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649ebcfb9ea64cc16737f53c | 4 | With the required quinoline tethers in hand, three aziridines 3a-c were prepared by previously reported methods and the compounds were reacted under Pd catalysis in order to form a small compound library. This proved broadly successful, with 1-substituted tethers 11a-c reacting as expected to form tricycles 7aa-cc in good to moderate yield (Table ). Yields are unoptimised except for that for the reaction forming 7ab, which was shown to be scalable to 1 mmol without reduction in yield. While reactions of tert-butyl substituted aziridine 3c proceeded somewhat more slowly, as we have previously reported, all reactions were found to be complete within 15 h at 100 °C. Increasing substitution of the quinoline necessarily leads to an increase in electron density (i.e. moving from 11a to 11c) and might thus be expected to impact on the rate limiting Diels-Alder cycloaddition within the cascade process; however, little difference in conversion vs time profile was observed, suggesting all quinoline moieties are effective in activating this step. Reactions involving 2-substituted tether 15 proved somewhat more challenging, with reactions proceeding significantly more slowly and redoxbased side reactions competing at higher temperatures. However, increased reaction times led to isolable levels of product formation in all cases. As expected, the reaction to form tert-butyl ester 7dc proved to be the most challenging; however, this was improved by pre-mixing tricyclic aziridine 3c with the catalyst prior to addition of allylic acetate 15 following this initial allylation step was followed by a separate cycloaddition step at higher temperature. These conditions enabled isolation of the desired product in 18% yield, with this improved yield from pre-mixing (c.f. 1% without) suggesting that a mismatch in rates of oxidative addition may be present in the case of allylic acetate 15. Further, the reduced rate within the Diels-Alder reactions to form series 7dx suggests that the 2-substituted allyl component is appreciably less activated, potentially due to either reduced conjugation of the alkene with the quinoline moiety or increased steric demand. However, despite some reduction in these latter reactions, the process gave broad access to the compounds shown in Table , tolerating significant changes in electron density of the activating quinoline moiety and providing a diverse range of compounds from seven easily prepared building blocks in a single step. With this family of twelve compounds now available the photophysical properties could be investigated. The focus was to explore TSCT between the nitrogen atom on the cage and the quinoline moiety. Since the general effect of protonation on the two nitrogen atoms was expected to be similar to quinine MeCN and 0.1 M H2SO4 were chosen as solvents to allow for study of the doubly protonated and unprotonated forms of the compounds. This would allow the SARs to be built up around the changing parameters of the number of methoxy groups and N-aryl distance. Figures and show the excitation and emission profiles of the compounds at 20 µM concentration in MeCN and 0.1 M H2SO4. The absorption spectra for the compounds in the respective solvents can be found in the Supplementary Information Figures and. For the doubly protonated species (0.1 M H2SO4) the emission profile is pretty much the same for all compounds. In 0.1 M H2SO4 both the nitrogen atom on the cage and the nitrogen atom on the quinoline unit will be protonated, meaning that there is very low potential for TSCT. Given the similarities in structure the emission properties are very similar with the doubly protonated/methylated quinine emission as reported elsewhere. Interestingly the number of methoxy units on the quinoline unit affects the PLQY of the emission (Table ). With the monomethoxy series (7cx) showing the highest PLQYs consistent and at times exceeding the PLQY for quinine in 0.1 M H2SO4. However, having zero methoxy units or having two methoxy units serves to reduce this quantum yield to either 6-8% or 25-30% respectively. The position of attachment to the cage also does not seem to affect the quantum yield with the 7dx series being almost identical to the 7ax series. The PLQY in MeCN is very low and similar for all compounds, with slightly better performance observed for the 7bx and 7cx series. Of greater interest however is the spectral character of the compounds in MeCN. In this solvent neither of the nitrogen atoms should be protonated and thus we can unpack the behaviour of the lone pair on the electronic properties of these compounds. Considering the 7cx series first it can be seen that in MeCN there is only locally excited emission with an onset of 3.77 eV. Removing a methoxy group such as in the 7bx series the emission is still predominantly dominated by the LE emission but there are some beginnings of charge transfer emission in the lower energy part of the spectrum. Moving to the zero methoxy compounds (7ax and 7dx) the charge transfer emission dominates in MeCN, with strong charge transfer character particularly in the 7dx series. This is consistent with the lone pair of the nitrogen being spatially closer to the quinoline unit in the 7dx series compared to the greater distance observed in the 7ax series. |
649ebcfb9ea64cc16737f53c | 5 | When comparing the emission bands of 7bx and 7cx to the mono-substituted quinoline (9b) and the di-substituted quinoline (9c) (Figure ) respectively in solution, we see that the emission in each case of is coming from the aromatic quinoline. 7cx emission bands match the more vibronic character of the di-substituted quinoline emission bands. When dissolved in 0.1 M H2SO4 the emission of 7cx at approximately 3 eV matches the energy of 9c emission. This is also the case for 7bx where the energies of both the doubly protonated and unprotonated compounds match the mono-substituted quinoline (9b), showing that the caged unit of all the compounds is only applicable when looking at the charge transfer behaviour of the molecule. Thus, tuning the position of the cage attachment and the number of the methoxy units on the quinoline affords great control over the strength of the CT state. Interestingly, varying the functionality α-to nitrogen (i.e. ketone, amide or tert-butyl) has very limited impact on the photophysical properties. This therefore enables variation of the pKa of the tertiary amine moiety while retaining essentially identical photophysical properties, suggesting such compounds may have useful function as pH sensors. A subsequent investigation into the position of the quinoline moiety in relation to the nitrogen atom within the caged species was performed to explore the effect of N-aryl distance on TSCT state formation. As mentioned previously, the quinoline moiety of the compound was shifted one place closer to the caged nitrogen atom in 7dx, compared to 7ax, to see whether this influenced the photophysical characterisation. 7aa and 7da were studied (Figure ) in five different solvents with increasing polarity to observe solvatochromism effects. The absorption and excitation profiles in these different solvents can be found in Figures and. Figure shows the emission of 7aa which has the quinoline at position 4 of the ring. We see little change in the emission peak on increasing the polarity of the solvents and there is only a slight red shift in the peak on dissolving the compound in acetonitrile. 7aa shows a more vibronic character in contrast to the 7da emission profile in Figure , which has a broader emission spectrum characteristic of CT states and a strong bathochromic shift with increasing polarity. 7da in methylcyclohexane has an emission peak of 3.1 eV which undergoes a 0.7 eV shift to 2.4 eV when dissolved in acetonitrile. This shift in emission can be rationalised through the position of the lone pair of the nitrogen being closer to the quinoline moiety and so giving clear indication of a TSCT between the two components. The switching on and off of TSCT through change in position by a single carbon bond shows the sensitivity of the formation of these states. |
649ebcfb9ea64cc16737f53c | 6 | Photophysical properties of the compounds were measured in solid state in both poly(methyl methacrylate) (PMMA) and poly(vinyl acetate) (PVA) polymer hosts. The PVA films were dropcast from 0.1 M H2SO4 to replicate somewhat the environment in 0.1 M H2SO4 solution. Supplementary Figures show the steady state absorption, excitation and photoluminescence profiles of all the compounds at 1 wt%. The 7ax series (Figure ) show poor emission in PMMA however in the PVA films the emission has higher intensity and is very similar to that observed in 0.1 M H2SO4 confirming that doubly protonated species in the PVA films have been achieved. In fact, all twelve compounds in PVA show emission very similar to that found in 0.1 M H2SO4, meaning that it is likely we have the doubly protonated compound dominating the emission in all PVA films. The weak emission of the 7bx series (the compounds with one methoxy group, Figure ) shows vibronic character in PMMA, albeit with a red shifted emission band. This is similar to what is observed in the 7cx PMMA films (See Figure ). We believe this additional red band is perhaps a result of aggregation or some CT species that may be activated in the packing of the PMMA films. The 7dx series (Figure ) behave very similar to the 7ax series with very weak emission in PMMA and the typical emission of the doubly protonated species in the PVA film. To re-emphasise, since the PVA films are made from 0.1 M H2SO4 the emission of the compounds in these films can be explained because of protonation of both the nitrogen atoms. The subsequent change in the electronic structure from protonation gives rise to the broader redshifted LE band as observed in solution. |
649ebcfb9ea64cc16737f53c | 7 | The PLQYs of the compounds (Supplementary Table ) in solid state are much lower than in solution, especially the 0.1M H2SO4 solution. For example, where 7bx series has PLQYs of 63.3-70.6% in 0.1 M H2SO4 it has PLQYs of 8.1-8.5% in PVA film. In the 0.1 M H2SO4 solution environment both nitrogen atoms are easily protonated and so the quantum yields are much higher. However, in the solid state the increased rigidity and lack of freely moving protons mean that the nitrogen atoms may not be sufficiently protonated, so we see a ten-fold reduction in the quantum yield. The spectral profile of the doubly protonated species remains the same in film or in solution. Moving to the PMMA films (which are akin to the MeCN measurements in solution) they are very different to the PVA films solidifying the argument that protonation has a significant part to play in PLQYs of these compounds. The compounds in PMMA do not rise above 2% whereas in PVA the 7bx series reaches almost 10%. Similarly, to the solution PLQYs, 7bx series has the highest quantum yields showing that the addition of a methoxy group affects the compounds PLQYs in solid state as well as in solution. The PLQYs for 7cx series of compounds is lower than those in the 7bx series despite them having an additional methoxy group. |
649ebcfb9ea64cc16737f53c | 8 | Overall, the compounds behave very similarly in the solid state. The spectral behaviour is very similar discounting the appearance of a redshifted band in the 7bx and 7cx series. The smaller PLQY values in the PVA films are more likely related to the ability to doubly protonate all molecules and are attributed to the particular equilibrium of unprotonated and doubly protonated species as a result. |
649ebcfb9ea64cc16737f53c | 9 | Clearly, the protonation of the caged and quinoline nitrogen atoms has a large part to play in the steady-state photoluminescence and the PLQYs of solid-state measurements. It reiterates the importance of the nitrogen lone pairs as well as the addition of methoxy groups in giving us control over the strength of TSCT emission, with little effect on the photoluminescence when adding different substituents to the cage attachment. |
649ebcfb9ea64cc16737f53c | 10 | Control of CT character is an important parameter that can have impact on a wide range of fields and applications from charge transfer in photosynthesis to the CT states that underpin phenomena such as TADF. In this work we have shown that fine control of the charge transfer character can be achieved through small alteration in the distance between a quinoline chromophore and aliphatic amine moiety. The important aspect of this work is that by simply changing the position of the cage nitrogen atom with respect to the quinoline unit the CT character can either be enhanced or reduced. If the nitrogen is closer to the quinoline a stronger TSCT transfer species can be obtained. Importantly for their application in sensors the pKa of the nitrogen atom on the cage can be modified and have minimal to zero effect on the emission profile. This provides an additional parameter for variation, potentially making these compounds extremely viable for use in biological sensors. |
6570cf90cf8b3c3cd7ee2117 | 0 | In the past 20 years, quantum chemistry has made great strides in describing chemical reactivity; widely-used methods such as density functional theory (DFT) and coupled-cluster methods (e.g., CCSD(T)) have become a rich source of data for the understanding of chemical reactions and the development of machine learning algorithms. However, despite their black-box nature, these methods face limitations on systems poorly described by a single electronic configuration, i.e. multiconfigurational or strongly correlated systems. A key example of these systems is familiar to most chemists: that of the transition state, in which the electronic character is often split between describing that of the reactant and the product. Given the ubiquitous nature of transition states in chemistry, it may then be a wonder how these approaches have proven successful in so many applications. The answer is that for many important cases these methods are simply able to overcome this difficulty despite the fundamental struggle with multiconfigurational character. Nevertheless, in automated applications of quantum chemistry such as reaction network exploration, the poorer description of multiconfigurational species can rear its head in key places and significantly impact results. |
6570cf90cf8b3c3cd7ee2117 | 1 | As such, describing strong correlation in transition states has long been poised as a potential application for multiconfigurational approaches such as complete active space selfconsistent field (CASSCF) theory. This approach overcomes the difficulty of describing multiconfigurational systems by describing the state as a superposition of the possible electronic configurations in an "active space" of orbitals and electrons: |Ψ CASSCF ⟩ = n 1 n 2 ...n L C n 1 n 2 ...n L |22...n 1 n 2 ...n L 00...⟩ (1) in which n 1 n 2 ...n L enumerates the possible occupations of the L active orbitals. With a good choice of active space, all static correlation can be addressed with far fewer configurations than FCI and comparable expense to DFT. However, despite the many academic applications of these approaches in the literature, the widespread adoption of these methods for reactivity has been hindered by the challenge of choosing a consistent and adequate active space along the reaction surface. The CASSCF energy expression is given by |
6570cf90cf8b3c3cd7ee2117 | 2 | where D pq and d pqrs are the CASSCF one-and two-body reduced density matrices. If the active space is chosen inconsistently between two geometries, one will obtain an unphysical "active space inconsistency error" (ASIE) resulting from the inconsistent treatment of correlation in the density matrices of equation 2. This error generally remains present even when addressing the remaining dynamic correlation perturbatively with methods such as CASPT2 or NEVPT2. The most common approach for reducing ASIE involves interpolating the active space orbitals between geometries, providing a continuous set of orbitals along the reaction coordinate. However, this approach is quite cumbersome: active orbitals often rotate in and out of the active space randomly during this procedure, and the active space may change size along a reaction coordinate, such as when moving from a fairly uncorrelated reactant to a correlated transition state. Furthermore, this interpolation scheme dramatically increases the cost of the calculation relative to approaches such as DFT, as CASSCF calculations are necessary along several points between the reactant and product, whereas KS-DFT only requires calculations at the individual end points. |
6570cf90cf8b3c3cd7ee2117 | 3 | Despite the fact that the KS-DFT determinant inevitably describes the density matrices of reactants and transition states with different accuracy (i.e., the exact two-body density matrices d pqrs differ more or less from the single-determinant D pq D rs ), KS-DFT is able to obtain good results in reactivity through use of an exchange functional of the density E xc [ρ]. This statement also applies to the success of "density corrected" DFT (DC-DFT), in which the densities used in the KS-DFT energy expression (eq. 3) come from HF determinants (i.e., the functional has no input on the density, but only the energy calculation). This leads to the hypothesis that the ASIE found in CASSCF may come in large part from unequal contribution of the density cumulant between two geometries, d pqrs -D pq D rs . A multiconfigurational approach that avoids use of the density cumulant by means of an exchange-correlation functional may inherit much of the equal-footing properties of KS-DFT and prove more robust against ASIE. |
6570cf90cf8b3c3cd7ee2117 | 4 | with two key differences: (i) the exchange-correlation functional is replaced with an "ontop" functional E ot which is a functional of both the density ρ and on-top density Π, and (ii) the density arguments D pq , ρ, and Π come from a multiconfigurational (generally CASSCF) wave function. In practice, the on-top functional is a "translated" functional (most often translated PBE, 28 tPBE) in which the density and on-top density are used to manufacture effective spin densities for use in the KS-DFT energy expression (eq. 3). Thus, as MC-PDFT more-or-less shares eq. 3 with KS-DFT, MC-PDFT appears promising for attenuating part of the active space inconsistency error, especially when paired with automated methods for choosing the active space in a reliable and consistent fashion. While MC-PDFT has been tested on a wide variety of systems and excitations, it has yet to be tested in a high-throughput fashion for reactivity. |
6570cf90cf8b3c3cd7ee2117 | 5 | Here we provide the first such test by applying automated MC-PDFT to the calculation of 908 automatically generated organic reactions in the RGD1 database. These data present a rich variety of organic reactivity and a challenging test for multiconfigurational approaches that is germane to reaction network exploration. Our results highlight the robustness of automated MC-PDFT in this domain compared to other perturbative multiconfigurational approaches such as NEVPT2 and outline the opportunity and challenges for applying multiconfigurational methods to high-throughput main-group reactivity. We find that combining APC with MC-PDFT produces robust results, with APC-PDFT reproducing DFT results for a set of single reference reactions. In addition, we show the deviation in relative energies from single reference are correlated to level of multiconfigurational character, with DFT and CCSD(T) becoming less reliable for strongly correlated systems (68% of reactions), and APC-PDFT providing better results in many of these cases. |
6570cf90cf8b3c3cd7ee2117 | 6 | The main barrier to automating multiconfigurational approaches is automatically selecting the active space in a robust fashion. Methods for automatically selecting active spaces continue to be an active research topic, and several approaches exist. Here, we employ approximate pair coefficient (APC) selection, in which candidate Hartree-Fock orbitals are ranked for the active space by means of their approximate pair coefficient interaction with other orbitals. Given doubly occupied orbitals i and virtual orbitals a, approximate pair coefficients are calculated as |
6570cf90cf8b3c3cd7ee2117 | 7 | Interactions with singly occupied orbitals are left uncalculated, and singly occupied orbitals are automatically given the highest possible entropy. Finally, due to the observed biasing of APC entropies towards doubly occupied orbitals a series of virtual orbital removal steps are employed N times in which the highest-entropy virtual orbital is removed from the sums in equations 6 and 7 and the entropies are recalculated; these highest-entropy virtual orbitals are then assigned the highest entropy at the end of the calculation. For small-to-medium sized organic systems we have found good results with N = 2, 12 which we have used here. |
6570cf90cf8b3c3cd7ee2117 | 8 | Implementation of APC is now available in PySCF. Candidate HF orbitals are then ranked in importance by their orbital entropies, with this ranking used to choose an active space meeting some user-defined size requirement (e.g., (12,12)). Here, to select consistent active space sizes between geometries we employ a simple size requirement in which for an (A,B) active space, the A/2 highest-entropy doubly occupied orbitals and the B -A/2 highest-entropy virtual orbitals are added to the active space; we refer to these active spaces as APC-(A,B). CASSCF calculations initialized from these active spaces in the cc-pVDZ basis were then carried out in PySCF. These CASSCF wave functions were then used for the calculation of MC-PDFT (tPBE) and NEVPT2 energies, also implemented in PySCF and PySCF-Forge. Multiconfigurational (or equivalently, multireference (MR)) character in the resulting wave functions is calculated via the M -diagnostic, which measures multiconfigurational character as a function of the natural orbital occupancies: |
6570cf90cf8b3c3cd7ee2117 | 9 | Here n HDOMO , n LUMO , and n SOMO are the average occupations of the highest doubly occupied, lowest unoccupied, and any singly occupied orbitals in the active space. An M diagnostic less than 0.05 is considered minimally multiconfigurational, 0.05 < M < 0.1 moderately MR, and M > 0.1 substantially MR. |
6570cf90cf8b3c3cd7ee2117 | 10 | Figure : Electronic energies of each state in the concerted transition state (CTS) and biradical reaction pathways relative to the reactants. Four methods are shown: APC(6,6)-tPBE (green, this work), hand-selected (6,6)-tPBE (black), HF-PBE (blue), and reference MR-AQCC results (red). The structures of each transition state and intermediate are displayed on the right. |
6570cf90cf8b3c3cd7ee2117 | 11 | As a first test of our methodology, we explore the performance of APC-tPBE on the Diels-Alder reaction between butadiene and ethylene. This reaction presents a well-studied series of transition states and intermediates that provide a clear challenge for automated multiconfigurational approaches, as all states contain a significant amount of multiconfigurational character (M > 0.1). Figure shows the tPBE results obtained with our automated APC (6,6) active spaces compared to previous literature results using hand-selected (6,6) active spaces, as well as reference MR-AQCC calculations. As is seen, the automatically selected active spaces are able to reproduce the tPBE results |
6570cf90cf8b3c3cd7ee2117 | 12 | (in good agreement with the MR-AQCC results) of the hand-selected active spaces in all transition states, despite not directly enforcing any consistency between active spaces beyond the size. For reference, we show the single-reference limit of MC-PDFT in which the CASSCF wave function densities are replaced with HF densities (equivalent to so-called "densitycorrected" PBE ); here we refer to this approach as HF-PBE. Unlike APC(6,6)-tPBE, HF-PBE dramatically overestimates the stability of the concerted transition state (CTS) while greatly underestimating the stability of the TS-Anti transition state and intermediate. Thus, our automated scheme successfully reproduces the important multiconfigurational results. |
6570cf90cf8b3c3cd7ee2117 | 13 | Given the success of our methodology in reproducing Diels-Alder results, we turn to the 908-reaction subset of RGD1 reactions for further testing. Our calculations show that this set of reactions shows a broad distribution of multiconfigurational character as measured by the M -diagnostic (Supporting Information), with 32% of reaction energies and 63% of activation energies demonstrating significant multiconfigurational character (M > 0.1), for a total of 68% overall. To account for the cases with the most multiconfigurational character, we have chosen large APC (12,12) active spaces for each state in these reactions. This active space size is significantly larger than necessary for most reactions in the dataset, resulting in inconsistent but unimportant orbitals between the reactants and products of some reactions. |
6570cf90cf8b3c3cd7ee2117 | 14 | These orbital inconsistencies represent a second test of the robustness of MC-PDFT. Figure shows the absolute deviation in the reaction energy, ∆E, and the activation energy, E a (both forward and backward), for all examined reactions from the single reference limit (SRL) for CASSCF (SRL: HF), tPBE (SRL: HF-PBE), and NEVPT2 (SRL: MP2). This deviation is stratified by three degrees of multirference (MR) character (low (M < 0.05), moderate (0.05 < M < 0.1), and high (0.1 < M ). As shown clearly, both the mean absolute deviation (MAD) from the SRL and overall spread of the data increases from the low M to the high M categories. In the cases with low multiconfigurational character, M < 0.05, tPBE successfully reproduces the single-reference limit with a mean deviation of ± 1.8 kcal/mol for ∆E and ± 2.8 kcal/mol for E a , with an average between these two of ± 2.2 kcal/mol. In contrast, CASSCF and NEVPT2 reproduce these limits with a mean deviation of ± 7.9 kcal/mol and 4.4 kcal/mol repectively, with much larger maximum deviations (as high as 20 kcal/mol). These results show that MC-PDFT is significantly more robust in the single-reference limit towards active space inconsistency error (ASIE) than competing multiconfigurational approaches, making it ideal for high-throughput application. Surprisingly, we find that this robustness carries over to the performance of hybrid PDFT as well, despite it being an admixture of CASSCF and tPBE; this point bears technical discussion and is discussed in the Supporting Information. A similar analysis, using the square of the coefficient of the leading configuration, C 2 0 , as the multireference diagnostic can also be found in the Supporting Information. Two examples where tPBE shows improved reliability for a single-reference reaction are shown in Figure . The first is a trimethylamine rearrangement reaction, where the APC(12,12)-CASSCF wave functions for the reactant and product are mostly well-described by a single determinant, with M diagnostics below 0.03. Thus, the overall reaction energy is expected to be similar between each MR approach and its single reference parallel. As is seen, APC-tPBE successfully reproduces HF-PBE to within 3 kcal/mol, a result that is similarly in-line with B3LYP-D3 and CCSD(T). Despite this, APC (12,12)-NEVPT2 shows a clear deviation from all other methods, overestimating the energy of the reactant by roughly tPBE. This drastic difference from the single-reference result is emblematic of ASIE, where orbital rotation between the product and reactant results in drastically unphysical results. |
6570cf90cf8b3c3cd7ee2117 | 15 | Here, all three states exhibit an M of less than 0.05, indicating both the reaction and activation energies should be well described by a single-determinant wave function. Despite this, both the forward and reverse barriers are predicted to be 20 kcal/mol lower with APC(12,12)-NEVPT2 than MP2. By comparison, APC-tPBE agrees to within chemical accuracy (1 kcal/mol) with the single-reference limit of HF-PBE and CCSD(T). Once again, the smaller APC(4,4) active space largely remedies this unphysical error with NEVPT2, demonstrating the error to be due to ASIE. An in-depth evaluation of the active space dependence of tPBE and NEVPT2 for these two reactions, as well as CASSCF is included in the Supporting Information. Figure presents a second case, in which the ring-opening of a 3-membered heterocycle forms an oxygen diradical with significant multiconfigurational character. As is seen, the HF determinant is completely incapable of describing this state, overestimating the energy of this product relative to the reactant by 60 kcal/mol -higher in energy than the transition state. Due to this terrible description given by HF, CCSD(T) inherits this error and also drastically overpredicts the energy of the reactant relative to the transition state. The unrestricted nature of B3LYP-D3 is able to account for the multiconfigurational character of the biradical somewhat, predicting a shallow barrier of 8.5 kcal/mol relative to the transition state. In contrast, APC-tPBE predicts a significantly more stable product, with a barrier of 31.3 kcal/mol relative to the transition state, and in much better agreement with the CCSD(T) reference values for the single-reference reactant and product. Here, we believe the APC-tPBE results give a much more accurate description than either DFT or CCSD(T), and are reproduced by NEVPT2 in a smaller active space containing only the correlating orbitals (Supporting Information). These results serve to highlight the necessity of multiconfigurational approaches for some reactions containing significant multiconfigurational character. |
6570cf90cf8b3c3cd7ee2117 | 16 | We have here presented the first large-scale automated multiconfigurational approach to the modeling of organic reactivity, which provides a compelling alternative to DFT and CCSD(T) for interrogating chemical space. These multiconfigurational methods have been held back from high-throughput application for decades due to the problem of active space inconsistency error (ASIE), which is here overcome through the increased robustness of the MC-PDFT method to ASIE and automated active space selection with the approximate pair coefficient (APC) approach. We have applied this automated APC-PDFT approach to the calculation of 908 main group reactions from the RGD1 database, which successfully reproduces the single-reference limit with ASIE of ±2.2 kcal/mol (similar to deviations between different density functionals) while providing more accurate multiconfigurational descriptions than DFT and CCSD(T) in many of the 68% of reactions containing multiconfigurational character. Taken at face value, these results make it possible to for the first time envision the high-throughput use of multiconfigurational methods in this domain, potentially increasing the accuracy of predictions at significantly lower cost (and possibly higher accuracy) than CCSD(T). |
6570cf90cf8b3c3cd7ee2117 | 17 | Of course, there are limitations. Firstly, there is no reason to expect good results if a sufficient active space is not chosen for all geometries. In the best case, one will reproduce HF-PBE, which may or may not be adequate. In the worst case, describing only some multiconfigurational states with good active spaces may result in an imbalanced treatment and actively worse predictions. How can one be sure that this is not the case? The APC (12,12) active spaces chosen in this work seem to have been sufficient for this application, but further development will be needed for application to larger organic complexes and transition metal systems. Ultimately, different approaches need to be tested on a wide variety of systems and investigated on a case-by-case basis to be trusted. |
6570cf90cf8b3c3cd7ee2117 | 18 | Secondly, the active space dependence of MC-PDFT may be larger than is comfortable in some sensitive systems. For example, previous work on H 2 dissociation has shown that the predicted dissociation energy of MC-PDFT can vary by over 10 kcal/mol increasing the active space size from a minimal (2,2) to (2,28). Nevertheless, this work has shown that cases such as this are more likely to be outliers than the norm; H 2 dissociation is a well-known failing of restricted HF and DFT, and thus the active space likely has an outsized impact on the performance of MC-PDFT in this case. The generally active-space-independent nature of APC-PDFT beyond a minimum size is further shown by recent studies calculating vertical excitation energies. Regardless of these remaining challenges, the throughput, automation, and robustness achieved here represent a milestone in applying multiconfigurational methods to main group reactivity and suggest further general-use implementations are possible. The next frontier involves extending this approach to encompass full reaction networks and larger compounds, promising a more comprehensive understanding of complex chemical processes. |
67a2ccb6fa469535b915b8fb | 0 | Vertically stacked twisted layers of two-dimensional (2D) materials provide a fruitful ground for the exploration of unique and novel quantum phenomena in van der Waals (vdW) material systems. Stacking of 2D vdW materials with a small twist angle θ (θ<~10°) and/or a slight lattice mismatch results in the reconstructed moiré superlattices (MSLs), accompanied by the enhanced interlayer coupling. These reconstructed MSLs especially with magic twist angles around θ≈1.1º can host flat electronic bands to form highly correlated phases, even showing superconductivity. In the small angle regime, the commensuration cell lattice constant can be equal to the moiré periodicity D, which is given by 𝐷 = 𝑎 2 sin 𝜃 2 (1), where a is the lattice constant of the constituent layer. For large twist angles (θ>~15°), on the other hand, the commensuration cell lattice constant is generally much greater than D. However, there exist a few special twist angles at, e.g., 13.2° and 21.8º for twisted hexagonal bilayers, where the "commensuration periodicityˮ is equal to D. Thus, from the view point of MSLs, any large twist angles except for the above special twist angles can be regarded as incommensurate twist angles. In the large angle regime, it is believed that atomic reconstruction hardly occurs, meaning that a rigid lattice model is a reasonable representation of the actual system. Although the interlayer coupling is supposed to be suppressed in these incommensurate MSLs, it has recently been revealed that this is not necessarily the case for 30°twisted vdW bilayers, forming quasicrystalline patterns with a 12-fold rotational symmetry. In these quasicrystalline layers, two twisted layers are coupled via Umklapp electronelectron scattering, which results in rich electronic structures, such as mirrored Dirac cones in graphene quasicrystals and mini-gaps near the valence band maximum in tungsten diselenide quasicrystals. Thus, incommensurate MSLs and related moiré potentials have attracted increasing attention, offering an interesting experimental platform to explore moiré physics beyond the small twist-angle regime. However, atomic-scale visualization of moiré potential is highly technically demanding. At present, scanning tunneling microscopy/spectroscopy (STM/STS) is one possible technique available for that purpose. Here we use an aberration-corrected high-resolution transmission electron microscopy (HRTEM) technique as a tool to explore the moiré potential in atomic scale. Although HRTEM has been often employed to obtain atomic resolution imaging of 2D materials and related MSLs, we show that this technique is also applicable for imaging the moiré potentials, which are reconstructed from the moiré diffraction spots in Fourier space. In previous works, the diffraction spots due to moiré potential have not been explicitly observed by HRTEM because of the general presence of hydrocarbon contaminants which are often trapped during the assembly of 2D stacked materials. These contaminants yield a severe background noise in Fourier space, obscuring weak moiré diffraction spots. Furthermore, any interlayer contaminants will modify the interlayer distance, leading to a fluctuation of moiré potential. In this work, we overcome the problem by developing a specially designed chemical exfoliation method to obtain atomically clean MSLs, which are ideal for the investigation of the moiré structure and the related potential by HRTEM technique. |
67a2ccb6fa469535b915b8fb | 1 | We develop a method to exfoliate atomically clean and strain-free hBN nanolayers from hBN particles. It has been well recognized that hBN nanostructures are characterized by their excellent thermal and chemical stability and unique electronic and optical properties, providing an ideal building block for the investigation of vdW potentials. Our exfoliation procedure is based on an intercalation-based method; however, unlike conventional methods, it does not require any sonication, sharing nor electrochemical process as a driving force, hence yielding mechanically intact and strain-free samples. Briefly, we start by creating hBN/H2SO4 intercalation compounds by heating hBN powders in an aqueous H2SO4 solution. The resulting solution is neutralized by a solution of NaHCO3 to form sodium sulphate salt in between the hBN layers. We found that this acid/base reaction leads to spontaneous exfoliation of high-quality hBN layers suitable for the characterization of moiré potentials by HRTEM (see the Supporting Information and Fig. for details). |
67a2ccb6fa469535b915b8fb | 2 | HRTEM and scanning TEM (STEM) observations were carried out on a JEOL JEM-ARM300F instrument equipped with a cold field emission electron gun and a spherical aberration (Cs) corrector at an acceleration voltage of 80 kV, under 1 × 10 -5 Pa in the specimen column. We analyzed strain of the exfoliated hBN layers based on the HRTEM images using the Peak Pairs Analysis (PPA) software package for Gatan Digital Micrograph. In order to calculate the interlayer electrostatic potential, we performed quantum chemical calculations using density functional theory (DFT) methods implemented in the Gaussian 16 suite of programs. In this work, hydrogen terminated clusters with various sizes and two different edges (zigzag and armchair) were used to model the local structure of twisted hBN bilayers with different twist angles. |
67a2ccb6fa469535b915b8fb | 3 | General characteristics of exfoliated hBN. Figure shows a typical AFM image of the exfoliated hBN sheets with a lateral size of a few m. Each sheet has a relatively smooth surface with a thickness t of 24 nm. Considering that the interlayer distance of hBN is ~0.33 nm, we can estimate that each nanosheet consists of ~515 BN layers. We show in Fig. a low-magnification annular dark field scanning TEM (ADF-STEM) image of the exfoliated hBN, showing a random stacking of micrometer-sized hBN layers. A high-magnification ADF-STEM image of non-twisted hBN layers is given in Fig. , illustrating 2D honeycomb structures of BN with asymmetric ADF scattering intensities. One may expect that three boron and three nitrogen atoms in each hexagonal ring are responsible for this asymmetric contrast, which can be in principle distinguished by their intensity based on the Z-(atomic number) contrast principle. However, we should note that our exfoliated hBN nanosheets are likely to have more than 5 AA-stacked BN layers, which are formed by stacking many anti-aligned layers B to N and N to B. In such layers, the expected Z-contrast will be averaged out to yield symmetric ADF scattering intensities. We hence assume that observed asymmetric ADF contrast results from a slight specimen tilt. To confirm the assumption, we performed simulations by changing x-tilt angle φ (for details, see Fig. ) using a comprehensive multipurpose crystallographic program Recipro. After several try-and-error attempts, we found that the specimen of t = ~8 nm and φ = ~1° yields the asymmetric contrast which is most comparable to that of the observed ADF-STEM image (see Fig. ). Although the thickness estimated from the simulation is somewhat greater than that obtained from an AFM image shown in Fig. , these estimated values are reasonably consistent with each other. Thus, we can conclude that the thickness of our exfoliated hBN sheets lies in the range from ~3 to ~8 nm, which will be thin enough to satisfy the weak phase object approximation (WPOA) especially for the samples consisting of light elements such as B and N. Under WPOA, the TEM image operated in the phase contrast mode at optimum focus directly reveals the projected potential. HRTEM images shown in Fig. ,b demonstrate that the resulting layers have a clean and adsorbates-free area extending several tens of nanometers (see also Fig. ). The corresponding fast Fourier transform (FFT) image yields six spots of 0.21, 0.12 and 0.11 nm spacings attributed, respectively, to 101 ̅ 0, 112 ̅ 0 and 202 ̅ 0 Bragg peaks (see the inset in Fig. ). Figure is the PPA strain mapping obtained for the HRTEM image shown in Fig. . As shown in Fig. , the strain tensor is estimated to be as low as 1 % over the entire region of interest (see Fig. for more details of the PPA analysis). |
67a2ccb6fa469535b915b8fb | 4 | Figure shows the edge area with four BN layers (see also the line profile in Fig. ). Any moiré patterns and the related rotational stacking faults are not present at the edge, indicating that the edges are not folded back bur rather exhibit the smallest possible scroll, as often observed in the edge structures of high-quality free-standing graphene layers. All the above results demonstrate that as far as the nontwisted hBN layers are concerned, atomically clean, flat and strain-free samples can be obtained by the present exfoliation procedure. |
67a2ccb6fa469535b915b8fb | 5 | TEM observations on twisted hBN layers. In addition to the non-twisted regions, we also found several contaminant-free twisted regions at different twist angles. We show in Fig. the HRTEM and the corresponding FFT images of the twisted hBN layers with four different twist angles of = 24.0º, 21.6º, 19.8º and 13.6 º. In this work, the twist angle was defined as the angle between the two closest 101 ̅ 0 spots, as often done in previous studies. The uncertainty of is within the range of ±0.4º. Note, however, that the alternative twist angle 𝜃 ̅ can be defined as the angle between the two next-closest 101 ̅ 0 spots, i.e., 𝜃 ̅ = 60°-𝜃. Since we cannot identify which definition is appropriate from the diffraction pattern alone, the selection of is just for convenience. We will show that this selection is not crucial for the discussion of this work in a later subsection.. The observed HRTEM images illustrate a variety of moiré patterns typical to twisted bilayers with large twist angles. The two of the observed twist angles (13.6 ° and 21.6°) are comparable to two of the commensurate angles of twisted hexagonal bilayers (13.2° and 21.8°) within the experimental uncertainty. Thus, in what follows, we will refer to the samples with =13.6 ° and 21.6° as nearly commensurate layers, whereas the rest of the samples as incommensurate ones. Note, however, that even in the incommensurate cases, the partially eclipsed interlayer atomic overlap, i.e., N nearly on N (or B nearly on B) configurations, is expected to be realized in the rigid lattice picture, as illustrated in Fig. . |
67a2ccb6fa469535b915b8fb | 6 | The FFT images given in Fig. are especially worth noting. We see that in addition to the two sets of 101 ̅ 0 Bragg spots defining a twist angle, there exist several extra spots especially in the inner region of the 101 ̅ 0 spots, which are located symmetrically with respect to the center spot. These extra spots have not been explicitly reported in previous HRTEM observations on MSLs. We also found that these extra spots are not observed in the TEM image of the twisted hBN layers with hydrocarbon adsorbates (Fig. ). This allows us to expect that clean and contaminant-free samples are necessary for the observation of the extra diffraction spots. |
67a2ccb6fa469535b915b8fb | 7 | What is the origin of these extra diffraction spots? One immediate answer is double diffraction, which often occurs in thick two-phase materials when a diffracted beam travelling through a crystal is rediffracted when it passes into a second crystal. Hence, it would be natural to expect that double diffraction induces several extra diffraction spots in MSLs. We, however, argue that the simple double diffraction process cannot account for the extra diffraction spots shown in Fig. . Double-diffraction spots occur around each of the primary reflections, including the direct beam spot, by keeping the symmetry of the constituent crystals. This general feature of double diffraction implies that as for twisted hBN layers, two types of primary reflections, each with 6-fold rotational symmetry, should be accompanied by a set of double diffraction spots with the same 6-fold rotational symmetry, as indeed observed in 10° twist angle double-multilayer of ~100-nm-thick hBN sample. Contrary to the above expectation from double diffraction, the extra diffraction spots given in Fig. does not show the 6-fold rotational symmetry except for the nearly commensurate sample at = 21.6°. Furthermore, for very thin specimens in which the WPOA holds, the double diffraction does not contribute to the entire diffraction process, as will be discussed below. |
67a2ccb6fa469535b915b8fb | 8 | For a better understanding of the extra diffraction spots, we analyzed the positions of these spots ke in reciprocal space. It has been revealed that ke can be found by connecting the two Bragg spots belonging to the different layers and translating the obtained vectors to the center of the diffraction pattern, as demonstrated in Fig. . The relationship can be written as ke = G1 G2, where Gi (i = 1, 2) represents the reciprocal vectors from two different layers. This relationship implies that the interlayer interactions are responsible for the generation of these extra diffraction spots indeed, but the question is, why do particular sets of the reciprocal vectors contribute to the extra diffraction processes? Here, one should remind that under WPOA, the contrast in HRTEM images is proportional to the projected specimen potential, convoluted with the impulse response of the instrument. Note, however, that diffraction peaks due to moiré structures (or double diffraction) cannot be observed when acquired at typical TEM electron energies (60300 keV) under WPOA, provided that the projected specimen potential consists only of the potentials of individual atoms in the respective layers (see 'Intensity of moiré peaks in diffraction pattern' section in the Supporting Information). We hence assume that the observed extra diffraction spots are originated from a well-defined moiré potential newly created by interlayer coupling. The moiré potential presumably has complicated spatial distributions and periodicity depending on the twist angle. When an electron beam is diffracted by the interlayer moiré potential, the resulting diffraction pattern will not necessarily have 6-fold rotational symmetry except for the commensurate MSLs but should be represented by the combination of a set of ke vectors with particular frequencies and amplitudes, accounting for the underlying characteristics of the extra diffraction spots with particular frequencies and intensities. |
67a2ccb6fa469535b915b8fb | 9 | Construction of the Moiré Potential. If the assumption mentioned in the previous subsection is valid, the inverse FFT (IFFT) of these extra spots will yield information on the spatial modulation of the moiré potential. It is hence interesting to reconstruct IFFT images from the FFT images by filtering in the frequency domain using the inclusive mask for the extra spots shown in Fig. , but excluding all the well-defined Bragg and center spots (for details, see Fig. ). Figure shows the thus obtained IFFT images using the FFT images shown in Fig. . We found that regardless of the twisted angles, the IFFT images exhibit a triangular lattice-like pattern. Note also that a similar pattern can be obtained even if the contrast of the respective IFFT images is inverted (Fig. ). Hence, the resulting images are not artefacts due to IFFT but will represent periodic-like 2D potential functions with comparable positive and negative amplitudes. As for the nearly commensurate cases at = 21.6° and 13.6°, the periodicities of the lattice are estimated to be ~0.6 nm and ~1.0 nm, respectively. These values are comparable to those deduced from Eq. ( ) (D = 0.66 nm and 1.08 nm for = 21.6° and 13.6°, respectively). The corresponding line profiles show distinct repeating patterns with positive and negative correlations along the three directions of the triangular lattice (Fig. ), which extends over the length scale of several to tens of nanometers (see Fig. for a wide-area IFFT image of = 21.6°). Thus, the commensurability of the MSLs is almost preserved in the IFFT image. |
67a2ccb6fa469535b915b8fb | 10 | Calculations of electrostatic potential. The present IFFT images presumably represent the interlayer moiré potential in our incommensurate and nearly commensurate hBN layers. However, additional theoretical support would be necessary to confirm this argument. In theoretical studies of 2D materials, two models are usually employed, i.e., a periodic model and a finite model. The periodic model is based on Blochʼs theorem and utilizes periodic boundary conditions to replicate the elementary cell. This approach is in principle applicable only to commensurate systems where (lower panels) with the same twist angle. These images are created by cropping and rotating the original images for the ease of comparison. |
67a2ccb6fa469535b915b8fb | 11 | the momentum is well defined. In the finite model approach, one performs, for example, quantum chemical calculations using a large enough finite cluster models, whose external dangling bonds are terminated usually by hydrogen atoms. Although the results of the finite models may suffer from edge effects, this approach can be applied both to commensurate and incommensurate systems and is useful for calculating electrostatic potential (ESP) in real space. Thus, in this work, we carried out a series of quantum chemical density functional theory (DFT) calculations using sufficiently large clusters of atoms modeling the hBN bilayers with different twist angles as well as the one with the untwisted AAstacking configuration (θ = 0°). Although the DFT calculations were performed on several model clusters with different sizes using various density functionals under the rigid lattice approximation, we only show the results on the (B111N111H42)2 cluster at the B97XD/6-31G(d) level, as explained in 'Computational details' section in the Supporting Information. |
67a2ccb6fa469535b915b8fb | 12 | Figure shows the resulting optimized structures of the H-terminated clusters with different twist angles, along with the 2D plot of the ESP in a plane bisecting the two hBN layers of the respective clusters. One sees from Fig. that as for the cluster with θ = 0°, the periodicity of the interlayer ESP matches that of the atomic configuration (for the crosssectional map perpendicular to the atomic planes, see Fig. ). The periodic pattern is created by the negative ESP on the N atoms and the positive ESP on the B atoms located exactly above (or below) the N atoms. As the twist angle increases from zero, the anti-aligned AA stacking (B on N or N on B) is altered to form various interlayer atomic alignments, such as N on N and B on B configurations, especially for the nearly commensurate clusters (Fig. ). From the 2D plot of the ESP shown in Fig. , one sees that such N/N (B/B) overlaps yield negative (positive) ESP. Consequently, the point where a fully eclipsed arrangement of N/N (B/B) shows the highest local negative (positive) ESP. This leads to the formation of triangular lattice-like patterns with pitches of 0.66 nm and 1.09 nm for θ = 21.6° and 13.6°, respectively, which are almost equal to those deduced from Eq. |
67a2ccb6fa469535b915b8fb | 13 | (1) (D = 0.66 nm and 1.08 nm for = 21.6° and 13.6°, respectively). Note also that even in the 2D ESP map of incommensurate clusters with θ = 24.0° (Fig. ) and 19.8°(Fig. ), a similar periodic pattern with a pitch of 0.66 nm is created due to periodicity of N nearly on N (or B nearly on B) configurations. Further worth mentioning is that as shown in Fig. , the triangular lattice-like patterns of the 2D ESP maps are very similar to those found in the IFFT images of the samples with the corresponding twist angles in terms both of the pitch and the pattern. A slight discrepancy between the observed and calculated pitch values may result from the rigid lattice approximation employed in the DFT calculations. This good correspondence confirms our assumption that a series of the IFFT images shown in Fig. represent the interlayer moiré potential created by the local interlayer atomic overlap in the respective hBN bilayers. Finally, we discuss how the interlayer ESP varies as the interlayer distance dint increases from its optimal value dint(opt). Figure shows a variation in the ESP with interlayer distance obtained for the cluster with θ = 24.0°, which is characterized by dint(opt) = 0.329 nm. One sees from Fig. that the positive ESP almost disappears for dint=0.375 nm, and the interlayer ESP eventually becomes almost structureless for din=0.475 nm. This probably accounts for the reason why in previous HRTEM studies on MSLs, the extra FFT diffraction spots, such as those observed in Fig. , have not been reported to occur. In the previous HRTEM measurements, it is likely that various adsorbates are trapped between layers during their assembly and sample handling, which prevents the observation of interlayer moiré potential. Thus, as mentioned repeatedly before, the preparation of adsorbate-free samples is a prerequisite to observe moiré potential as FFT diffraction spots. The chemical exfoliation procedure developed in this work is one useful method for obtaining clean hBN nanolayers and hence observing their moiré potential. We are now applying the present method to graphite and transition metal dichalcogenides. Currently, studies are in progress to confirm its applicability to other vdW systems. |
67a2ccb6fa469535b915b8fb | 14 | We fabricated strain-and contaminant-free hBN layers with different twist angles using the intercalation-based exfoliation technique and observed their HRTEM images. The FFT of the HRTEM images allowed us to recognize moiré diffraction spots, and their IFFT computations provided information about the interlayer moiré potential, as corroborated by the DFT calculations. Also, the DFT calculations highlight the importance of the local interlayer atomic overlap in establishing the moiré potentials both in the commensurate and incommensurate cases. The present results not only pave the way for observing the moiré potentials in twisted hBN layers, but they also expand the application of electron microscopy to visualizing the moiré potential in a variety of MSLs especially with large twist angles. |
67a2ccb6fa469535b915b8fb | 15 | Boron Nitride was purchased from Kojundo Chemical Lab. Co., Ltd. (purity ∼99%, particle size ∼10 μm) without any additional treatment. We confirmed that the sample powders show Bragg X-ray diffraction peaks attributed only to the hBN phase. Sulfuric acid (95 %) was obtained from Wako Pure Chemical Industries, Ltd. and was used as purchased. We prepared h-BN/H2SO4 intercalation compounds according to the scheme shown schematically in Fig. . A 30 mg amount of h-BN was added to 0.5 mL of sulfuric acid in a 50 mL Teflon-lined stainless steel autoclave. The autoclave was heated at 200 °C for 24 h, and then naturally cooled to room temperature, producing a slightly brownish slurry. The slurry was transferred into a test tube and was neutralized with an aqueous solution of NaHCO3, resulting in an opaque solution. During neutralization, sodium sulfate salt (Na2SO4) is expected to be formed in between the hBN layers, leading to spontaneous exfoliation of hBN layers The solution was centrifuged at 15000 rpm for 45 min to remove insoluble materials, and then the supernatant was transferred to a new test tube. The thus obtained supernatant is an aqueous solution containing Na2SO4 and exfoliated hBN nanosheets. A solvent extraction method was utilized to isolate the exfoliated hBN nanosheets from the supernatant solution. That is, the solution was mixed with an equal volume of organic solvent in a separatory funnel, leading to migration of hBN nanosheets into the organic solvent. We found that 1-pentanol is the most suitable solvent for the present purpose. Although the extracted 1-pentanol solvent was transparent, a colloidal dispersion of the exfoliated hBN nanosheets was confirmed by the Tyndall effect (Fig. ). |
67a2ccb6fa469535b915b8fb | 16 | For the TEM observations, the extracts of a volume of ~20 mL were concentrated to a volume of about 0.7 mL, then ethanol of 20 mL was added. This solvent exchange is useful to minimize the amount of hydrocarbon adsorbates on the sample. Then, 5 μL of the suspension was collected with a pipette and drop casted onto a TEM microgrid. The TEM grid was dried in vacuum using a dry pumping station for ~2 h to remove solvent. |
67a2ccb6fa469535b915b8fb | 17 | Atomic-resolution HRTEM and STEM observations were carried out on a JEOL JEM-ARM300F instrument equipped with a cold field emission electron gun and a spherical aberration (Cs) corrector at an acceleration voltage of 80 kV, under 1 × 10 -5 Pa in the specimen column. Typically, we adjusted the Cs value to 1 μm. All HRTEM images were recorded with an exposure time of 4 s on a Complementary Metal-Oxide-Semiconductor (CMOS) camera (Gatan OneView, 4096 × 4096 pixels). In ADF STEM imaging, the probe size was 0.07 nm, the convergence angle was 32 mrad, and the inner and outer collection angles were 45 and 180 mrad, respectively. Although the operated voltage appears to be higher than the knock-on radiation damage threshold reported for h-BN (78 kV), we did not observe any radiation damage during the TEM observations. Image processing including the fast Fourier transformation (FFT) and inverse FFT (IFFT) was carried out by Gatan Digital Micrograph. |
67a2ccb6fa469535b915b8fb | 18 | We analysed strain of the exfoliated hBN layers using the Peak Pairs Analysis (PPA) software package (HREM research) for Gatan Digital Micrograph. For the analysis, we employed low-pass filtered HRTEM images of the non-twisted hBN layers. The peak positions were determined on the filtered image, and the relative displacement fields (ux, uy) of the measured lattice with respect to a reference basis vector were calculated. The components of strain tensor 𝜀 𝑥𝑥 , 𝜀 𝑥𝑦 , 𝜀 𝑦𝑦 , mean dilatation ∆ 𝑥𝑦 , rotation 𝜔 𝑥𝑦 (in radians) are defined as follows: |
67a2ccb6fa469535b915b8fb | 19 | where 𝛷(𝑥, 𝑦) is the sample phase shift, 𝜎 is the interaction parameter, 𝑉(𝑥, 𝑦) is the projected potential of the entire sample. The interaction parameter 𝜎 is given by σ = 2𝜋𝑚𝑒𝜆 ℎ 2 , where m is the relativistic mass of the electron, e is the elementary charge, is the wavelength of the electrons, and h is the Planckʼs constant. Eq. (S1) can further be approximated by the first order Taylor series as 𝑡(𝑥, 𝑦) ≈ 1 -𝑖𝜎𝑉(𝑥, 𝑦) (S2) under the weak-phase object approximation (WPOA), which is applicable to very thin crystals of light atoms, as in the case of hBN nanolayers. |
67a2ccb6fa469535b915b8fb | 20 | where 𝑉 𝑡 (𝑥, 𝑦) and 𝑉 𝑏 (𝑥, 𝑦) are the projected potentials of the top and the bottom layers, respectively. The last term describes the overlap of the top-and bottom-layer potentials, which can, in principle, contribute to the formation of moiré peaks in the diffraction pattern. In high-energy (20 300 keV) electron microscopy, however, the related moiré peaks are not observed because of the following reasons. From Eq. (S3), one sees that the second and third terms, which describes the intensity of the main peaks, are proportional to 𝜎, whereas the last term to 𝜎 2 . Note, however, that for typical TEM electron energies (20 300 keV), the value of 𝜎 is relatively small, e.g., 𝜎 = 0.81 (keV • Å) -1 at 100 keV. Consequently, the last term proportional to 𝜎 2 becomes negligibly small, as compared to the second and third terms, resulting in the absence of moiré peaks in conventional TEM mode. When the electron energy is reduced below ~100 eV, moiré peaks should be visible as 𝜎 becomes relatively high, 55 e.g., 𝜎 = 25.61 (keV • Å) -1 for 100 eV. However, atomic-scale imaging is not possible for such low electron energies. |
67a2ccb6fa469535b915b8fb | 21 | Finally, we take account of the interlayer moiré potential in the electron transmission process. We assume that the interlayer moiré potential is created in between the top and bottom layers as a result of the interlayer coupling and also that this potential explicitly contributes to the phase shift. The resulting transmission function of the twisted bilayers can be described as: |
67a2ccb6fa469535b915b8fb | 22 | where A represents a nucleus, and 𝑍 A and 𝑹 A are the charge and position of the nucleus A, respectively. The ESP is generally insensitive to the level of sophistication, e.g., the size of the basis set and the level of electron correlation, since it depends directly on the electron density (ρ = |Ψ| 2 ). 2D ESP was rendered by Visual Molecular Dynamics (VMD) and/or Gaussview 69 software packages. |
67a2ccb6fa469535b915b8fb | 23 | The effect of density functional on the optimized structure and ESP is also of interest. Figure shows the optimized values of dBN and dint obtained for the (B111N111H42) This suggests that the long-range electron-electron exchange interactions are reasonably incorporated in the B97XD functional. The interlayer ESPs calculated at the B3LYP-D3/6-31G(d) and ωB97XD/6-31G(d) levels for the (B111N111H42)2 cluster with = 21.6° and 13.6° are given in Fig. . We did not find any critical differences between the ESPs at the B3LYP-D3/6-31G(d) and ωB97XD/6-31G(d) levels, although these two levels of calculations result in somewhat different values of dint. This implies that the underlying features of the interlayer ESP are insensitive to the DFT functional. Hence, in the main text, we only show the ESP map for the (B111N111H42)2 cluster calculated at the ωB97XD/6-31G(d) level. |
671fbd3c83f22e421475dc8a | 0 | Structural DNA nanotechnology has emerged as a versatile tool to build elaborate nanostructures in a convenient, biocompatible and user-friendly way. By exploiting specific DNA base-pairing principles, it is now possible to program the assembly of cocktails of synthetic DNA strands into virtually any desired 2D or 3D morphologies. The resulting structures are not only obtained at a high yield with great precision, but they can also be used as universal scaffolds to spatially organize bound entities (proteins, particles, etc.) with subnanometric resolution, leading to a vast range of applications, from materials science to biomedicine. The underlying DNA self-assembly principles impose however some limits. First, most approaches rely on the use of a scaffold, as in the case of DNA origamis, which strongly limits the size of the final self-assembled structures, typically up to around 100 nm, unless specific additional protocols are applied. Additionally, despite the recent development of isothermal DNA self-assembly principles, the vast majority of methods rely on a thermal annealing step to ensure flawless assembly between the multitude of DNA strands. This temperature treatment, consisting in heating the system above the melting temperature before a slow cooling down ramp, takes usually hours to days, thus imposing strong temporal constraints on the assembly. To expand the potential offered by programmable DNA self-assembly, it would be highly valuable to identify principles orthogonal to basepairing rules, in which DNA nanostructures could be assembled into well-defined superstructures, both extended in space and produced in a rapid manner. We suggest to approach such a goal by getting inspired by the fact that, in nature, DNA is usually present in a variety of higher-ordered structures not solely relying on Watson-Crick-Franklin interactions. For instance, genomic DNA of viruses, eukaryotes and prokaryotes are highly organized thanks to a combination of interactions where electrostatics plays a major role. It has been shown in particular that double-stranded DNA, which adopts an elongated coil conformation in water due to the strong electrostatic repulsions between the phosphate groups along its backbone, undergoes a dramatic transition into highly ordered structures, such as toroids, when small multivalent cations, including naturally occurring polyamines such as spermidine and spermine, are added. We envisaged that this principle could be used to rapidly reorganize self-assembled DNA nanostructures into higher-order superstructures. The exploitation of electrostatic interactions for such a purpose has already been explored but only in a few notable cases. In the case of DNA origamis, solid substrates were used to generate electrostatically tunable lattices or induce intramolecular suprafolding transition in the case of soft cationic polymer layer. The requirement of solid substrates limits however the versatility and applicability of the resulting assemblies. In bulk, intramolecular reconfiguration upon addition of positively charged proteins and intermolecular assemblies mediated by cationic nanoparticles were reported. However, DNA origamis, remaining small building blocks, are not well suited for the construction of extended 3D assemblies. For their elongated geometry and possibility to reach micrometric dimensions, DNA nanotubes obtained by the self-assembly of single-stranded or double-crossover tiles, appear as more promising starting materials. For instance, the addition of crowding agents or magnesium ions induced the formation of asters or bundles, respectively, while specifically designed macromolecular star-shaped cationic crosslinking agents led to contractile rings. Surprisingly, the use of naturally occurring polyamines for the assembly of DNA nanotubes has never been explored. Moreover, although DNA condensation is a reversible process, the possibility of dynamically disassembling DNA nanotubes superstructures has been overlooked. Here, we used a simple cocktail of 5 DNA strands leading to long self-assembled nanotubes and studied how they reorganized upon addition of two naturally occurring polyamines known as DNA condensing agents, the triamine spermidine (noted SPD 3+ ) and the tetraamine spermine (noted SPM 4+ ), and compared with the effect of magnesium ion (Mg 2+ ). Using fluorescence and electron microscopy, we revealed the reproducible formation of a diversity of superstructures, including bundles, rings as well as novel organizations into extended networks. We established phase diagrams highlighting the importance of counter-ion valency rather than specific interactions and proposed methods to reversibly disassemble the superstructures into nanotubes through monovalent salt addition. We also explored the possibility of photocontrolling the superstructure formation in the presence of a photosensitive DNA condensing agent. |
671fbd3c83f22e421475dc8a | 1 | We used DNA nanotubes obtained by the thermal annealing of 5 short DNA strands (500 nM each, including a fluorescently labelled one) in a so called TAMg buffer (Trizma base 40 mM, acetic acid 20 mM, MgCl2 12.5 mM). We hypothesized that the addition of multivalent cations capable of DNA condensation would induce the formation of superstructures that could be disassembled with a further addition of monovalent ions in a sufficiently large excess (Fig. ). Initial nanotubes appeared as elongated filaments freely fluctuating in solution as observed by fluorescence microscopy (Fig. left, top image and Movie S1). Transmission electron microscopy (TEM) revealed that they were well individualized (Fig. left, bottom image) with a uniform diameter of 12 ± 3 nm (Fig. ), in agreement with previous reports. We first added spermine (noted SPM 4+ ), a natural tetraamine, and observed the resulting structures in bulk by fluorescence microscopy. Addition of millimolar amounts of SPM 4+ led to immediate formation of arrested structures of large dimensions floating in solution, with a low fluorescence background indicating that most nanotubes were engaged in these clustered structures (Fig. right, top image and Movie S1). Similar assemblies were observed in the past using high concentrations of Mg 2+ or crowding agents and will be referred to as "bundles". Moreover, TEM revealed a local organization into thick elongated structures (Fig. right, bottom image) with an average diameter of 63 ± 26 nm (Fig. ) where individual nanotubes could not be distinguished anymore, indicating a very strong attraction mediated by SPM 4+ . Interestingly, TEM revealed that individual nanotubes could be distinguished and were found to locally organized into aligned assemblies (Fig. middle, bottom image), showing inter-tube attraction, but without strongly condensing as in the bundles. |
671fbd3c83f22e421475dc8a | 2 | It is known that electrostatic condensation of a semi-flexible polyelectrolyte like double-stranded DNA (dsDNA) leads to the formation of toroids with a diameter (≈ 100 nm) around twice its persistence length (50 nm), inside which dsDNA double-helices are parallelly packed in a nearly crystalline manner with an interspacing of about 2.4 nm. We thus scrutinized in more detail the regime of bundle formation ([SPM 4+ ] = 2.5 mM). First, we used cryo-electron microscopy (cryo-EM) to reveal the internal structure of the DNA assemblies before and after bundle formation (Fig. ). Without SPM 4+ , we could distinguish the DNA strands in the repeating tile motif forming hollow nanotubes with a diameter in agreement with TEM observations. Notably, after SPM 4+ addition, hollow nanotubes could not be distinguished anymore. Instead, the inner structure of the bundles revealed a tightly packed parallel DNA arrangement with an interspacing of around 3 nm, i.e., a value close to a double-helix diameter (2 nm). This feature, structurally reminiscent to the internal organization of condensed DNA in toroids, confirms the role of SPM 4+ to induce electrostatic condensation of the nanotubes. Moreover, using TEM we detected that the condensed nanotubes also existed in the form self-closed structures similar to DNA toroids but of much larger dimensions (Figs. ). These rings were also observed by confocal microscopy coexisting with bundle fragments adsorbed on the microscopy cover slip surface (Fig left, white arrows). Using super-resolution fluorescence imaging allowing a 120 nm lateral resolution, rings appeared with a single dense contour (Fig. right), in agreement with cryo-EM (Fig. ) and TEM (Fig. ) data, confirming the compact longitudinal assemblies of the nanotubes in these structures. The ring diameter was found to typically vary between 1 and 10 µm (Fig. ), with a mean ± SD value of 2.0 ± 1.7 µm (Fig. ), which is smaller yet of the order of twice the persistence length of nanotubes (≈ 4 µm) . It is also in agreement with a recent report using a large synthetic star-shaped multicationic crosslinking agent. Our results thus show that electrostatic DNA condensation by counter-ion condensation is enough to generate the spontaneous formation of rings and, notably, does not require specific crosslinking interactions. To both understand the physico-chemical mechanisms underlying the formation of the different superstructures and analyse how general this behaviour could be, we established a diagram reporting the nature of the obtained superstructures for different multivalent cations added to DNA nanotubes. The diagram was plotted as function of both the condensing agent concentration (Fig. ) and the charge ratio ρ (Fig. ), which was defined as the concentration of charges brought by the condensing agent normalized by that of DNA (Text S1). Starting with spermine (SPM 4+ ), we observed the formation of networks from [SPM 4+ ] = 0.2 mM (ρ = 7.14) to 0.4 mM (ρ = 14.3) (Fig. ). For larger concentrations, nanotubes were organized into bundles coexisting with a fraction of rings, in agreement with Figs. . |
671fbd3c83f22e421475dc8a | 3 | Using spermidine (SPD 3+ ), a trivalent polyamine, a similar nanotube-network transition was observed but at a higher concentration (5 mM, Figs. ). Interestingly, this concentration increase was larger than a simple compensation of valency as revealed by the larger charge ratio at the transition (ρ = 143, Fig. ). We compared the effect of these two polyamines to the simple dication Mg 2+ and found the same behaviour, at even a larger concentration (50 mM, Figs. ) and ρ (ρ = 1190, Figs. 3, S5), confirming not only the importance of valency in driving the process but also that such nanotube assembly mainly relies on electrostatic attraction rather than specific chemical interactions. For SPD 3+ , bundles were observed for higher concentrations and charge ratios but were smaller in size that with SPM 4+ while we could not detect bundles in the highest magnesium concentrations tested in our experiments. This further highlights the importance of a high condensation agent valency to get large and dense assemblies of DNA nanotubes. For a given valency, the evolution observed in all these phase diagrams is in agreement with the assembly of rigid negatively charged polyelectrolytes, such as actin filaments or microtubules, forming bundles in the presence of sufficiently high concentrations of multivalent cations, as shown in the past both experimentally and theoretically. The valency-dependence is also reminiscent to the compaction of double-stranded DNA by multivalent cations, where the neutralization of the DNA backbone through counter-ion condensation drives the process. According to the Manning-Oosawa picture, 36,37 counter-ions of valency z condense on the DNA backbone leading to an average charge neutralization θ = 1 -d/(zlB) where d is the average distance between DNA charges (0.17 nm) and lB is the Bjerrum length (lB = e 2 /(4πεkBT), with the e the elementary charge, ε the dielectric constant of the solvent, kB the Boltzmann constant and T the temperature). In water at 25 °C, lB = 0.7 nm and the neutralization only depends on z: θ = 1 -0.24/z. Therefore, adding multivalent cations to double-stranded DNA induces an entropically favourable counter-ion exchange and a progressive neutralization of DNA leading to its compaction when θ becomes too large (≈ 0.89). The higher the valency, the more entropically favorable the counter-ion exchange is, the more efficient DNA neutralization becomes, and the lower is the charge ratio necessary to induce DNA compaction. Notably, the same evolution was observed in the nanotube condensation diagram where transitions to higher-order structures were systematically observed at a lower ρ when z increased (Fig. ). |
671fbd3c83f22e421475dc8a | 4 | Knowing that our buffer contained a significant amount of Mg 2+ (12.5 mM), we performed the same study in a buffer composed of solely monovalent cations. To get stable nanotubes, we replaced MgCl2 by a high concentration of NaCl (100 mM). Interestingly, we obtained the same types of superstructures by adding increasing amounts of SPM 4+ (Fig. ), including the formation of rings (Fig. ) having dimensions similar to those obtained in the regular Mg 2+ -containing buffer (Fig ). All these results showed that the multivalent counter-ions were the main driving force for the superstructure formation. Note that the frontiers for the transitions were shifted to higher charge ratios ρ when Na + was used (ρ = 21.4 for the nanotube-network and ρ = 89.3 for the network-bundle transition, Fig. ) instead of Mg 2+ (ρ = 7.14 and ρ = 14.3, Fig. ), attributed to the large concentration of monovalent cations competing for counter-ion exchange and DNA neutralization. |
671fbd3c83f22e421475dc8a | 5 | The reversibility of DNA condensation led us to explore if the nanotube superstructures could be disassembled after their formation. It is known that adding an excess of monovalent cations on condensed DNA can compete with the DNA neutralization by multivalent counter-ions leading to DNA decompaction. Following this principle, nanotubes were first assembled into networks by introducing [SPM 4+ ] = 0.4 mM prior to adding NaCl (100 mM) to the solution. Notably, right after Na + addition, nanotubes were observed freely fluctuating in solution in a state comparable to that before spermine introduction (Fig. , Movie S2). To achieve further control with an external stimulus without having to change the chemical composition of the medium, we implemented AzoTAB, a photosensitive DNA condensing agent. AzoTAB is a cationic amphiphilic molecule neutralizing DNA in a photodependent manner, the trans isomer inducing DNA condensation at a lower concentration than the cis isomer. We used an AzoTAB solution kept in the dark (-UV, trans-rich state) or irradiated at 365 nm for 1 min (+UV, cis-rich state). Starting from individual nanotubes obtained by thermal annealing in TAMg buffer, we added different amounts of AzoTAB, without or with UV, and analyzed the resulting assemblies (Fig. ). Regardless of irradiation conditions, nanotubes at a low concentration of AzoTAB (0.1 mM) were freely fluctuating in solution and appeared similar to nanotubes without AzoTAB (Figs. S8, 1B left, and Movie S1). Without UV, increasing AzoTAB concentration to 0.5 and 1 mM led to the formation of clustered nanotube assemblies presenting some similarities with the networks obtained with multivalent cations. Notably, with UV, nanotubes remained individual at |
671fbd3c83f22e421475dc8a | 6 | [AzoTAB] = 0. 5 mM and coexisted with a small fraction of restricted networks at [AzoTAB] = 1 mM (Fig. ). Like for DNA condensation, AzoTAB was thus found to induce nanotube association into superstructures at a higher concentration when a short UV irradiation was applied. As a consequence, we could identify an AzoTAB concentration (0.5 mM) where the system organized into individual nanotubes (+UV) or superstructures (-UV) in a photodependent manner (Movie S3). This creates ground for dynamic photoactuation of nanotube higher-order organization and superstructure formation. |
671fbd3c83f22e421475dc8a | 7 | We have shown that self-assembled DNA nanotubes of micrometric length condense into superstructures upon addition of sufficient amounts of multivalent cations, such as Mg 2+ , the triamine spermidine and the tetraamine spermine. We demonstrated the strong analogy with the phenomenology of DNA condensation, through i) the crucial role of counter-ion valency (the higher the valency, the lower the charge ratio indeed to induce a transition) and ii) the formation of rings the size of the order of the nanotube persistence length resembling the toroids formed by DNA condensation and with similar internal DNA organization. In term of the structures obtained, the system also recapitulated some of the known features obtained with other semi-flexible or rigid polyelectrolytes such as actin filaments and microtubules, with the formation of networks and bundles, thus reinforcing knowledge of the electrostatic assembly of polyelectrolytes as well as opening perspectives for building cytoskeletoninspired materials. Mainly driven by electrostatics, the assembly principles explored here provide a ubiquitous basis for the formation of superstructures independent of their detailed chemistry. It is therefore not only a means of building higher-order superstructures combining nanoscale DNA programmability with extended dimensions, but also a strategy for organizing bricks other than DNA. |
6712802812ff75c3a1cd714b | 0 | In materials and surface science, the prevalence of activated atomic-scale processes with barriers exceeding several k B T makes rare-event type dynamics more the norm than an exception. In corresponding systems, the dynamics is characterized by long residence times in a basin of the potential energy surface (PES), and infrequent crossings of PES transition states (TSs) to access another basin. The longer-term time evolution is then suitably described by a Markovian Master equation, which coarse-grains the continuous dynamics into discrete Markov jumps between the respective metastable system states and where the short-time dynamics within each basin is appropriately condensed into the rate constants k i j for individual jumps from state i to another state j. Rate theories thereby provide the link between the PES and the rate constant, within harmonic transition state theory (hTST) for instance k i j = ν i j exp(-∆E act i→ j /k B T ) with ν i j a vibrationalfrequency dependent prefactor and ∆E act i→ j the activation barrier connected with the TS. |
6712802812ff75c3a1cd714b | 1 | Among a variety of approaches to approximately solve the Master equation for practical systems , kinetic Monte Carlo (kMC) enjoys increasing popularity as a general and versatile methodology . As a stochastic technique, kMC works by generating an ensemble of state-to-state trajectories, whose average yields the correct time evolution. For any nontrivial system, this implies excessive queries of the possible jumps out of states i visited along a trajectory, i.e. the locations of the TSs leading out of the corresponding PES basin, as well as the concomitant rate constants k i j . In particular if the PES is evaluated by first-principles electronic structure theories like density-functional theory (DFT), the dominant solution to nevertheless keep the computational costs tractable is to determine a number of considered involved states i as well as all jumps aka the elementary processes connecting them before the actual kMC simulation. In a corresponding microkinetic model , two-sided TS searches like the climbingimage nudged-elastic band (CI-NEB) method can then efficiently be employed to comprehensively compute all barriers ∆E act i→ j and thus have the resulting list of rate constants k i j accessible in look-up tables during the kMC simulation itself. Corresponding (first-principles) kMC simulations have been successfully employed for a wide range of applications, including surface catalysis , molecular depo-sition , crystal growth and diffusion in solids . Such works typically also map the system onto a lattice model, to further reduce the number of non-equivalent elementary processes for which rate constants need to be computed as well as to exploit efficient local updating of discrete data structures and other numerical accelerators in high-end lattice kMC codes . |
6712802812ff75c3a1cd714b | 2 | While highly efficient, the well-known downside of this prevalent look-up table approach to kMC is the necessity to a priori establish the microkinetic model. This is typically done manually, i.e. the involved scientist merely chooses the considered metastable states and the connecting elementary processes based on more or less deep insight into the system. The human bias toward intuitive processes (often involving only a minimum number of atoms) may then result in overlooking potentially crucial processes. This has for a long time fueled efforts toward alternative, less error-prone kMC strategies. One recurrent idea is to mitigate the excessive computational costs of on-the-fly TS searches at each step of the kMC simulation by building up process catalogs for all already visited system states. Here, a number of one-sided TS searches like the dimer method or the activationrelaxation technique (ARTn) would be employed to more systematically establish elementary processes that lead out of a current system state i. These processes and their rate constants would be stored, and whenever state i is revisited in the state-to-state kMC trajectory the look-up entries rather than new TS searches would be employed. |
6712802812ff75c3a1cd714b | 3 | While conceptually elegant, realizations of this adaptive (on-the-fly or self-learning) kMC idea stand and fall with the number of system states and how well an already visited state is recognized. An intractable total number of TS searches along the kMC trajectory is only avoided, if state revisits quickly become dominant. State revisits are also much easier recognized, if the system is confined to a lattice model. Yet, it might a priori not be clear whether a lattice model might suit a system, or if so which one. If complete off-lattice kMC is performed, imperfect state recognition can instead quickly lead to a strong redundancy of TS search efforts for in principle actually equivalent system configurations. In practice, applications of such adaptive kMC have therefore to date been restricted to rather simple systems or to systems where state recognition is readily achieved. |
6712802812ff75c3a1cd714b | 4 | In a new attempt to overcome empiricism in establishing the elementary processes considered e.g. in traditional lookup table kMC, we here present a versatile workflow that is motivated by adaptive kMC but differs in two central aspects. First, we separate the process exploration step from the actual kMC simulation. This allows us to select the system's atomic configurations on which TS searches are conducted beyond the confines of the kMC algorithm. If the process list resulting from the automated exploration step motivates a suitable lattice mapping, our separated workflow furthermore enables the use of existing optimized lattice kMC codes. Second, our initial automatized process exploration (APE) approach exploits a fuzzy machine-learning (ML) classification to specifically focus the TS searches around atoms within the selected system configurations that exhibit non-equivalent and hitherto unexplored local atomic environments. Simultaneously respecting fundamental symmetries and being agnostic to insignificant differences in atomic positions, this minimizes redundancies in the TS searches and allows application of our workflow to more complex systems. |
6712802812ff75c3a1cd714b | 5 | We demonstrate this APE framework using island diffusion on a Pd(100) surface as a characteristic application example. APE readily identifies a plethora of non-intuitive collective, yet low-barrier processes far beyond traditionally considered surface hopping and exchange diffusion mechanisms. That this happens even for such a seemingly simple system underscores the limitations of prevalent look-up table kMC approaches. Subsequent lattice kMC simulations reveal a significant influence of identified collective processes on island diffusivity and point in particular at the relevance of hitherto unrecognized sliding motions of entire rows of atoms. |
6712802812ff75c3a1cd714b | 6 | The initial process exploration phase of the APE workflow is schematially summarized in Fig. . It starts from any given atomic configuration of the system, and we use our previously described fuzzy classification algorithm DECAF to group all atoms of this configuration into equivalence groups of essentially identical local atomic environments. In brief, DECAF achieves this labeling by first converting the local environment around each atom into a smooth overlap of atomic positions (SOAP) descriptor . It then embeds this high-dimensional descriptor using multidimensional scaling to perform the categorization with mean shift clustering (MSC) on the resulting low-dimensional embedded vector. Through the use of SOAP, it thus naturally encodes relevant rotation and species permutation symmetries, while the fuzzy classification based on the embedded vector allows atoms with approximately equal atomic environments to still end up in the same equivalence group. What is approximately equal is thereby critically determined by the MSC bandwidth. At large values of this hyperparameter, the fuzzy classification would in the present example merely distinguish terrace, step or corner atoms (essentially resolving their different coordination number). At smaller values, subclasses like different step atoms start to be resolved. Further discussion of DECAF and the alternative choice of using the MACE descriptor instead of SOAP are provided in the SI. |
6712802812ff75c3a1cd714b | 7 | As a next step we establish a to-do list of local atomic environments for which TS searches are to be performed. Each entry in this list consists of the total atomic configuration of the system and one highlighted atom within this configuration which exhibits the local atomic environment that is to be explored. The initial entries all concern the starting atomic configuration and have as highlighted atom one randomly chosen atom of each equivalence group. For one entry after another, a specified number of dimer searches is executed, each initialized by randomly perturbing the positions of all atoms within a sphere around the highlighted atom. We note that the APE package is constructed in a modular way and alternative onesided TS search algorithms like ARTn could equally be implemented and used. For each identified TS, local geometry optimization determines the final state (FS) structure, i.e. the system's atomic configuration after execution of the corresponding elementary process. Calculation of the local Hessian of all atoms within the finite sphere around the highlighted atom at initial state, TS and FS provides the prefactors ν i j and ν ji for the forward and backward process. Finally, the process data in form of initial and final total atomic configuration together with hTST forward and backward rate constant, k i j and k ji , are stored in an ever expanding identified-process list. |
6712802812ff75c3a1cd714b | 8 | Each FS structure is subjected to the DECAF classification. If this signals one or more new equivalence group(s), i.e. atom(s) with atomic environments that differ in the embedded low-dimensional space by more than the employed finite MSC bandwidth, then this yields corresponding new entries in the to-do list of local atomic environments. These entries now contain the identified atom with a distinctly new environment as highlighted atom and the FS structure as the total atomic configuration of the system. This way, the progressively performed TS searches crunch through the to-do list entries and -if indicated -generate new entries with novel atomic environments. The new entries are sorted in order of increasing energy of the stored atomic configuration of the system, and if several entries concern new equivalence groups that fall within their mutual MSC bandwidth, then only the lowest energy entry is retained. This thus prioritizes the search on lower-energy system states, while simultaneously minimizing TS search redundancy as searches centered on more than one representative atom of each equivalence group (aka local atomic environment) are never performed. |
6712802812ff75c3a1cd714b | 9 | This local atomic environment driven exploration phase continues until no entry is left in the to-do list (or a given computational budget on TS searches is spent). Rather than randomly choosing atomic configurations or primarily exploring atomic configurations that differ by low-energy processes as in traditional adaptive kMC, the APE workflow thus optimally focuses its TS searches on structures that contain unexplored and non-equivalent atomic environments. The final outcome of the exploration phase is a list of elementary processes that was automatically generated without human bias. In a subsequent extraction phase, the APE framework now FIG. . Schematic illustration of the automated process exploration (APE) workflow. Starting from an initial atomic configuration of the system, the DECAF algorithm fuzzily classifies all atoms into equivalence groups with approximately equal local atomic environments. Randomly choosing one atom per equivalence group yields the first entries in a to-do list of local atomic environments on which dimer TS searches are performed. If these searches yield elementary processes that create novel local atomic environments in their final structure, then the corresponding atom in this system atomic configuration is added to the to-do list. This workflow continues until there are no more entries in the to-do list and thus no processes leading to new atomic environments have been found anymore. The APE result is an automatically generated list of elementary processes that is curated by removing (symmetry-equivalent) duplicates in a subsequent extraction phase. |
6712802812ff75c3a1cd714b | 10 | curates this process list to remove (symmetry-equivalent) duplicates. For this, we first use the stored initial and final total atomic configuration to determine all atoms that have been significantly displaced in the given elementary process. Due to the nearsightedness of chemical interactions, these atoms typically form compact, finite-size clusters in the initial and in the final atomic configurations. Considering the significantly displaced atoms, these clusters constitute in fact nothing else but local atomic environments around these atoms. We can therefore readily use the DECAF fuzzy classification again to filter the total process list into groups of equivalent processes that lead from approximately equal initial to approximately equal final local atomic environments, barring rotation, mirror and species permutation symmetries. In the curated process list we then keep only one of these equivalent processes per group and assign to each such unique process the mean of the k i j (and k ji ) of the processes in the respective group. Effectively, this thus averages out differences in the atomic configurations beyond the finite cluster aka considered local atomic environment -in surface applications often denoted as long-range lateral interactions. We note that there could be less common cases where more than one TS connecting the same initial and final state has been found. In this case, our current procedure would assign the mean of the corresponding rate constants to the extracted elementary process. |
6712802812ff75c3a1cd714b | 11 | The finally extracted process list yields the microkinetic model. Specific for every individual system, a lattice representation can ideally be found for this model to ultimately enable efficient lattice kMC simulations. At present this representation has to be found by hand and we view the generation of an automatized and versatile workflow that achieves a suitable lattice mapping starting from a list of symmetry-reduced, unique elementary processes as an intriguing challenge for future methodological work. |
6712802812ff75c3a1cd714b | 12 | To automatically obtain the processes for the island diffusion application example, we choose as initial atomic configuration a (4 × 4) square monolayer island plus one isolated adatom at a Pd(100) surface as already depicted in Fig. above. The surface is described as a four layer slab in a (10 × 10) periodic boundary condition supercell, and we al-low the adatom, all atoms of the island and all atoms of the first Pd(100) layer to freely move during the TS searches. The PES is determined with an embedded atom potential and we perform 100 TS searches for each entry in the to-do list, i.e. for each equivalence group denoting one distinct local atomic environment. DECAF with two-dimensional embedding and a cluster bandwidth of 0.048 , identifies ten equivalence groups in the initial atomic configuration. Detailed settings for the dimer search and prefactor calculations are provided in the SI. In the APE exploration phase, this is extended to 120 distinct equivalence groups that spread over a total of 46 different total atomic configurations that were generated as final state structures of identified processes. From 120 × 100 = 12000 TS searches launched, the outcome of the exploration phase are thus 7247 TSs with barriers within 20 k B T from the lowest barrier found (corresponding to a maximum absolute barrier of 1.36 eV). For further illustration, a part of the APE workflow is explicitly shown step by step in the SI. For the curation of this process list in the ensuing extraction phase we use a simple threshold of 0.55 Å to identify the significantly displaced atoms in each process. Again employing DECAF with the same settings, this extracts 777 unique processes as the central result of the APE framework. For comparison, we also ran the akMC code EON in different settings starting from the same initial state structure. After having spent the same computational budget in form of 12000 TS searches, EON had only identified less than a third of the unique process classes found by APE, with full details and a critical discussion on the use of akMC provided in the SI. As to be expected, the list of these APE identified unique processes contains the classic on-surface and exchange diffusion mechanisms . For an isolated adatom on Pd(100), on-surface diffusion proceeds via a TS at the bridge site to end up in a nearest-neighbor (NN) hollow site. In contrast, in exchange diffusion, the adatom pushes one of its directly coordinating Pd atoms of the topmost surface layer out into a second NN hollow site and takes its place instead. Including analogs of these two mechanisms at the perimeter of the island as e.g. illustrated in Fig. , this constitutes a group of 149 unique processes. With all likelihood, this group of processes would have been what a human researcher would have enumerated manually in the look-up table kMC strategy based on our current view of Pd island surface diffusion. |
6712802812ff75c3a1cd714b | 13 | Intriguingly, this is but a fraction of the processes identified by APE. Analysis of the process lists reveals another group of 213 processes in which atoms access the top of the island, and a group of 360 processes that involve initial or final states that are clearly beyond the fcc-type structure of crystalline Pd(100). Such processes would ultimately lead to the nucleation of multi-layer islands, as well as restructuring, roughening and amorphization of the surface. These are highly interesting topics in their own right, and the APE framework establishes a means to systematically access the underlying atomic-level processes. Kinetically, such corresponding surface evolution would be penalized though, and will likely only kick in at elevated temperatures. Some of these intriguing offlattice or multi-layer processes are explicitly showcased in the SI. Much more intriguing is therefore a final group of 55 unique collective processes. These processes involve more atoms than the single-atom surface hopping or two-atom exchange diffusion mechanisms, yet all atoms in the initial and final states remain in fcc lattice positions. As illustrated in Fig. , they often correspond to sliding motions of entire rows of atoms. As also apparent from the example in the figure, many of these processes exhibit barriers in the same range as those of the classically considered diffusion mechanisms. |
6712802812ff75c3a1cd714b | 14 | The effect of just these hitherto unconsidered collective processes on island diffusivity is illustrated next with two microkinetic models for lattice kMC simulations. The humanintuition model only considers the 149 surface hopping and exchange diffusion type processes a human researcher would likely have enumerated, whereas the APE model additionally considers the 55 collective processes. Both models are implemented in the lattice kMC code kmos3 to run kMC simulations for varying island sizes in the range 16 ≤ N ≤ 144 Pd atoms. Each simulation is performed in a (40 × 40) periodic boundary condition simulation cell containing one island as shown in Fig. , and we extract the diffusion coefficient D N from the migrating island center of mass position during one kMC trajectory. Convergence of D N to within ±5 % was generally reached in O(10 9 ) kMC steps. We note that the total number of kMC steps executed to obtain the data summarized in Fig. is thus O(10 11 ). In the above described EON akMC runs, the system evolved only over ∼ 80 -90 steps within the computational budget of 12000 TS searches spent for APE. This underscores the necessity to separate the process exploration from the actual microkinetic simulations to even only address systems of such moderate complexity. |
6712802812ff75c3a1cd714b | 15 | As apparent from Fig. , the collective processes lead to a consistent increase in the simulated diffusivity. This increase applies globally, i.e. it is roughly similar over the entire studied island size range. The additional processes do thus not affect the pronounced non-monotonous behavior in the nonscalable regime up to N ≈ 100 , nor the close-to-one exponential size scaling for larger islands (D N ∝ N -β , β = 1.02 ± 0.05 and 0.95 ± 0.05 for the APE and humanintuition models, respectively, cf. Fig. ). The oscillation in diffusivity with island size is well observed in other computational studies and arises from the pronounced stability of islands with perfect square or nearsquare rectangular ground-state shape at T = 0 K (N = n 2 or n × (n + 1)) . Further sensitivity analysis regarding the individual impact of these collective processes is provided in the SI. Overall, these findings are thus perfectly consistent with the effect of other collective diffusion mechanisms that had been proposed for island diffusion on coinage-metal fcc(111) and fcc(100) surfaces before . In the past though, such collective mechanisms have typically been identified through cost-intensive molecular dynamics simulations for smallest islands or clusters of atoms, whereas here they result automatically from the APE framework. |
6712802812ff75c3a1cd714b | 16 | In summary, we have shown that the presented APE framework provides a general and straightforward approach to systematically assemble elementary process lists beyond human intuition and bias. The focus on ever new local atomic environments minimizes the redundancy in the underlying one-sided TS searches and renders APE applicable to larger system sizes and complexities that also span non-crystalline off-lattice configurations. At present we simply employ a fixed, large number of TS searches per local atomic environment. Adapting this number on-the-fly to a decreasing success in finding novel TSs or including some form of active learning, e.g. penalizing TS revisits, might create a further gain in efficiency. Nevertheless, the total number of PES evaluations required for moderately complex systems like the present Pd(100) showcase will likely strain computational budgets if directly based on first-principles electronic structure calculations like DFT. To this end, we view the emergence of machine-learned interatomic potentials (MLIPs) as a game-changing development. Combining MLIPs as fast surrogate for the DFT-PES with the efficiency of APE (and its negligible computational overhead) will make predictive-quality first-principles kMC simulations for reactive systems feasible. We have followed this path in work on the initial oxidation of Pd steps, with APE readily identifying close to 3000 unique elementary processes . Among these are numerous low-barrier collective processes that enable an O-induced step restructuring that is facile enough to introduce fluxionality aspects to the operando evolution of Pd surfaces in oxidation catalysis. This -as well as already the much simpler, but hitherto nevertheless unrecognized collective sliding motions of atomic rows in the presented Pd(100) island diffusion example -gives only but a taste for the surprising non-intuitive elementary processes that have likely been missed in the prevalent human created look-up tables so far. |
60c752b4842e65c8e3db3df8 | 0 | spiro [2,2]-pentane ring is a structural fragment of many biologically active compounds , including highly efficient insecticides . In the recent years, strong physiological activity has been revealed in the series of conjugated spiro [2,2]-pentane carboxylic acid esters derivatives, and interest in these compounds has increased considerably . Almost all known syntheses of such rings are based on a combination of -unsaturated carbonyl derivatives and in situ generated gem-dichlorocarbene to generate gemdichlorocyclopropane derivatives which further undergo annealation to give spiropentane carboxylic acid derivatives. Indeed, gem-dihalocyclopropane derivatives are useful synthetic intermediates because they can be readily transformed into cyclic, acyclic, heterocyclic and macrocyclic compounds including natural product precursors . |
60c752b4842e65c8e3db3df8 | 1 | The scope and generality of this addition protocol was investigated (Table ). A wide range of α,β-unsaturated amides used tested and found that unsubstituted 2a, gives mixture of diastereomers 3a, 3b respectively. the major diastereomers 3a is 1S based on steric grounds that carbenes like dichlorocarbene would approach the double bond from the side opposite to that of the N-phenyl substituent on chiral pyrazolidinone. The beta phenyl substituent 2b converted to β-phenyl substituted esters in beta-phenyl single diastereomer 4a with 61% yield . The -ester 2c did not give the product, the n-propyl 2d and methyl 2e substituents gives single diastereomer 5a and 6a in 62 and 67 % yield, respectively. Further the 6a structure was confirmed by single x-ray crystals, where methyl group is trans to chiral amide, the trans orientations of starting material remains intact, it indicates that dichloro carbene is in singlet state and reaction proceeds in single step. The presence of additional carbons as branched chain at beta position, isopropyl 2f, tertiary butyl 2g and b,b-substituents 2h, motifs did retard the desired spiro reaction (for 3f-3h). The presence of a bulky β-aryl group that can destabilize the resulting alkyl radical intermediates was envisioned to account for the above no reaction selectivitively. |
60c752b4842e65c8e3db3df8 | 2 | we next turned our attention to study the reaction with α,β-substituted substrate 2i, gives excellent yield, but product is limited to gem dichloro cyclopropane 7c only. The product 7c is further confirmed as 1S, 2R by ORTEP, where the beta-methyl is trans orientation with chiral amide. This method is far superior to reported method where resolution is used to separate the required product . In case of -alkyl-substituted substrate 2j, the product is not only limited to dichloro cyclopropane 8c but with low yield, even after prolong reaction time. The 8c were isolated with similar yield by resolution by reported method . |
60c752b4842e65c8e3db3df8 | 3 | The product 8c is characterized by ORTEP as 1S. The -bromo substituents 2k gives inseparable multiple products. This method is supervisor over reported method where direct substitution of halogen from gem-dihalocyclopropanes is limited and dialkylation with a new 'cyclocuprate' species to yield spiro compounds is possible if the reaction is performed in the presence of a lithium acetylide . |
60c752b4842e65c8e3db3df8 | 4 | where used for C-alkylation to achieve the intermediates of biologically active molecules . Herein we treated O-protected oxime 2l with dichlorocarbene and obtained the product 9a, minor product, and major product 9b is debenzylated, whose cyclopropane proton and NH are combined shows as mulltplet . The cleavage of benzyloxy group due to excess of reagent in reaction medium, which is consistent with reported methods where unprotected oxime under similar condition gives nitrile . |
60c752b4842e65c8e3db3df8 | 5 | The product 10d is further confirmed by single crystal data. The -ester 2b substituent gives products with 12% yield, along with decarboxylated product 9d in 55% yield. The -, ,-and ,-substituents did not react due to steric addition of trichlorocarbene. In case of -substituents only 5% yield of product 8c where isolated. Overall, the use of trichloro acetate in combination with TBAC is limited to olefin and -ester and to some extent to -substituents only. |
60c752b4842e65c8e3db3df8 | 6 | we have developed a stereoselective reaction for synthesizing the gemdichlorocyclopropane and its annulated products, tetrachloro spiro [2,2] pentane carboxylic acid derivatives, by using -unsaturated amides and O-protected oxime 2al derived from a chiral camphorpyrazolidinone as a acceptor of in situ generated dichlorocarbene, depending on the substituents and its position on unsaturated carbonyl substrates, -substituents forms selectively spiro [2,2] pentane whereas -substituents and ,-substituents shows gem-dichlorocyclopropane. The O-protected give dichloroaziridine after cleavage of benzyloxy group. This efficiency was demonstrated without using any metals and non-anhydrous reactions conditions. |
65d898779138d23161ce552c | 0 | Benzylsuccinate synthase belongs to the family of fumarate-adding enzymes (FAE) which is itself part of the growing superfamily of glycyl radical enzymes (GRE) . GRE are involved in surprisingly different, but always chemically demanding reactions in anaerobic metabolic pathways of Bacteria, Archaea, and Eukarya. In addition to FAE, the currently known families of GRE consist of the pyruvate formate lyases (PFL) , type III anaerobic ribonucleotide reductases (ARNR) , glycerol or diol dehydratases , |
65d898779138d23161ce552c | 1 | hydroxyproline dehydratases , arylacetate decarboxylases , choline and isethionate lyases . Their common reactive feature is either the formation, cleavage, or rearrangement of C-C, C-O, C-N, or C-S bonds in biomolecules via radical-based addition or elimination mechanisms . Most GREs contain a homologous large subunit of approximately 100 kDa, which forms a conserved fold, consisting of a 10-stranded -barrel with strands of alternating orientations, and two finger loops protruding towards the center and facing each other from opposite sides of the inner wall. Each of these loops carries a strictly conserved amino acid at its tip which are crucial for the reactivity of GRE: a glycine residue located close to the C-terminus and a cysteine at around the middle of the sequences of the primary subunits (see . All GRE are initially synthesized in a catalytically inactive state and need to be converted to the active, radical-containing state by a separate activating enzyme, which is a member of the S-adenosylmethionine (SAM)-dependent radical enzymes. The activating enzymes contain a bound SAM cofactor at a special Fe4S4 cluster in their active centers and form a productive reaction complex with the conserved Gly residues of the corresponding GRE, which are assumed to be pulled out of the folded GRE structures together with their C-terminal ends during activation . The activating enzyme then transfers one electron from a lowpotential donor like ferredoxin or flavodoxin to the bound SAM cofactor, reducing it to methionine and a Fe-bound deoxyadenosine radical, which in turn removes the pro-S hydrogen of the conserved Gly residue while being reduced to 5'-deoxyadenosine . |
65d898779138d23161ce552c | 2 | Subsequently, the C-terminus of the GRE refolds, the activating enzyme dissociates, and the GRE is now in its active, radical-containing state. Because of mesomeric interchange with the electrons of the peptide bond, the glycyl radical is highly stabilized, but only under strictly anaerobic conditions . Any contact of an activated GRE with molecular oxygen results in irreversible destruction by oxygenolytic cleavage of the peptide bond at the site of the glycyl radical, as demonstrated for PFL and BSS . This apparently complicated indirect method of initiating a radical reaction is especially advantageous for catabolic reactions occurring multiple times: instead of the high cost of converting one SAM cofactor to methionine and 5'-deoxyadenosine with every reaction of a SAM radical enzyme, this occurs only once per catabolic GRE during its activation. The introduced stable glycyl radical is continuously recycled, allowing a multitude of reactions to proceed without re-activation. The general mechanism of GRE is initiated by substrate binding, which closes the active site and triggers a cascade of hydrogen atom transfer steps, leading to a succession of radical intermediates in the reaction mechanism. Starting with the glycyl radical, a more reactive thiyl radical is generated at the conserved Cys, which then reacts with the bound substrate to create an enzyme-bound substrate radical. To be able to do that, the active site Cys simultaneously needs access to the glycyl radical outside and to the bound substrate within the active site cavity (Fig. . insert) and therefore needs to pass the border of this cavity. This substrate radical then undergoes the intended conversion reaction, which is typically not possible in the non-radical state, producing an enzyme-bound product radical species. Finally, the hydrogen atom transfer reactions are repeated in a reverse cascade via the thiyl and glycyl radical intermediates, generating the product in the active site. These reactions are believed to require a tightly closed enzyme-substrate complex to protect the radical intermediates from reacting with interfering molecules from the solvent. Only when the stable glycyl radical state is reached again, the active site can safely be opened to release the product and bind new substrate(s). |
65d898779138d23161ce552c | 3 | While most GRE contain only the conserved Gly and Cys residues as obvious active site elements, some are equipped with additional components required for activity. In particular, the PFL family contains two consecutive conserved Cys in place of just one in all other GRE (Cys418 and 419 in Escherichia coli), which leads to an extended hydrogen atom transfer cascade with two thiyl intermediates instead of the single one involved in other GRE. Both Cys are essential for the mechanism, as Cys419 is needed as 'radical hub' thiyl, which is involved in various intermediary partial reactions, while Cys418 binds covalently to the carbonyl carbon of pyruvate to activate the substrate for C-C cleavage to a formyl radical and an acetyl thioester, which is transferred to CoA . A second exception is known in ARNR because ribonucleotide reduction requires an additional redox step in addition to the radicaldependent activation reaction. Therefore, in addition to the bound ribonucleotide triphosphate, the active site accommodates an additional formate molecule as a reductant, which is intimately involved in the reaction mechanism . Moreover, the enzyme contains an Zn-binding domain missing in other GRE. Finally, the enzymes of the BSS and aromatic acid decarboxylase families contain additional subunits carrying FeS-clusters. In case of BSS, two small subunits with one Fe4S4 cluster each have been observed , whereas 4-hydroxyphenylacetate decarboxylase contains one small subunit with two Fe4S4 clusters . In either case, the functions of these subunits are still unclear. The glycyl radical has been characterized by EPR spectroscopy in many of these enzymes and they show remarkably similar spectroscopic features (Table ). The remaining H-atom at C of the glycyl radical residue causes a characteristic pronounced hyperfine splitting of the observed EPR spectra of 1.5 mT (1.7 mT for radiation-induced glycyl radicals in small model substrates ). In PFL and BSS, this hydrogen atom has been reported to be rapidly exchanged to deuterium in D2O-based solvents, while such an exchange did not occur in ARNR . For PFL, the activation reaction has been shown to be highly enantiospecific for the removal of pro-S hydrogen of glycine , while one of its two conserved cysteines (Cys419) was shown to be involved in the observed H/D isotope exchange of the glycyl radical . However, the detailed mechanism of this process is still unknown for any GRE. |
65d898779138d23161ce552c | 4 | In this study, we report on computational modeling of the radical transfer steps between the active site Gly and Cys that are involved in activating the bound substrate, using BSS as a model system with bound substrates or product and the apo enzyme as a reference. From these models, we infer a hypothesis as to why isotope exchange of the hydrogen atom of the glycyl radical site has been observed in some, but not in all GRE. |
65d898779138d23161ce552c | 5 | with some minor modifications. For the preparation of this medium, the main solution was made anaerobically and autoclaved separately, containing 816 mg/L KH2PO4 and 5920 mg/L K2HPO4, 530 mg/L NH4Cl, 200 mg/L MgSO4, 1000 mg/L KNO3, 25 mg/L CaCl2 x H2O. After autoclaving, the medium was supplemented with 10 mL/L trace elements, 5 mL/L vitamins solution and 1 mL/L sodium selenite/sodium tungstate stock solution, stock solutions were (1000 x). The precultures of Aromatoleum sp. were prepared in Thb medium supplemented with 4 mM sodium benzoate, allowing the bacteria to reach the stationary stage before inoculating it into a medium with 0.025 % toluene in a larger volume (1-2 L). To prevent toluene toxicity, paraffin oil was added to the medium in the final concentration of 2%. Further on, the culture was supplemented with 0.1% toluene in the final volume when needed, based on monitoring nitrate and nitrite levels, assuming a 1:4 ratio of toluene and nitrate consumption. |
65d898779138d23161ce552c | 6 | Fully-grown cultures were opened under anaerobic conditions (97:3 N2:H2) and moved into centrifugation beakers. Cells were harvested at 4500 x g 4 °C for 45 min. The cell pellet was resuspended in a 1:1 ratio with 20 mM TEA/HCl buffer pH 7.8 and homogenized with ultrasonication (20 mHz, 20% amplitude, 3 s pulse with 9 s pause for 20 min; Sonifier 250, Branson) while cooled with solid ice packs to prevent denaturation. Permeabilized cells were ultra-centrifuged at 100 000 x g, 4 °C for 1 hour. The supernatant was collected and the obtained cell-free extract was stored at -80 ⁰C until use under the blanketing atmosphere of N2/H2. The protein concentration of the cell extract was determined in a 2 L spectroscopic method (280 and 260 nm, BioTek with Take3 plate) yielding 39 ± 0.9 mg/ml. |
65d898779138d23161ce552c | 7 | L were collected at 0, 5, 10, 15, and 20 min, and the reaction was stopped by mixing these in a 1:1 ratio with acetonitrile. These diluted supernatants were processed as described above and analyzed with LC-DAD, while samples to be analyzed by LC-MS/MS were 20 times diluted with acetonitrile. All experiments were carried out in triplicates. |
65d898779138d23161ce552c | 8 | Samples were analyzed on an Agilent 1260 UHPLC coupled with DAD and an Agilent 6460 The quantitative analysis of benzylsuccinate was conducted using a DAD detector at 210 nm and external calibration (Fig. ) for samples diluted 1:1 with acetonitrile. This method was used for the determination of enzyme activity with toluene and d8-toluene. |
65d898779138d23161ce552c | 9 | Samples for the EPR monitoring of H/D exchange on the glycyl radical were prepared by exchanging the solvent via passage over PD-10 gel filtration columns (1.5 x 5 cm, GE healthcare). These were made anoxic by washing with water containing 5 mM dithionite, then equilibrated with either anoxic water or D2O. After applying 0.5 ml of cell extract, the columns were eluted with either anoxic water or D2O, resulting in an initial exchange of water to D2O and a second exchange back to water. The recovered protein-containing eluates did not show significant dilution. The exchange of protium to deuterium was also confirmed by mixing the cell-free extract in a 1:1 ratio with anoxic D2O, using non-treated cell extract as a control sample. Extracts were transferred into EPR tubes under anaerobic conditions, secured with a clamped rubber tube, and gently frozen in liquid nitrogen. The samples were stored in liquid nitrogen until measured. |
65d898779138d23161ce552c | 10 | The EPR spectra for H/D exchange of the glycyl radical and the reverse exchange were observed in cell extracts of toluene-grown Aromatoleum toluolicum strain T. They were recorded with an EMX-6/1 X-band spectrometer (Bruker, Karlsruhe, Germany) with a standard TE102 rectangular cavity and an ESR-900 helium flow cryostat with variable temperature (Oxford instruments, Oxford, UK) or a liquid-nitrogen finger dewar as described in . The H/D exchange at glycyl radical in D2O was also confirmed by EPR spectra of extracts of toluenegrown cells of an Aromatoleum sp. which were recorded by a Bruker Elexsys E580 spectrometer and SHQ4122 resonator equipped with ESR900 cryostat (Oxford Instruments) (see SI for details). |
65d898779138d23161ce552c | 11 | The initial structure of the BSS T1 apoenzyme was obtained from the crystal structure of the apoenzyme (PDB code: 4PKF) . The water molecules as well as and subunits were removed and the model was protonated with H++ at pH 7.4 . The overall charge of the model was -3 which was equilibrated with sodium ions. |
65d898779138d23161ce552c | 12 | The AMBER parameters for radical Gly829 were taken from Barone et al . The BSS models were solvated with explicit water molecules (10 Å radius around the protein, 23,324 or 24,215 water molecules, respectively for holo-and apoenzyme) and the calculations were conducted in a periodic-boundaries box (119.6 Å × 86.3 Å × 96.8 Å). The AMBER parameters for radical Cys493 were derived according to standard protocols . All AMBER parameters of enzyme ligands and non-standard residues were provided in Supplementary Information. |
65d898779138d23161ce552c | 13 | All classical MD simulations were performed for holo and apo BSS models using the AMBER ff03 force field . The calculations were conducted with AMBER 18 according to the previously described protocol . The stable parts (i.e. final 20 ns) of the 50-60 ns simulation trajectories, i.e., exhibiting stable RMSD of the main chain (Fig. ), were analyzed with clustering using the k-means method taking into consideration heavy atoms of the active site residues (see SI). |
65d898779138d23161ce552c | 14 | For apoenzyme, the optimal number of 6 clusters was selected based on the DBI and pSF indexes. A structure for further QM:MM calculations was selected based on the following criteria: the size of the cluster (the higher the better), cluster tightness (the average distance from the centroid, the lower the better), silhouette (the higher the better), and the agreement of the Cys493 C-Cα-Cβ-Sγ dihedral angle with its median value observed during MD simulation. |
65d898779138d23161ce552c | 15 | For the enzyme-substrate complex, we analyzed the last 35 ns of the stable trajectory using the same approach. However, in this case, clustering yielded geometries with toluene at the entrance of the active site, far from Cys493. Therefore, for QM:MM calculations, we selected the frame with the shortest distance (3.23Å) of the toluene group to the SH group of Cys493 which belongs to the first cluster which described the majority (54%) of the analyzed frames. |
65d898779138d23161ce552c | 16 | For simulations of the enzyme with radical Cys493, we conducted three 60 ns simulations with toluene and monoprotonated fumarate as well as with monoprotonated (R)-benzylsuccinate, while for apoenzymes two 100 ns simulations (Fig. ). For the sections of trajectories with stable RMSD, we analyzed the distances between C atoms of Gly928 and Cys493 (Fig. ). |
65d898779138d23161ce552c | 17 | All QM:MM calculations were conducted using the Gaussian16 C.01 program .The QM:MM models obtained from MD simulations were stripped from sodium ions and most of the water molecules, leaving only H2O molecules penetrating a 20 Å radius from Cys493. The positions of all residues and water molecules above the 15 Å radius from Cys493 were frozen in geometry optimization. The overall charge of the QM:MM models were -7 and -3 for holo-and apo-BSS models, respectively. The fumarate was modeled in the monoprotonated state according to previous docking studies . Two sizes of high layer (HL) were used in the study a small one (S-HL, Fig. ) used for geometry optimization and vibrational analysis and a big one (B-HL Fig. ), used for single point correction of the energy. |
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