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HomeChemistrycell2mol: encoding chemistry to interpret crystallographic information

cell2mol: encoding chemistry to interpret crystallographic information

The algorithm

The characterization of a unit cell with cell2mol solely requires its crystallography file (i.e., the cif). After an preliminary formatting with the cif2cell code38, the characterization proceeds in two principal steps (see detailed workflow in Supplementary Be aware 1). The objective of step is to acquire the details about the stoichiometry of the completely different molecules within the unit cell. This data shouldn’t be instantly obtainable from the.cif file because the molecules aren’t but acknowledged as such. Furthermore, they are usually severely fragmented in smaller teams of related atoms (field A in Fig. 1). These are put collectively by way of the development and block-diagonalization of the adjacency matrix (A), with Aii = 1, and Aij = 1 if the gap between atoms i and j is beneath a threshold, in any other case zero. Thus, A is evaluated primarily based on interatomic distances on account of its simplicity and effectivity39, whereas extra correct and costly alternate options exist primarily based on Voronoi partitioning schemes40,41. After block diagonalization, the ensuing blocks correspond to both molecules or fragments (i.e., a portion of a molecule). Molecules are preserved, whereas fragments bear translations within the three crystal instructions forming greater fragments till all molecules are totally reconstructed (field B). Lastly, ligands in TM complexes are recognized utilizing the same block-diagonalization course of, with AMj=AjM= 0 for all metallic (M) and ligand atoms (j) (field C).

Fig. 1: Simplified workflow of cell2mol.
figure 1

Simplified workflow of cell2mol.

In step , cell2mol proceeds to assign the connectivity (C) and formal cost (Q) for all species within the unit cell exploiting the cost neutrality rule. All ligands and any non-metallic species (i.e., counterion or lattice-solvent) are interpreted and their C and the related formal complete cost (Q) and atomic prices (qi) are retrieved. Inside cell2mol, the idea of connectivity is mathematically dealt with because the Bond-order matrix C representing a Lewis construction. Mainly, C provides the bond order (e.g., single, double bond) data to A. The creation of C from A is completed by way of a modified and expanded model of the xyz2mol code developed by Jensen and coworkers primarily based on earlier work by Kim42. Using C to outline the molecular graph gives improved capabilities with respect to different codes primarily based on A29,30. Lewis buildings give entry to qi and Q, and allow superior sub-structural searches together with particular bond patterns or practical teams. Whereas the adopted equipment gives a transparent benefit, the variety of doable C (i.e., Lewis buildings) grows very quick with rising the variety of atoms, particularly in conjugated backbones. Because of this, along with the issue to deal with periodic connectivities, cell2mol can’t be utilized to periodic buildings, for which different approaches primarily based on A can be found29. Nonetheless, the technology of C requires a identified Q, which is exactly our unknown variable. Due to this fact, our strategy is to generate a number of C ranging from a listing of candidate preliminary prices, and to pick out these which might be believable (field D). The standards to generate and choose one of the best C is identical for non-complex molecules (e.g., solvent, counterions) and ligands. Nonetheless, for ligands, there’s a key preliminary step. To compensate for the lacking M-L bonds when producing C, some related ligand atoms (i.e., these which might be coordinated to the metallic) should be saturated, sometimes with H atoms. It is a difficult a part of the algorithm because of the ligand’s giant chemical range and completely different coordination modes. A complete record of guidelines is laid out in cell2mol to this activity, coping with a big number of denticity -and hapticity- modes for each terminal and bridge ligands. For some ligands, particularly polydentate ones with giant, conjugated moieties, the choice to saturate related atoms is especially tough, as a result of a chemically significant C might be achieved with and with none extra protonation. Thus, a number of protonation states are created and, for every of them, a number of C are generated (see Supplementary Be aware 2).

From the pool of C, those who reduce the overall variety of atomic prices, and absolutely the complete cost earlier than and after correction (for the removing of the added H+), are thought of believable and are pre-selected. As soon as believable C are collected for all non-metal species within the unit cell, these are mixed with a listing of widespread OS for all metallic species (see Supplementary Be aware 3), producing cost distributions. When just one cost distribution fulfils cost neutrality, it’s chosen, and the unit cell is efficiently interpreted (field E). When a number of do, the unit cell is taken into account “unresolved” (see Supplementary Be aware 4 for an in depth evaluation of errors in step ). That is more and more widespread in unit cells with a number of redox-active species, corresponding to in bi- or poly-metallic complexes (A0/B+1 vs. A+1/B0). Choices are at the moment being explored to enhance the interpretation of these methods (see Supplementary Be aware 5).

Instance: YOXKUS

As an instance the interpretation capabilities of cell2mol, we take YOXKUS43 for instance (see Fig. 2). In accordance with cell2mol, YOXKUS has 4 an identical mono-metallic Re complexes and no counterion or solvent molecules within the unit cell. Every complicated has three kinds of ligands. The primary ligand is interpreted as being related to the Re ion by way of two teams of atoms. One group consists of a substituted Cp ring with η5 hapticity and the opposite is the P atom of a diphenylphosphine, with κ1 denticity. cell2mol assigns this ligand a complete –1 cost, after creating one protonation state, producing its connectivity underneath 5 doable prices (0, ±1, ±2), and deciding on probably the most believable one. The second ligand is an iodine atom with −1 cost and seems twice, and the third is a impartial CO ligand, with a − 1 and a + 1 formal cost within the C and O atoms, respectively, and a triple bond between them. All this data is saved in variables and saved in a python object containing the interpretation of the entire unit cell. From this file, a person can simply export the Cartesian coordinates of the complete reconstructed unit cell, in addition to the cell parameters, to organize a solid-state QC computation. Alternatively, the person can extract the Q, R, and C of any of the person molecules, or that of the remoted ligands/metals/atoms of these molecules. Certainly, non-metal species will also be accessed by way of their respective Rdkit mol objects, which gives an unprecedented degree of management within the ultimate dataset, with all the possibly related data (i) for a substructure/similarity search (utilizing C), (ii) to set any QC computation (utilizing Q and R), or (iii) for the technology of chemoinformatics (e.g., SMILES44) or QML-based45 representations for ML fashions (utilizing Q, R, and C).

Fig. 2: Diagram of the CSD entry YOXKUS.
figure 2

Diagram of the CSD entry YOXKUS.

Efficiency of cell2mol

The capabilities of cell2mol are demonstrated by deciphering crystallographic data extracted from the CSD repository. For simplicity, datasets are constructed individually for eight TM ions, together with probably the most electronically difficult ones from the 3d block (Cr, Mn, Fe, Co, Ni, Cu) and representatives from the 4d (Ru) and 5d (Re) blocks. The information is initially extracted from the CSD software program ConQuest. The one filters utilized at this stage are the presence of the respective TM ion, and the absence of any so-called polymeric bond. Thus, periodic methods are discarded, for which different approaches supply wonderful topological evaluation instruments, or the prediction of metallic OS25,26,29. General, our databases cowl molecular crystals of organometallic and coordination complexes. No different limitation on the factor varieties (besides f-block), molecular dimension, or complexity is about. The ensuing entries are exported from ConQuest in .cif format, and duplicate CSD-refcodes are discarded. Aiming at an entire interpretation of the unit cell, cell2mol is weak to experimental uncertainties. Entries with dysfunction or lacking H atoms can’t be interpreted appropriately and are thus filtered out (see Fig. 3 and Supplementary Be aware 3). This pre-filtering step is essential to acquire extra dependable statistics of cell2mol. Much less evident errors can solely be recognized after retrieving the connectivity, which remains to be unknown at this stage. As an example, assessing whether or not an O atom is lacking a proton (OH vs. O vs. O) will depend on the connectivity (−OH vs. =O vs. −O) of all molecules, and on fulfilling the cost neutrality criterion.

Fig. 3: Normal workflow of cell2mol efficiency evaluation.
figure 3

Normal workflow to arrange the success fee and reliability of cell2mol, together with values for the Fe-based database of mono-metallic complexes.

To judge the efficiency of cell2mol we use two metrics: the success fee and the reliability. The previous quantifies the proportion of CSD entries for which a believable interpretation is given, and is said to the quantity of chemical range that the code can deal with with out errors. The latter, which is a very powerful parameter to generate curated databases, measures how usually is the proposed interpretation appropriate. Whereas assessing the reliability primarily based on your entire record of properties which might be extracted for every CSD entry shouldn’t be doable, most have a direct impression on the task of the metallic OS. The metallic OS is thus chosen to estimate the success fee and reliability of the cell2mol interpretation (see Fig. 3), and is in comparison with the metallic OS given within the.cif file, which is taken as a reference. As mentioned hereafter, the reference values are generally misguided, which implies that the reported reliability estimates are barely underestimated (~1%) for all strategies. Additionally, instances of error compensation are doable, by which the cell2mol interpretation is wrong in any of its variables, whereas not affecting the metallic OS prediction. In any case, all CSD entries for which the OS reference is accessible are collected within the check set, whereas the opposite entries are collected in what is known as the prediction set, on condition that cell2mol predicts its properties primarily based on the obtainable crystallographic information. Lastly, each subsets are additional break up in mono-, bi-, or poly-metallic complexes46. To simplify the dialogue, we deal with mono-metallic complexes though complementary evaluation on the opposite subsets can be found in Supplementary Be aware 5.

Greater than 75% of crystal buildings containing mono-metallic complexes are univocally interpreted by cell2mol (see Desk 1). This share raises to 94% for a pool of randomly chosen purely natural crystals, and reduces to 71% for Re-based complexes, owing to their larger range in OSs and metal-ligand coordination modes. So successful fee is akin to what has been reported for the CSD interpreters, and largely outperforms different common strategies to assign the metallic OS corresponding to BVS, particularly for Cr, Ru, and Re (see Supplementary Be aware 6). Much more essential, the reliability is very excessive for all metals, particularly for these with one dominant OS corresponding to Cu (98%) or Ni (97%), and diminishes to 90% in Re complexes, owing to its bigger variety of widespread OS. Entries with a disagreement are discarded from the ultimate printed datasets. Nonetheless, handbook inspection reveals that solely about one-third of these instances are on account of an error in cell2mol (see Supplementary Be aware 7). Generally, the disagreement is because of incomplete or misguided data within the.cif file, which suggests the potential use of cell2mol as a diagnostic instrument. Additionally, the reliability of cell2mol is way bigger than BVS (ca. 74%), which tremendously underperforms right here as compared with what is often reported within the literature, because of the a lot larger range of our datasets. Lastly, to evaluate the efficiency of ML fashions for a similar dataset, we skilled a Random Forest (RF) ML mannequin to foretell the metallic OS primarily based on its native setting (see Strategies for particulars). The accuracy of this mannequin reaches ca. 94%, much like what Smit and coworkers report for the applying of their ML mannequin to metallic complexes (ca. 90%)25, and much like cell2mol itself (see Desk 1). We thus conclude that cell2mol gives comparable reliability, whereas offering not solely the metallic OS (such because the ML and BVS strategies) however a complete interpretation of the unit cell. The benefits of cell2mol turn out to be even clearer when deciphering the CSD entries within the prediction set (vide infra).

Desk 1 Outcomes on the cell2mol characterization of unit cells with mono-metallic TM complexes included within the check set (See Supplementary Be aware 5 for unit cells with bi- and poly-metallic complexes).

Chemical range

For 31019 CSD entries included within the check set, cell2mol supplied a unit cell interpretation that coincided with the metallic OS supplied within the.cif file. For these entries, two-dimensional maps of their chemical area have been constructed (see Strategies), highlighting the cost and connectivity distribution (see Fig. 4 for Fe and Supplementary Notes 1013 for different metals). These maps assist establish construction–property correlations with none a priori assumption. As an example, (i) most Fe-based haptic compounds have Fe(II) or Fe(0) metallic ions, (ii) Mn reveals a transparent correlation between construction and OS, or (iii) Cu complexes with coordination quantity 3 are virtually completely related to Cu(I). General, the eight metallic facilities might be present in 2407 completely different coordination sphere varieties (e.g., FeN4O2), and are coordinated to a pool of 13,819 distinctive (i.e., non-repeated) ligands with complete prices that vary from –6 to +2, and together with 8 completely different hapticity modes (see Fig. 5). These ligands are collected in a separate database that features their coordinates, record of related atoms, cost (Q), and bond community (C) representing their Lewis construction. On one hand, C permits us to find out, by way of a structural search, that on this pool of ligands there are, as an example, 6909 secondary amines, or 988 rings containing an O atom. Then again, the remaining information could possibly be used to re-assemble46 these ligands into new complexes to create a bottom-up database encompassing a good broader area of chemical area. As an example, the 4942 distinctive bi-dentate ligands within the database might be mixed to generate about 20 billion octahedral complexes48. Equally, the re-assembled molecules could possibly be mixed, in a modular vogue47, with the recognized 1246 distinctive non-complex molecules (i.e., solvent, counterions) to generate new candidate unit cells fulfilling cost neutrality. Whereas the steadiness and form of those new unit cells must be assessed48,49, we count on that cell2mol is also exploited to generate chemical range on the supramolecular degree.

Fig. 4: Evaluation of the chemical area lined by the Fe database and ML mannequin efficiency.
figure 4

Illustration of the chemical area within the Fe mono-metallic dataset utilizing the t-SNE projection. Every level is one TM-complex within the database. Complexes are clustered by similarity within the native SLATM illustration of their metallic heart describing the construction and chemical composition of the primary coordination sphere (see Strategies). Within the high panel, for the check set we present a the distribution of metallic OS (0 = inexperienced, 2 = pink, 3 = cyan), Oxidation State (Check Set), b the presence of at the least one haptic ligand (inexperienced = no, blue = sure), Hapticity (Check Set), c the 385 coordination sphere varieties for Fe, Coord. Sphere (Check Set), and d the coordination variety of the metallic, with haptic ligands counting 0 in direction of this quantity (inexperienced = 0, cyan = 3, purple = 4, navy = 5, pink = 6), Metallic Coord. Quantity (Check Set). Within the beneath panel, we present the e the utmost chance related to the ML prediction of the metallic OS, as a measure of its confidence (yellow = 1, degrading to inexperienced = 0.5 and blue = 0) Max. ML chance (Check Set), and the f overlap between the prediction (pink) and check (blue) units, that are additionally proven individually in g and h. The black circle signifies a area with poor overlap. See Supplementary Notes 1013 for different metals.

Fig. 5: Chemical range within the ligands database.
figure 5

Distribution of (left) complete prices and (proper) hapticity modes within the database of 13,819 distinctive ligands. The inset reveals the only case of a ligand with −5 cost, in QORFAG.

Mining the CSD

We’ve got proved that cell2mol is ready to interpret molecular crystals and assemble databases with nice chemical range. To this point, this has been performed completely for what we outlined because the check set, which quantities for ca. 50% of the overall CSD entries. Ideally, databases could be constructed from the entire of CSD, and never be restricted to a fraction of its chemical area. Not being a statistical technique, the success fee and reliability established above for the check set ought to, in precept, maintain for the prediction set, supplied that the set of chemical guidelines in cell2mol is transferable sufficient. To show it, we used 1000 mono-metallic randomly-selected CSD entries for every metallic. As anticipated, comparable success charges are obtained for all metals (ca. 73%, see Supplementary Be aware 8). To judge the reliability within the absence of metallic OS data within the.cif file, right here we in contrast the metallic OS predicted by cell2mol with the one supplied by the ML mannequin. Each strategies coincide with about 90% of CSD entries with Mn, Fe, Ni, Cu, and Ru, which is near the reliability reported for each strategies within the check set (see Desk 1). Nonetheless, the settlement surprisingly drops to 70% for Cr, Co, and Re (see Fig. 6). Guide inspection of as much as 100 instances with disagreement reveals that cell2mol is often appropriate, which hints at deficiencies of the ML mannequin (see Supplementary Be aware 9) that may be defined by the next two causes. First, some metals exhibit a really poor correlation between construction (together with chemical composition) and their OS (see Fig. 4a and Supplementary Be aware 10), which decreases the arrogance of the ML mannequin when assigning the OS (see Fig. 4e and Supplementary Be aware 12) and therefore its accuracy (89% vs. 96 of settlement in Fe vs. Mn). Second, the chemical panorama might be very completely different within the check vs. prediction units (see Fig. 4f–h and Supplementary Be aware 13), which implies that the ML mannequin usually has to extrapolate. When each issues cooperate, corresponding to in Cr, Co, and Re, the ML fashions lose accuracy. Contemplating that we used the entire obtainable information in CSD to coach this mannequin, this conduct is probably going unavoidable, and factors to a elementary drawback that statistical strategies have when mining the wealthy chemical range in your entire CSD. This stresses the relevance of non-statistical alternate options corresponding to cell2mol. Certainly, probably the most promising route for future work is the mixture of a deterministic technique for the great interpretation of the unit cell (e.g., cell2mol) with an area statistical technique for the analysis of particular properties of species when a couple of doable interpretation is feasible (e.g., the metallic OS in unresolved CSD entries). Future work will deal with the implementation of this scheme, in addition to on the development/extension of the chemical guidelines to know M-L connectivity, and the incorporation of f-block metals.

Fig. 6: Efficiency of the ML mannequin for the check and prediction units.
figure 6

Comparability of the efficiency of the skilled ML mannequin (see Strategies) at predicting the metallic OS. In blue, the reliability of the mannequin, established by comparability with the.cif information within the check set. In pink, the settlement between cell2mol and the ML mannequin within the assignation of metallic OS for the prediction set.


We offered cell2mol, a instrument that encodes chemical ideas and guidelines to interpret crystallographic information, and extract complete details about the person molecules contained in unit cells. cell2mol can efficiently interpret about 75% of the CSD entries containing mono-metallic complexes with a reliability of over 95%. We demonstrated that these metrics surpass different common strategies devoted to the task of metallic OS (BVS and ML), with cell2mol being rather more versatile. Additionally, we confirmed that our software program can generate top-down and bottom-up QC-ready databases with incomparable chemical range. To reveal its capabilities, we’ve got used cell2mol to generate a publicly obtainable database of 31,019 complexes containing eight completely different metallic facilities (Cr, Mn, Fe, Co, Ni, Cu, Ru, Re). Moreover, we generated a separate database of 13,819 constituent ligands that may be rearranged to generate billions of reasonable new chemical buildings. All content material is totally searchable and interoperable utilizing chemoinformatics software program (e.g., Rdkit, SMILES-based instruments). We count on that cell2mol, with doable subsequent enhancements, will pave the way in which in direction of making all crystallographic repositories solely usable for molecular and supplies design functions.



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