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60c73f85ee301c7b01c78902 | 31 | If SMARTY is successful, it will discover SMARTS strings that identify these types (Figure ), starting from a chemically undistinguished initial hydrogen base type. Finding all five reference types simultaneously would give a 100% total score, but we would also consider discovering SMARTS patterns that receive a 100% partial score for all of these types during different parts of a simulation a success. Partial success might come from distinguishing four for the five types instead. |
60c73f85ee301c7b01c78902 | 32 | The chemical perception trees sampled in both SMARTY and SMIRKY were scored against the typing in existing force fields (Section 2.1.1). For SMARTY, we used a traditional indirect chemical perception force field specification as the reference, namely, AMBER's parm99 with the parm@Frosst 97 extension. For SMIRKY, we used the direct chemical perception force field smirnoff99Frosst, which was generated by hand to closely follow the parameters in the parm99/parm@Frosst force field. |
60c73f85ee301c7b01c78902 | 33 | For the first set, our goal was to have a small set of molecules with minimal complexity to test whether these tools could work as intended. Thus, this set was limited to molecules composed of carbon, oxygen, and hydrogen atoms, with only single bonds; that is, to alkanes, ethers, and alcohols and the compounds were drawn from the AlkEthOH compound set. The specific set of compounds used here comprises 42 molecules, with a total of 803 atoms. We refer to this minimal set as AlkEthOH in our results. |
60c73f85ee301c7b01c78902 | 34 | The second set, PhEthOH, is the first set additionally supplemented with aromatic compounds, and comprises 200 molecules with a total of 7,185 atoms. Chemically, the difference in these sets is that PhEthOH includes aromatic rings, along with alkanes, ethers, and alcohols. AlkEthOH has one atom type not found in PhEthOH, namely H3, corresponding to a hydrogen bound to a carbon which is connected to three electron withdrawing groups. The aromatic groups in PhEthOH introduce two atom types not found in AlkEthOH -specifically, CA for aromatic carbons and HA for the hydrogens connected to those carbons. However, PhEthOH has more bond, angle, and fragment types than AlkEthOH. |
60c73f85ee301c7b01c78902 | 35 | The third set of molecules was obtained by filtering DrugBank, a free database of drug and drug-like molecules. Molecules with fewer than three or more than 100 heavy atoms were removed, as were any molecules with metals or metalloids. Next, the molecules were assigned parm99/parm@Frosst atom types, and any molecule that could not be typed was removed. The molecules were then also typed with smirnoff99Frosst version 1.0.5 and any molecules assigned a generic parameter, for example any bond ("[*:1]∼[*:2]"), were also removed. Finally, we selected a reduced set of compounds that include all atom and fragment types in the reference force fields used in DrugBank after this filtering. The final set, termed MiniDrugBank, has 371 molecules containing 15,678 atoms, and is available separately on GitHub (). |
60c73f85ee301c7b01c78902 | 36 | A series of tests were performed to evaluate success for each tool described above -the original SMARTY sampler (SMARTY ), the elemental SMARTY sampler (SMARTY ), and SMIRKY -in discovering chemical perception of the complexity in existing force fields. Each test was run on each of the three molecule sets described above, AlkEthOH, PhEthOH, and MiniDrugBank. For SMARTY , tests were performed for each element with more than one atom type in the molecule set. Using the elemental sampler on elements with only a single atom type (such as halogens) would not provide useful insight since even a generic SMARTS pattern could match the relevant chemical perception. SMIRKY tests were performed for bond, angle, proper torsions, and nonbonded (vdW) fragment types. While the SMIRNOFF format and SMIRKY support improper torsions, there are a very limited number in smirnoff99Frosst so those were not tested. |
60c73f85ee301c7b01c78902 | 37 | MC sampling was run at eight effective temperatures: 0, 10 -6 , 10 -5 , 0.0001, 0.001, 0.01, 0.1, and 1. Ten initial tests of 10,000 iterations were performed for each combination of molecule set, temperature, and tool. These were followed by three additional tests with first 50,000 and then 100,000 iterations for MiniDrugBank with SMIRKY, since the search space for fragment types is so large. Output for both tools was saved in two ways: a human-readable log of the run, and a comma-separated trajectory file which stores the partial score for each reference atom or fragment type and the total score at each iteration. |
60c73f85ee301c7b01c78902 | 38 | A central goal of this study is to test the ability of the SMARTY and SMIRKY sampling methods to discover type definitions closely matching those in existing force fields. As detailed above, if successful, we would recover SMARTS and SMIRKS patterns matching all atom or fragment types, by achieving total scores of 100% or partial scores of 100% for all reference types (Section 2.4). However, we would consider high total scores along with a 100% partial score for most reference types to also indicate success, showing promise for expanding these algorithms for sampling chemical perception trees beyond the proof of principle in this paper. Both methods were tested on three molecule sets of increasing complexity -AlkEthOH, PhEthOH, and MiniDrugBank (section 2.4). |
60c73f85ee301c7b01c78902 | 39 | We performed 10 SMARTY runs, of 10,000 steps each, for each of the three molecule sets, at effective temperatures of 0, 10 -6 , 10 -5 , 0.0001, 0.001, 0.01, 0.1, and 1, using both the original SMARTY sampler (SMARTY ) and the elemental sampler (SMARTY ). The results of these calculations are analyzed in the following two subsections. |
60c73f85ee301c7b01c78902 | 40 | We first tested SMARTY on the AlkEthOH and PhEthOH sets. Although these have only eight atom types, some of the five hydrogen types used in these sets require multiple atoms in the beta position, so they still provide a significant challenge. For the AlkEthOH set run at effective temperatures between 10 -6 and 10 -2 , the original sampler, SMARTY , yielded total scores, averaged across the 10 runs, of > 90% (Table ), and the lowest average score is still fairly high, at 69%. The degradation of performance at lower and higher temperatures is reasonable for the MC method, as low temperatures can lead to trapping in local maxima, while high temperatures can lead to a lower preference for favorable states. Figure provides sample plots of total score against step number for MC runs at various temperatures. As expected, the higher temperatures lead to greater score fluctuations. Equivalent results were obtained for the PhEthOH set (Table ), which has a similar number of atom types (Section 2.4). To summarize results, we also report total scores for the initial atom types used in each simulation and the maximum total score received across all simulations (Table ). Overall, these results strongly support the ability of SMARTY to sample chemically relevant ensembles of atom types. Analysis of the partial scores offers a finer-grained view of these overall results. Thus, we made heat maps showing the frequency of generating a partial score of 100% for each reference atom type (Figure ), at the various simulation temperatures. These show that some reference atom types are easier to discover than others. This can be for multiple reasons, including because they have simpler specifications, and because they occur more frequently. Also, although low to moderate temperatures yield the best results for most atom types, higher temperatures worked better for atom type HC, at least for the PhEthOH molecule set. |
60c73f85ee301c7b01c78902 | 41 | Figure shows a sample working atom type hierarchy tree (top panel) that was generated during a SMARTY simulation, with levels of the hierarchy represented by different colors. The bottom panel shows which reference atom types are matched by each SMARTS pattern, and the partial score for each match. It is worth noting in this regard that SMARTY's hierarchical approach to sampling dramatically simplifies the complex search problem. For example, in the parm99/parm@Frosst force field for AlkEthOH, there are four atom types for hydrogens bound to carbon, differing in the number of electron withdrawing groups bound to the carbon atom (i.e., in the beta position). As mentioned before, these hydrogens provide a significant challenge to SMARTY. With hierarchical sampling, SMARTY can first discover less specialized SMARTS and then proceed to more complex derivative types further down the tree (Figure ). SMARTY would not be able to find H1 ("[#1$(*-[#6]-[#8])]"), a carbon with one electron withdrawing group, without first discovering HC ("[#1$(*-[#6])]"), because moves are made one atom at a time. This also highlights the importance of the hierarchy when matching; if the more complex child SMARTS patterns were placed above their parents, then all hydrogen atoms would be assigned to the more general "[#1]" type; the more complex pattern is only valuable when it is a child of and placed below the less complex pattern. |
60c73f85ee301c7b01c78902 | 42 | This point is further illustrated by considering the additional hydrogen types used in AlkEthOH. The We plot the fraction of simulation time that each reference atom type (x axis) is matched by a SMARTS pattern with a partial score of 100%. We tested eight different temperatures (y axis) and ran 10 simulations of 10,000 iterations each. Darker colors imply a higher rate of matching 100% of that reference atom type; see color bars at right. If we never found the reference atom type, the corresponding cell would be white, but this does not occur here. |
60c73f85ee301c7b01c78902 | 43 | This figure shows the final hierarchy achieved in one SMARTY simulation with the AlkEthOH set at = 0.0001 after 10,000 iterations. The top shows the hierarchy of SMARTS strings discovered where each color represents a different level. For example, the initial types are represented in light blue, and the yellow squares are the working atom types derived from the initial types; the same logic applies for the other colors. For hydrogen, we see SMARTS patterns that match the parm99/parm@Frosst reference types HC (yellow), H1 (light green), H2 (lilac), and H3 (light red). The bottom (large gray box) shows all final working types and their respective reference atom types as well as partial score for that pairing. Here we determine the first iteration at which each sampler achieves a 100% total score (numerical values, out of 10,000 in total), then average this number for all runs which were successful in achieving a score of 100% at some point (out of 10 trials in total). The y axis shows which sampler was used (SMARTY for all atoms versus SMARTY for hydrogen and oxygen) and the x axis shows the temperature employed. In general lighter colors indicate higher success rates, and lower numbers indicate success was achieved more rapidly. Results for SMARTY for carbon is not shown since AlkEthOH has only one carbon atom type (CT). |
60c73f85ee301c7b01c78902 | 44 | hydrogen atom types used by parm99/parm@Frosst are relatively complex because previous work concluded the nonbonded parameters for these atoms need to be different, and thus SMARTS patterns to match these must also be fairly complex. Specifically, these atom types require SMARTS strings extending out far enough to describe multiple atoms in the beta position. If SMARTY did not use SMARTS patterns already generated as parent types, finding these complex patterns would be impossible. Here, the relevant atom types cover hydrogen attached to carbon with zero (HC), one (H1), two (H2) or three (H3) electron withdrawing groups (Figure ). For example, a SMARTS pattern which can recognize H3 (in AlkEthOH as shown in Figure |
60c73f85ee301c7b01c78902 | 45 | . But arriving at H3 directly from HC ("[#1$(*-[#6])]" ) would be impossible without very complex move proposals (yellow to red in Figure ). Instead, a move in SMARTY could use HC as a parent type and propose a move to create H1. A subsequent move could take H1 as a parent and generate H2 as a child then the same for creating H3 from H2. Of course, this will only work if uncovering each new intermediate type provides some incremental increase in total score, which it does here. Our assumption is that the chemistry of more diverse sets can be described in a similar way, starting with the most simple (or generic) SMARTS and then extending that pattern only where necessary. |
60c73f85ee301c7b01c78902 | 46 | The analysis so far has focused on the original SMARTY algorithm, which samples over all elements simultaneously. This approach is comprehensive, but leads to a combinatorial sampling problem. Imagine we want to find the hydrogen atom types in AlkEthOH. The most complex of these is H3, which requires specifying one atom in the alpha position and three atoms in the beta position (Figure ). When adding either an alpha or beta substituent, the probability of choosing a specific base type (i.e. correct element) is approximately 0.15. This means it could potentially take SMARTY more than 0.15 -4 ≈ 1, 000 moves to find H3 when starting with a hydrogen parent type. Including the necessity of choosing the correct parent element decreases the probability of each move to 0.015, meaning it could take SMARTY on the order of 10,000,000 moves to generate the correct SMARTS pattern for H3. The elemental SMARTY method, SMARTY , speeds the search by sampling only one element (base type) at a time. Thus, fewer iterations are required to first discover a SMARTS with a total score of 100%, as shown for AlkEthOH in Figure . |
60c73f85ee301c7b01c78902 | 47 | The MiniDrugBank molecule set was drawn from the DrugBank database, and contains a similar diversity of atom types in a smaller number of molecules (Section 2.4). Initial and maximum scores across all SMARTY simulations for MiniDrugBank are shown in Table . The total number of reference atom types represented in MiniDrugBank, 37, is considerably larger than the number of reference atom types in AlkEthOH or PhEthOH, making this a more challenging test case. As a consequence, the average total scores run lower, often at 70-80%, than in the case of the simpler test sets (Table ). We therefore focus further evaluation on the the elemental SMARTY sampler (SMARTY ), which reduces the combinatorial explosion of types and thus is particularly suitable for bigger and more complex molecule sets. Accordingly, the evaluation of these results is in terms of partial scores, rather than total scores (Section 2.4). |
60c73f85ee301c7b01c78902 | 48 | We find that SMARTY is capable of finding SMARTS patterns for the majority of reference atom types For SMARTY for MiniDrugBank, we plot the fraction of simulation time where the partial score is 100% for a given parm99/parm@Frosst atom type. The elements shown here are (a) hydrogen, (b) carbon, (c) nitrogen, and (d) oxygen. We used 10 simulations of 10,000 iterations each to construct the plots at different temperatures (y axis). At high temperatures, most of the reference atom types reach 100% partial score. However, at low temperatures, there are more well populated reference atom types but also more which never achieve 100% at any iteration. |
60c73f85ee301c7b01c78902 | 49 | (Figure ). Overall, SMARTY is more likely to match 100% of all reference atom types at relatively high temperatures. When we decrease the temperature, SMARTY's behavior changes and no longer finds many reference atom types (shown by white in the heat maps), but it matches 100% of some atom types more frequently (darker colors), until the temperature becomes too low. |
60c73f85ee301c7b01c78902 | 50 | SMARTY is able to generate multiple different SMARTS patterns matching typical reference atom types in MiniDrugBank. In 10 runs of 10,000 iterations each, we found 16,564 unique SMARTS strings which match at least some fraction of any reference atom type. When we look at the SMARTS patterns which match 100% of any reference atom type, the number is still rather large, at 801 unique SMARTS strings. This was true even for simple atom types, such as CM, which is represented by "[#6X3]" in parm99/parm@Frosst. For CM, SMARTY found 24 different SMARTS strings that matched 100% of this reference atom type. Some of these 24 SMARTS are very generic, such as "[#6]", others more complex ("[#6X3$(*-[*])$(*=[#6])]"). Our goal was not to replicate exactly the same SMARTS patterns written by human experts, but instead to determine what extent automated sampling can capture equivalent -or at least similar -chemical perception. SMARTY's ability to discover a wide diversity of SMARTS patterns corresponding to each reference atom type appears to demonstrate success in this regard. We illustrate how SMARTY scores working atom types (red on the left) compared to reference atom types (blue on the right) using a bipartite graph. (a) When there is only one generic SMARTS string ("[#6]"), this pattern is assigned to both CT and CA atom types through the PATTY-adapted scheme, but it will be matched only to the more populated reference atom type (CT highlighted in yellow); (b) when SMARTY creates a new set of working types, containing both "[#6]" and "[#6X4]", the generic atom type will not match CT anymore, since it chemically matches the new working atom type ("[#6X4]") instead. |
60c73f85ee301c7b01c78902 | 51 | When working types have only very generic SMARTS pattern they will match the most populated reference atom type due to our typing scheme and scoring function. The scoring function uses a bipartite graph where the matching is based on the maximum total weight and the weight on each edge is determined by the number of atoms assigned that working and reference type (Section 2.1.1). For this reason, a reference type with the highest population is more likely to be matched with a generic working type. To understand the implications of this, consider the frequency of two of the carbon types in MiniDrugBank, CT and CA. The parm99/parm@Frosst atom type CT is assigned to 2213 atoms, while CA is used for 2097. If we have only one carbon SMARTS string, such as the generic one "[#6]", all carbon atoms in the molecule set will be assigned as "[#6]", and after scoring, the SMARTS pattern will match the reference atom type CT because it leads to the highest total score. In that case, CA (and all other carbon atom types) are not matched to any SMARTS. But, if we discover a new working atom type that matches CT only, such as "[#6X4]", then the generic SMARTS will match CA (Figure ). |
60c73f85ee301c7b01c78902 | 52 | For MiniDrugBank we were only partially successful; we were not able to find a 100% partial score for the HX, N2, C*, and HP atom types with SMARTY. It is worth briefly examining these types to understand why. HX was created to address a very specific problem occurring with hydroxyl hydrogens; to match it, a SMIRKS pattern would need to describe an atom in the gamma position (3 bonds away from the primary), but SMARTY sampling extends out only to the beta position. N2 requires multiple SMARTS patterns to be able to match 100% (it combines several different chemical groups into a single atom type) and the bipartite graph matching only allows one working atom type per reference atom type, meaning that SMARTY will never discover it. C* is very similar to other five-membered ring carbon atom types (CW, CC, and CR) in our tests; it also occurs less frequently which would require SMARTY to generate and keep highly specialized SMARTS patterns that match the other atom types uniquely before it could be discovered. In order to find HP, the SMARTS pattern would need a decorator in the beta position, but SMARTY does not currently add decorators to the beta position making it impossible to match this particular atom type. More details about all of these atom types and why they never get a partial score of 100% can be found in the Supporting Information. Nevertheless, SMARTY was fairly successful finding a 100% partial score for most reference atom types in parm99/parm@Frosst with only a few exceptions. In our tests, we were able to find patterns matching 33 out of 37 parm99/parm@Frosst atom types with a 100% partial score -overall an 89.2% success rate. While some reference atom types are not found, this seems to be less a commentary on our chosen sampling algorithm and move set; but a byproduct of the complex human decisions made in constructing parm99/parm@Frosst. The very complex atom typing employed in parm99/parm@Frosst may provide a further argument in favor of moving toward a force field with direct chemical perception and away from those with human defined atom types. |
60c73f85ee301c7b01c78902 | 53 | SMIRKY extends SMARTY, testing our ability to sample over chemical perception trees used for fragment types in SMIRNOFF format force fields. It automatically samples SMIRKS patterns for fragment types for bond, angle, torsion, and nonbonded types then compares the fragment type SMIRKS with that in a reference force field for the same set of molecules. As with SMARTY, the overall goal with SMIRKY is to ensure we can find SMIRKS patterns that sample comparable chemical complexity to that used in our reference force field, smirnoff99Frosst. Scoring works the same as with SMARTY-we evaluate both the total score and the partial score for each iteration. In the case of SMIRKY, a partial score of 100% corresponds to SMIRKY discovering a SMIRKS pattern that matches a single reference fragment type (Equation ). |
60c73f85ee301c7b01c78902 | 54 | With SMIRKY, we were at least partially successful with all molecule sets as evidenced by our ability to find high total scores and 100% partial scores for the majority of fragment types in smirnoff99Frosst. Initially, we performed simulations of comparable length with SMIRKY as with SMARTY; however, increased complexity made longer simulations necessary. Specifically, we began by performing 10 simulations with 10,000 iterations for each fragment type at all eight temperatures (0, 10 -6 , 10 -5 , 0.0001, 0.001, 0.01, 0.1, 1). However, because SMIRKY goes beyond atom types to fragment types, it necessarily must sample more complex chemical perception trees. For example, torsion fragment types require at least four atoms and potentially substituents as well; decorators may also be required for all these atoms. This results in SMIRKS patterns which involve four or more atoms (three or more bonds) all with decorators-a challenging problem. In SMARTY, the combinatorial problem of discovering sufficiently complex SMARTS patterns was tackled by creating the elemental sampler in order to limit the chemical space being searched. But with SMIRKY, we cannot currently sub-divide the chemical space for these more complex fragments (Section 2.3), so we instead increased the number of iterations. For the most complex molecule set, MiniDrugBank, we increased the number of iterations to 50,000 and then 100,000. In each case, we performed three simulations at each temperature for each fragment type. To summarize our results, we report total scores for in the initial fragment types used in each simulation and the maximum total score received across all simulations (Table ). We also report the fraction of reference fragment types to receive a 100% partial score during any simulation (Table ). |
60c73f85ee301c7b01c78902 | 55 | As with SMARTY, AlkEthOH provides a useful toy example for testing our methods, and SMIRKY is successful based on total scores for all fragment types. In smirnoff99Frosst, there are nonbonded parameters corresponding to the same hydrogen parm99/parm@frosst atom types discussed above (Section 3.1.1). To distinguish all of these types, multiple beta position atoms must be identified. a total score of 100% for all smirnoff99Frosst fragment types in AlkEthOH (Table ). An average total score of > 90% at multiple temperatures provides further evidence of SMIRKY's success (Table ). While SMIRKY is quite successful in general, its success is not universal at all temperatures. At moderate temperatures, SMIRKY is able to discover SMIRKS patterns complex enough to agree with the fragment typing used in smirnoff99Frosst, achieving a successful total score of 100%. But, as is expected with an MC algorithm, we achieve relatively poor scores both at = 0 and at the high temperature of 0.1. However, at the intermediate temperature of 0.001, SMIRKY eventually generates torsion SMIRKS with a 100% score and maintains that high score (Figure ). In addition to the examples depicted here, multiple simulations at the temperatures of 10 -6 , 10 -5 , and 0.0001 also reached a 100% total score. The fact that multiple temperatures reach a total score of 100% indicates we have been successful in automatically sampling the chemical perception trees for torsion parameters in AlkEthOH. Details for all simulations are included in the Additional Information. |
60c73f85ee301c7b01c78902 | 56 | PhEthOH adds a small amount of complexity relative to AlkEthOH, including aromatic rings in addition to alkanes, ethers, and alcohols. It requires a total of 10 bond, six angle, 16 torsion, and nine nonbonded smirnoff99Frosst parameters. As with AlkEthOH, we performed 10 SMIRKY simulations at each temperature for each fragment type. This small increase in complexity also increased the difficulty of matching all reference types simultaneously, as shown by the drop in average total score for all fragment types (Table ). For bonds, angles, and nonbonded fragment types, SMIRKY is able to achieve a 100% total score; however, the same could not be said for torsions (Table ). However, SMIRKY is able to find a 100% partial score for all torsions at most temperatures (Table ). |
60c73f85ee301c7b01c78902 | 57 | A 100% partial score is evidence that SMIRKY can generate the SMIRKS of the same chemical complexity found in the smirnoff99Frosst. As with SMARTY, we examine the partial score for each reference torsion type and consider the fraction of iterations spent at 100% (Figure ). For all but one reference torsion type (t2), SMIRKY is able to achieve a partial score of 100% for at least a fraction of time at all temperatures. It does achieve a 100% partial score for t2 at most temperatures, only failing at temperatures of 0 and 0.1. However, PhEthOH is slightly more challenging, as evidenced by the fact that heat map colors are lighter in general. Unlike in AlkEthOH, SMIRKY was not able to achieve a total score of 100% when sampling torsions in PhEthOH (Table ). PhEthOH only has six more torsion types, yet these make it substantially more challenging to find and keep sufficiently complex SMIRKS. In Section 3.1.1, we estimated the number of moves required to generate certain SMARTS patterns. When considering fragment types with more atoms, the combinatorial problem grows further since there are multiple atoms and bonds that require decorators. The lower frequency of 100% partial scores for torsions in PhEthOH is our first example of the implications of this combinatorial problem. For PhEthOH, we are able to generate SMIRKS for all reference torsions during at least some fraction of most simulations. However, if we are going to effectively sample chemical perception trees for the development of force fields, future move proposals will need to move through chemical space more efficiently. We will examine this problem more closely when analyzing SMIRKY's results on MiniDrugBank (Section 3.2.3). |
60c73f85ee301c7b01c78902 | 58 | Future move proposal engines could be made more efficient by taking advantage of basic chemical information. For example, if a double bond was already specified between a carbon and another atom, that carbon atom cannot have four bonds; however, as currently implemented, SMIRKY will occasionally propose moves which attempt to add a "X4" decorator to that carbon. We could take this concept one step further by learning which decorators can productively be applied to which atoms. For example, hydrogen can only have one bond and it is always single, so adding decorators to a hydrogen atom or its connecting bond will never usefully impact the separation of fragment types. Currently, SMIRKY makes many naïve moves, wasting many of its iterations generating SMIRKS patterns that cannot help separate fragments for these and other reasons. |
60c73f85ee301c7b01c78902 | 59 | MiniDrugBank covers significantly more chemical space than either of the other molecule sets with 73 bond, 34 angle, 136 proper torsion, and 26 nonbonded parameters from smirnoff99Frosst. It uses all parameters employed in molecules from the DrugBank database that can be atom typed by the parm99/parm@Frosst force field, as described in Section 2.4. This is a more complex set, so despite considerable success, we are often unable to obtain a total score of 100%. Specifically, we were unable to find a total score of 100% for bonds, angles, torsions or nonbonded fragment types with 10,000 iterations. We also saw a significant decrease in the average total score for all fragment types during our ten simulations (Table ) relative to other molecule sets. For this reason we repeated the simulations with 50,000 and then 100,000 iterations. SMIRKY still did not find a total score of 100% during the longer simulations. However, overall, SMIRKY was partially successful for MiniDrugBank. We achieve total scores over 90% for nonbonded, bond, and angle types for the highest scoring iterations (Table ). The highest total score for torsion types is 76%, which is still promising considering the large combinatorial problem. |
60c73f85ee301c7b01c78902 | 60 | On combining the results from every iteration in all simulations (10,000, 50,000, and 100,000 iterations at all temperatures) we find a 100% partial score for the majority of smirnoff99Frosst reference fragment types (Table ). Heat maps for MiniDrugBank, like the examples shown for torsions in AlkEthOH and PhEthOH (Figure ), are available in the Supporting Information. There are five bond, two angle, 19 torsion, and one nonbonded reference fragment types where SMIRKY never finds a 100% partial score. Potential reasons for missing these fragment types are summarized in this section and discussed in further detail in the Supporting Information. While it would be ideal to find all the fragment types, SMIRKY is able to find SMIRKS patterns that agree with 91% of the smirnoff99Frosst fragment types, indicating that we do recover a great deal of the target chemistry. As with SMARTY, there are a few fragment types that SMIRKY never recovers. In the Supporting Information we provide information about these missing fragment types, exploring in more detail why some are so challenging and why others are undiscoverable with SMIRKY's current algorithm. In the following paragraphs we summarize the categories where SMIRKY's algorithm could be improved in order to discover these missing types. |
60c73f85ee301c7b01c78902 | 61 | The order of the fragment type hierarchy and relationship between parent and child types could help explain some missing types. The two missing angle types, a6 ("[*:1]∼;!@[*;r3:2]∼;!@[*:3]") and a12 ("[*:1]∼;!@[*;r5:2]∼;@[*;r5:3]"), highlight the importance of where newly generated SMIRKS are placed in the hierarchy. In smirnoff99Frosst these patterns always match carbon atoms in 3-and 5-membered rings, but atoms 1 and 3 can be any element, meaning it is easy to lose progress made toward these two patterns when patterns lower in the hierarchy also match the ring carbon. SMIRKY requires that when a child SMIRKS pattern is created the parent SMIRKS still matches at least some molecules. In most cases this prevents the creation of unnecessarily specific SMIRKS, but in some cases makes it impossible to OR decorators together. For example, we would be unable to find the exact pattern for n7 ("[#1:1]-[#6X4]∼[*+1,*+2]") because creation of a child with a second OR type on the beta atom will always empty the parent. This is also true for many of the other 19 missing torsions. SMIRKY is not trying to discover the exact SMIRKS patterns used in smirnoff99Frosst so it is possible our algorithm could still succeed finding SMIRKS matching these reference types using a different combination of moves. However, allowing moves to combine SMIRKS decorators could make distinguishing this type of chemistry easier. Another possible solution is allowing a child to completely replace a parent when the generated SMIRKS matches a larger section of chemical space, but not when it types the same group of fragments the parent typed. |
60c73f85ee301c7b01c78902 | 62 | The combinatorial problem that occurs in SMARTY is exacerbated in SMIRKY since multiple atoms may require decorators or alpha or beta substituents. It is difficult to identify a specific reason SMIRKY does not reach a 100% partial score for some of the torsion types and the five missing bond types. This suggests that the combinatorial problem described above (Section 3.2.2) is the most likely source of failure. Thus it seems likely that chemical perception sampling tools in future force field parameterization will need improved move sets with higher acceptance rates. |
60c73f85ee301c7b01c78902 | 63 | To estimate the size of the search problem posed by torsions in SMIRKY, we considered an example reference torsion t78 ("[*:1]-,:[#6X3:2]=[#7X2:3]-[*:4]"), a deceptively simple example where SMIRKY never reaches a 100% partial score. SMIRKY simulations for torsions are initialized with the center two atoms specified and no bond information provided, so the initial torsion relevant to t78 is "[*:1]∼[#6:2]∼[#7:3]∼[*:4]" -that is, a carbon atom connected by any bond to a nitrogen atom. For the purpose of this exercise we will assume we want to generate this exact same SMIRKS; while that is not actually the goal of SMIRKY, it is a helpful example to illustrate the scope of the combinatorial problem. In this case, the probability of adding any one particular atom or bond decorator is approximately 0.01. In t78, there are an additional two atom decorators (X3 on carbon and X2 on nitrogen) along with four extra bond decorators. For each SMIRKY step, one torsion type from the working set is chosen (this is the parent type) and then the child fragment is created by making changes to this parent type (Figure ). In order to generate this particular SMIRKS we also need to include the probability of choosing the correct parent type, which is about 0.02. Even if we assume the order of adding each decorator is unimportant, it will typically take SMIRKY over 1 billion steps to generate this exact SMIRKS pattern. |
60c73f85ee301c7b01c78902 | 64 | One way to simplify the combinatorial problem in SMIRKY or future packages for sampling chemical perception trees would be creating a more efficient move set. As discussed in Section 3.2.2, SMIRKY currently considers all possible decorators for the atoms and bonds, whether or not they make chemical sense, and thus wastes considerable time proposing patterns that do not match any molecules. Considering the low probability of picking a given decorator, the fact that SMIRKY is able to find SMIRKS patterns which match 120 (88%) of the reference torsions is further evidence that we have been fairly successful in sampling the chemical perception tree effectively. However, if we could increase the probability of picking good decorators, we could decrease the number of moves required to sample the requisite chemistry. Future progress of these tools should leverage moves which only employ chemically reasonable combinations of decorators. For example, a double bond decorator should never be allowed next to a tetrahedral carbon which only has single bonds. This information would not necessarily need to be provided by a human expert; instead, molecule sets used for training could be used to extract this information. |
60c73f85ee301c7b01c78902 | 65 | SMARTY and SMIRKY have proven capable of automatically sampling chemical perception trees relevant to general small molecule force fields. Both of our tools were tested first with relatively simple sets (AlkEthOH and PhEthOH) and then using MiniDrugBank, which provided a test set of molecules encompassing the diversity of the DrugBank database. SMARTY generated SMARTS patterns which resulted in a 93% total score for MiniDrugBank, and 100% for AlkEthOH and PhEthOH. SMIRKY achieved a total score of over 90% for nonbonded, bond, and angle fragment types in MiniDrugBank. |
60c73f85ee301c7b01c78902 | 66 | In some cases, the significant chemical complexity encoded in certain existing atom types limits our ability to find these types via individual SMARTS patterns. This may in part be because of overly complex atom typing, which, in traditional force fields, needs to encode the chemistry required for all force field parameter types simultaneously. Switching to direct chemical perception may allow for much more straightforward parameter assignment. Our SMIRKY tool for working with direct chemical perception also had considerable success. SMIRKY generated SMIRKS patterns which capture more than 90% of the fragment types in smirnoff99Frosst for MiniDrugBank and 100% for AlkEthOH and PhEthOH. Coverage was less than perfect in part because there is a significant combinatorial problem in sampling chemical perception trees. This combinatorial problem is most pronounced in SMIRKY's results on torsions, where many atoms and bonds may require multiple decorators. The ability to automatically recover the chemical perception in these existing force fields is a promising first step toward sampling over chemical perception as part of force field parameterization. |
60c73f85ee301c7b01c78902 | 67 | SMARTY and SMIRKY are prototypes created as a part of the Open Force Field Initiative, which aims to create open source parameterization tools that can provide accurate force fields without human experts being required in the parameterization process. The overall initiative is expected to have a significant impact on the quality of biophysical modeling and molecular design for a variety of fields, and facilitate force field science. |
60c73f85ee301c7b01c78902 | 68 | Historically, many force fields used atom types, a form of indirect chemical perception, where all atom types were generated by hand by an expert. As discussed in the Introduction, the complexity of these atom types has been a major contributor to the difficulty of force field development and a barrier to crosscomparing force fields. The new SMIRNOFF format, with direct chemical perception, is an important step forward, but as currently implemented still uses hand-encoded SMIRKS patterns to assign parameters. In order to automate force field development, the generation of these SMIRKS patterns must be done automatically. SMARTY and SMIRKY are able to generate SMARTS and SMIRKS with comparable chemical complexity to parm99/parm@Frosst and smirnoff99Frosst. These tools are a promising first step to determining chemical perception for general force fields without relying on human expertise. |
60c73f85ee301c7b01c78902 | 69 | While SMARTY and SMIRKY both show considerable promise, they both face challenges with the size of the combinatorial search problem, suggesting room for further improvement. The combinatorial problem becomes especially important for fragment types involving the most potential atoms and decoratorsangles and torsions. One step to improving performance could include a better optimization algorithm, such as simulated annealing. Here, however, the sampling problem is exacerbated by the fact that move proposals are not necessarily chemically sensible, so future work will need to make more reasonable chemical moves to improve efficiency. Before introducing a new optimization algorithm, the move set needs to be improved. Particularly, instead of using any SMARTS decorator, these tools should take advantage of basic chemistry. For example, no molecule will have a tetrahedral carbon with a double bond, so such a move should never be proposed. |
60c73f85ee301c7b01c78902 | 70 | Our ultimate goal is to move past comparisons to existing force fields and to develop new force fields which hopefully provide improved accuracy. While SMARTY and SMIRKY are both promising examples of tools which sample over chemical perception trees, our work here used them in the context of existing force fields. Longer-term, they will instead be used to help sample over chemical perception as well as force field parameters, since our real goal is to improve force fields. New scoring functions will be used to evaluate SMIRKS patterns and parameters in the SMIRNOFF format compared to experimental and/or quantum chemical reference data. These tools will allow the development of next generation force fields in a completely automated way. |
62544ac05b90092c0e0af962 | 0 | The reaction of unsaturated substrates with hydrogen gas enriched in the para spin isomer leads to products with a high degree of nuclear singlet spin order. This leads to greatly enhanced NMR signals, with important potential applications such as magnetic resonance imaging (MRI) of metabolic processes. Although parahydrogen-induced polarization has the advantage of being cheap, compact, and mobile, especially when performed in ultralow magnetic fields, efficiency is lost when more than a few protons are involved. This strongly restricts the range of compatible substances. We show that these difficulties may be overcome by a combination of deuteration with the application of a sinusoidally modulated longitudinal field as a well as a transverse rotating magnetic field. We demonstrate a six-fold enhancement in the 13 C hyperpolarization of [1-13 C, 2,3-d 2 ]-succinic acid, as compared with standard hyperpolarization methods, applied in the same ultralow field regime. |
62544ac05b90092c0e0af962 | 1 | Magnetic Resonance Imaging (MRI) represents a versatile, noninvasive diagnostic tool, but suffers from low sensitivity, due in part to the very low levels of equilibrium nuclear spin polarization. Very large (∼ 10 5 ) polarization enhancements are available by hyperpolarization techniques , leading to the possibility of imaging low-concentration metabolites, with important clinical applications . Hyperpolarization is particularly advantageous for 13 C-labelled substances, since 13 C nuclei often have relatively long relaxation times compared to the abundant protons, allowing the hyperpolarization effect to persist longer, as well as a large chemical shift range, facilitating compound-specific imaging. For example, hyperpolarization of 13 C-labelled metabolites such as pyruvate, fumarate and succinate (1,4-butanedioic acid, see figure ) allow monitoring of the tricarboxylic acid (TCA) cycle, exposing metabolic anomalies which are indicative of disorders such as cancer . |
62544ac05b90092c0e0af962 | 2 | Most applications of hyperpolarized compounds for in vivo metabolic imaging currently use the Dynamic Nuclear Polarization (DNP) technique, for which commercial apparatus exists . However, the DNP technique suffers from high capital and running costs, low throughput, large footprint and technical complexity. This has stimulated interest in compact, mobile and less expensive methods such as parahydrogeninduced polarization (PHIP) . Although less general than DNP, PHIP-based techniques do not require high magnetic fields or cryogenic equipment, and also have high potential throughput. |
62544ac05b90092c0e0af962 | 3 | Parahydrogen-induced polarization of a 13 C-labelled target substance is achieved by catalytic hydrogenation of a suitable precursor with para-enriched hydrogen gas (pH 2 ). The proton pairs in the reaction product acquire a high degree of nuclear singlet order. The non-magnetic nuclear singlet order is con- -succinic acid. The spin-spin couplings have been reported previously , except for those involving deuterium, which are estimated. The labile protons are ignored. |
62544ac05b90092c0e0af962 | 4 | The conversion of proton singlet order into 13 C magnetization is a crucial step. Methods exist for implementing this transformation either in the high magnetic field of an NMR magnet, or in low magnetic field. Low-field procedures are preferred for real-world applications, since they allow the use of relatively inexpensive, compact, and mobile equipment . Recently, purified solutions of highly polarized [1-13 C]-fumarate have been produced using a low magnetic field sweep for singletto-magnetization conversion . However, [1-13 C]-fumarate is a favourable case since it has a very simple spin system, containing only three coupled spins-1/2. |
62544ac05b90092c0e0af962 | 5 | The application of such procedures to more complex spin systems is problematic. Every additional spin doubles the spin dynamical complexity and decreases the transformation efficiency. For example, [1-13 C]-succinate contains 5 coupled spins-1/2, and has 4 times as many quantum states as [1-13 C]-fumarate. In general field-sweep methods perform poorly for multiple-spin systems, since it is hard to maintain control of the highly complex nuclear spin dynamics, especially through the multiple level crossings associated with field sweeps . |
62544ac05b90092c0e0af962 | 6 | The number of coupled protons may be reduced by selective chemical replacement of protons by deuterons. An example is shown for [1-13 C, 2,3-d 2 ]-succinic acid in figure . Although this leads to a beneficial simplification of the proton spin system, deuteration introduces problems in the context of ultralowfield NMR, where the spin-spin couplings are of the same order of magnitude as nuclear Larmor frequencies. In this regime, the rapid quadrupolar relaxation of the deuterium nuclei induces rapid decoherence of the entire spin system, resulting in substantial polarisation losses . Furthermore, singlettriplet mixing effects induced by heteronuclear couplings lead to further losses . Conventional heteronuclear decoupling is inapplicable in the ultralow-field regime, since the nuclear Larmor frequencies are not sufficiently distinct. In order to fully leverage parahydrogen-induced polarization in the microtesla regime, polarization transfer strategies are required that not only decouple disruptive deuterium nuclei, but also suppress singlet-triplet mixing effects, in the regime of ultralow magnetic fields. |
62544ac05b90092c0e0af962 | 7 | In this article we demonstrate efficient singlet-tomagnetization conversion in the microTesla regime, while simultaneously achieving deuterium decoupling and suppression of singlet-triplet mixing. This is done by applying two periodically modulated fields at the same time. The first field is a sinusoidally modulated longitudinal field, as in the recently described Weak Oscillating Low Field (WOLF) technique . The second field rotates in a plane perpendicular to the first, as in the recently described Singlet-Triplet Oscillations through Rotating Magnetic Fields (STORM) method . We show that the combination of these two fields achieves selective polarization transfer with suppression of deuterium-induced relaxation. We achieve a 13 C polarization of ≃6.1% for a 50 mM solution of [1-13 C, 2,3-d 2 ]-succinic acid, in the case of a modest parahydrogen enrichment level of 50%. This result is encouraging for the application of low-field parahydrogen-induced polarization to a wide range of deuterated molecular systems. |
62544ac05b90092c0e0af962 | 8 | To demonstrate the technique, 30 mg (0.25 mmol) of [1-13 C, 2,3-d 2 ]-fumaric acid (Sigma-Aldrich) and 18.1 mg (0.025 mmol) of the [Rh(dppb)(COD)]BF 4 catalyst were dissolved in methanol-d 4 (5 mL). 50%-para-enriched H 2 was prepared by passing hydrogen gas at a pressure of 10 bar over iron oxide at 77 K. Each experimental run started by transferring 250 µL of the stock solution to a high-pressure NMR tube and heating the sample to 75 ○ C in the ambient magnetic field of the laboratory (110 µT). The heated sample was transferred to a magnetically shielded chamber (three concentric walls of mu-metal, from Twinleaf LLC, USA) equipped with magnetic field coils. Paraenriched hydrogen gas was dissolved in the solution by bubbling. This initiated the catalytic hydrogenation of the [1-13 C, 2,3-d 2 ]fumaric acid precursor, generating the singlet-polarized target substance [1-13 C, 2,3-d 2 ]-succinic acid. As discussed below, several methods were evaluated for the conversion of the proton singlet order into hyperpolarized 13 C magnetization. Immediately after singlet-to-magnetization conversion, the level of 13 C polarization was assessed by rapidly inserting the sample into a conventional 9.41 T NMR magnet, followed by generation of the 13 C NMR spectrum by applying a single π/2 pulse and Fourier transformation of the free-induction decay. Further details of the experimental implementation are given in the supplementary information. |
62544ac05b90092c0e0af962 | 9 | Figure shows the three alternative protocols that were evaluated: (a) a conventional field-ramp procedure for magnetization-to-singlet transformation ; (b) a STORM procedure for the magnetization-to-singlet transformation, suppressing the effects of deuteron relaxation; (c) magnetization-tosinglet transformation by STORM, combined with suppression of singlet-triplet mixing during hydrogenation by simultaneous application of STORM and WOLF. |
62544ac05b90092c0e0af962 | 10 | Protocol (a) in figure uses a conventional field-ramp procedure for singlet-to-magnetization transfer . This was performed as follows: Para-enriched H 2 was bubbled through the solution for an interval of duration τ B , in the presence of a static bias field of 50 µT, in order to separate the Larmor frequencies of the different isotopes, helping preserve the proton singlet order. The magnetic field was then swept linearly from ≃0 µT to ≃1 µT over a duration τ T , to induce the singlet-tomagnetization transfer. As shown in table 1, experimental optimization of the bubbling time (τ B = 7 s) and the transfer time (τ T = 90 ms) resulted in a 13 C polarization of p = 0.98% ± 0.04% for the [1-13 C, 2,3-d 2 ]-succinic acid reaction product. A representative spectrum for protocol (a) is given in figure . The moderate level of 13 C polarization level is not surprising, since the conventional field-ramp protocol is subject to interference from both deuterium quadrupolar relaxation and singlet-triplet mixing. |
62544ac05b90092c0e0af962 | 11 | Protocol (b) in figure employs the rotating-field STORM technique for the polarization transfer. After bubbling with para-enriched H 2 , the transverse rotating STORM field was applied for a duration τ T in the presence of a longitudinal 6 µT bias field. The amplitude of the rotating STORM field was B STORM = 3.9 µT. The rotation frequency of the STORM field was ω STORM /2π =72.5 Hz. As discussed in the supplementary material, this choice of field parameters decouples the proton spins from the deuterium spins during the transfer step. Figure shows the resulting 13 C spectrum for an optimal STORM duration of τ T =100 ms. The final 13 C polarization was estimated to be p =1.70%±0.22%, which is significantly higher than that for protocol (a). Since the bubbling protocols are identical in procedures (a) and (b), we attribute the increase in the 13 C polarization level to the robustness of the STORM pulse with respect to interference from fast deuterium relaxation. |
62544ac05b90092c0e0af962 | 12 | Although the use of a rotating-field STORM suppresses the deleterious effects of deuteron relaxation during the singlet-tomagnetization transfer, the problem of singlet-to-triplet mixing remains. In the current context of very low magnetic fields, this mixing is caused by differences in the J-couplings of the two protons to heteronuclei such as 13 C and 2 H (see the coupling network in figure ). As a result of these couplings, proton singlet state is not a Hamiltonian eigenstate for the succinic acid product. Reaction of the fumaric acid precursor with para-hydrogen therefore initiates coherent oscillations of the spin density operator. Since the hydrogenation reaction is relatively slow, these |
62544ac05b90092c0e0af962 | 13 | Fig. Timing diagrams for (a) hydrogenation followed by a conventional field sweep for polarization transfer; (b) hydrogenation followed by polarization transfer using a STORM pulse; (c) hydrogenation under simultaneous WOLF+STORM fields, followed by polarization transfer using a STORM pulse. In (a) para-enriched hydrogen is bubbled through the sample for a duration τ B in the presence of a static bias field (B 0 ) along the laboratory frame z-axis. During the period τ T the field is linearly increased from 0 µT to a target value Bsweep. In (b) the linear field sweep is replaced by the application of a rotating magnetic field generated by two orthogonal transverse coils. The amplitude of the transverse rotating field is given by B STORM . In (c) the bubbling period is conducted under the simultaneous application of a small bias field B bias , a transverse rotating field of amplitude B STORM and an oscillating longitudinal field of amplitude B WOLF . The singlet-to-magnetization polarization transfer is initiated by turning off the longitudinal WOLF field, while retaining the rotating transverse STORM field. In all three cases, the sample is transferred to a high-field NMR apparatus immediately after the polarization transfer, followed by a π/2 pulse and signal acquisition on the 13 C channel. tests this hypothesis by applying simultaneous WOLF and STORM pulses during the hydrogenation interval, in order to suppress singlet-triplet mixing in the product molecules. At first this seems counter-intuitive, since a lone STORM pulse induces singlet-to-magnetization polarization transfer from the proton pair to the 13 C nucleus, as demonstrated in protocol (b). Such a process would be undesirable during the slow hydrogenation reaction, since the premature transfer of singlet order to 13 C magnetization would lead to a loss of spin order, when summed over all reacting molecules. However, as discussed in the supplementary material, the superposition of a resonant STORM pulse with a suitably chosen WOLF pulse suspends the polarization transfer until the hydrogenation is complete, while preserving the deuterium-decoupling properties of the STORM pulse, and also suppressing singlet-triplet mixing effects during hydrogenation. |
62544ac05b90092c0e0af962 | 14 | For the experimental implementation of protocol (c) we kept the STORM pulse parameters identical to protocol (b), but added a WOLF pulse with amplitude B WOLF = 20 µT and frequency ω WOLF /2π = 800 Hz during the hydrogenation interval. The WOLF pulse parameters were based on the analysis given in the supplementary information. The pH 2 bubbling period was optimized to τ B = 15 s for protocol (c). The resulting 13 C spectrum is shown in figure , which corresponds to a 13 C polarization of p =6.13%±0.07%. As highlighted in table 1, this represents a factor of 6 improvement over a conventional field sweep procedure. |
62544ac05b90092c0e0af962 | 15 | The molar polarization (product of polarization level and concentration) has been proposed as a more useful hyperpolarization metric than the polarization level alone . The molar polarization achieved in the current experiment is estimated to be 6.12% × (49 ± 1) mM = 3.00 ± 0.06 mM (see Supporting Information). Figure compares the observed 13 C-polarization as a function of bubbling time τ B , for protocols (b) and (c). Since these protocols use the same singlet-to-magnetization conversion procedures, differences in performance may be attributed to the chemical and spin dynamics during the hydrogenation. The markers represent experimental data, whereas the solid curves represent numerical simulations. For protocol (b), which has no special intervention during the hydrogenation, the 13 C-polarization quickly reaches a plateau at a relatively low level. For the WOLF+STORM approach (protocol (c)) the build-up of 13 C- polarization continues to longer times with a plateau reached at τ B = 15 s. No significant reduction in 13 C-polarization was observed even beyond 20 seconds of bubbling. These data support the hypothesis that the simultaneous WOLF+STORM fields suppress singlet-triplet mixing during hydrogenation. The solid lines in figure show simulations derived by a Monte-Carlo procedure which combined many spin dynamical trajectories initiated at random times, according to a statistical model of the chemical kinetics. Details are given in the Supporting Information. An acceptable match between experiment and simulation is attained for both protocols (b) and (c), assuming an effective hydrogenation rate constant given by k eff = 0.05 ± 0.01 s -1 and a singlet order decay time constant T S of at least 60 seconds. This indicates that singlet spin order accumulates on the proton pair during the hydrogenation under WOLF+STORM irradiation. |
62544ac05b90092c0e0af962 | 16 | To summarize, we have demonstrated that it is possible to hyperpolarize the 13 C nuclei of isotopically labelled succinate using a compact, low-cost apparatus which exploits para-enriched hydrogen gas, a cheap and readily available substance. The achieved level of ∼ 6% 13 C-polarization could readily be increased to ∼ 18% by using pure para-H 2 gas. This polarization level is competitive with dissolution-DNP procedures but is achieved far more rapidly and with much less cost. This suggests the feasibility of this method for producing hyperpolarized 13 C- succinate for metabolic imaging applications. Further improvements in the yield and throughput are likely to be possible, for example by operation at higher pressure and temperature . |
62544ac05b90092c0e0af962 | 17 | We anticipate that this proof-of-concept experiment should open up the technique of ultralow-field parahydrogen-induced polarization to a much wider range of compounds than is currently accessible. Related hyperpolarization techniques such as side-arm hydrogenation are also likely to benefit, allowing the use of deuteration to simplify the spin systems and improve spin-dynamical efficiency, while avoiding the problems associated with rapid deuterium relaxation. |
6388eb71836cebd8f26f1b02 | 0 | Metal organic frameworks (MOFs) are hybrid and crystalline materials composed of metal centers connected by organic ligands. The resulting 3D frameworks exhibit ultrahigh porosity and large surface areas that can be modulated for specific applications due to the wide availability of metalligand combinations. For this reason, MOFs have been extensively studied for applications in many different fields of science such as catalysis, drug delivery or gas adsorption, separation, 8,9 sensing 4,10-12 and storage, among others. One of the applications that has attracted the most attention in recent years is the capture of polluting gases emitted from anthropogenic sources. Special attention has been paid to carbon dioxide due to its strong impact on the greenhouse effect. Other gases, like carbon monoxide, can also play an important role in climate change and the development of capture strategies is interesting not just for environmental concerns but also for the possibility of reusing them in other industrial chemical processes. Hofmann-like clathrates with general formula Fe(pz)[M(CN)4] (pz = pyrazine, M = Ni, Pd, Pt) are a versatile class of MOFs with octahedrally coordinated Fe(II) centers connected by cyanide ligands, CN -, to a square-planar openmetal site, M(II). The resulting Fe[M II (CN)4]∞ layers are pillared by bidentated aromatic ligands resulting in threedimensional networks. These materials are interesting for gas capture applications due to the combination of openmetal M(II) sites and bistable Fe(II) spin-crossover centers. These can undergo a spin-state switch under the influence of external stimuli such as temperature, pressure, light or incorporation of guest molecules. The presence of unsaturated metal centers can, potentially, enhance the adsorption capacity, whereas their bistability can be used for sensing applications. Several studies of gas adsorption have been published since their discovery in 2001, including the interplay between spin-crossover and guest molecules. Recently, the member of the series Fe(pz)[M(CN)4] with M = Pt(II) has shown a significant higher CO2 and CO uptake capacities compared to other MOFs with larger surface areas. In this work, we focus our interest in these Hofmann-like clathrates upon CO2 and CO loading. We report a detailed study of gas adsorption mechanism of CO and CO2 in Fe(pz)[Pt(CN)4] in the low-spin state by means of neutron scattering techniques and density-functional theory calculations. We identified the two adsorption sites, on top of the open-metal site and between the pyrazine rings, and the most stable orientational configuration of the guest molecules and the pyrazine ligands of the framework was determined. The inelastic neutron scattering results assisted by DFT calculations, show signatures of a hindrance of the pyrazine libration and the out-of-plane movement of cyanide ligands when the gas is adsorbed. Together with the computed binding energy and a molecular orbital analysis, these results agree with a physisorption mechanism for both gases. |
6388eb71836cebd8f26f1b02 | 1 | Neutron experiments were performed in the high-intensity two-axis diffractometer D20 installed on the hot neutron source of the high-flux reactor at the Institut-Laue Langevin (ILL) in Grenoble, France. A wavelength of 1.54 Å was used. The empty and gas-loaded samples were measured at 100 K. Rietveld refinements and calculations of the structures were performed using the FullProf suite of programs. The schematic illustrations of the crystal structures and magnetic arrangements were obtained with the VESTA program. Inelastic Neutron Scattering. Inelastic neutron scattering experiments were performed in the indirect geometrytype spectrometer IN1-LAGRANGE installed on the hot neutron source of the high-flux reactor at the Institut Laue Langevin (ILL) in Grenoble, France. Monochromators of Si(111), Si(311) and Cu(220) were selected to collect the data for energy transfers of [8-129], [92-215] and [173-427] cm -1 , respectively. The measurements were done at 30 K for both the empty and loaded materials. A post-processing treatment of normalization to monitor counts and subtraction of the empty sample holder was done using LAMP. Gas adsorption The powder samples were placed inside a cylindrical aluminium sample holder connected to a sample stick adapted for gas adsorption. A manifold gas pumping system was attached to the stick through a capillary and the temperature control was achieved using either a closed-cycle cryostat (IN1-LAGRANGE) or an Orange cryostat (D20). The samples were loaded to saturation by initially injecting the gas doses at room temperature and then lowering the temperature of the sample holder (to 100 K for CO and 200 K for CO2), creating a cold point to force the gas to move towards the sample and facilitate the adsorption. For CO2, the saturation loading is about 1.5 mol of CO2 per Fe mol, as determined experimentally from adsorption isotherms. In the absence, to the best of our knowledge, of published absorption isotherms for CO, we estimate the saturation loading at about 2 CO mol / Fe mol from the kinetic uptake experiments reported by Ibarra et al. Our ND, DFT and INS results are consistent with these saturation loading values (vide infra). |
6388eb71836cebd8f26f1b02 | 2 | Computational details. The DFT calculations were performed with the Quantum Espresso package (v 6.4) within the generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof (PBE) and long-range interactions described with the semiempirical approach proposed by Grimme (PBE+D2). We use the Rappe-Rabe-Kaxiras-Joannopoulos ultrasoft (rrkjus) pseudopotentials without semicore states in valence. The convergence threshold on forces is 0.0001 Ry/Bohr and the wavefunctions and charge density cutoffs are set to 100 and 1000 Ry, respectively. All the calculations are performed using the low-spin (S = 0) electronic configuration for the Fe(II) atoms. The Brioullin zone is sampled using a 3 × 3 × 3 Monkhorst-Pack k-point grid. The Becke-Johnson (BJ) damping scheme together with the D3 Grimme approach (PBE+D3+BJ) was also used to perform a Barder charge analysis in the loaded MOFs. The same pseudopotentials, force thresholds, Monkhorst-Pack k-point grid, wavefunctions and charge density cutoffs than for PBE+D2 were used for this functional. |
6388eb71836cebd8f26f1b02 | 3 | where G(ω) is the generalized phonon density of states defined elsewhere, 48 M = l M l /N, n is the thermalequilibrium occupation number of the vibrational state and < n + 1 >= exp exp(ℏωβ)-1 with β = 1 K B T . The exponential term is the Debye-Waller factor for neutron attenuation by thermal motion and ω the phonon frequencies obtained by employing the ph.x package in Quantum Espresso. Q corresponds to kinematical range of IN1-LAGRANGE. A convolution with a Gaussian function is also applied to account for the resolution of the monochromators with a standard deviation of 3.0 cm -1 for the range [0 -478] cm -1 and around 0.01ω for [478 -4033] cm -1 , close to the experimental resolution of IN1-LAGRANGE which is 0.02-0.03ω. Orientation of the pyrazines. The orientational configuration of the pyrazine rings depends on the nature and amount of the guest molecules incorporated in the material. Recently, the present authors reported an ordered structure for the empty Hofmann clathrate Fe(pz)[Pt(CN)4] with the pyrazine ligands oriented in a perpendicular configuration. The ordered structure is found below the spin-transition temperature (ca. 285 K), whereas at higher temperature the Fe(II) atoms switch to HS and the pyrazines display a dynamic disorder. In presence of adsorbed molecules, the orientation of the pyrazines can remain perpendicular or change to a parallel configuration as reported for water, depending on the type and amount of adsorbed gas. To study this, we have collected diffraction data on the deuterated homologue, taking advantage of the sensitivity of this technique to the deuterium position and consequently to the pyrazine orientation. The different configurations where explored also by DFT calculations by studying an increasing number of adsorbed CO and CO2 molecules: 1, 1.5, and 2 molecules per formula unit (f.u.) both in the parallel and the perpendicular configuration of the pyrazines. To accomodate the perpendicular configuration, a supercell with lattice parameters a ′ = √ 2a and b ′ = √ 2b is used, where a and b are the lattice parameters of the primitive cell. The PBE+D2 lattice parameters of the bare MOF are a = 10.096 Å, b = 10.097 Å, and c = 6.711 Å. |
6388eb71836cebd8f26f1b02 | 4 | Neutron diffraction We used neutron diffraction data collected on gas-loaded Fe(d4-pz)[Pt(CN)4] to get insight into the configuration of the pyrazine moieties. The absence of the peaks characteristic of a perpendicular configuration (Figure ) is a strong indication to discard this possibility. Additionally, some peaks related to the parallel configuration show an increase (although this could be also in part correlated with the presence of gas molecules in the structure). Therefore we used the parallel configuration as starting model, which is consistent with DFT calculations (see below). In subsequent refinements, some disorder was allowed between the possible positions of the pyrazine. The residual scattering density obtained when the initial model of the bare Fe(pyrazine)[Pt(CN)4] with parallel pyrazines is compared to the experimental neutron diffraction pattern of the gas-loaded compounds (see Figure for the case of CO) allows us to distinguish two bonding sites for the guest molecules: (i) On top of the open-metal site (site A) and (ii) between the pyrazine rings (site B). The higher density is found in site A, which is an indication of a preference for this site. The residual density observed, located mainly in the z = 0 plane, is indicative of a position of the gas molecules in parallel to the Pt[CN]4 plane. The guest molecules were then incorporated to the model. Initially, these molecules were placed disordered in two perpendicular positions (see Figure ), and 2 and 1.5 molecules per f.u. were considered for CO and CO2, respectively (with site A always fully occupied, since it shows a significantly higher residual density). With this model, the disorder of the pyrazine rings between their two possible positions was estimated by a fit to the gas-loaded Fe(d4-pz)[Pt(CN)4] patterns, with refined values of 35(2) and 30(3) % for CO and CO2, respectively. This disorder was then fixed in the ensuing refinements. Finally, constrained fits (due to the quality of the data and the number of parameters) of the gasloaded Fe(pyrazine)[Pt(CN)4] patterns (see details in the SI) yielded the structural models presented in Figure . The structures present a slight monoclinic distorsion (of ca. 0.5 • in γ for both CO and CO2) , in agreement with DFT results (vide infra). The ordering of the pyrazine rings in a pref-erentially parallel configuration implies the existence of two non-equivalent B sites, one with more space available than the other. Attempts to introduce gas molecules in the site with less available space produced worse fits. A total occupancy of 2 CO molecules per f.u. gave the best agreement for the CO-loaded material, with both A and B sites fully occupied. |
6388eb71836cebd8f26f1b02 | 5 | For CO2, the best fits are obtained with a total occupancy of 1.69(6) CO2 molecules per f.u. (the A site was considered fully occupied while the occupancy of guest molecules in the B site was allowed to vary). The refinement of the disorder among the possible orientations of the guest molecules allowed by the proposed model did not give significant improvement of the fits, thus the disordered configurations were retained. |
6388eb71836cebd8f26f1b02 | 6 | Predicted geometry DFT calculations are used to resolve the most stable configuration in the ground state. For CO, we find a perpendicular orientation of the pyrazines upon adsorption of 1 molecule per f.u. while for 1.5 and 2 CO per f.u. a parallel orientation is predicted. The energy differences between the two configurations are 0.029 eV, 0.007 eV, and 0.119 eV, respectively, per formula unit. Therefore, for the predicted saturation loading of 2 CO per f.u., the parallel orientation of the pyrazine ring is the most stable. This is consistent with the neutron diffraction patterns of CO-loaded Fe(d4-pz)[Pt(CN)4]. For 1.5 and 2 CO per f.u., the two binding sites obtained in our calculations agree with neutron diffraction: on-top of the open-metal site (site A), and between the pyrazine rings (site B). The occupancy of site B is 0.5 for 1.5 CO per f.u. and 1.0 for 2 CO per f.u. The A site is always fully occupied. The CO molecules are oriented perpendicular to the pyrazine planes and parallel to the Pt[CN]4 plane (see Figure ), regardless of the amount of gas. The unit cell presents a monoclinic distortion (γ = 89.55 • ), in agreement with the neutron diffraction results. In the case of CO2, the orientation of the pyrazines is parallel for 1 and 1.5 CO2 per f.u. with a corresponding energy difference between parallel and perpendicular of 0.016 and 0.036 eV per f.u., respectively. Only the parallel configuration could be converged for 2 molecules suggesting that large interatomic forces could prevent a perpendicular configuration in this case. For a loading of 1 CO2 per f.u. the molecules are located only on site A and are perpendicular to the pyrazine planes. When 1.5 and 2 molecules per f.u. are considered, CO2 locates in both sites A and B. The molecules in site A are again perpendicular to the pyrazine planes, while the molecules in site B are almost parallel to the pyrazine planes and perpendicular to the neighbouring CO2 (Figure ). While molecules in site B are parallel to the Pt(CN)4 plane for a loading of 1.5 CO2, for a 2 molecule-loading, the CO2 the are tilted off-plane. In the first case, the molecules on-top of the platinum in site A move slightly off the metal position (see Figure ). Also in this case, the structure is monoclinically distorted (γ = 89.51 • ), consistent with the neutron diffraction results. Amount of gas adsorbed. Neutron diffraction on the deuterated compound suggests that most of the pyrazines are in parallel orientation for both the CO-and CO2-loaded materials. DFT confirms that this configuration only occurs when 1.5 or 2 molecules of CO are adsorbed per openmetal-site. Therefore, we can deduce that more than one molecule has been adsorbed. Since adsorption isotherms are not available for CO, we estimate the saturation loading at about 2 CO mol / Fe mol from kinetic uptake experiments which are in agreement with our neutron diffraction results. The combination of INS and DFT calculations is consistent with this loading value. In the case of CO2, a parallel configuration is predicted by DFT for all the loading values considered. We have retained the value of 1.5 molecules per f.u. in our calculations, which is consistent with the saturation loading for CO2 determined experimentally from adsorption isotherms (about 1.5 mol of CO2 per Fe mol ), and with the refined value of ca. 1.7 obtained |
6388eb71836cebd8f26f1b02 | 7 | The experimental spectra for the empty MOF and upon CO and CO2 adsorption are shown in Figure (upper panel) together with scattering function computed using eq. 1 panel). For the bare material the pyrazines are considered perpendicular in agreement with previous calculations and experimental findings. The scattering function upon CO adsorption in Figure is computed by adopting the configuration described in the previous section with 2 molecules per f.u. and pyrazines in a parallel orientation. For CO2, we consider 1.5 molecules per f.u. and a parallel orientation of the pyrazines. |
6388eb71836cebd8f26f1b02 | 8 | The experimental errors are reported in Figure and Figure upon CO and CO2 adsorption, respectively. Data were collected up to 427 cm -1 . The measurements below 100 cm -1 are not optimized at IN1 and no clear peaks are observed in this region. We note that at low energy the assignation of the vibrational modes from the calculations is more challenging compared to higher energy (see for example the intense peak at 100 cm -1 as compared to that at 400 cm -1 ). While at around 400 cm -1 a good agreement between experiment and DFT is found, low energy modes present larger relative errors possibly due to the underlying approximations (basis set and functional choice may affect this part of the spectra). |
6388eb71836cebd8f26f1b02 | 9 | At higher energies (not reported here), the vibrational modes of the pyrazine [700-1500] cm -1 and cyanide stretching modes [2100-2200] cm -1 which appear with intense and well-defined peaks, were found to undergo negligible changes upon SO2 adsorption. The experimental data show two well defined peaks for the bare MOF centered at ca. 96 and 396 cm -1 and less resolved peaks between them. The first peak at 96 cm -1 blueshifts and becomes broader and less intense upon CO and CO2 adsorption. It blueshifts to 133 cm -1 for CO and to ca. 116 cm -1 for CO2. The second peak at 396 cm -1 redshifts upon CO adsorption while it is negligibly affected by the CO2 uptake. |
6388eb71836cebd8f26f1b02 | 10 | To assist the analysis of the inelastic scattering data, we compute the partial G(ω) for each atom or group of atoms in the case of CO and CO2 adsorption (see Figure ). The distribution of the specific contributions to the total G(ω) is similar in the two cases, and to the case of SO2 . Below 100 cm -1 the spectra are dominated by vibrations of the heavy atoms, Fe and Pt, with the Pt being the dominant one. A minor contribution from the pyrazines and cyanides can be observed as well, together with the vibrational modes of CO or CO2 (mainly rotational or translational modes). For the intense peak which is found in the experiment at ca. 96 cm -1 and predicted around 150 cm -1 , the main contributions arise from the pyrazine, cyanides and the Pt atoms. In the region [100-400] cm -1 we find vibrations from all the atoms. In this region, Felix et al. identified the characteristic Fe-Npz and Fe-NCN stretching modes using Raman and nuclear inelastic scattering for Fe(pz)[Ni(CN)4] at 306 and 381 cm -1 , respectively. We identified these modes upon CO adsorption at 311.3 and 318.0 cm -1 for Fe-Npz stretching and at 374.7 and 386.4 cm -1 for Fe-NCN. For CO2, Fe-Npz stretchings appear at 309.25 and 320.11 cm -1 and Fe-NCN stretchings at 387.97 and 375.16 cm -1 . Finally, the peaks at 400 cm -1 have a strong contribution from the pyrazines and a smaller contribution from CN and Pt. |
6388eb71836cebd8f26f1b02 | 11 | Signature at 100 cm -1 . Upon CO and CO2 adsorption, the peak at 96 cm -1 blue-shifts giving rise to a broader and less intense peak. The gas adsorption results in a larger shift for CO (37 cm -1 ) than CO2 (20 cm -1 ) and the previously studied SO2 molecule (29 cm -1 , see ref. 48). This is well reproduced by the computed S(ω) (see Fig 6). In this region, the calculations predict two peaks centered at ca. 107 cm -1 and 138 cm -1 for the bare MOF. The first one corresponds to a libration of the pyrazine ligand around the z-axis, while the second, named A in Figure , contains three vibrational modes: (i) a collective mode involving in-plane and out-ofplane movements of the CN groups and a libration of the pyrazine around the z-axis at 137.8 cm -1 , (ii) a rigid out-ofplane twisting of the Fe(CN)4N2 octahedra at 138.5 cm -1 and (iii) an out-of-plane vibration of the cyanide together with a small libration of the pyrazine at 139.2 cm -1 . The first peak at 107.9 cm -1 blue-shifts to 134.3 cm -1 (under peak A ′ ) upon CO adsorption and to 116.6 cm -1 (under peak A ′′ ) upon CO2 adsorption. In the new mode, the initial pyrazine libration is coupled with a libration of the CO and with a small translation of the CO2, respectively. The shift is substantially larger for CO. We attribute the blue-shift to the hindered rotation of the pyrazines. As shown in more detail in the next section, this mode is the most sensitive to both the amount of adsorbed gas and the type of molecule. The band A ′ that arises upon CO adsorption includes two additional modes at 131.0 and 135.1 cm -1 . The first one results from a pure libration of the CO. The second one is the result of the red-shift of the mode located at 137.8 cm -1 in peak A, i.e. mode (i) described above. A similar situation is found for CO2: the mode at 137.8 cm -1 under peak A red-shifts to 130.9 cm -1 , under peak A ′′′ . Because the shift of the mode at 107 cm -1 is significantly smaller for CO2 (9.6 cm -1 ) than for CO (27.4 cm -1 ), two separate peaks (A ′′ and A ′′′ ) are observed for CO2 and one for CO (peak A ′ ). The peak A ′′ includes as well two additional translational modes of CO2 at 122.5 and 114.4 cm -1 . The other two vibrational modes under peak A, i.e. (ii) 138.5 and (iii) 139.2 cm -1 , undergo a blueshift to 146.6 (142.3) and 151.5 cm -1 (141.3), upon CO adsorption (CO2), respectively, resulting in peak B ′ (B ′′ ). For these modes, a larger blueshift is found for CO (8 and 12.3 cm -1 ) than CO2 (3.8 and 2.1 cm -1 ). This blue-shift can be attributed to the increase in the cyanide out-of-plane bending force constant due to steric hindrance. For the bare MOF, the two vibrational modes under peak B, at 147.9 and 152.2 cm -1 , correspond to an in-plane movement of the Pt atoms together with a rigid back-and-forth movement of the pyrazines and Fe atom. Upon CO adsorption, we observe a small blue-shift to 148.1 and 154.4 cm -1 , respectively, (peaks B ′ and C ′ ). In the case of CO2, the first red-shifts by 0.8 cm -1 (peak B ′′ ) and the second blue-shifts by 0.7 cm -1 (beginning of peak C ′′ ). Finally, under peak C, two vibrational modes are found at 159.7 and 161.2 cm -1 for the bare MOF. These are similar to the modes of peak B but in this case the rigid displacement of the pyrazine together with the Fe atoms occurs in-plane. A shift to lower energies is found upon CO (CO2) adsorption from 159.7 to 156.7 (156.5) cm -1 and from 161.2 to 157.5 (159.6) cm -1 under peak C ′ (C ′′ ). In the case of CO adsorption, a new vibrational mode located at 160.9 is found under peak C ′ . This corresponds to a collective mode consisting of a libra-tion of the pyrazines and the CO and an in-plane movement of the Pt. |
6388eb71836cebd8f26f1b02 | 12 | Signature at 400 cm -1 . The intense peak centered at 396 cm -1 in the experiment undergoes a red-shift to 383 cm -1 and a small decrease in intensity upon CO adsorption, while no significant change is found upon CO2 adsorption. In this region, the computed S(ω) for the bare MOF predicts an intense peak at ca. 400 cm -1 , named D, and a smaller peak at ca. 411 cm -1 . Upon CO adsorption, peak D shifts to lower energy and splits into peak D ′ at 385 cm -1 and D ′′ at 396 cm -1 (see Figure ). For CO2, the computed S(ω) exhibits a single peak, named D ′′′ , located almost at the same position as D (ca. 399 cm -1 ). For both molecules, we see a small peak centered at around 413 cm -1 which moves negligibly with respect to the bare material. |
6388eb71836cebd8f26f1b02 | 13 | For the bare MOF, peak D is a combination of seven vibrational modes (400.0, 400.3, 400.4, 400.4, 400.9, 403.6 and 405.0 cm -1 ). Two of these, at 403.6 and 405.0 cm -1 , dominate the intensity of the S(ω) and are associated with a torsion of the pyrazines. With CO, they undergo a red-shift by 18.4 and 8.7 cm -1 , giving rise to peak D ′ at 385.1 cm -1 and peak D ′′ at 396.3 cm -1 , respectively. For CO2 the associated red-shift is smaller (7.0 and 6.4 cm -1 ) and gives rise to peak D ′′′ (two modes at 396.6 and 398.6 cm -1 ). This result differs from the case of SO2 adsorption where the two modes are almost unchanged. The intensity of the other five modes under peak D is a factor of two lower and only two of them (400.0 and 400.3 cm -1 ) undergo a noticeable shift upon gas adsorption. These involve large displacements of the two Fe atoms and result in tilting and distortion of the octahedra together with an in-plane movement of the Pt atoms. Upon CO (CO2) adsorption, the first blue-shifts by 7.5 (8.6) cm -1 from 400.0 to 407.5 (408.5) cm -1 and falls under peak D ′′ (D ′′′ ). The second one red-shifts by 13.6 (12.3) cm -1 from 400. and between 362 and 425 cm -1 (right panel). The spectra of the empty Fe(pz)[Pt(CN) 4 ] (black) and after CO (red) and CO 2 (green) adsorption are reported. The computed S(ω) is reported in the middle (for bare and CO) and lower panels (bare and CO 2 ). For a better visualization, the vertical lines represent the normal mode frequencies ω with intensity S(ω) and no convolution with the Gaussian function. |
6388eb71836cebd8f26f1b02 | 14 | D ′ (D ′′′ ). The two remaining modes at 400.4 cm -1 under peak D are out-of-plane movements of CN groups which are anti-symmetric with respect to the Fe atom and result in a rigid movement of the Fe(N)4 planar complex. They undergo a small blue-shift to 401.1 and 401.8 cm -1 for CO and 401.1 and 401.4 cm -1 for CO2, respectively. Finally, the vibrational mode at 400.9 cm -1 consists of distortions of the two octahedra resulting primarily from the movement of the Fe atoms which are almost unchanged after adsorption (400.1 cm -1 for CO and 399.9 cm -1 for CO2). |
6388eb71836cebd8f26f1b02 | 15 | Effect of amount of adsorbed gas on the spectral features. In Figure we show a comparison of the computed G(ω) for 1, 1.5 and 2 CO adsorbed molecules with the experimental INS data (see Figure ). In the presence of a single molecule, it can be observed that neither of the two characteristic signatures of occurs. The peaks at around 108, 138 and 400 cm -1 do not undergo any displacement, whereas in the other two cases, both peaks are shifted upon adsorption. We performed a similar comparison for 1 and 1.5 CO2 molecules adsorbed per f.u. (see Figure ). In an attempt to differentiate the steric effect from the nature of the binding, we report the shift of the 6 most characteristic and intense modes as a function of the volume occupied by the adsorbed molecules. The computed van der Waals volume is considered in each case. Specifically, we report the shift upon adsorption for the mode at 107.9 cm -1 (upper panel), for the three modes under peak A (middle panel) and for the two modes dominating the intensity of peak D (lower panel) in Figure . |
6388eb71836cebd8f26f1b02 | 16 | The energy of mode at 107.9 cm -1 exhibits the strongest dependence on the occupied volume upon adsorption, reaching a maximum displacement of 27 cm -1 when 2 CO per f.u. are adsorbed. Interestingly, when 1 SO2 (point c, 23.8 cm 3 /mol) and 1.5 CO per f.u. (point d, 24.2 cm 3 /mol) are considered, the displacement of this mode differs considerably by 9.7 cm -1 even though the occupied volume is similar in the two cases. This indicates a dependence not only on the volume but also on the nature of the gas and the associated interactions established within the cavity. For the three modes under peak A (137.8, 138.5 and 139.2 cm -1 ) we find overall a smaller shift upon adsorption and the correlation between energy shift and occupied volume is weaker, in particular for the mode at 137.8 -1 (black data) which exhibits the weakest correlation with the gas volume. |
6388eb71836cebd8f26f1b02 | 17 | 1.5 CO / f.u. ). In the case of CO2 on top of the metal site, we find no mixing of the metal-molecule orbitals, as expected from an electrostatic/dispersion interaction (see PDOS in Figure ). The strength of the π-acceptor interaction was computed by performing a Bader charge analysis using PAW pseudopotentials and the PBE+D3+BJ functional. For the CO on site A, the analysis revealed a small charge transfer from the MOF to the molecule of 0.05 electrons, confirming a . Energy shift with respect to the bare material of the 6 most characteristic modes plotted versus the van der Waals volume occupied by the guest molecules. We report the mode at 107.9 cm-1 (purple data, upper panel), 137.8 (black), 138.5 (light blue), and 139.2 cm -1 (orange, middle panel), 403.6 (green) and 405.0 cm -1 (red, lower panel). The points in the abscissa correspond to a=16.2 (1 CO/f.u.), b=20.2 (1 CO 2 /f.u.), c=23.8 (1 SO 2 / f.u.), d=24.2 (1.5 CO/f.u.), e=30.3 (1.5 CO 2 / f.u.), and f=32.4 (2 CO/f.u.) cm 3 /mol. |
6388eb71836cebd8f26f1b02 | 18 | For CO, the metal-ligand charge transfer causes a decrease of the C-O bond order due to the antibonding character of the π * -LUMO orbitals. This is confirmed by the C-O bond distances being always larger for the CO adsorbed on site A (1.142 Å) than in site B (1.139 Å). The longer C-O bond distances can cause a red-shift of the stretching CO frequency with respect to the free CO. The stronger the backbond-ing, the weaker the C-O bond and the lower the stretching frequency. The computed C-O stretching frequency for gas phase CO appears at approx. 2123 cm -1 while upon adsorption on site A it is around 2092 cm -1 . The typical red-shift for a strong backbonding interaction is normally more than 100 cm -1 , e.g. the experimental shift for Cr(CO)6 is of ca. 143 cm -1 . As expected, the stretching frequencies of the CO located between the pyrazines remain unchanged upon adsorption consistent with the absence of backbonding. In the case of CO2, a backbonding interaction would increase the O-C-O bond distances due to the antibonding character of the π * -LUMO orbitals, resulting in lower stretching frequencies. Here, the O-C-O distances remain almost unchanged with respect to the free CO2 (1.172 Å versus 1.174 Å) and the symmetric and antisymmetric stretching frequencies shift by less than 10 cm -1 . |
6388eb71836cebd8f26f1b02 | 19 | The predicted binding energies for CO and CO2 using PBE+D2 are 0.277 and 0.435 eV, respectively. These decrease to 0.029 and 0.002 eV when the PBE functional is used without the Grimme correction, indicating that van der Waals interactions are dominating the binding in both cases. In order to further assess the role of the open metal site in the binding mechanism, we computed the binding energy of CO and CO2 adsorbed between two [Pt(CN)4] planes (representing site A) and between two pyrazines (representing site B) and removing the rest of the framework. This is done by fixing the atomic coordinates to the relaxed geometry in the MOF and by removing the pyrazine ligands and the planes respectively. We imposed cell parameters of a=b=c= 20 Å in both cases to avoid interactions between periodic images. We employed PBE+D2 for this comparison. For CO, the computed binding energies are 0.190 and 0.088 eV for the molecule adsorbed respectively on pseudo-site A and B. For CO2 these are 0.256 and 0.142 eV, respectively. This comparison indicates a stronger contribution of the [Pt(CN)4] plane to the binding energy. This is different for SO2, where a larger decrease in binding energy (by 64.4 %) was predicted (see table ) than for CO (31.4 %) and CO2 (41.1 %) when comparing the full MOF and the [Pt(CN)4] fragments. |
6388eb71836cebd8f26f1b02 | 20 | By combining neutron scattering data and DFT calculations we determine the gas adsorption sites and fully characterize the adsorption mechanism of CO and CO2 in the Fe(pz)[Pt(CN)4] Hofmann-type clathrate. When the MOF adsorbs 2 CO molecules per f.u. these orient parallel with each other and parallel to the Fe[Pt(CN)4]∞ but perpendicular with respect to the pyrazine rings. In contrast, when the uptake is 1.5 CO2 per f.u., the molecules adsorbed on top of the open-metal cation (site A) orient perpendicular to the pyrazines, while the molecule in the center of the pore (site B) are pseudo-parallel resulting in 'T'-shape configuration of neighbouring CO2. In both cases the guest molecules are parallel to Fe[Pt(CN)4]∞ planes. The main signatures of the INS spectra upon adsorption of 2 CO and 1.5 CO2 per f.u. occur in the peaks located at ca. 100 cm -1 and 400 cm -1 . The first blue-shifts upon CO and CO2 adsorption, with a larger shift for CO, while the second red-shifts only in the presence of CO. DFT calculations confirm these signatures and allow us to characterize the blue-shift as due to a hindered libration of the pyrazine and the out-of-plane movement of cyanide ligands when the gas is adsorbed. The red-shift of the peak at 400 cm -1 is caused by the steric effect of the guest when the pyrazines display a torsion movement. The DFT-predicted energy of the modes yielding the most intense INS features is studied with respect to the pore volume occupied upon adsorption by different amounts and types of gas. The predicted shift of these modes shows that those at ca. 107.9 and 403.6 cm -1 are the most sensitive upon volume and the nature of the gas. Consistent with a fully occupied d z 2 orbital of the Pt(II) that prevents a molecule/metal σ-donor/-acceptor interaction, the adsorption mechanism in both cases is of electrostatic and van der Waals nature (physisorption) with the latter dominating the binding. A weak backbonding metal-to-ligand charge transfer is predicted for the CO located on site A while no charge transfer was predicted for CO2. In conclusion, this work reports the gas adsorption mechanism of CO and CO2 in the Hofmann-like clathrate Fe(pz)[Pt(CN)4] for which large adsorption capacities were previously reported when compared to other MOFs with larger surface areas. We have made use of the information obtained from neutron diffraction, inelastic neutron scattering and density-functional theory calculations in a complementary way. The results suggest that only a few modes depend on the nature of the adsorbed gas and, although the use of these modes as a reference to selectively detect one gas over the other seems complicated, the experimental signatures are clearly different when the saturation points are reached. |
60c743b6469df4007bf43256 | 0 | Molecular mechanics (MM) force fields for biomolecular simulations have been under continuous development for many years. In traditional transferable force fields, every atom in a molecule is assigned a type based on its atomic number, bonding and local chemical environment. The atom type then dictates the parameters that are used to model that atom's interactions. The force field parameters for each atom type are stored as a library, which is built by carefully reproducing the experimental or quantum mechanical properties of a benchmark set of small molecules. Due to the infeasibility of accurately parameterizing all of chemical space, a balance must be made between the size of the library and potential inaccuracy due to transferring parameters to molecules outside the fitting set. In many cases, it is acknowledged that transferable force fields are not sufficiently accurate. When building force fields for small molecules, the atomic charges are usually assigned in a system-specific or "bespoke" manner, using methods such as RESP, CM1, or AM1-BCC. This is because it is well-known that atomic charges polarize in response to their chemical environment (for example, the presence of electron donating or withdrawing groups). Bespoke charges are usually assumed to be compatible with the fixed Lennard-Jones parameters of the force field, although these themselves have also been shown to be dependent on the local environment of the atom. Although proteins must also experience polarization effects in both the charges and Lennard-Jones parameters, protein force field parameters have always, to date, been assigned from a transferable library. This leads to an inconsistency in the parametrization strategy used for protein force fields and bespoke small molecule force fields. This is potentially problematic when studying properties that depend on the electrostatic potentials of proteins, such as their interactions with small molecules, and there is no clear way around this using traditional force field fitting methods. |
60c743b6469df4007bf43256 | 1 | To improve the consistency between charge and Lennard-Jones parameters, and also reduce the reliance on fitting to experimental data, one could either directly fit non-bonded MM parameters to reproduce quantum mechanical (QM) energies and forces, or derive the non-bonded parameters of the force field directly from QM. In the latter approach, the QM interaction energy may be broken down into physically motivated components using intermolecular perturbation theory, though these methods are limited to quite small system sizes. Encouragingly, Grimme's quantum mechanically derived force field (QMDFF) method is capable of outputting bespoke non-bonded force field parameters for molecules comprising more than 100 atoms. Despite using fixed point charges, with no explicit polarization term, the bespoke force field reproduces both QM inter-and intramolecular energies to an accuracy of around 1 kcal/mol for small molecule benchmarks. |
60c743b6469df4007bf43256 | 2 | In recent years, we have been following a similar strategy to Grimme's QMDFF, focusing more on condensed phase properties and heterogeneous systems. The basis of this approach is the density derived electrostatic and chemical (DDEC) atoms-in-molecule (AIM) scheme, which partitions the total electron density into approximately-spherical atomcentered basins. Atomic charges are derived by integrating the atomic electron density over all space and, in contrast to direct fitting of the QM electrostatic potential (ESP charges), it is possible to derive chemically-meaningful DDEC atomic electron densities and charges for both surface and buried atoms. A further advantage of this approach is that the Lennard-Jones parameters may also be computed directly from the atomic electron densities, using methods based on the Tkatcheko-Scheffler relations that are commonly used to incorporate dispersion effects into density functional theory (DFT) calculations. Similar to the Grimme approach, these non-bonded parameters are derived from a single QM optimized structure, which would be problematic if the charges show strong conformation dependence. However, Manz and Sholl have demonstrated that DDEC charges are transferable between different conformations of a molecule (as measured by their ability to recreate the QM electrostatic potential), and they conclude that the charges are suitable for the construction of flexible force fields. Furthermore, it should be noted that atoms-in-molecule electron density partitioning lends itself naturally to the derivation of both off-site charges to model electron anisotropy (such as lone pairs and σ-holes) and atomic polarizabilities, though we have not yet investigated a fully polarizable force field. |
60c743b6469df4007bf43256 | 3 | In keeping with our goal of deriving force field parameters directly from QM, rather than fitting to experiment, we have supplemented the atoms-in-molecule non-bonded parameters with harmonic bond and angle parameters derived directly from the QM Hessian matrix. There are a number of methods available for deriving bonded parameters from the QM Hessian matrix, but our recent adaptation of the Seminario method (which we name the modified Seminario method) is conceptually quite straightforward whilst yielding parameters that reproduce QM vibrational frequencies with a mean unsigned error of 49 cm -1 , below that of OPLS (59 cm -1 ). Collectively, we have named these methods the QUantum mechanical BEspoke (QUBE) force field. This name reflects the fact that force field parameters are derived by the user specifically for the small molecule under study, directly from QM calculations. We have released a software toolkit (QUBEKit) that facilitates the derivation of small organic molecule force field parameters, and also allows the user to derive the positions of off-site charges to model anisotropic electron density and to fit dihedral parameters to QM torsion scans. QUBE force fields have been derived for 109 small organic molecules, and yield mean unsigned errors of 0.024 g/cm 3 , 0.79 kcal/mol and 1.17 kcal/mol in computed liquid density, heat of vaporization and free energy of hydration. These results are competitive with standard transferable force fields, which have been extensively fit to properties such as these. |
60c743b6469df4007bf43256 | 4 | To achieve our goal of employing the QUBE force field in computer-aided drug design applications, we require a compatible protein force field. Since the non-bonded parametrization strategy employed in QUBE is very different to that used in the standard biomolecular force fields (e.g. AMBER, OPLS, CHARMM), there is no reason to believe that they are compatible. However, by implementing the atoms-in-molecule non-bonded parameter derivation methods in the ONETEP linear-scaling density functional theory (DFT) software, we have shown that it is feasible to derive these charges and Lennard-Jones parameters for entire proteins. In this way, the number of fitting parameters is substantially reduced, and we have a consistent parametrization approach that can be applied to both small and large molecules, including entire biomolecular assemblies. Since, in this approach, all non-bonded parameters are derived from a single QM calculation, both the charge and Lennard-Jones parameters naturally include the native state polarization effects of the environment. Importantly, we have shown that protein charges derived using DDEC electron density partitioning recreate the underlying QM electrostatic potential with high accuracy, and that charges derived for a NMR ensemble of BPTI protein structures are not too conformation-dependent (standard deviations per residue less than 0.04 e). This is in contrast to the performance of RESP charges, which have been shown to be significantly more conformation-dependent for an ensemble of polypeptide structures. Additional simulations demonstrated the feasibility and advantages of deriving bespoke parameters for a protein-ligand complex. The computed relative binding free energy of indole and benzofuran to the lysozyme protein using the environment-specific force fields (-0.4 kcal/mol) was in excellent agreement with experiment (-0.6 kcal/mol), and was substantially more accurate than standard force fields (-2.4 kcal/mol). However, the force field was in need of further development as the bespoke non-bonded terms were used in combination with standard OPLS-AA bonded parameters. |
60c743b6469df4007bf43256 | 5 | In standard transferable force fields, the torsional component is typically parameterized using QM dihedral energy scans, with the difference between analogous MM and QM energy scans minimized by fitting the torsional parameters. Reparameterization of the torsional terms has been shown to be a crucial step in improving the accuracy of force fields and this has recently been demonstrated for AMBER ff15ipq, CHARMM36 and OPLS-AA/M. Bond and angle reparameterization has also been shown to be an essential stage in improving the accuracy of biomolecular force fields, 2,36 although it is not so frequently carried out. |
60c743b6469df4007bf43256 | 6 | Since it is not currently feasible to derive accurate QM Hessian matrices for entire proteins, we have used the modified Seminario method to compute a complete set of bond and angle parameters for the twenty naturally occurring amino acids. This work focuses on the remaining component of the force field, namely the re-fitting of key torsional parameters that describe the backbone and sidechain dynamics of an amino acid. The methods and validation tests broadly follow the approaches employed in the development of OPLS-AA/M, the latest OPLS force field. Torsional parameters are fit by minimizing the differences between multiple QM and MM potential energy scans of dipeptide backbone and sidechain dihedral angles. Our overall goal is to test the extent to which bespoke non-bonded parameters may be combined with libraries of bonded parameters to produce a protein force field that is compatible with our QUBE small molecule force field for use in computer-aided drug design applications. |
60c743b6469df4007bf43256 | 7 | The performance of the QUBE protein force field is tested through comparisons between experiment and molecular dynamics (MD) simulations for a set of twenty dipeptides, the glycine tripeptide and alanine pentapeptide, and a range of small folded proteins. This benchmark testset is similar to those used in the development of protein force fields such as AMBER ff15ipq, AMOEBA, CHARMM36 and OPLS-AA/M. As we shall show, the QUBE protein force field is competitive with standard transferable force fields for the dipeptide set and alanine pentapeptide, while retaining the experimental structures of small folded proteins reasonably well. To encourage further testing of the QUBE protein force field, MD input files for the molecules studied, as well as the necessary scripts to convert the QM electron density to QUBE force field format have been made available (). Finally, in the conclusions, we outline a roadmap for future improvements to QUBE. |
60c743b6469df4007bf43256 | 8 | The functional form of the standard biomolecular force field has five components. Covalent interactions between atoms are modelled using harmonic bond stretching and angle bending parameters, while rotations about a bond are described by anharmonic 4-body torsional terms. Non-bonded interactions are described by a sum of Coulombic interactions between (usually) atom-centered point charges and a physically-motivated Lennard-Jones interaction, which combines a short-range repulsive r -12 potential with a longer-range attractive r -6 interaction. We now provide an overview of how these various components are parameterized in the QUBE protein force field, and contrast the approaches to those used in standard transferable force fields. Since the methods used to parameterize the non-bonded, and bond and angle terms have been extensively described elsewhere, we focus here on the derivation of the torsional parameters. |
60c743b6469df4007bf43256 | 9 | The non-bonded components of a molecular mechanics force field aim to describe the quantum mechanical electrostatic, dispersion and exchange-repulsion interactions in a computationally efficient manner. The charge parameters are generally fit to the quantum mechanical electrostatic potential of small molecules. The Lennard-Jones parameters are then fit to reproduce experimental data, such as liquid densities and heats of vaporization. The aim of QUBE is to move away from the requirement for transferable force field parameters, and instead to derive bespoke parameters for molecules directly from QM calculations. First, a QM simulation of the molecule under study is performed. From the output of the QM calculation, the total electron density of the molecule is partitioned onto individual atoms using an atoms-in-molecule (AIM) weighting scheme. There is no unique method to perform this partitioning, but we favor the density derived electrostatic and chemical (DDEC) scheme, which is a weighted combination of the iterative stockholder atoms and iterative Hirshfeld approaches. With the electron density partitioned to individual atoms, the atom-centered charges can be simply found by integrating the electron density over all space (and adding the nuclear charge). We have implemented the DDEC approach in the ONETEP software package, which allows us to perform QM calculations of, and assign parameters to, systems comprising thousands of atoms. The derived charges have been shown to be suitable for use in flexible force field design in multiple works, because they are able to reproduce the underlying QM electrostatic dependence while exhibiting low conformation-dependence. The charges are specific to the system under study and, by performing the QM calculation in the presence of an implicit solvent model, polarization of the charges in the condensed phase can be included in the model. The dispersion and exchange-repulsion interactions are described using a Lennard-Jones potential with a form: |
60c743b6469df4007bf43256 | 10 | , can then be used to determine heteroatomic dispersion coefficients. The A ij parameter, which describes the short-range repulsion between overlapping electron clouds, cannot be readily calculated directly from the electron density. Instead it is computed by requiring that the minimum in the interatomic Lennard-Jones potential coincides with the estimated van der Waals radius of the atom in the molecule. This non-bonded parameter derivation scheme requires just one fitting parameter per element (corresponding to the van der Waals radius of the free atom in vacuum). |
60c743b6469df4007bf43256 | 11 | The parameterization approach used to determine bond and angle harmonic force constants in traditional force fields, such as OPLS and AMBER, is to fit them to reproduce QM data or experimental normal mode frequencies. This creates interdependencies in the force field parameters. That is, bond and angle parameters depend on the non-bonded and torsional parameters used during the fitting process, and therefore they cannot be easily transferred to the QUBE force field. Instead, we derive bond and angle force constants directly from the QM Hessian matrix of the molecule under study, while equilibrium bond lengths and angles are taken from the optimized geometry of the molecule. This method is a modification of the Seminario method, and is based on the computation of the eigenvalues and eigenvectors of the partial Hessian matrix, k AB : |
60c743b6469df4007bf43256 | 12 | Similar methods may be used to derive the angle force constants, and we introduce a correction to the standard Seminario method which takes into account the geometry of the molecule under study. Consistent improvements in the computed normal modes were demonstrated using this modified Seminario method for a range of molecules. In particular, QM vibrational frequencies for a set of dipeptides were reproduced with an accuracy of 40 cm -1 , which compares favorably with the OPLS force field (47 cm -1 ) and the original Seminario method (104 cm -1 ). Since the derived bond and angle parameters do not depend on the choice of non-bonded and torsion parameters, the derived parameters are suitable for use in the QUBE protein force field. Since large-scale polarization effects are expected to be significantly less important for bond and angle parameters than for charges, we use the library of bonded parameters provided previously (and the same atom types as those used for OPLS-AA/M 1 ). |
60c743b6469df4007bf43256 | 13 | Whilst preparing the protein simulations, it was found that our library was missing parameters for the disulfide bridge between pairs of cysteine residues. These bond and angle parameters were therefore derived using the QM Hessian matrix of dimethyl disulfide and are supplied in Section S2.3 of the Supporting Information. With new bond, angle and non-bonded parameters derived, all that remains to complete the QUBE protein force field is to obtain the torsional parameters. Unfortunately, it is infeasible to derive torsional parameters from QM simulations that are specific to each protein. |
60c743b6469df4007bf43256 | 14 | where the sum runs over all dihedrals (k) in the molecule and V k 1-4 are parameters to be fit. We focus on reparameterizing the backbone (φ, φ , ψ and ψ ) and sidechain (χ 1 , χ 1 , χ 2 and χ 2 ) torsional parameters (Figure ). Re-fitting of the remaining torsional and improper parameters are beyond the scope of the current work, and these parameters are instead taken from the OPLS-AA/M force field. However, parallel efforts are being made to develop a toolkit for automated parameterization of small molecules using the QUBE force field, which will facilitate derivation of the remaining parameters in future. When fitting torsional parameters, the main objective is to minimize the difference between MM and QM gas phase dihedral energy scans. However, weighting schemes and regularization can also be used to change the form of the error function that is minimized. |
60c743b6469df4007bf43256 | 15 | Regularization is a technique generally used to prevent overfitting to data. There are multiple forms of regularization that can be applied to improve fitting. In this work we use a harmonic restraint that is added to the error function. This penalty term ensures that torsional parameters do not deviate significantly from their initial value unless a significant improvement in the agreement with the QM energy surface is observed. As we will show, even with low levels of regularization (a small λ value), a sizeable increase in performance is observed for the QUBE force field. The general form of the error function used in this study is given by: |
60c743b6469df4007bf43256 | 16 | where k B is the Boltzmann constant, T is a weighting temperature, n is the number of points at which the energy is evaluated, W j is the contribution from the weighting scheme, λ is the regularization coefficient (this term is independent of n and can take any positive value), V i is the torsion parameter being optimized and V 0 i is an initial estimate of the torsion parameter. Where we have used a harmonic restraint, we have used V 0 i = 0 as the initial guess as previously suggested. The V 4 term was set to zero throughout the fitting procedure to avoid overfitting. 1 E j QM and E j M M are the QM and MM optimized energies at each sampled dihedral angle relative to the lowest QM or MM energy. MM scans allow all other degrees of freedom to optimize, and so the structures are similar, but not identical, to the QM structures. Weighting schemes are used to prioritize accuracy in particular regions of the dihedral scan, for example in the β-sheet region of the Ramachandran plot. A range of weighting schemes has been previously used, including schemes that prioritize the lowest QM energies 1 or that prioritize regions that have been shown experimentally to be most populated by proteins. 3 Methods |
60c743b6469df4007bf43256 | 17 | Torsional parameter fitting followed the general strategy employed in the development of the OPLS-AA/M force field, 1 amongst others, in which parameters are fit to reproduce QM gas phase potential energy surfaces. Fitting and validation was performed using dipeptides of the form (Ace-X-NMe), where X is the amino acid, Ace is an acetyl group and NMe is the N-methyl group. |
60c743b6469df4007bf43256 | 18 | The ground state electron densities of the dipeptides were computed using the ONETEP linear-scaling DFT code with the PBE exchange correlation functional and standard parameter settings, (Supporting Information S2.2). Since the reference QM potential energy scans are performed in the gas phase, we have decided to derive QUBE force field charges and Lennard-Jones parameters from the vacuum electron density (rather than in an implicit solvent). The assumption here is that the required correction to the MM potential energy surface is approximately the same in the gas and condensed phases. |
60c743b6469df4007bf43256 | 19 | Charge and Lennard-Jones parameters were derived from the QM ground state electron density using the DDEC scheme as implemented in the ONETEP code (Section 2.1). As discussed previously, DDEC charges show low, but non-zero, conformational dependence. To account for this, the non-bonded parameters were derived for multiple conformations of each dipeptide and averaged. Input files for the full set of dipeptide structures are provided in the Supporting Information. Non-bonded parameters on identical atoms (for example, hydrogen atoms in a methyl group) were symmetrized. It should be noted that only atom-centered charges were used in this work, though off-site charges to model anisotropic electron density distributions, particularly on sulfur atoms, may lead to improvements in future work. Bonded parameters were assigned to the dipeptides from the library developed using the modified Seminario method using OPLS-AA/M atom typing rules. |
60c743b6469df4007bf43256 | 20 | The torsional potential energy scans of alanine, glycine and all sidechains are the same as those used in the development of the OPLS-AA/M force field, as described previously. In brief, structures were relaxed in the gas phase using Gaussian 09 with a ωB97X-D functional and a 6-311++G(d,p) basis set. Dihedral angles were scanned in 15 • increments from -180 • to 180 • . A single point energy calculation was then performed on the optimized structure using the double hybrid functional B2PLYP-D3(BJ) and the Dunning basis set aug-cc-pVTZ. |
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