2.1. Bonding Descriptor Syntax

In simplelinear polymer segments, the repeat units may be written in a waysuch that the strings for each repeat unit may be directly concatenatedtogether in any order or orientation to form a representation of apolymer molecule.Figure2 includes a representation of one such hypothetical polymersegment; however, in many cases (such as polymers synthesized viaring-opening polymerization with repeating units always in a specificorientation, or if there exist multiple sets of orthogonal reactionsthat prohibit the formation of a certain connection between some repeatingunits), more complex bonding patterns can arise. To differentiateand clearly specify different connectivity patterns between repeatingunits, two types of bonding descriptors are introduced.

Thefirst type of connection is AA type bonding, where connections canoccur between any two bonding moieties within a group of possiblemoieties. This is commonly found in the bonds formed from chain polymerizationof vinyl monomers, where each polymerized vinyl carbon can in principleconnect to any other polymerized vinyl carbon found in other repeatunits (allowing for head-to-head, tail-to-tail, and head-to-tail addition).Section SI (p S2) in the Supporting Informationgives a more detailed discussion of this feature. For this type ofconnectivity, the “$” notation is used. For example,for a linear polymer segment formed from vinyl monomers ethylene and1-butene, the stochastic object reads

As illustratedby the example, in general, there are multiple equallyvalid representations for each repeating unit, and the bonding siteto other repeating units (the position of symbol “$”)can be placed at any position in the repeating unit. Furthermore,there can be more than two such sites per repeat unit, which becomesuseful when the notation is generalized to represent branched polymers.For example,Figure S2a (p S11, SectionSIV in the SI) gives a representation for branched polyethylene usingbranching units with three or more connection sites to the other repeatingunits. It should be emphasized that the list in the BigSMILES stochasticobject is defined based on repeating units rather than monomers. Therefore,for monomers such as isoprene, which may have up to four isomerizationstates upon polymerization,³¹ each isomerizationstate is treated as a distinct repeating unit in the stochastic object,as illustrated inFigure3b.

If multiple orthogonal sets ofAA type connections exist withinthe same molecule, the symbol “$” can be appended witha positive integern into “$n” to distinguish between different sets of connections. Bydefault, “$” represents a single bond connection; however,if the repeating units are connected by other bonds, the bond typeor bond order can be specified by using the SMILES bond order representation,with “$=n” for double bonds, “$#n” for triple bonds, and “$\n” and“$/n” for explicitly specifying the cis–transisomerization states of single bonds directly adjacent to double bonds,respectively. Note that integer IDsn should serveas unique identifiers for the different sets of bonds and thereforenot be reused within the same stochastic object. Since the scope ofthis identifier is only within the stochastic object (between thecurly brackets), identifiers within different stochastic objects aredistinct even if the IDs appear to be identical. Furthermore, whileexplicitly stating the additional bond order in every bonding descriptorenhances clarity, the first occurrence of the bond of a particularID is treated as the definition for the connectivity pattern associatedwith the ID, and the details of the bond order can be omitted forsimplicity in later occurrences. If there is only one group of bondswithin the stochastic object, the integer ID can be dropped for simplicityif no additional descriptor (such as the bond order) is needed forthe bond. In the special case where there are just two connectivesites per repeat unit, and only one type of AA bond of bond orderone exists, if the repeat unit is written such that these two sitesare at the termini of the repeat unit, the symbol “$”may be omitted altogether, as in the case illustrated inFigure3a,b. This providesa substantial simplification for a very wide range of common polymersand is referred to as the “simplified representation.”

In the $ representation of AA bonding, any bond indicated by “$n” can be joined to any other bond “$n”, and the repeating unit in the polymeric structureneed not connect in the orientation specified in the repeat unit list.Therefore, structures with repeat units in the flipped orientationare implicitly included. For instance, this bonding descriptor canbe used for representing vinyl polymers, for which both the head-to-headand the head-to-tail configurations need to be included so the overallBigSMILES representations capture the full ensemble of the possibleconfiguration of the polymer (Figure S1, p S2). Including both configurations is especially important indescribing polymers such as poly(vinyl alcohol) or fluorinated vinylpolymers, for which there are known to be a significant number ofhead-to-head oriented pairs along the chain.³² However, it is emphasized that while the bonding descriptor specifiesthe ensemble of possible configurations, it does not provide informationon the relative weights for each of the configurations.

Forthe second type of bonding, AB type bonding, a bonding moietycannot connect directly to other moieties within the same group butcan only connect to moieties in another conjugate group. This is commonlyseen in monomers polymerized with condensation reactions. For example,in a polyamide, the amide bonds between monomers are always betweenan acid moiety and an amine moiety but never between two acid or twoamine moieties. In this case, angle brackets “<”and “>” are used to indicate the bonds, where bondsmust form between conjugate pairs of brackets. For example, the polymericsegment of nylon-6,6, as shown inFigure3c, may be represented in BigSMILES as

As the asymmetric bonding descriptor represents bonds and connectivityresulting from the reaction of a pair of conjugate end groups, suchas polymers synthesized from the polycondensation reaction of a pairof end groups, conjugate symbols are selected for each of the twobonds. For instance, in the nylon-6,6 example, all the amine endsare denoted by the symbol “>”, whereas the carboxylends are denoted by the opposite symbol “<”; similarly,the amine ends on the polypeptide inFigure3d share the symbol “>”,andthe carboxyl ends are denoted by the opposite symbol “<”.Similar to the “$” symbol, if multiple groups of ABtype bonds exist, or higher bond order is needed, the notation canbe extended to “<bn” or and “>bn”, whereb is either “–”,“=”, “#”, “\”,or “/” depending on the bond order or bond type, andn is a positive integer. Again, for single bonds, whereb is “–”,b can beomitted for simplicity. Practical examples on the usage of the bondingdescriptors and common errors in encoding BigSMILES strings are, respectively,provided inSection SIX (pp S45–S53)andSection SII (pp S6–S9) of theSupporting Information.

2.2. Fragment Name DefinitionNotation

In BigSMILES syntax, repeating units are representedby an extendedversion of SMILES strings. While this design ensures that BigSMILESstrings are standalone and self-descriptive, in some cases it mightbe more beneficial to have some portions of the BigSMILES representationsbe replaced by more abstract but compact proxies, for example, thenames of repeating units. This is especially helpful when the structureis complex, and the resulting BigSMILES representation becomes long.To facilitate understanding, a definition of molecular fragments thatassociate user-defined names with partial BigSMILES strings is allowedin BigSMILES using the following syntax:

The definitionof repeat unit names is placed at the end of theentire BigSMILES string, with each definition of fragment enclosedby curly brackets and delimited by periods. When fragments are usedwithin the original BigSMILES object, a square bracket should be enclosedto avoid potential confusion of # with triple bonds. Note that thefragments should conform to the BigSMILES syntax and produce a syntacticallyvalid BigSMILES string when embedded within the original BigSMILESobject through a substring replacement. In addition, while havingcomplete (fully bracketed on both sides) BigSMILES stochastic objectswithin the fragment definition is allowed, no bonding descriptors(except for those within fully bracketed stochastic objects) shouldbe included within the fragment definition, so that all occurrencesof the bonding to other repeating units appear explicitly in the BigSMILESstochastic objects. In many cases, the fragment definition notationcan significantly increase the readability of the BigSMILES strings;two such examples are illustrated inFigure4. Fragment notation also provides a way ofintroducing monomer libraries to improve the readability of BigSMILES.An initial library illustrating a wide variety of examples is providedin the Supporting Information (Section SI, p S3,Table S1).

2.3. Concatenation and Nestingof Stochastic Objects

The BigSMILES stochastic object definedearlier represents polymericfragments. In principle, as in the SMILES language, the adjacent stringsoutside the stochastic object concatenated to the string within thestochastic object form a continuous chemical structure. However, toensure chemical validity, how the termini connect to exterior stringsshould be specified using leading and trailing bonding descriptorswithin the curly brackets:

The additional bonding descriptorsindicate how the exterior atomsare connected to the fragment. Therefore, they should be conjugatesto the specific desired terminal; i.e., the additional descriptorshould be “>nb” if the desired terminalbond type is “<nb”. This syntaxis especially useful for explicitly specifying how polymers with ABtype bonds connect to the exterior. For example, if the end groupsbracketing the terminals of the nylon-6,6 inFigure3c are explicitly specified, with both endsterminated by carboxylate group, additional “>” wouldneed to be added to both ends of the stochastic object to indicatethat the terminal bonds are of connected to the carbon on the carboxylategroup rather than the nitrogen on the amine group:

It shouldbe noted that this concatenation syntax only allows upto two connections to the exterior. In some cases, because of thenature of the repeating unit, by specifying the ending bonding orientation,the bond type at the beginning of the object is also determined. Thisis common in polycondensation of AB type monomers or ring openingpolymerization, where the connectivity on one end completely determinesthe connectivity pattern on the other end. For example, if the endgroups OH were to be positioned on the left of the stochastic objectrepresenting a glycine alanine copolymer, only the C-to-N orientationof the polyamide makes sense given the placement of the end group.In these cases where at least one end of the polymer is capped byexternal groups, if all repeating units within the stochastic objectshave only a pair of conjugate connective sites belonging to the sameAB bond group, and all repeating units are written so that the sitesare placed at the termini with the same orientation, then “<”and “>” at the termini of the repeating units maybeomitted to simplify the representation. With this simplification,the PEG example inFigure3e may be simplified aswhereas the previous glycine alanine copolymercan be simplifiedasAlthough the N-terminus of the polymer seems uncapped, thereis an implicit hydrogen that terminates the polymer. Collectively,these simplifications for AB bonding are also referred to as the “simplifiedrepresentation.”

The SMILES feature that allows stringconcatenation to representa continuous chemical structure enables blocks of polymeric structurein a copolymer to be written as the direct concatenation of severalstochastic objects. For example, a polyethylene-block-polystyrene structure shown inFigure4c can be easily encoded by concatenatingthe two polymers segmentsSimilarly, this representation can begeneralized to representmultiblock copolymers, such as the triblock poly(ethylene glycol)-block-poly(propylene glycol)-block-poly(ethyleneglycol) (PEG-b-PPG-b-PEG) illustratedinFigure4d. Notethat, in this triblock copolymer example, the syntax is greatly simplifiedwith the omission of the terminal “<” and “>”in the repeating units.

In the BigSMILES syntax, it is possibleto nest multiple levelsof stochastic objects within a stochastic object to create more complexstructures. To illustrate the syntax of nesting, consider synthesisof a polyurethane through polycondensation of 1,3-propanediol, ethyleneglycol oligomers, and toluene diisocyanate (TDI), as illustrated inFigure4e. The ethylene glycololigomers are encoded as one stochastic object, and this can be nestedin a second stochastic object representing the overall polyurethanepolymer:This example can be easily generalized to describe polymersresulting from the polycondensation of more than two types of oligomersor repeating units.

Another scenario that demonstrates the convenienceof nesting isthe representation of graft polymers. Consider polyisobutene-graft-poly(methyl methacrylate) (PIB-g-PMMA)synthesized by grafting from the linear copolymer of poly[isobutene-co-(m-bromomethylstyrene)], illustratedinFigure4f, as anexample. With the polymer graft nested within the backbone, the graftpolymer can be represented byor, separately defining the polymer graftwith the syntaxprovided in the previous section, the polymer can also be representedasWhen possible, readability and ease of comprehension willusually benefit from encoding a polymer in a non-nested way.

2.4. Branched Polymers and Polymer Networks

Up to now, allexamples have been focused on linear polymer segments,where each repeat unit has two attachment points corresponding tothe start and end of its SMILES string. However, the stochastic objectcan also be generalized to represent randomly branching polymers.For example, consider a low-density polyethylene (LDPE) molecule withlong chain branching (Figure S2a, p S11,Section SIV). Its BigSMILES representation is

Unlike otherrepeating units discussed up to this point, the secondand third repeating units each have functionality larger than two(and therefore the “$” symbols cannot be omitted). Therefore,they serve as branching points, and the entire stochastic object representsa randomly branching structure, which resembles the structure of LDPE.Note that while linear segments of the LDPE molecule can have an oddnumber of carbons because of branching, the overall linear backboneof LDPE must have an even number of carbons. Hence, the repeatingunits in this case consist of molecular fragments with two carbons.In practical cases, the fraction of the last repeat unit should bevery small compared to the other two repeating units, and this unitis retained in the list here for completeness. Other branched polymersor polymer networks can also be encoded similarly. InSection SIII (pp S10 and S11) of the SupportingInformation, more examples, including hyperbranched polymers, end-linkedpolymer networks, and vulcanized networks, are given; additional discussionon noncovalent or dynamic networks can be found inSection SIV, pp S12 and S13 of the SI.

2.5. End Groups

In BigSMILES, there aretwo valid ways of specifying end groups. The first way is to explicitlyappend the end groups around the polymeric fragment represented bythe stochastic object; this method allows specification of a deterministicend group. This was used in the previous section to specify the structurefor a methacrylate terminated PEG, as illustrated inFigure3e. The other way is to appendthe list of possible end groups as a comma-delimited list to the endof the list of repeating units, separated by a semicolon:

The end groupsare represented as if they are also repeating units,with the same bonding descriptors “$nb”,“<nb”, or “>nb” as repeating units that indicate the allowed connectivitypatterns between repeating units and the end groups. However, thenature of end groups dictates that they should have only one possiblebond to another repeating unit, to terminate the structure. For example,in the nylon-6,6 case, two different end groups are possiblewhere the carboxylicand amine end groups are included withinthe list of repeating units. Note that, in this example, hydrogenatoms are explicitly written for clarity. When end groups are specifiedusing this representation, it means that all the unconnected bondson the molecular fragment generated using the list of repeating unitswith two or more connections to other repeating units are capped withthe specified end groups. This representation can be especially usefulwhen there are multiple possible end groups. For instance, the variabilityof the end groups on the two ends of nylon-6,6 synthesized from polycondensationof adipic acid and hexamethylenediamine is implicitly considered byusing this representation. The effectiveness of the latter representationis especially demonstrated by the following example. Consider linearpolystyrene synthesized from AIBN initiated radical polymerization.It could have three different end groups depending on the route oftermination:

The possible terminal structures are illustrated inFigure5a. In this example,the SMILESstring leading to the random fragment is synonymous with specifyingthat the fragment already has one of its two ends capped by an initiator,indicated by the leading [$]. Therefore, it leaves only one unconnectedbond on the fragment. The other end group can be one of the threeend groups trailing the ethylene monomer in the list. The first possiblecase is that the other end group is also the initiator, which correspondsto the second entry on the list (first one in the end group list).This happens when termination by coupling takes place. The styrenerepeating unit within the end group is written in a reversed orientationto emphasize the preferred configuration in polymerization. On theother hand, when termination from disproportionation occurs, the endof the polymer can be capped by either of the two groups at the endof the list.

When randomly branched polymersare considered, the representationthat includes end groups into the list of repeating units has largeadvantages. Consider the hyperbranched polymer example inFigure S2b (p S11, Section SIV); if the end groupfor the #B moiety is #E, then theend groups of the hyperbranched polymer can be easily specified usingthe following representation:Note that, in this case, it is impossibleto explicitlyappend end group #E to the polymer fragment, becausedifferent members of the ensemble of molecules represented by thestochastic fragment have different numbers of unclosed bonds.

2.6. Macrocycles

For macrocycles thatare well-defined, such as the cycle structures in ring polymers, themacrocycles are encoded using the usual syntax for describing cyclesin SMILES. To illustrate this, consider a polystyrene ring synthesizedthrough alkyne azide click chemistry, as illustrated inFigure5b. In this case, since ringsand cycles within repeating units do not extend beyond a single repeatingunit, the macrocycle associated with the ring polymer can be treatedwith the usual SMILES ring closure syntax. The integer identifierthat was used within the repeating units for ring closure is consideredto be independent of any ring closure ID that was used in other partsof the BigSMILES string. Therefore, the BigSMILES representation forthis polymer readswhere the ring closure for the macrocycle is selected tobe between the sulfur atom and its neighboring atom. Meanwhile, thering closure denoted by 2 and 3 describes the ring closure in thephenyl group and the ring with nitrogen atoms. It should be emphasizedthat, similar to the ID used in bonding descriptors, the scope forring indiceswithin a stochastic object is localto the object, and independent of other ring indices not within thestochastic object. In principle, other well-defined, nonstochasticcycles can be encoded in a similar manner. For example, a ring polymersynthesized with ring expansion metathesis polymerization (REMP) developedby Grubbs and co-workers³³ can also beencoded with similar syntax, as illustrated inFigure5c.

On the other hand, randomly formedcycles, such as the random loops in polymer networks, cannot be explicitlyenumerated because each cycle requires indexing in the SMILES language.While the examples shown inFigure S2b–d (p S11, Section SIV in the SI) do not explicitly present the possibilityof macrocycle formation, the rules of connectivity implicitly allowit, and enumeration of molecular states represented by the BigSMILESstructure according to algorithms for generating gel connectivity,such as the algorithms adopted by Stepto and co-workers,³⁴ Eichinger and co-workers,³⁵ or Olsen and co-workers,^36,37 will includethe formation of these cyclic structures. Examples of BigSMILES stringsfor such structures are included inSection SIV (pp S10–S11) of the Supporting Information.

2.7. Ladder Polymers and Repeating Units with MultiatomConnections

The syntax up to this point assumes that neighboringrepeating units are always connected through a single pair of atoms.However, for some materials, such as ladder polymers, this conditiondoes not hold. To represent ladder polymers or other polymers withmultiple connections between a single monomer pair, the bonding descriptorsare nested by the following syntax:

The outerlayer (everything except the part bracketed by “[...]”)encodes the connectivity between the repeating units with the samesyntax as detailed in previous sections. Atoms on a repeating unitconnecting to the same neighboring repeating units are indicated byan identical outer layer bond type, bond orderb andbond IDn. For detailed examples of the use of nestedbonding descriptors, please refer to p S14,Section SV in the Supporting Information.

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Supplementary Materials