. This type of error scaling makes ab initio results very amenable to improvement using the CBH approach.
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and the corresponding errors in HOFs (Table ) show that the magnitude of the CBH-2 correction derives from the HOF error of CH 2 --C --CH 2 (7.7 kcal/mol) which is considerably larger than, and opposite in sign from, the errors in HOF of the remaining fragments (-1.1 to -4.1 kcal/mol).
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For R19 the HF-3c Dev-2 error is -33.5 kcal/mol, much larger in magnitude than other Dev-2 error for HF-3c. For comparison the corresponding value for HF/STO-3G is -12.0 kcal/mol. In R19 an oxirane ring is formed, which may pose a special challenge to minimal basis sets that may not offer sufficient flexibility to describe the ring strain. Indeed, the Dev-2 error for the first reaction shown in Figure is -14.6 and -12.6 kcal/mol for HF-3c and HF/STO-3G, respectively. While these errors are similar to the HF/STO-3G Dev-2 error for R19, they are still significantly smaller than the HF-3c Dev-2 error for R19, so we performed similar calculations for the second reaction shown in 2a, which is more similar to R19. The HF-3c and HF/STO-3G errors are -16.4 and -11.7 kcal/mol, respectively. The source of this increased difference in error between HF-3c and HF/STO-3G can be understood by decomposing the Dev-2 error into contributions from the two "half-reactions" (2c). The HF-3c and HF/STO-3G Dev-2 errors for the "product reaction" are very similar (-12.5 and -11.5 kcal/mol), while the HF-3c error is 4.0 kcal/mol higher than that for HF/STO-3G for the reactant reaction. Thus, the higher Dev-2 error observed HF-3c is primarily due to a higher error for the reactant. So, one possible explanation for -33.5 kcal/mol error for HF-3c is that roughly 13 kcal/mol comes from the oxirane ring in the product while the remaining error comes from the four rings in the reactant (4(4.0) = 16 kcal/mol).
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HF-3c differs from HF/STO-3G in several ways: HF-3c uses the MINIX basis set instead of STO-3G and has three empirical corrections accounting for dispersion (E disp ), basis set superposition error (E BSSE ), and bond length errors (E SRB ). These three corrections contribute 1.1 and 4.8 kcal/mol to the errors in the product and reactant half-reactions, respectively. Thus the larger error compared to HF/STO-3G for the product half-reaction is primarily due to the difference in basis set. This observation is also consistent with the fact that the HF/MINIX Dev-2 error for the R19 is -24.8 kcal/mol kcal/mol.
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The connectivity-based hierarchy (CBH) protocol for computing accurate reaction enthalpies developed by Sengupta and Raghavachari 1 is tested for fast ab initio methods (PBEh-3c, HF-3c, and HF/STO-3G), tight-binding DFT methods (GFN-xTB and DFTB), and NDDO-based semi-empirical methods (AM1, PM6, PM6-DH+, PM7, and OM2) using the same set of 25 reactions as in the original study. As observed by Sengupta and Raghavachari 1 , the CBH-1 correction scheme, which reflects the change in bonding, provides only a modest improvement in accuracy and for many of the semi-empirical methods the error actually increases. For the CBH-2 scheme, which reflects the change in the immediate chemical environment of all the heavy atoms, the MUE relative to G4 of PBEh-3c is 1.9 kcal/mol which is very similar to the 1. While the accuracy is lower for the minimal basis set and semiempirical methods are lower than for PBEh-3c, they are significantly more computationally efficient with HF-3c and HF/STO-3G being roughly 10-50 times faster and the semiempirical methods being roughly 1000 times faster, depending on system size. It is worth noting that GFN-xTB is roughly 10 times faster than the other semiempirical methods, which can lead to significant time savings when dealing with thousands of molecules. However, significant changes in bonding and/or unusual bonding still presents are challenge to these faster methods as evidenced by the presence of outliers.
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More generally, our analyses show that while the errors in HOF computed by ab initio and tight-binding DFT methods tend to be larger in magnitude than for the NDDO-based semiempirical methods, the magnitude tends to scale systematically with the number and types of bonds in the molecule, which make them very amenable to improvement using the CBH approach. The NDDO-based semi-empirical methods are optimized by reducing the absolute HOF-error independent of system size and, as a result, the HOF-error of an individual molecule tends to be relatively random both in sign and magnitude, which makes them less amenable to improvement using the CBH approach. A better approach may be to parameterize the semiempirical methods by minimizing the CBH-corrected error and presenting the CBH-corrected energies to the user. For example, while NDDO-based methods would parameterize by minimizing the HOF-error of propane (∆HOF(propane)), a CBH-1-based scheme would minimize [∆HOF(propane)-(∆HOF(ethane)-∆HOF(methane)] and present the CBH-1 corrected HOF to the user. This approach might make it easier to find more generally applicable parameters that better and systematically minimize the error, since the underlying HF approach "naturally" gives larger errors for larger systems and we are no longer asking the parameters to "undo that" by searching for small errors independent of system size.
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geometries supplied by Sengupta and Raghavachari 1 (some molecules related to R2, R5 and R16 were missing and build from scratch). Enthalpy corrections are not included for the NDDO-based methods, because they are parameterized to reproduce enthalpies of formation. We computed enthalpies of formation, for analysis-purposes, using the method outlined by Curtiss et al. . The PBEh-3c and HF-3c are performed with ORCA , the DFTB calculations with GAMESS , the xTB calculations with the xTB program 11 , the OM2 with MNDO 27 and the remaining NDDO-based methods are performed with in MOPAC .
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The versatility of arynes as reactive intermediates continues to spur advances in organic synthesis including the discovery and development of asymmetric reactions and access to complex scaffolds. Although deprotonation/elimination was one of the earliest methods to generate arynes, the past several decades have been dominated by fluoride induced elimination of o-trimethylsilylaryl triflates because this has proven to be an exceptionally mild strategy (Scheme 1a). Notwithstanding the functional group compatibility of this approach, the primary limitation lies in the multi-step synthesis of o-trimethylsilylaryl triflates (Scheme 1a). The commercial availability of these reagents is therefore limited and the cost exorbitant relative to other arylation reagents. Moreover, the synthetic sequence to access o-trimethylsilyl aryl triflates requires strong bases and consequently the functional group compatibility of these aryne precursors is actually quite limited with respect to the aryl substituents (R-group in Scheme 1a). On balance, although generation of arynes is mild, otrimethylsilyl triflates do not provide efficient access to diversely substituted arynes and novel aryne precursors are needed to continue advancing synthetic capabilities with these reactive intermediates.
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Aryl "onium" reagents have emerged as aryne precursors during a resurgence of methods based on orthodeprotonation/-elimination (Scheme 1b). These aryne precursors include those based on halogen leaving groups such as iodonium, bromonium, and chloronium, as well as chalcogen leaving groups such as sulfonium and oxonium (Scheme 1b). In several cases, these "onium" leaving groups permit the use of mild bases such as potassium and cesium carbonate and potassium phosphate to generate arynes, and these approaches rival or even exceed the functional group compatibility of fluoride-induced aryne generation of otrimethylsilyl triflates. Although aryl "onium" reagents have provided a mild way to generate arynes via deprotonation, they have not universally improved the generality and efficiency of accessing arynes. For instance, cyclic diarylhalonium salts specifically deliver biaryl-derived arynes and therefore lack broad generality. Additionally, triaryloxonium salts require a substantial time and material investment to synthesize similar to that of otrimethylsilylaryl triflates. Unsymmetrical aryl(Mes)iodonium and aryl thianthrenium salts are uniquely positioned within this class of aryne precursors to effect both mild and efficient access to arynes (Scheme 1b).
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Simple arenes are unconventional aryne precursors because they lack complimentary electrofugal and nucleofugal leaving groups for a redox neutral elimination event. Yet, the dehydrogenation of simple arenes represents an expansive source of latent aryne intermediates and even has the potential for late-stage functionalization of active pharmaceutical ingredients and agrochemicals. In 2023 we merged the C-H functionalization of arenes via thianthrenation and deprotonative aryne generation for a net dehydrogenation of simple arenes as an efficient way to access arynes (Scheme 1c). In our early optimization, we found that aryl thianthrenium salts were more easily accessed than aryl(Mes)iodonium salts and we therefore developed a two-step sequence in which the aryl thianthrenium salts were isolated and subsequently used as aryne precursors (Scheme 1c). Although the isolation of aryl thianthrenium salts is relatively straightforward, only involving trituration and filtration, it does represent an additional, and potentially unnecessary, manipulation (Scheme 1c). Moreover, we found gaps in scope including simple feedstocks (i.e., benzene, toluene, anisole), polysubstituted arenes (i.e., 1,3-disubstituted arenes) including heteroarenes, and several useful functional groups such as triflate, nitro, and ester (Scheme 1c). Scheme 1. Overview of access to arynes.
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Herein, we describe a conceptual shift to access arynes from reagents that rely on pre-functionalization to those that only bear hydrogen substituents at the eventual aryne site (Scheme 1d). The methods we describe in this work uses simple arenes to generate arynes, which substantially expands the breadth of arynes that are accessible. Moreover, we increase the efficiency of this approach so that a simple arene may be converted into a trapped aryne within hours and no isolation of aryl thianthrenium intermedi-ate species is needed. Additionally, we show that tuning the C-H functionalization by installing iodonium leaving groups expands the scope of arenes that participate in these transformations. Finally, mechanistic analysis reveals the complementarity of sulfonium and iodonium leaving groups and this is specifically highlighted in a "user's guide" to employing simple arenes to access arynes.
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Increasing efficiency. An overarching goal of this line of research is to convert simple arenes into arynes. We partially achieved this goal by developing a two-step procedure to install a thianthrenium leaving group followed by ortho-deprotonation and -elimination (Scheme 1c). To further advance this goal, we re-evaluated this process to develop a one-pot procedure in which a simple arene can be selected from a chemical inventory and converted into a trapped aryne within several hours and without isolation of any intermediate species (Scheme 2). There were two major hurdles to merging the two-pot process into a onepot procedure: 1) two different solvents were used and 2) the acidic and basic conditions of the two steps are incompatible. We selected 4-chloroanisole 1a as the simple arene for study and the conditions presented below in entry 1 of Table are the result of a large number of experiments to rectify the challenges described above. Under these conditions 1a and TTO are dissolved in MeCN followed by the addition of triflic anhydride (Tf2O) at 0 °C to yield a homogenous light purple solution (Table ). After stirring for 30 minutes at room temperature, solid potassium phosphate is added to the vial, which results in a loss of the purple color and the reaction mixture is stirred for an additional five minutes. Furan 2a and solid sodium tertbutoxide are added to the vial and it is placed in a preheated (65 °C) aluminum block for 60 minutes. The trapped aryne product 3aa is observed in 86% 1 H-NMR yield from 1a; 3aa is obtained in 73% isolated yield after purification by column chromatography when the reaction is conducted on 0.5 mmol scale of 1a (Table ). A summary of experiments to demonstrate the relevance of each component in the reaction sequence is shown in Table (entries 2-8). Toluene was used in our prior work in the aryne forming step, however when the one-pot sequence is performed in toluene only trace (< 5%) amounts of 3aa were observed in the crude 1 H NMR spectrum (Table , entry 2). Triflic acid is a by-product of the C-H thianthrenation step and therefore leaving out the neutralization step (K3PO4) results in a greatly diminished yield of 3aa even with excess base in the second step (23%; Table , entry 3). Two other methods were tested to activate the TTO reagent under the one-pot conditions (Table , entries 4 and 5). The strongly acidic conditions involving a combination of TFAA and TfOH resulted in low yield (10%) of 3aa whereas conditions with the mixed anhydride TFAOTf resulted in comparable yield (83%) to those with Tf2O (Table , entries 4 and 5). The mixed anhydride TFAOTf, however, is substantially more expensive than Tf2O. Two other sulfonium salts were also tested as intermediates in this reaction (Table , entries 6 and 7). The tetrafluorinated analog of TTO, TFTO, resulted in low yield of 3aa (26%), though the dibenzothiophene analog, DBTO, resulted in a similar, but slightly lower, yield to that obtained with TTO (75%; a Conditions: 1a (0.1 mmol, 1 equiv.), TTO (0.1 mmol, 1 equiv.), Tf2O (0.12 mmol, 1.2 equiv.), MeCN (0.4 mL), 0 °C -r.t., 30 min; K3PO4 (0.1 mmol, 1 equiv.), r.t., 5 min; 2a (0.5 mmol, 5 equiv.), NaOt-Bu (0.2 mmol, 2 equiv.), 65 °C, 60 min.; yields determined by H NMR spectroscopic analysis of crude reaction mixtures with 1,3,5-trimethoxybenzene as internal standard. b Isolated yield on 0.5 mmol scale of 1a.
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The scope of the one-pot method to convert simple arenes into trapped arynes was evaluated with ten different arenes and nine different arynophiles (Scheme 2). Six of the arenes used in the one-pot method had also been previously used in our two-pot method (1a-d, g, i; Scheme 2). In four of the cases, the yield is higher in the one-pot method than the two-pot method by 6-24% (3aa, 3ba, 3da, and 3ia; Scheme 2). In the two cases in which the yield is not higher for the one-pot method, it is within 5% and the greater efficiency and reduced waste of the onepot method make it preferable (3ca, 3ga; Scheme 2). Several new arenes were also evaluated in the one-pot method including 2-cyanoanisole (1e), a benzoimidazolone derivative (1f), and trisubstituted arenes (1h and 1j; Scheme 2). A range of different arynophiles were also compatible in the one-pot procedure, including those that undergo [3+2] cycloaddition such as benzyl azide 20 (2b) and a nitrone (2c); as well as those that participate in [2+2] cycloaddition such as cyclic enol ether (2d) and cyclic enamine (2e; Scheme 2). The later reaction converts simple arenes into densly functionalized racemic benzocyclobutenes (3cd and 3ae; Scheme 2). Amines are one of the strongest arynophiles known, and are compatible in this one-pot procedure. Both aromatic and aliphatic (2f-h) amines trap Scheme 2. Scope of one-pot net dehydrogenation of arenes.
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During evaluation of the scope of the one-pot method we found that several feedstock arenes resulted in low yield (Figure ). Specifically, when we attempted to use benzene, toluene, anisole, or 1,3-dimethoxybenzene in this reaction we only observed trace (< 5%) yield of trapped aryne product (Figure ). However, C-H thianthrenation of these arenes is well-established; moreover, we have independently synthesized the corresponding aryl thianthrenium salts and observed trace yield when we attempted to generate and trap the corresponding arynes. Increased scope. In order to address the observed gaps in the scope of arenes for the one-pot net dehydrogenation via aryl thianthrenium intermediates, we considered alternative "onium" leaving groups. Our prior work in the area of generating arynes from aryl "onium" reagents suggested that iodonium leaving groups might be a viable intermediate to dovetail these missing arenes and their corresponding arynes. Although, several aryliodonium leaving groups are known in the context of generating arynes, including phenyl, mesityl, 8,14-17,22 and 2,4,6trimethoxyphenyliodonium, we hypothesized that the mesityliodonium is uniquely suited to this role for two key reasons. First, the 2,6-dimethyl groups of mesityl block deprotonation on the mesityl ring and lead to selective aryne formation on the other ring of the diaryliodonium salts; this scenario is not necessarily predictable with the phenyliodonium leaving group. Second, the mesityliodonium group may be installed by C-H functionalization of arenes using commercially available mesityliodine diacetate; this scenario is not generally possible for installation of the 2,4,6-trimethoxyphenyliodonium group. We modified Dohi and Kita's conditions to synthesize and isolate aryl(Mes)iodonium salts and then used these as reagents to generate arynes and trap them with furan; in all cases the reported yields are for the two-step procedure from the simple arene (Scheme 3). We were unable to develop a one-pot procedure, as in the case of aryl thianthrenium intermediates, because we found that both the synthesis of and use of diaryliodoniums as aryne precursors is substantially more sensitive to solvent effects and low yields were observed in acetonitrile as the sole solvent. In the case of benzene we used commercially available phenyliodine diacetate (PIDA) because, consistent with Dohi and Kita's prior observations, benzene is unreactive with mesityliodine diacetate, even under forcing acidic conditions. The symmetrical diphenyliodonium triflate was used to generate benzyne which was trapped with furan in 59% overall yield (3la; Scheme 3). Toluene, anisole, and diphenyl ether were all compatible under the standard conditions and generated trapped arynes in high overall yields (3ma, 3na, 3pa; Scheme 3). Several 1,2-disubstituted arenes were also compatible including those bearing functional groups that were not compatible with a thianthrenium leaving group, including triflate (1q), nitro (1s), phenyl (1t), and ester (1w) groups (3qa, 3sa, 3ta, 3wa; Scheme 3). We did not observe competitive loss of the triflate group in the case of 3qa (Scheme 3). In the case of a trifluoromethyl substituent, 1r-TT resulted in trace aryne adduct in our hands, though the isomer 4trifluoromethyl anisole has been successfully used by others. Additionally, aryl(Mes)iodonium reagent 1r-IMes yielded an approximate 10: 1 mixture of inseparable regioisomers due to competitive deprotonation at the 3-and 5position (Scheme 3). When we replaced furan with a nitrone 2c to trap the aryne, a similar mixture of regioisomers were formed, yet were separable by chromatography and the major one isolated in 76% overall yield from 1r (3rc, Scheme 3). We have noted previously that substitution patterns impact the reactivity of aryl "onium" aryne precursors, and those derived from 1,3-substituted arenes are the least reactive. We found that using the aryl(Mes)iodonium intermediates and LiHMDS as base Scheme 3. Increased scope of arenes via two-step net dehydrogenation with aryl(Mes)iodonium intermediates.
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successfully generated arynes from these substrates which were trapped with furan (3ua, 3oa and 3va; Scheme 3). In the case of arene 1u, an 8:1 mixture of 1u-IMes isomers is obtained from iodination at the 4-and 6-positions, respectively, and when this mixture was carried forward a 10:1 mixture of isomers was obtained for the aryne adduct. The major isomer 3ua shown results from aryne formation at the 4,5-position and the minor isomer results from formation at the 5,6-position (Scheme 3). Similar isomer ratios were obtained for the synthesis and use of 1u-TT as an intermediate, but the yield of aryne adduct from 1u-TT is notably lower (3ua, 56%; Scheme 3). The use a aryl(Mes)iodonium salts has also provided access to a trapped pyridyne (3va) and to the best of our knowledge this constitutes the first example of a pyridine to pyridyne process (Scheme 3).
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Synthetic Applications. The ability to efficiently convert arenes into arynes is aptly suited to late-stage functionalization. We have demonstrated this concept on O-methyl triclosan 1x, the methylated derivative of an anti-bacterial agent found in many consumer products (Scheme 4a). In this case we subjected 1x to our standard one-pot conditions via the in situ generated aryl thianthrenium and the trapped aryne 3xa was isolated in 74% yield (Scheme 4a). We have also shown that aryne intermediates can be used to access several naphthalene derivatives, namely naphthoquinones, naphthalenes, and naphthols (Scheme 4b). Arene 1a was used as the starting material in all three cases. First, a one-pot method to transform 1a into the corresponding naphthoquinone is achieved in 66% yield when 2j is used in the aryne trapping step and the crude reaction mixture is stirred with trifluoroacetic acid (4; Scheme 4b). Second, the aryne adduct 3aa can be converted into a naphthalene via "oxygen deletion"; the two-pot process for generating naphthalene 5 from arene 1a proceeds in 43% overall yield (Scheme 4b). Finally, the oxabicyclic ring of 3aa can be ring opened with HCl to generate the functionalized 1-naphthol 6; this process can be conducted in a single-pot and 6 can be isolated in 60% overall yield from 1a (Figure ). Alternatively, 6 can be carried forward in the same flask to generate a derivative of propranolol (highlighted in grey on 7) in 34% overall yield from 1a (Figure ). Mechanistic Analysis. Our synthetic studies (vide supra) suggest that the two strategies described here for net arene dehydrogenation, one using aryl thianthrenium intermediates and the other using aryl(Mes)iodonium intermediates, have complementary arene scope. We have performed experiments to probe the mechanism of each step, C-H functionalization and aryne formation, and we have compared and contrasted the results for each strategy. We used deuterium kinetic isotope effects (DKIE), competition experiments, and Density Functional Theory (DFT), and our mechanistic analysis corroborates the suggestion of our synthetic studies; each step of the reaction has mechanistic subtleties that contribute to complementary overall scope based on the two aryl "onium" intermediates employed.
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The first step of the net dehydrogenation is the installation of the "onium" leaving group, and given that this occurs at an aromatic C-H bond we used DKIE analysis to probe this step. A mixture of toluene 1m and deuterated toluene 1m-d8 was subjected to the first step of the standard conditions for each strategy (Scheme 5). Thianthrenation of toluene via activation by Tf2O in acetonitrile yielded a DKIE of 1.6 (Scheme 5a). This result is consistent with Wang's DKIE of 1.4 obtained for the same system albeit conducted in DCM, but stands in contrast to the DKIE of 2.7 obtained by Ritter when TTO is activated by a combination of TFAA and TfOH. Ritter has suggested that the stability of TT +• as a persistent radical and, therefore, the fast and reversible formation and cleavage of the C-S bond relative to slow deprotonation of the Wheland intermediate is the cause of the primary DKIE of 2.7. However, the substantially lower DKIE obtained by us and Wang, 1.6 and Scheme 4. Synthetic applications of net dehydrogenation of arenes into arynes.
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1.4, respectively, suggest that the mode of activation may also impact the kinetic relevance of the C-H bond cleavage step. That is, the mode in which TTO is activated may generate distinct thianthrenium electrophiles and impact the relative barriers for C-S bond formation and C-H bond cleavage; the latter appears to be less kinetically relevant when TTO is activated by Tf2O (Scheme 5a). We also performed a DKIE analysis on the formation of tolyl(Mes)iodonium triflate, 1m-IMes, by the same method (Scheme 5b). In this case, we obtained a DKIE of 1.5, a value similar to the DKIE obtained for arene thianthrenation (Scheme 5b). These data suggest that the kinetic relevance of the C-H cleavage step is similar for thianthrenation and iodination steps and points toward the existence of a Wheland intermediate in both cases that undergoes relatively fast deprotonation. Scheme 5. DKIE analysis for the formation of aryl "onium" species.
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To further probe the existence of a Wheland intermediate, we considered a Hammett analysis via one-pot competition experiments for both the formation of aryl thianthrenium and aryl(Mes)iodonium salts. However, our initial attempts to construct a Hammett plot in both cases were unsuccessful because electron-rich arenes, such as anisole and toluene completely out competed benzene in the case of thianthrenation. Moreover, we, and others, have found that benzene is unreactive with iodomesitylene diacetate under the conditions we used for the first step of the net dehydrogenation mediated by iodonium leaving groups. Therefore, we conducted a series of competition experiments to construct a qualitative scale of relative arene reactivity for the formation of the two different aryl "onium" species (Scheme 6). We used an equal excess of the two competing arenes relative to TTO or MesI(OAc)2 (Scheme 6). Although the scales for the two processes appear similar, there are some important distinctions that warrant further comment. The order of arene relative reactivity for general classes of arenes is consistent for the two processes: benzene, toluene, chloroanisoles, anisole, dimethoxybenzenes is the order from least to most reac-tive. Additionally, thianthrenation has a broader scope of compatible arenes than iodination (Scheme 6). Although Hammett plots provide a -value which can be a useful metric to describe the electronic properties of the arene during the rate determining step, individual plots must be constructed for a series of substituents at a given position (meta or para). In our relative reactivity scale, we have included polysubstituted arenes which demonstrates how the position and electronic effects of multiple substituents impacts reactivity. For instance, 2-, 3-and 4chloroanisoles, 1c, 1u and 1a, respectively, have relative reactivity between toluene 1m and anisole 1n (Scheme 6). Therefore, although chloro is a deactivating substituent, the combination of chloro (deactivating) and methoxy (activating) is more reactive than a methyl (activating) substituent. Additionally, the relative position of the substituents has an impact on reactivity, which was not necessarily consistent between thianthrenation and iodination (Scheme 6). Again, considering the 2-, 3-and 4chloroanisoles, the 1,4-substitution pattern was the least reactive in both thianthrenation and iodination reactions, in fact 4-chloroanisole 1a was not a viable substrate for iodination (Scheme 6). In the case of thianthrenation, 2chloroanisole 1c was slightly more reactive than 3chloroanisole 1u; though this order was reversed for iodination (Scheme 6). The trends observed for dimethoxybenzenes shared some similarities with those of chloroanisoles. For example, 1,4-dimethoxybeznene 1y was not a viable substrate for thianthrenation or iodination. Moreover, 1,2-dimethoxybenzene 1d was only compatible with thianthrenation but not iodination. In the case of thianthrenation, the 1,3-substitution pattern 1o is more reactive than 1,2-substitution pattern 1d (Scheme 6).
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The relative reactivity of 1,3-and 1,2-dimethoxybenzene 1o and 1d in thianthrenation and the lack of reactivity of 1,4-dimethoxybenzene 1y in both reactions prompted us to take a closer look at these substrates (Scheme 7). Electron-rich arenes, such as these, are known to be reductants via single electron transfer (SET), and arene radical cations have been suggested as intermediates in the formation of both aryl thianthrenium and diaryliodonium salts. 1,3-Dimethoxybenzene 1o has a reduction potential of 1.50 vs SCE, and readily forms 1o-IMes and 1o-TT in high yields (Scheme 7a). 1,2-Dimethoxybenzene 1d is a stronger reductant with a reduction potential of 1.43 vs SCE, and is only compatible in the thianthrenation reaction (Scheme 7b). In the case of iodination of 1d, both 1d and Me-sI(OAc)2 are completely consumed in the reaction, but no product is formed (Scheme 7b). Moreover, a competition experiment between 1d and 1o in the formation of aryl(Mes)iodonium salts results in neither 1d-IMes or 1o-IMes. This data suggests that 1d inhibits the formation of 1o-IMes by decomposing MesI(OAc)2 via SET. A similar scenario is observed for the attempted formation of an aryl(Mes)iodonium salt from 1,4-dimethoxybenzene 1y; both the arene and MesI(OAc)2 are consumed, but no product is observed (Scheme 7c). 1,4-Dimethoxybenzene 1y also inhibits the formation of 1o-IMes in a competition experiment. Thianthrenation of 1y is somewhat different from iodination. Although thianthrenation of 1y is unsuccessful and 1y is completely consumed, it does not inhibit Scheme 6. Arene relative reactivity scale for the formation of aryl thianthrenium and diaryliodonium salts. a,b a Conditions: 1 (1 mmol, 1 equiv.), MesI(OAc)2 (MIDA) (1 mmol, 1 equiv.), TfOH (1 mmol, 1 equiv.), MeCN (1 mL), r.t., 3 hours. b Conditions: 1 (0.5 mmol, 1 equiv.), TTO (0.5 mmol, 1 equiv.), Tf2O (0.6 mmol, 1.2 equiv.), MeCN (2 mL), 0-25 °C, 30 minutes. the formation of 1o-TT in a competition experiment. Collectively, the data presented in Scheme 7 suggest that there is a key difference in the mechanisms for forming aryl thianthrenium and aryl(Mes)iodonium salts. Although both reactions are somewhat sensitive to the reduction potentials of arene substrates, thianthrenation reactions are not inhibited by strongly reducing arenes. This may suggest that arene radical cations are not productive intermediates in the formation of diaryliodonium salts.
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The aryne forming step of the net dehydrogenation involves deprotonation of an aromatic C-H bond and elimination of the "onium" leaving group. We used competition and DKIE experiments as well as DFT to analyze and compare this process for aryl thianthrenium and ar-yl(Mes)iodonium salts. Our synthetic and mechanistic analysis of the formation of aryl "onium" species revealed that aryl thianthrenation is broader in arene scope than aryl iodination (vide supra). Our experimental evidence suggests that the formation of arynes from aryl(Mes)iodonium salts is broader than from aryl thianthrenium salts. In order to gain direct evidence for the relative reactivity of aryl thianthrenium and aryl(Mes)iodonium salts as aryne precursors, we performed a competition experiment with deuterium labeled substrates (Scheme 8). 2-Fluorophenol was trideuteromethylated with DMSO-d6 to generate 1z-d3. The deuterated and non-deuterated analogs of 1z-TT and 1z-IMes were synthesized and used in competition experiments to generate and trap the corresponding aryne, ultimately leading to 3za and 3za-d3 (highlighted in pink, Scheme 8). Both scenarios of the deuterium label on the aryl thianthrenium or the aryl(Mes)iodonium salts were performed and in both cases the product 3za derived from the aryl(Mes)iodonium salt was the major product by ~ 2.5: 1 (Scheme 8). These data provide direct evidence that aryl(Mes)iodonium salts are more reactive aryne precursors than the corresponding aryl thianthrenium salts.
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Chalcogen leaving groups are relatively rare in aryne forming reactions, but "onium" groups based on these have received increased attention in the past year in C-H deprotonation/-elimination sequences. As such there is relatively little known about the mechanism of this process, and nothing known when aryl thianthrenium salts are used. We measured the DKIE by one-pot competition experiments to glean an understanding of the kinetic relevance of the C-H deprotonation step in the formation of arynes from aryl thianthrenium and aryl(Mes)iodonium salts (Scheme 9). We synthesized a deuterated analog of 1b-TT and 1m-IMes to obtain the DKIE from aryl thianthrenium and aryl(Mes)iodonium salts, respectively (Scheme 9). In the case of 1b-TT and its deuterated analog, we observed a small DKIE of 1.4 (Scheme 9a), which is similar to the value obtained by Smith and co-workers for aryne formation from triaryloxonium ions. On the other hand, when we performed a competition experiment between 1m-IMes and its deuterated analog we observed a much larger DKIE of 4.9 when NaOt-Bu was used as base and 5.2 when LiHMDS was used (Scheme 9b). These data demonstrate that the C-H deprotonation step is more kinetically relevant in aryne formation from aryl(Mes)iodonium salts than from aryl thianthrenium salts. Scheme 9. DKIE experiments for aryne formation from aryl thianthrenium and aryl(Mes)iodonium salts.
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To gain further insight into the C-H deprotonation/elimination sequence from aryl thianthrenium and aryl(Mes)iodonium salts, we performed DFT calculations on several different substrates 10 and Figure ). All intermediates and transition state structures were optimized with the M06-2x functional and the Def2-tzvpp basis set with SMD solvation (toluene) using Gaussi-an09. Given the range of solvents used in the experimental methods to access arynes from aryl thianthrenium and aryl(Mes)iodonium salts we survey solvation models (Table ), and ultimately selected toluene as a single and representative solvent for DFT analysis. Our DFT analysis revealed that aryne formation from aryl thianthrenium and aryl(Mes)iodonium salts occur through distinct reaction pathways (Scheme 10). All aryl thianthrenium substrates analyzed by DFT (1b-TT, 1l-TT and 4-chlorophenyl thianthrenium) were found to generate a stable zwitterion (A, Scheme 10) upon deprotonation with tert-butoxide and passing through TS1 (Scheme 10 and Figure ). In the case of A, derived from 1b-TT, protonation (the reverse of the initial step) is lower in energy than elimination of the thianthrenium group through TS2 by 2.5 kcal/mol (Scheme 10, left). Therefore, the C-H deprotonation is reversible and TS2 is the highest energy point on the reaction pathway (Scheme 10, left). Conversely, the computed reaction pathway for all aryl(Mes)iodonium salts analyzed (1m-IMes, 1l-IMes and 4-chlorophenyl(Mes)iodonium) proceed through a single transition state (Scheme 10 and Figure ). In the transition state, epitomized by TS3, C-H and C-I bond cleavage is concerted but asynchronous; the C-H bond is elongated by 30% whereas the C-I bond is elongated by only 5%. Nevertheless, no zwitterionic intermediate could be found as TS3 collapses to the aryne dedihydro-1m as well as tert-butanol and mesityl iodide (Scheme 10, right). With these pathways established, the DKIE were calculated from the optimized geometries of the reactants and transition states for each reaction step. The overall DKIE for the two step aryne formation from 1b-TT was calculated based on equation SF1, and both values were found to be in relatively good agreement (Scheme 10). The DKIE calculated from the DFT data for 1b-TT was 1.0 compared to the DKIE of 1.4 obtained from the wet lab experiment (Scheme 9 and 10, left). The relatively small DKIE reflects the reversible C-H deprotonation followed by rate-limiting thianthrene elimination, and thus the separation of the C-H deprotonation and rate-limiting steps. The DKIE calculated from the DFT data for 1m-IMes was 4.5 compared to the experimental value of 4.9 (Scheme 9 and 10, right). This much larger DKIE reflects C-H bond cleavage in the rate-limiting step of the reaction.
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User's guide to accessing arynes from arenes. Collectively, our observations over the course of these studies can be distilled down to a user's guide for generating and trapping an aryne derived from a simple arene. We have demonstrated that the two strategies, using an aryl thianthrenium or an aryl(Mes)iodonium salt as an intermediate, are essentially complimentary with respect to the arene scope. For several classes of arene only the aryl thianthrenium salt can be synthesized obviating the use of aryl(Mes)iodonium salts for these substrates; in other cases the aryne cannot be accessed from the aryl thianthrenium and therefore the aryl(Mes)iodonium salts critically expand the arene scope. Our general strategy, shown in Scheme 11a, involves either a one-pot (for aryl thianthrenium) or two-pot (for diaryliodonium) process for net dehydrogenation and functionalization of arenes. The site of aryne formation largely depends on the substitution pattern of the arene and in most cases very high selectivity is observed (Scheme 11b). In mono-substituted arenes the aryne is formed exclusively at the 3,4-position (highlighted blue) because both thianthrenium and iodonium groups are installed with very high para-selectivity (4-position) and deprotonation occurs exclusively ortho to the leaving group (3-position; Scheme 11b). In mono-substituted arenes, no aryne formation is observed at the 2,3-position. Scheme 10. Calculated reaction landscape for aryne formation from 1b-TT and 1m-IMes. a a Intermediates and transition states were optimized at M06-2x/Def2-tzvpp with SMD solvation in toluene using Gaussian09. In 1,2-disubstituted arenes the major site of aryne formation is at the 3,4-position. This selectivity is again initiated by high para-selectivity (4-position) for installation of thianthrenium and iodonium groups; this is followed by generally high selectivity for deprotonation at the 3position (Scheme 11b). In a few cases, we have observed a minor product from deprotonation at the 5-position (i.e., 1r-IMes and 1t-IMes, Scheme 3), but an aryne is not formed at the 5,6-position for 1,2-substituted arenes; this numbering scheme is predicated on the strongest paradirector at the 1-position. In 1,3-substituted arenes, the site of iodination may be impacted by the relative steric effects of the EDG and the R-group at the 3-position (Scheme 11b). When the R-group is a chloride as in 1u we observed preference (8:1) for installation of the iodonium at the 4-position over the 6-position (Scheme 11b). Subsequently, because the 3-position is blocked, deprotonation occurs at the 5-position. The minor aryne adduct arises from iodination at the 6-position and deprotonation at the 5-position (Scheme 11b). There is only one site for aryne formation to occur with 1,4-substituted arynes and it is at the 2,3-position (Scheme 11b). However, in this case it is important to point out that the aryne is flanked by two substituents and in these cases we have shown that the nature of the two substituents impacts the selectivity of nucleophilic addition to the aryne; that is, the site of thianthrenation is not necessarily the site of nucleophilic addition. It should also be noted that higher substitution patterns can be treated as an extension of disubstituted arenes. That is, 1,2,3-substituted arene react similarly to 1,2-substituted arenes (cf. 3ha and 3da, Scheme 2) and 1,2,4-substituted arenes react similarly to 1,4-substituted arenes (cf. 3ia and 3aa, Scheme 2).
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Broadly, there are relatively few arenes for which there is overlap in the use of aryl thianthrenium and aryl(Mes)iodonium salts as intermediates to mediate the net dehydrogenation of arenes (Scheme 11c). 1,2-Disubstituted arenes hold this unique position and we rec-ommend using the one-pot method via aryl thianthrenium salts (Table and Scheme 2) as it is the most efficient approach to convert arenes into arynes. Other substrates for which aryl thianthrenium salts are the preferred mediator are aryl halides, and in this case we recommend using our first-generation two-pot method as the aryl halide is used as the solvent in the C-H thianthrenation step. Additionally, 1,4-substituted arenes and very electron-rich arenes, such as 1,2-dimethoxybenzene 1d, require the use of the corresponding aryl thianthrenium salt as an intermediate (Scheme 11c, yellow oval). The use of aryl(Mes)iodonium salts as an intermediate is recommended for the formation of arynes from mono-substituted feedstocks, such as toluene and anisole, 1,3-substituted arenes, including pyridines, and useful functional handles such as triflate, nitro and ester (Scheme 11c, purple oval). CONCLUSIONS Herein, we described a general approach for accessing arynes from arenes. Two distinct strategies were discussed that depend on the arene substitution pattern and electronic effects. In the first case, a one-pot procedure, which passes through in situ generated aryl thianthrenium salts, was used. This is especially useful for generating arynes at remote sites on aryl halides and on 1,2-and 1,4-substituted arenes, as well as those arenes that are strong reducing agents. In the other case, a twopot process, which passes through an isolated aryl(Mes)iodonium salt, was used. This is especially useful for generating arynes from mono-substituted arenes, 1,3-substituted arenes, and a substituted pyridine. Collectively, these two strategies provide mild and efficient access to arynes within several hours from the unfunctionalized arene thereby substantively expanding the scope of arynes that are accessible. Moreover, these strategies provide opportunities for late-stage Scheme 11. User's guide to accessing arynes from arenes via net dehydrogenation.
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a EDG = electron-donating group. functionalization (triclosan) and access to a range of benzenoid-based scaffolds such as naphthoquinones, 1naphthols, and naphthalenes; including the streamlined synthesis of pharmaceutical derivatives (propranolol). The net dehydrogenation of simple arenes is based on two distinct steps: C-H functionalization and C-H deprotonation/-elimination. Mechanistic analysis via competition and DKIE experiments, as well as DFT reveal that there are both similarities and differences depending on the intermediate (thianthrenium or iodonium) enroute to the aryne. C-H functionalization via thianthrenation is broader in scope than iodination; however, mesityliodonium are more reactive leaving groups than the corresponding thianthrenium. C-H functionalization by both thianthrenation and iodination occur with very high para-selectivity and have small observed DKIE consistent with reversible formation of a Wheland intermediate and fast deprotonation. However, the iodination reaction is especially sensitive to SET events and the formation of aryl radical cations, whereas thianthrenation appears to be largely insensitive to this feature. Aryne formation from aryl thianthrenium salts and aryl(Mes)iodonium salts have distinct reaction pathways. Aryl thianthrenium salts undergo reversible deprotonation to generate a stable zwitterion that proceeds through rate-limiting thianthrenium elimination to produce the aryne. Aryl(Mes)iodonium salts undergo a concerted but asynchronous deprotonation/elimination event to generate the aryne. In both cases, experimental and computational determined DKIE values are consistent with these pathways. We envision that these platforms for generating arynes will engender new synthetic applications of arynes and increase the breadth of arynes that are accessible.
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Automated chemical synthesis and measurement devices have begun to be recognized as indispensable tools for improving efficiency and speed in experiments, enabling control and recording of experimental systems with high precision, reproducibility, and efficiency . The research of automated experiments have a history of several decades, but recent advances in information science have ushered in a new paradigm . Typical achievements include the use of image recognition systems for assessing experimental conditions , prediction of experimental results through models that learn structures and property correlations from large datasets , and suggesting experimental conditions using search algorithms like Bayesian optimization and sparse modeling .
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Since around 2022, large language models (LLMs, or foundation models) trained on vast amounts of text have gained attention . While they still do not match human inference capabilities, LLMs such as the Generative Pretrained Transformer 4 (GPT-4) are capable of natural language-based reasoning, allowing for more reliable predictions and chemical proposals compared to previous AI that did not adequately consider linguistic or scientific theories . GPT-4 also possesses exceptional programming capabilities. For example, it can generate scripts to control automated experimental devices based on the text described in experimental sections . Multimodal models, including GPT-4, capable of image recognition have also emerged, proposing their use in automated collection of experiments .
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There are two main options for implementing automated experiments with AI and robots: a) building dedicated experimental devices, and b) utilizing general-purpose robotic arms . Dedicated experimental devices include flow devices often used in organic synthesis . Devices specialized for organic synthesis experiments are commercially available, and high-throughput screening proposals are also being made in the polymer field . However, specialized hardware has issues with customizability and cost, and is not always practical in experimental research phases where experimental operations are prone to change .
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This study proposes a system for automatically synthesizing polyimide precursor particles using a handmade dispensing device specialized for liquid handling combined with a general-purpose robotic arm (Fig. ). Inspired by the design of standard 3D printers , we have created an inexpensive and easily customizable dispensing machine. Additionally, we have coordinated a robotic arm that can move sample bottles to any location to add scalability and future expandability to synthetic experiments. Cameras continuously monitor chemical reactions. Furthermore, experimental procedures and observation results are analyzed using a multimodal language model that supports image input, automatically generating detailed experimental notes. The obtained experimental records can be used to compare different experiments and suggest experimental conditions to be conducted next. It is also possible to consider why experiments do not go well from images taken during the experiment. These preliminary results suggest the practical role of foundation models in lab automation and present a new pathway for the experimental cycle with a versatile, reproducible, and objective AI robot system.
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All purchased chemicals were used as received unless otherwise specified. Pyromellitic dianhydride (PMDA) and 4,4'-oxydianiline (ODA) were purchased from Tokyo Chemical Industry Co. and sublimated before use. Acetone was obtained from FUJIFILM Wako Pure Chemical Co. A typical experimental procedure for synthesizing polyamic acid is as follows. Initially, a human chemist prepared a 200 mmol/L solution of ODA in acetone and a 5.12 mmol/L of PDMA in acetone solution and placed them in the dispensing system. A 39 mL solution of PDMA was added to an empty sample bottle containing a stir bar rotating at 1000 rpm. The dispensing system automated the subsequent addition of reagents and stirring operations. The reaction was initiated by adding 1 mL of ODA solution so that the molar amounts of each became 0.2 mmol. A camera periodically recorded the state of the sample, and after stirring for one hour, the reaction was finished. After the reaction, an evaporator or a hot plate removed the solvent to obtain the microparticles, which were analyzed by scanning electron microscopy (Hitachi High Technologies, S-5500).
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The authors created the dispensing system inspired by 3D printer systems. A configuration of belts and servo motors controlled the arm's X, Y, and Z coordinates. A screw-type actuator and servo motors controlled the pushing mechanism of the micropipette. The micropipette holder was created using a 3D printer. A microcomputer (Arduino) installed with control software called Grbl controlled the motors' behavior. Arduino and the main computer were conducted via serial communication through a USB connector. The dispensing system has a USB camera directly connected to the computer. The series of devices is controlled by an interface written in Python.
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A 4-axis robot arm, DOBOT Magician (Dobot Robotics, Inc.), was used to move the reagent bottles. The standard suction cup in the kit was adopted as the end effector. As an extension part of the robot, a rail with a working range of 1 meter was mounted on the arm. A USB camera for position control is mounted on the tip of the arm.
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All the sample bottles used in the experiment are stored in containers made of a 3D printer. The containers have ArUCo markers attached for identification and coordinate recognition. These markers are recognized through the OpenCV library and are used to control the arm coordinates. Detailed design and programming codes about the constructed system can be provided upon inquiry to the corresponding author. responses used in this study are shown in the Supplementary Information. We have recorded the results primarily based on interactions with GPT-4. The inputs and outputs of GPT-4 omni (GPT-4o), the latest version released on May 13th, are also presented in the Supplementary Information, but no significant differences in output accuracy were observed between the two versions.
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We have constructed a customizable, handmade automatic reaction system (Fig. ). This system comprises two main parts: the dispensing system and a rail-operated robotic arm. The dispensing system has a control mechanism with XYZ axes, which determines the spatial coordinates of the micropipette. The device incorporates a universal micropipette, and a servo motor controls the liquid extrusion button. The parts making up the device are the same as those used in open-source general-purpose 3D printers, costing the raw components approximately $1000.
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The robotic arm mechanism for moving sample bottles comprises commercially available products intended for research and education. The body of the arm and the movable rail each cost about $1300, suitable for constructing a rapid prototyping system. The arm is equipped with a suction cup, which allows it to transport objects while suctioning them, and nominally, it can transport objects up to about 500 grams.
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The sample bottles for the chemical reactions are mounted inside specialized containers made by a 3D printer. The container is affixed with a square barcode-like marker called an ArUco marker. The ArUco marker, developed for robotics, not only enables the identification of the labeled object but also allows the estimation of three-dimensional relative coordinates between the marker and the camera. The robotic arm and dispensing device operate by referencing the position of the ArUco marker. Such simple yet accurate robot control based on visual feedback allows for the construction of a robust system that is adaptable to changes in the experimental environment. The system features liquid handling, observation of samples, and moving containers (Fig. ). Leveraging its high customizability, in this study, we have incorporated a four- unit stirrer into the machine. We adopted a mechanism to control the dispensing operation of a universal 1 mL micropipette with a servo motor, controlling the volume of liquid aspirated by the depth to which the pipette's extrusion button is pressed. To determine how accurately the unofficial usage, not anticipated by the manufacturers, could control the volume aspirated, we experimentally verified the relationship between the button's pressing distance and the volume of liquid (Fig. ). Water was chosen as the standard sample for preparing the calibration curve, and the volume of liquid was estimated from the weight and specific gravity. Linearity was confirmed between the aspirated volume and the pressing distance, with an average error of 3.4 μL.
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This prototype device uses a micropipette instead of a syringe for dispensing operations, making it unsuitable for reaction systems that require strict inert conditions for reagent addition. Also, as no special spectrophotometric devices have been incorporated, there are limitations in tracking reactions that do not show visible light changes. To capitalize on the device's strengths and target a chemically unique reaction system, we focused on a precipitation polymerization reaction to obtain polyimide precursor particles (Scheme 1) . The reaction system is a typical polycondensation reaction where pyromellitic dianhydride (PMDA) and 4,4'-oxydianiline (ODA) bond through amidation . In this reaction system, while the monomers dissolve, the polyamic acid is known to form unique particle structures by choosing an appropriate insoluble solvent. These products can be utilized as polyimide particles through a dehydration cyclization reaction induced by heating or applied to high nitrogen-containing carbon materials through high-temperature sintering .
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We attempted the automated synthesis and observation of polyamic acid using our custom-built dispensing system and the assistance of the multimodal large language model GPT-4 (Fig. ). This study emphasizes the operational verification of the dispensing device and the proof of principle of automatic observation, so it is important to note that the design is not yet a fully autonomous, closed-loop system.
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We executed the following experiment: 1) 39 mL of PDMA solution was added to an empty reagent bottle, 2) 1 mL of ODA solution was added, 3) the solution was stirred for one hour while being observed by a camera, and 4) after the reaction finished, the reaction mixture was transported out of the dispensing system. One advantage of this system over manual experimentation is its ability to precisely specify and record the timing and details of experimental operations on a second-by-second basis. In organic chemical reactions, significant signs, such as noticeable changes in the color of the solution, occur immediately after reagent addition. On the other hand, in manual operations, it isn't easy to wholly and continuously record what operations were performed at what exact time or what significant events occurred. This deficiency in information would undermine strict documentation and reproducibility.
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One of the interesting findings of this study is the automatic text generation of recorded information from automated experiments. While means to record the state of reaction systems using cameras and measurement devices have existed , they have not been widely adopted in experimental chemistry. The primary reason is the lack of sufficient methods to convert the data obtained into an information format that is easily understandable by humans. Although languages are useful tools for describing experiments, traditional lab automation and measurement systems lack mechanisms for linguistic information conversion and compression .
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GPT-4 is a multimodal large language model that can handle images as input data. We have found that this model is capable of performing even some experimental observations (Fig. ). By inputting a) a description of the chemical reaction, b) experimental setup conditions, c) an operation log automatically generated by the synthesis system, and d) images captured by the camera (showing changes over time) into the language model and issuing appropriate instructions, it can generate textual observations of experimental notes that link changes in the state of the reaction mixture to chemical reactions. For instance, the GPT-4 observations in this reaction system indicated that turbidity appeared around 370 seconds after reagent addition and progressed further between 400-2600 seconds. This description generally matched the observations made by humans. The reason for the turbidity, attributed to the formation of polyamic acid, was also proposed by GPT-4 in a chemically reasonable analysis. The quality of the generated texts was sufficient for inclusion in a standard experimental notebook.
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GPT-4 could also convert observation records obtained by photography into semi-quantitative measurement data (Fig. and). When instructed to estimate the turbidity of the reaction mixture on a scale of 0 to 5, turbidity estimates were returned for each time point. Human observations indicated turbidity began when observation started (1 s, turbidity: 1) and reached a maximum level after approximately 700 seconds. On the other hand, GPT-4's observations showed a gradual increase in turbidity over about 2500 seconds, reaching a level of 4 to 5. The general trend was similar to humans but was slightly different.
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The difference in evaluation may be largely attributed to variations in observation conditions. Humans can observe the solution from various angles during experiments, allowing for a more accurate estimation of turbidity. In contrast, due to the limitations of the robotic system, GPT-4 can only capture images from directly above, making it difficult to accurately assess factors such as light transmission. A system that can observe samples from multiple angles, similar to the movement of a human neck and head, might be necessary. Attention should be given to accurately measuring turbidity in situ during a reaction, which is not necessarily straightforward with traditional methods . The most common approach for measuring turbidity involves observing the state of scattering against laser light . While light scattering methods show sufficient quantification and reproducibility under strict measurement conditions, their suitability for liquids undergoing stirring and chemical reactions is limited. This limitation arises because stirring can cause convection, an additional factor in light scattering, and chemical reactions may proceed while measurement conditions are being adjusted. Moreover, meticulous calibration and stringent environmental settings are required to accommodate light sources and ambient light changes. Such stringent setups solely to observe the state of a solution in routine experiments are too costly and, hence, not widespread in everyday experiments.
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While GPT-4, with careful prompting, can suggest the subsequent experimental conditions , this preliminary study manually selected the reaction conditions for improved suggestions. In the conditions mentioned earlier (Run 1), the reaction was conducted by dissolving 0.2 mmol of monomer in 40 mL of solution. In Runs 2 and 3, the amount of monomer was reduced to 0.1 and 0.05 mmol, respectively (Table ). As the concentration of the reaction solution was lowered, the time it took for the solution to become cloudy increased (Fig. and). For example, the mixture appeared at about 740 seconds opaque at 0.2 mmol (Run 1), partially opaque at 0.1 mmol (Run 2), and almost transparent at 0.05 mmol (Run 3). These differences are due to a decrease in polymerization speed due to lower concentrations and a reduction in the absolute number of particles that cause light scattering.
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The differences in cloudiness due to the different Runs could also be semi-quantified from photographs using GPT -4's multimodal capabilities (Fig. ). For verification, we re-input the experimental records and images of the reaction solution generated by GPT-4 for Runs 1 and 3 into a multimodal model. We instructed it to output the turbidity levels as table data (see Supplementary Information for the prompt).
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). The match indicates that, despite the observation images' suboptimal resolution and shooting conditions, the multimodal model can perform experimental observations close to human capabilities. Still, as pointed out, the model might have slightly underestimated the turbidity levels in Run 1. The discrepancy could stem from the facts that the observation system was not fully optimized and that GPT-4 was not explicitly designed for chemical experiment applications. Moving forward, we aim to develop a foundation model that is more closely integrated with automated experimental hardware.
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We evaluated the relationship between reaction conditions and the diameter of particles produced by SEM (Fig. , Table ). Spherical particles with diameters less than 1 µm were observed under all conditions, supporting the progression of precipitation polymerization . In the experiment with the highest concentration (Run 1), the particle diameter was approximately 0.4 µm. In contrast, in Runs 2 and 3, where the concentration during polymerization was reduced, the particle size decreased to 0.5 and 0.4 µm, respectively. As the concentration of the monomer decreases, the rate of nucleation and growth of particles slows down while the solubility improves. Because the product's particle size is determined after such complex interactions, there is no simple rule to connect the experimental conditions, the reaction solution's appearance, and the product's structure . In the future, we plan to comprehensively analyze the effects of monomer concentration, solvent conditions, temperature, and other factors on microparticles' precipitation behavior and particle size. The experiments will be automatically done by robots, and foundational models should support analysis.
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To determine whether experiments performed by robots yield the same results as humans, we carried out manual tracer experiments using the same stirrers and glassware. Contrary to our initial expectations, there were apparent differences in the appearance of the particles obtained by robots and by manual processes (Fig. , Table ). We had anticipated that particles produced by automated experiments would be more homogeneous, but the opposite was true. In every run, while the average size of the particles did not differ significantly between the robotic and manual experiments, the size distribution was smaller in the human experiments. SEM observations also showed that in robotic experiments, there were many small or agglomerated particles (Fig. ).
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The authors, experienced chemists, speculate that the difference between the two experiments could be due to differing stirring conditions. Although stirring was conducted at 1000 RPM in both conditions, it was noticed that in robotic experiments, the sample bottle was not placed exactly in the center of the magnetic stirrer (Fig. ). As a result, the stir bar frequently collided with the glass bottle, leading to irregular stirring of the reaction mixture, which should have significantly affected the particle size distribution. Furthermore, it is technically feasible to develop systems capable of autonomously recording and interpreting every aspect of an experiment, including auditory elements such as collisions between a glass bottle and the stir bar . In this experiment, we did not record audio data. However, GPT-4o, released on May 13, 2024, supports audio input and has improved output generation speed. The capability highlights an important nuance often emphasized by skilled chemists: the significance of being attentive to the sounds of the experiment.
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We conducted a simple synthesis experiment of polyamic acid particles using a handmade robotic device and a multimodal foundation model. The robotic mechanism allowed for control and recording of the experimental process, after which the multimodal AI appropriately analyzed the automatically generated information, demonstrating the ability to output content akin to an electronic lab notebook. The high level of abstraction provided new pathways for low-cost and comprehensive input and output of process information, observational records, and measurement results. Moreover, the foundation model could also compare the appearance of reaction solutions based on image data and understand the misalignment of the sample bottle's position to analyze why the experiments were unsuccessful. In the long term, a lab automation system combining optimized hardware with cutting-edge AI is expected to provide benefits such as accumulating tacit and experiential knowledge that was difficult to store as objective data. We are advancing methodologies to enable robots to explicitly control operations by capturing and codifying laboratory expertise and implicit knowledge. Our approach centers on leveraging the multimodal capabilities of large-scale language models, with the goal of achieving comprehensive and autonomous system control through next-generation AI. We are conducting a polycondensation reaction using pyromellitic dianhydride (PMDA) and 4,4'-oxydianiline (ODA).
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This reaction system generates precipitated microparticles of polyamic acid when ODA solution is added to the PDMA solution. Based on the experimental protocol automatically output by a robot and the measurement results from a camera, please provide a detailed description of the observations, considerations, and the next steps for the experiments.
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-Glass bottle 2 contains a 200 mM ODA acetone solution. The images you've provided document the progression of a polycondensation reaction involving pyromellitic dianhydride (PMDA) and 4,4'-oxydianiline (ODA). These images illustrate the reaction over time, as ODA solution was added to a PDMA solution. Let's walk through the observations and their implications:
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• Rate of Addition: The timeline shows that the addition of ODA to PDMA was controlled (taking place between 21:53 and 21:55), which is essential for managing the reaction kinetics and particle formation. o Chemical Composition: Verify the chemical structure of the microparticles using spectroscopic methods like FTIR or NMR to confirm the formation of polyamic acid.
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Based on the observations, further fine-tune the reaction conditions such as concentrations, temperature, and solvent system to optimize the yield and quality of the microparticles. . Application Testing: Depending on the intended application of the polyamic acid microparticles, perform application-specific testing, for example, testing in filtration systems, drug delivery matrices, or as reinforcing agents in composites.
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This reaction system generates precipitated microparticles of polyamic acid when ODA solution is added to the PDMA solution. Based on the experimental protocol automatically output by a robot and the measurement results from a camera, please provide a detailed description of the observations, considerations, and the next steps for the experiments.
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Quantitative Analysis: To better understand the reaction kinetics and product composition, consider conducting a particle size analysis and other spectroscopic measurements (like IR or NMR) to confirm the structure and purity of the polyamic acid. o Stirring Speed: Alter stirring speeds to investigate the effect on particle size distribution and reaction homogeneity.
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This reaction system generates precipitated microparticles of polyamic acid when ODA solution is added to the PDMA solution. Based on the experimental protocol automatically output by a robot and the measurement results from a camera, please provide a detailed description of the observations, considerations, and the next steps for the experiments.
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• Rate of Addition: The timeline shows that the addition of ODA to PDMA was controlled (taking place between 21:53 and 21:55), which is essential for managing the reaction kinetics and particle formation. 6. Scale-up: If the process needs to be scaled up, consider the impact of mixing efficiency and heat transfer on the particle formation.
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This reaction system generates precipitated microparticles of polyamic acid when ODA solution is added to the PDMA solution. Based on the experimental protocol automatically output by a robot and the measurement results from a camera, please provide a detailed description of the observations, considerations, and the next steps for the experiments.
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This reaction system generates precipitated microparticles of polyamic acid when ODA solution is added to the PDMA solution. Based on the experimental protocol automatically output by a robot and the measurement results from a camera, please provide a detailed description of the observations, considerations, and the next steps for the experiments.
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By following these steps, you can gain a comprehensive understanding of the polycondensation reaction mechanism, optimize the reaction conditions, and characterize the resulting polyamic acid microparticles for further applications. In experiments conducted by humans compared to those by robots, better products were obtained from the human experiments. Consider the reasons for this based on the state of the glass bottles placed on the stirrer.
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Van der Waals dispersion interactions play a crucial role in nature, determining the structure and functionality of molecular systems and materials, two examples being the deviation from the ideal gas law observed in real gases and the ability of geckos to stick to walls. These inherently quantum-mechanical interactions originate from the non-local electronic correlation among distant densities and their accurate description is crucial for a reliable computational modelling of matter. As a consequence of the underlying nonlocal electronic correlation, Kohn-Sham (KS) Density Functional Theory (DFT) is unable to model dispersion interactions and expensive wavefunction-based methodologies are usually required. In this connection, three-body Symmetry Adapted Perturbation Theory (SAPT) approaches have been shown to provide very accurate evaluations of dispersion energies. However, these methods are computationally challenging for large systems with scalings ranging from O(N 7 ) for HF-SAPT to O(N ) for SAPT(DFT) . To retain the attractive performances of DFT methods, several dispersion-corrected functionals have been proposed where dispersion is added via empirical pairwise London contributions. This simple and computationally appealing approach has proven successful in including dispersion effects within the DFT framework although the semiempirical nature of exchange-correlation functionals may have effects on their overall accuracy. One limitation of the meanfield pairwise approach in modelling dispersion interactions is the impossibility of capturing many-body dispersion (MBD) effects: many evidences have in fact demonstrated the importance of a non-additive treatment of dispersion interactions in modelling supramolecular complexes , clusters of atoms , one-dimensional wires , extended systems as well as in molecular crystals. The non-additive long-range character of dispersion interactions has been modelled, among the many different approaches , via a set of coupled fluctuating dipoles (CFD) or alternatively by quantum Drude oscillators , the former being preferred over the latter for computational reasons. In recent years, Tkatchenko et al. have formulated the MBD@rsSCS model based on the CFD and introducing the rangeseparation of the self-consistent screening (rsSCS) of polarizabilities which are related to each of the quantum harmonic oscillator in the system. In particular, the model relies on ab initio derived input quantities thus almost removing the presence of empirical parameters. Moreover, the self-consistent screening procedure improves the physical description of the polarizability anisotropy which strongly depends on the atomic environment.
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The MBD@rsSCS model can be summarized into three main steps. Firstly, a set of atom-in-molecule static dipole polarizabilities are obtained from the partitioning of the molecular electron density. Secondly, the polarizabilies are made frequency-dependent via Padé approximation and subsequently a Dyson-like self-consistent screening linear equation is solved for a selected set of frequencies. Lastly, the set of screened frequency-dependent polarizabilities are employed in the solution of Casimir-Polder integrals and the outcoming screened atomic charateristic excitation frequencies are then employed to compute the target MBD energy.
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The MBD@rsSCS model coupled to DFT methods involves a small additional computational cost compared to the solution of the KS equations, however, for increasingly large systems where linear-scaling DFT methods are employed, the O(N 3 ) scaling of the diagonalization procedure as well as the solution of the self-consistent screening equations becomes no longer negligible. In the present work, we considerably extend the applicability of the MBD@rsSCS model via a novel computational resolution of its equations. A robust and efficient linear-scaling scheme for the iterative solution of the self-consistent screening equations is introduced together with a stochastic approach allowing for a linear scaling estimation of the MBD energy which bypasses matrix diagonalization. The article is organized as follows: first the MBD@rsSCS model is briefly reviewed at the beginning of the Theory section. Later in the same section the theoretical aspects of the efficient solution of rsSCS equations are presented as well as the theoretical foundations of the linear-scaling stochastic estimator of the MBD energy. A detailed discussion of the algorithms and of their massively parallel implementations are presented in the Numerical Result section that is followed by the Conclusion.
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To identify the set of { ωi } we start by introducing a corresponding set of bare isotropic and static atomic polarizabilities {α i (0)} which, in the original Tkatchenko-Scheffler scheme , is obtained by partitioning of the total electron density via the Hirshfeld decomposition or, alternatively, via an iterative Hirshfeld scheme. The static polarizabilities are turned into frequency-dependent ones by employing the [0/2] Pade approximants' form in Eq. (3). ω 0 j is the free-atom resonant frequency which is defined in terms of the free-atom's first dispersion coefficient and static polarizability, C 0 6, j and α 0 j (0) respectively. We note in passing that both quantities can be obtained from accurate ab initio calculations.
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In the above equation, R vdw i represents the atom-in-molecule van der Waals radius for atom i which is obtained from the atom-in-molecule static polarizability α i (0), the free-atom static polarizability α 0 i (0) and the free-atom van der Waals radius R 0,vdw i , the latter defined for noble gases as half of the distance between two atoms where exchange-repulsion balances London's dispersion attraction.
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We note that the resulting set of screened polarizabilities { ᾱ j (iν)} are not isotropic due to the effect of self-consistent screening. Finally, the screened resonant frequencies used in the zero-point energy E 0 , are defined similarly to Eq.( ): this time instead, screened quantities are used and the screened dispersion coefficients must be explicitly computed via the Casimir-Polder integral, Eq. (14).
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The overall computational cost involved in the evaluation of the MBD correlation energy arises from the N ν -times solution of Dyson-like self-consistent screening equations (Eq.( )) as well as from the eigendecomposition of V MBD both of which being as O(N 3 ) in scaling. In the following part of this section we first describe a robust and linear-scaling iterative self-consistent screening algorithm as well as a linear-scaling stochastic estimation of E int based on a state-of-the-art linear algebra numerical algorithm.
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The set of screened polarizabilities ᾱ j (iν), key quantities in the aforedescribed MBD@rsSCS model, are typically obtained by partial-contraction of the screened super-polarizability Ā(iν). We propose, instead, to first contract Dyson-like rs-SCS equation prior its iterative solution which directly provides the set of screened polarizabilities. This approach not only involves a reduced number of variables with the consequent reduction of memory requirements but also allows us to obtain screened polarizabilties in a linear-scaling fashion as it will be discussed profusely.
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By projecting C on both the left sides of Eq.( ), we obtain a partially contracted rs-SCS set of equations, Eq.( ), where P and P represent the (3N, 3) arrays gathering all bare and screened atomic polarizabilities respectively. ĀC = AC -AT SR ĀC P = P -AT SR P ( )
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The overall computational cost of Eq.( ) arises from the AT SR p[k] σ matrix-vector products involved in the iterative procedure, where the diagonality of A allows the computation of AT SR on the fly at nearly no cost. The matrix-vector products described above can be performed very efficiently by exploiting the short-range nature of T SR , i.e. its sparsity. This is achieved by building specific short-range neighbor lists based on a cut-off radius which choice will be discussed and motivated in the numerical results section. A further aspect to consider in improving the matrix-vector products' efficiency is the way the T SR elements are built. We remind that Eq.( ) should be solved as many times as the number of frequencies (N ν ) needed in the GL quadrature employed to solve Eq. (14). In this regard it is possible to compute the purely geometry-dependent parts of T SR once and this allows their re-use in the on-the-fly building of frequency-dependent elements. This, as it will be analyzed later, decreases considerably the computational cost. Efficient matrix-vector products would be of little help if the overall convergence required a large number of iterations: it is therefore important to make use of a robust and efficient iterative scheme. The simple self-consistent solution of Eq.( ) can be considered as a fixed-point iterative procedure where the previous iteration's result is used as input for the next one. The rate of convergence of fixed-point iterative algorithms can be generally improved by constructing, at each iteration, a guess vector being a linear combination of previous iterations' resulting vectors where the coefficients of the linear combination are determined to minimize in a least squares sense the error. This extrapolation scheme known as diret inversion of the iterative subspace (DIIS) was introduced with the aim of accelerating and stabilizing the convergence of the Roothaan-Hall self-consistent field equations. The application of the DIIS together with fixed-point iterative methods in solving linear systems of equations makes the overall procedure equivalent to the Generalized Minimal Residual method (GMRES) which, belonging to the Krylov subspace class of iterative methods, is known for its fast and robust convergence properties. We mention that the coupled fixed-point/DIIS iterative schemes have proven successful in the context of modelling many-body polarization interactions and this motivates the use of this mixed procedure in the solution of Eq. (25). Finally, when the px , py and pz arrays are converged for all the N ν frequencies, the frequency-dependent screened atomic polarizabilities are isotropized (second equality in Eq.( )) and the set of { ωi } constituting the zero-point energy E 0 are obtained via Eqs.( ) and (2) respectively.
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We propose, in the following, an alternative approach bypassing the diagonalization step. We first express E int in terms of the trace of √ Λ: by recognizing the trace invariance under any change of basis, the interaction energy is written as shown in Eq.( ) which, at this point is still exact. For simplicity, the MBD lower script is dropped from now on.
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The E int expression is now turned into the evaluation of the trace of a square-root matrix function: this very problem has been recently tackled by Ubaru, Chen and Saad by means of a stochastic Lanczos (SL) trace estimation. For the sake of generality, the algorithm is discussed for Tr [ f (V)], where f denotes a general analytic function inside a closed interval.
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To estimate Tr [ f (V)], the proposed algorithm inkoves Hutchinson's stochastic trace estimator , Eq.( ), where v l is one of the R normalized random vectors of dimension D (in our case D = 3N), which elements follow a Rademacher distribution, i.e. they can assume values of either 1 or -1 with equal probability.
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The overall computational cost of the SL algorithm is to be mainly addressed to the construction of the tridiagonal matrices ∆ (l) via the Lanczos algorithm which, however, only relies on matrix-vector products and can thus be performed in a linear-scaling fashion. On the other hand, the computational cost required by the diagonalization of ∆ (l) is negligible as the (M + 1) number of quadrature points (and therefore the dimension of the tridiagonal matrix to be diagonalized) is very small, typically not exceeding 50, regardless of the system size. Moreover, the exact diagonalization of small tridiagonal matrices can be performed efficiently by means of several O(N) efficient libraries. We finally note that the SL algorithm is embarrassingly parallelizable with respect to the R random vectors as they involve independent processes thus requiring minimal communication.
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The presented algorithms have been implemented in the massively parallel Tinker-HP molecular dynamics package . Atomsin-molecule quantities were computed with the Multiwfn software by partitioning DFT electron densities generated with the Gaussian quantum chemistry software at the PBE/cc-pVQZ level. Free-atom parameters are taken from reference except for noble gases' van der Waals radii which have been taken as the half of the equilibrium distance obtained from accurate reference potential energy surfaces. .
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Before the discussion and analysis of the newly proposed algorithms, we validated the implementation of the standard model which will then represents our target reference. This was done by selecting, from the S66 57 dataset, 9 structures for which dispersion plays a major role in inter-molecular interaction energies. For these selected dimers the implemented model generates MBD energies being in agreement (average deviation of 0.4 kcal/mol, Supporting Information) with the ones computed with the MBD correction implementation included in the Q-Chem package. We note however, that the Hirshfeld partitioning can give as output slightly different parameters according to the software implementation employed thus leading to potentially small discrepancies.
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We start by analyzing the iterative self-consistent solution of the reduced Dyson-like screening equation from which the set of frequency-dependent screened polarizabilities are obtained and subsequently used in the solution of the Casimir-Polder integral in Eq.( ). Before proceeding with the numerical analysis it is first important to understand the adequate number of quadrature points (i.e. frequencies) to be used in the GL quadrature. While a too low number of quadrature points may lead to numerical errors, a too large one, on the other hand, would lead to an unnecessary increase of the computational cost as well as memory requirements and a balance must be therefore found. The analysis reported in the Supporting Information shows that a ten-points GL quadrature leads to errors in the order of 10 -6 and this number of choice will be embraced throughout the discussion.
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We are now in position to analyze numerically the proposed algorithms, starting from the convergence rate for the iterative solution of Eq.( ) which is schematically summarized below. In this and in the following section, argon clusters are taken as test systems as this only involves free-atom parameters and decouples the MBD model from the Hirshfeld partitioning, thus allowing to easily work with increasingly large system sizes without facing the DFT computational bottleneck.
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The rate of convergence is studied on a cluster of 30 argon atoms where the inter-atomic distance is, on average, less than the half of the argon-argon equilibrium distance. This high-density system allows for the testing the algorithm's robustness under high screening regimes. Figure ?? shows the convergence of the screened frequency-dependent polarizabilities in terms of the logarithm (base 10) of the residual defined in Eq.( ) for a single frequency ν n , as function of the number of iterations in the case of a simple fixed-point solution of Eq.( ) where line 18 in Algorithm 1 is skipped.