Assessing Greenness of Chemical Reactions and Synthesis Plans

Research Article pubs.acs.org/journal/ascecg

Assessing Greenness of Chemical Reactions and Synthesis Plans through Posetic Landscapes Guillermo Restrepo*,†,‡ and Peter F. Stadler*,∥,⊥,#,∇,○,◆ †

Bioinformatics Group, Department of Computer Science, Universität Leipzig, Leipzig, Germany Laboratorio de Química Teórica, Universidad de Pamplona, Pamplona, Colombia ∥ Bioinformatics Group, Department of Computer Science, and Interdisciplinary Center of Bioinformatics, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany ⊥ Institute for Theoretical Chemistry, University of Vienna, Währingerstraße 17, A-1090 Vienna, Austria # Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, D-04103 Leipzig, Germany ∇ RNomics Group, Fraunhofer IZI, Perlickstraße 1, D-04103 Leipzig, Germany ○ Center for Noncoding RNA in Technology and Health, University of Copenhagen, Grønnegårdsvej 3, DK-1870 Frederiksberg, Denmark ◆ The Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, New Mexico 87501, United States ‡

S Supporting Information *

ABSTRACT: Chemical reactions can be prioritized according to either their attributes or according to properties of their substances. Such a prioritization can be extended to entire synthetic routes and thus makes it possible to assess synthesis plans and look for suitable reactions. The combination of properties of substances to evaluate objects such as chemical reactions or synthesis plans yields partial orders and defines fitness landscapes over the universe of chemical reactions. Three green chemistry examples are used to illustrate the approach: reactions of 3-benzyl-1,3-oxazinan-2-one using environmental information on their synthetic routes and for phenol and caffeine using environmental attributes of the involved substances. KEYWORDS: Chemical reactions, Synthesis plans, Partially ordered sets, Dominance degree, Separability degree, Prioritization, Fitness landscapes, Caffeine

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separately. While  is totally ordered, i.e., any two configurations can be compared unambiguously, as in ranking processes, this is not true in a MOEA setting, where f takes values in a partially ordered set (poset). Posetic landscapes and its basic properties were explored by Stadler and Flamm,6 and here, we analyze them for a particular kind of configuration space (X,R): chemical reactions, which are assessed in green chemical contexts through their attributes and those of their substances. As substances, reactions and reaction paths are terms used in the ensuing discussion; we define them in the next section. Reactions and Reaction Paths through Their Attributes. We start by assigning real-valued attributes to every chemical substance s ∈ S. Formally, we have

INTRODUCTION Evolutionary algorithms have been adapted to optimize problems with respect to several objectives, with applications ranging from engineering1 to medicine2 and chemistry.3,4 Chemical questions like “which substances shall one study from a large library of chemicals, meeting conditions of solubility, toxicity, etc.?” or “how can one “tune” chromatographic variables to attain a good separation?” are solved by applying multiobjective evolutionary algorithms (MOEA).5 In the current paper, MOEA concepts are combined with elements of order theory to solve questions like “which is the greenest reaction from or to a particular chemical?” Optimization problems are conveniently represented as fitness landscapes (X,R,f), where X is a nonempty set of configurations, each of which is assigned a usually real-valued “fitness” f : X → . The relation R of X specifies a notion of similarity or reachability among the configurations. In MOEA, f is usually replaced by a tuple (f1,f 2,...,f m) of m distinct objectives, each of which is supposed to be optimized © XXXX American Chemical Society

Received: December 7, 2015 Revised: February 12, 2016

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DOI: 10.1021/acssuschemeng.5b01649 ACS Sustainable Chem. Eng. XXXX, XXX, XXX−XXX

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ACS Sustainable Chemistry & Engineering

Figure 1. Three fitness landscapes. (A) (Xr, R, f): for chemical reactions, where Xr = {r1, r2, r3}, being ri the i-th chemical reaction; R is the relation of, e.g., being reactions used in a chemical industry, and f is given by attributes of the reactions. (B) (S, R, f): for chemical substances, where S = {s1,..., s7}, being si the i-th substance, e.g., atom economy, reaction yield, etc.; R is the relation of being substances involved in the chemical reactions of Xr, and f is given by attributes of substances, e.g., ozone depletion potential, water solubility, etc. (C) (Xr, R, f), for chemical reactions based on substances, where Xr is as defined in (A), R gathers the order relations of substances found in (S, R, f), and f is given by the handling of those ordering relationships. Details on arrow values are given in the Supporting Information.

Order Theory. Definition 5. For a nonempty set X whose elements x ∈ X are characterized by f(x) = ( f1(x),f 2(x),...,f n(x)), f i(x) being the i-th attribute of x; it is said that y ∈ X dominates x, in symbols , if (1) f i(x) < f i(y) for all i or if (2) f i(x) < f i(y) for at least one i and f i(x) ≤ f i(y) for all other i of the index set. Definition 6. Two elements x, y ∈ X are comparable if either , otherwise they are incomparable, (x∥y). Definition 7. A subset A ⊆ X is an antichain if x∥y for all x,y ∈ A. Definition 8. A binary relation on X is a partial order if for x, y, z ∈ X:

As shown in Figure 1, attributes characterizing substances are, e.g., ozone depletion potential and water solubility. Each attribute fi : S →  defines a “fitness landscape” on the set S of substances. Definition 1. A chemical reaction r is a transformation rule7 of the form ∑s∈Sc−r,Ss → ∑s∈Sc+r,Ss, where S is a nonempty set of substances s, and c−r,S and c+r,S are stoichiometric coefficients. For a chemical reaction r, Er and Pr are further defined: Er ≔ {s ∈ S | c−r,S > 0} and Pr ≔ {s ∈ S | c+r,S > 0} are the sets of educts (reactants) and products of r, respectively. Thus, for reaction r1 (Figure 1), where, for the sake of simplicity, stoichiometry is disregarded, Er1 = {s1, s2} and Pr1 = {s3}. For our purposes, two chemical reactions are distinct if Eri ≠ Erj or Pri ≠ Prj. Definition 2. Two distinct chemical reactions ri and rj are adjacent if In Figure 1, r1 and r2 are not adjacent but r2 and r3 are. Definition 3. A reaction path p = (r1,r2,...,rl) is a sequence of chemical reactions such that ri and ri+1 are adjacent for 1 ≤ i < l. In Figure 1, r2 and r3 form a reaction path. Definition 4. A reaction r is characterized as follows: (1) through its attributes: f(r) = (f1(r),f 2(r),...,f m(r)), with f i being the i-th attribute of r. (2) through attributes of its substances: r is associated with the matrix of q rows and m columns, with q being the number of substances in r and m the number of attributes characterizing substances. Hence, each entry f ij(r) of the matrix shows the j-th attribute of substance si ∈ r. Reactions of Figure 1 are characterized through their attributes atom economy and reaction yield (Definition 4.1). They are also characterized by attributes of their substances (Definition 4.2) such as ozone depletion potential and water solubility. The reaction path p = (r2,r3) may be characterized by the attributes of r2 and r3 (Definition 4.1) and also by the attributes of s4, s5, s6, and s7 (Definition 4.2). As our aim is to prioritize chemical reactions and reaction paths on the basis of their attributes, to this end, we introduce some concepts of order theory.8

A binary relation ≤ on X is a total order if it holds antisymmetry, transitivity, and totality, i.e., x ≤ y or y ≤ x. The couple is called a partially ordered set. , its Hasse diagram H Definition 9. Given a poset is the digraph with vertex set X and arc set A such that (x,y) ∈ A if and only if (i) x ≠ y, (ii) , and (iii) implies u = x or u = y, with u ∈ X. In the Supporting Information, a toy example is included, which shows how a Hasse diagram is built up. Every partial order can be extended to a total order ≤ implies x ≤ y.9 This extension is known as on X such that a topological sorting and ensures that the Hasse diagrams can be drawn in the Euclidean plane such that the vertical coordinate of y is larger than that of x if . Conventional drawings thus show the arcs of the Hasse diagram as undirected edges since their direction is implicit in the vertical coordinates. A natural approach to prioritizing reactions is through the available ordering information about their substances. It is straightforward in principle to think of partial orders of the power set of X. For example, one might say that if Xi,Xj ⊆ X are substances of two reactions or reaction paths, Xi is dominated by Xj if holds for all x ∈ Xi and y ∈ Xj. However, this definition is too stringent for our purposes. Instead, we use a relaxed notion: the degree of dominance and of separability.10 Definition 10. Given two subsets Xi,Xj ⊆ X, the degree of dominance Dom(Xi,Xj) and the degree of separability Sep(Xi,Xj) are given by: B


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Figure 2. Four synthetic reactions (r1 to r4) of 3-benzyl-1,3-oxazin-2-one.

Figure 3. (a) Atom economy (AE), reaction yield (ε), reciprocal of the stoichiometric factor (1/SF), material recovery parameter (MRP), and reaction mass efficiency (RME) of the reactions r1 to r4 depicted in Figure 2, after Tonilo et al.12 (b) Hasse diagram of the reactions characterized by ε and 1/SF.

In the following, we develop a methodology for prioritizing chemical reactions and reaction paths by using the reaction’s or substance’s attributes. Prioritizing Chemical Reactions by Order theory. In this section, we show how the hypothetical cases of Figure 1 are realized by considering three practical cases. Prioritization necessarily requires a context. In utility-based approaches, this is implicitly encoded in the weighting scheme. Here, we advocate to make the context explicit by subselecting attributes that are relevant for a particular decision-making process. In the context of environmental protection the key attributes will be those describing environmental impact such as toxicity, longevity, biodegradability, and so on. In the context of an economical decision between industrial processes, production attributes such as price, availability, storage modalities, and legal regulation will take center stage. One strength of the order theoretic approach is that the effect of different choices of attribute subselections can be studied explicitly. Prioritizing Reactions through Reaction Attributes. This case considers different synthetic routes to a target product. As an illustrative example, we use the four reactions (Figure 2) to 3-benzyl-1,3-oxazin-2-one, used in Alzheimer treatment, recently analyzed regarding their environmental impact.12 Toniolo et al.12 characterized each of the reactions of Figure 2 by five environmental attributes (all of them varying in the real interval [0,1]): atom economy13,14 (AE), reaction yield (ε), reciprocal of the stoichiometric factor14 (1/SF), material

Degrees of dominance and of separability range in the real interval [0,1]. Dom(Xi,Xj) = 1 indicates that all elements in Xi dominate all elements in Xj, while Sep(Xi,Xj) = 1 indicates no single dominance relation among members of Xi and Xj, i.e., they are incomparable. We show, in the Supporting Information, how to calculate dominance and separability degrees for the case of chemical reactions. The advantage of using order theory to assess chemical reactions is that this approach avoids any a priori aggregation or weighting of attributes, which lies at the heart of alternative methods such vector magnitude ratio11 (VMR). Hence, there is no single utility function whose numerical value would be used for ranking. The definition of aggregating utility functions involves subjective choices of both the algebraic form (as a sum, product, or one of many possible choices of averages over individual attributes) and of a collection of weight parameters. VMR, for example, opted for the summation of squares of attribute values. Once these choices have been made, the relative contribution of, and the conflicts between, attributes is hidden in a single number. The order theoretic approach, in contrast, focuses attention on the agreements and disagreements of the attributes. C


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Figure 4. (a) Smog formation SFP, abiotic resource depletion ARDP, and acidification−basification ABP potentials11 for the substances used in four industrial synthetic paths to phenol. (b) Hasse diagram of substances of the paths to phenol using SFP, ARDP, and ABP.

recovery parameter15 (MRP), and reaction mass efficiency (RME) (Figure 3a). The greenest and the worst reactions are those reaching 1 and 0, respectively, for all five attributes. AE indicates to which extent the atoms of the reactant molecules are used to build up the desired product; ε shows how close the amount of product is to the expected amount of material; 1/SF quantifies how near is the reaction to the case of not wasting reactants; MRP regards the amounts of other materials used in the reaction such as solvents and catalysts and RME is a composite indicator of the four previous attributes. The resulting Hasse diagram (derived and analyzed with PyHasse16,17) is an antichain, indicating that at least two attributes order the reactions in a totally different way, e.g., AE , while ε yields . This yields indicates that by considering the five attributes it is not possible to claim which synthesis is better than another. But if the interest lays, e.g., on actually producing the expected amounts of substance, wasting the least amount of educts, the new poset must be based on ε and 1/SF, whose Hasse diagram is shown in Figure 3b. This indicates that there are two reactions (r1 and r2) with low yields and high wasting of reactants, while reaction r4 is the preferred one, for it holds better yields and wastes less educts than all other synthesis. Route r3 is “better” than r1 and r2, but it is dominated by r4. This example shows the connection between fitness landscapes, chemical reactions, and posets and its use in prioritizing reactions. It entails characterizing reactions based on information recovered once they have taken place, i.e., the characterization is a posteriori. However, it is of importance for synthesis plans and for chemical industry to have methods allowing the a priori selection of particular reactions based on theoretical or estimated attributes or on experimental information on the involved substances. In the following example we show how to do it. Prioritizing Reaction Paths (Synthesis Plans) through Attributes of Substances. Here, the ordering of reactions is attained by ordering substances involved in reactions. We show the application of the procedure to the synthesis of phenol, an important industrial chemical precursor of many substances. Andraos11 recently analyzed some industrial reaction paths to phenol where each substance was characterized by different attributes. In the current example, we selected three environmental attributes (potentials) from Andraos’ study11 to define

an environmental context for the study: smog formation (SFP), abiotic resource depletion (ARDP), and acidification−basification (ABP), which are shown in Figure 4a for the most representative substances of each synthetic path. High values for each attribute are environmentally worrisome, while low values are sought for. The four paths are the following: Path 1 (p1) Benzene + H 2SO4 → [C6H5SO3H] + H 2O [C6H5SO3Na] + Na 2SO3 → [C6H5SO3Na] + SO2 + H 2O [C6H5SO3Na] + NaOH → [C6H5NaO] + Na 2SO3 + H 2O [C6H5NaO] + SO2 + H 2O → Phenol + Na 2SO3

Path 2 (p2) Benzene + Cl 2 → [C6H5Cl] + HCl [C6H5Cl] + NaOH → [C6H5NaO] + NaCl + H 2O [C6H5NaO] + HCl → Phenol + NaCl

Path 3 (p3) Benzene + HCl + O2 → [C6H5Cl] + H 2O [C6H5Cl] + H 2O → Phenol + HCl

Path 4 (p4) Benzene + 1‐propene → 1‐methylethyl‐benzene 1‐methylethyl‐benzene + O2 → [C6H5C(CH3)2 OOH] [C6H5C(CH3)2 OOH] → Phenol + Acetone

The associated Hasse diagram to the most representative substances (according to Andraos11) of the synthesis of phenol is shown in Figure 4b, where it is observed that the most problematic substances are H2SO4, HCl, phenol, and 1-propene and that there is no “worse” substance (none of them dominates all the others), but there is a “greenest” chemical, namely, NaCl, dominated by all others. D


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that it is the only path including NaCl, which is the greenest of the substances considered (Figure 4b). Prioritizing Reactions through Attributes of Substances (Derivatization Reactions). The coffee industry is constantly looking for strategies for adding value to its products, and a chemical way of doing it is through chemical transformation of coffee substances.18 In addition, caffeine is an environmental pollutant,19 and reactions addressing its transformation are sought for. In this example, we take caffeine and explore its chemical reactions reported in the literature. On March 12, 2015, we retrieved from SciFinder20 the 661 chemical reactions where caffeine is one of the educts; reactions whose yields were greater or equal to 70% were selected, which led to 220 reactions. As there were several reactions appearing several times in SciFinder, we selected one of them and dropped the others. There were also reactions with same educts, same products but varying in their yields, and we selected the reaction with the highest yield and dropped the others. This procedure led to 176 reactions involving 296 different chemicals. The context to order reactions was environmental and by using the Estimation Program Interface (EPI) Suite21 from the U.S. Environmental Protection Agency, we estimated (in some cases access to experimental data was possible) environmental attributes of the substances. Given EPI constraints, multicomponent substances and salts with no experimental information were excluded, which led to 249 substances that were characterized by the logarithm of the octanol−water partition coefficient (log Kow) and the Henry law constant (HLC), two attributes that are correlated with several other environmental attributes and used for further estimation. Log Kow is a dimensionless attribute calculated through the substance’s concentration ratio between equal volumes of noctanol and water and indicates the distribution of a substance in polar and nonpolar solvents;22 the higher log Kow, the higher the probability of accumulation in nonpolar phases, e.g., lipid portion of organisms or river soils. Log Kow values for the substances here studied ranged from −3.540 to 8.390, i.e., from

With ordering information regarding substances the question that arises is whether is possible to prioritize synthetic paths. This can be achieved by classifying substances belonging to the same path and comparing the order relationships between classes by means of dominance and separability degrees. A stepby-step procedure of how to do this is shown in the Supporting Information. Substances of each one of the synthetic paths to phenol were grouped forming classes pi, with i indicating i-th path. The degrees (dominance and separability), calculated with PyHasse,16,17 are summarized in Figure 5a, which also shows a diagram (Figure 5b) depicting the information. For simplicity, we only depict dominances greater than 0.3. See Supporting Information for more details.

Figure 5. (a) Dominance degree of the synthetic paths pi over pj, the value of each cell corresponds to Dom(pi,pj); Sep(pi,pj) is shown at the bottom. See the Supporting Information for the details of the calculations. (b) Network depicting dominance degrees greater than 0.3, where arc tails and heads indicate dominating and dominated synthetic paths, respectively.

Figure 5b shows that there is no worse synthetic path, for none of them dominates the others. However, there is a green path (although not the greenest), namely, p2, as it is dominated by p3 and p4. Although each substance contributes to the comparison, an important reason for the green behavior of p2 is

Figure 6. Histogram of dominance degree values for 134 chemical reactions where caffeine is an educt. E


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Figure 7. Network depicting dominance degrees greater than 0.8, where arc tails and heads indicate dominating and dominated reactions, respectively. Reactions ri that are dominated by others with a dominance greater than 0.8 are shown in Figure 8. Yellow reactions indicate those involved in dominance degrees greater than 0.9.

hydrophilic to hydrophobic (not readily bioavailable) substances. HLC is the ratio of a substance concentration in the gas phase to that in the aqueous phase at equilibrium;22 it is expressed as atm m3 mol−1. HLC is used as a proxy for chemicals volatility from water and gives indication of potential environmental partitioning between aqueous and gaseous phases. HLC values of the substances studied ranged from 7.96 × 10−23 to 1.83 × 10−1 atm m3 mol−1, i.e., from nonvolatile to volatile substances in an aqueous matrix. In the present study, high values of both attributes are considered worrisome in environmental terms as they are related to mobility and global distribution of the substances. In particular, they indicate substances that may be concentrated in lipid fractions (such as human tissues) and which are highly volatile posing risks, e.g., by inhalation. The Hasse diagram of the 249 chemicals has 2,585 incomparabilities and 16,918 comparabilities and given its complexity23 it is not depicted here. To be able to order reactions, complete information (log Kow and HLC values) of their chemicals is needed. By excluding reactions with missing information, 134 reactions (10 reactions with only caffeine as educt and 124 with caffeine plus another educt) were retained. Upon them, dominance degrees (for short dominances) were calculated. The histogram depicting the distribution of dominance values (Figure 6) shows that most of the values lay below 0.4, i.e., there are few reactions dominating, to a big extent, many other reactions. As the chemical industry’s interest is on environmentally friendly reactions, we looked for highly and frequently

dominated reactions, which we set up as dominances greater than 0.8. This led to the network of Figure 7, analyzed and drawn with Pajek.24 The in-degree of a node in a network is the number of arc heads pointing to the node.25 By exploring the in-degree distribution of Figure 7, it was found that only 19 reactions (Figure 8) have in-degrees different from zero, i.e., only those reactions are dominated by others with a dominance greater than 0.8. In fact, out of the 341 dominances greater than 0.8, 82% are accounted by reactions r107, r80, r17, r50, and r119. The respective in-degrees of these reactions are 100, 100, 52, 17, and 10. Such reactions are those posing less environmental risk, in fact their substances are all hydrophilic and nonvolatile from water. As expected, reactions with only one educt have greater likelihood of posing low risks, as the number of comparabilities contributing to the dominance is lower than that for reactions with more educts. In fact, all 10 single-educt reactions appear among the most dominated reactions. The nine two-educt reactions posing less risk are shown in the right-hand-side of Figure 8. Yellow nodes of Figure 7 depict those reactions whose dominances are greater than 0.9, which shows that only eight reactions, r107, r80, r50 r17, r119, r125, r94, and r74, are strongly dominated by others. The respective in-degree values are 11, 11, 11, 11, 10, 2, 2, and 2, which shows that the first five reactions are those most dominated and correspond to oxidation, methylation, demethylation, chlorination, and isotope labeling of caffeine. F


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Figure 8. Nineteen chemical reactions ri where caffeine is an educt, whose dominance degree values make them less hazardous reactions. Percentages indicate reaction yields.

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By further exploring SciFinder, it is found that the oxidized product of r107 is commercialized by 26 companies; however, its use for further chemical synthesis is still incipient. The methylated product of r80 has been produced without solvents26 and is used in drug design; the product is commercialized by 22 companies. The most commercialized green caffeine product is the resulting from r50 (theobromine), which is the precursor of many substances of pharmacological interest, and it is a metabolic product of caffeine. Another highly commercialized green caffeine product results from r17, sold by 90 companies, and also a precursor of pharmacological substances. A product of more scientific interest, which may result also in novel commercial possibilities for the coffee industry, is the deuterium-labeled caffeine, product of r119, which is used in metabolic studies27 and so far is not commercially produced.

CONCLUSIONS AND OUTLOOK

The idea introduced in this paper is that chemical reactions and even entire pathways and synthesis plans can be ordered by the reactions’ attributes as wholes or by analyzing attributes of their parts (substances). By so doing, three fitness functions are introduced as mapping elements of chemical reactions (either substances or reactions) to posets. For chemical companies where several reactions are already systematized and from which production attributes are at hand, the straightforward application is the ordering of reactions based on those attributes, as exemplified for 3-benzyl-1,3oxazinan-2-one. If syntheses have not been systematized and different synthesis plans for a particular product are regarded, the G


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ordering of reactions based upon substances is an interesting option, helping in the decision of which synthetic path to select. This was exemplified for phenol. The same approach may be used when designing routes to obtain products from a source substance, as shown with the caffeine case. Grzybowski et al.28 have developed interesting algorithms to discover one-pot reactions and to detect synthetic pathways leading to dangerous chemicals. However, those pathways and reactions are not environmentally assessed. Those algorithms combined with the methodologies here presented would be a step forward in discovering green chemical reactions. The examples here considered form connected networks of chemical reactions, where either a target or starting substance is the source of connectedness. However, the methods devised may be applied to unconnected networks, e.g., 100 reactions with no common substance(s) produced by a company and whose environmental impact wants to be assessed. When characterizing reactions by the attributes of their substances, the differentiation between educts and products is disregarded. If further refinement is needed, e.g., more emphasis on products than in educts, the respective orderings among educts and among products of the reactions considered need to be worked out, which leads to split dominance and separability of any two reactions into subdominances and subseparabilities for educts and for products, opening the door for further ordering studies. There are several questions that can be addressed through partial orders regarding synthesis, e.g., which values are required for the attributes to make one synthesis better or worse than another? How probable is it that one synthesis comes out better or worse than another? Which attribute most affects the ordering? The methods to address questions of this sort are found in refs29−31 and can be computed with PyHasse.17

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ASSOCIATED CONTENT

* Supporting Information S

This material is available free of charge via the Internet at http://pubs.acs.org/. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssuschemeng.5b01649. Examples for building up Hasse diagrams and for calculating dominance and separability degrees. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected],grestrepo@ unipamplona.edu.co (G.R.). *E-mail: [email protected] (P.F.S.). Notes

The authors declare no competing financial interest. The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Guillermo Restrepo thanks the Universidad de Pamplona and the Alexander von Humboldt Foundation/Stiftung for supporting this research.

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REFERENCES

(1) Prada, D.; Bellini, M.; Stevanovic, I.; Lemaitre, L.; Victory, J.; Vobecky, J.; Sacco, R.; Lauritzen, P. On the Performance of Multiobjective Evolutionary Algorithms in Automatic Parameter H


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Assessing Greenness of Chemical Reactions and Synthesis Plans

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