Critical Evaluation of Published Algorithms for Determining Material

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Critical Evaluation of Published Algorithms for Determining Material Efficiency Green Metrics of Chemical Reactions and Synthesis Plans John Andraos ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.5b01554 • Publication Date (Web): 04 Mar 2016 Downloaded from http://pubs.acs.org on March 11, 2016

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ACS Sustainable Chemistry & Engineering

1 Critical Evaluation of Published Algorithms for Determining Material Efficiency Green Metrics of Chemical Reactions and Synthesis Plans John Andraos*, CareerChem, 504-1129 Don Mills Road, Toronto, ON M3B 2W4 Canada ([email protected])

Abstract In this paper we evaluate seven published algorithms on determining material efficiency green metrics for individual chemical reactions and synthesis plans with respect to their implementation by professional chemists and chemical engineers. Specifically, we compare and contrast calculation outputs, visual displays, and ease of use. For a direct head-to-head comparison of algorithm performances, thereby establishing consistency, all methods are tested on the same set of chemical examples taken from Organic Syntheses and journal articles that first introduced the algorithms in the literature. For brevity, the Supporting Information contains detailed instructional notes and calculation outputs and visuals for each example highlighted. Misconceptions and misinterpretations of applying materials metrics analysis when making claims of greenness for reactions and synthesis plans are also discussed.

Keywords: algorithms, green chemistry engineering, metrics analysis, sustainability metrics

Introduction For chemical professionals introduced to the field of green chemistry for the first time, the topic of metrics may at first appear daunting and somewhat overwhelming for several reasons. Nevertheless, understanding this topic and its associated tools is important not only for grasping concepts in green chemistry, but also for legitimizing the subject as a serious branch of chemical science. The primary problem is the apparent large number of undifferentiated metrics that have been advanced, many of which have similar definitions yet are often described with different names depending on the author. For example, the term “experimental atom economy”1 is synonymous with “kernel reaction mass efficiency (RME)”2, the term “balance yield (bilanzausbeute)”3 is synonymous with “overall or global RME”2, the term “mass index”4 is identical to the reciprocal of overall RME2, the term “mass intensity”5 is synonymous with

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2 “process mass intensity”6, and the term “effluent load factor”7 is synonymous with “E-factor”8. This lack of standardization makes it difficult to choose which metrics are meaningful and useful to amply describe the performance of a chemical reaction or sequence against another. It also gives the false impression that the choice of metrics is arbitrary or that certain material efficiency metrics are inferior to others in properly describing input material utilization, or conversely, waste production. Such a notion whose underlying assumption is that a set of material efficiency metrics are treated as separate unconnected entities, suggests a hierarchy among them where some are favored more than others. For example, reaction yield, conversion, and selectivity, which are well-known and appealing metrics to synthetic organic chemists, may be sufficient to describe the efficiency of converting a given substrate to a desired target product under a given set of reaction conditions but appear to be insufficient in accounting for all of the waste production since all auxiliary materials are ignored. On the other hand, atom economy describes the synthesis design efficiency in planning a reaction to a given product so as to minimize reaction byproducts, but appears not to account for both reaction yield performance and auxiliary material consumption, namely, reaction solvents. In reality, when all of the essential material efficiency metrics are integrated together through the use of balanced chemical equations, in a simple input-output mass balance analysis, they become equally important because there is an underlying mathematical connection between them. Hence, arguments that suggest, for example, that atom economy is less important or less informative than global reaction mass efficiency miss the point of integrated understanding. After nearly two decades of various reports appearing in the literature advancing stand-alone metrics to describe material efficiency either in terms of input material utilization or waste material production, the consensus is that process mass intensity (mass ratio of all input materials used versus desired product) has now become the best metric to parameterize overall material efficiency performance. More importantly, this metric can be mathematically decomposed into its constituent contributing metrics mentioned earlier that were originally introduced as separate entities. Part 1 of the Appendix at the end of this paper shows this decomposition explicitly for any given chemical reaction, and therefore emphasizes that all of the essential material metrics are equally valued. This strong foundational connection implies that true optimization toward greenness via PMI is achieved when each of the contributing metrics to PMI are optimized in an orchestrated fashion in the same positive direction. This unified strategy sharply contrasts one that treats each metric


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3 separately and attempts to optimize any one contributing metric at the expense of others. Moreover, a reviewer has emphasized that “a significant disadvantage of material-efficiency metrics is that they are nearly useless for determining the greenest synthesis because they treat all materials as equally damaging or hazardous on a per unit mass basis.” This point will be elaborated on and addressed in the subsequent paper dealing with a comparison of algorithms that include environmental and safety-hazard metrics, as well as material efficiency metrics, thereby differentiating substances beyond mass. One impediment that has helped to fuel these misinterpretations is that since the mid-2000s, authors have published new algorithms without comparing their performances against prior published works using the same chemical examples. This oversight has slowed progress both in wide implementation of any individual algorithm and in standardization of green metrics calculations in general. In this paper we address this gap in the literature with a view to compare and contrast seven published algorithms which practicing chemists and chemical engineers can implement directly in their work whenever green chemistry issues arise. Specifically, we address the following issues: correctness and completeness of the calculations, the presence and quality of visual aids, user friendliness, strengths and limitations of each method, areas of further study and common errors to avoid. We argue that any discussions of reaction or synthesis plan optimization are fundamentally discussions about green chemistry principles. Furthermore, we have recently demonstrated that the most effective way of conveying green chemistry concepts is through rigorous quantitative analysis that concretizes them through worked examples 9. The seven algorithms discussed herein are the following: Environmental Assessment Tool for Organic Synthesis (EATOS) 4,10,11-, Andraos algorithm 2,12-16, Augé algorithm 17-19, American Chemical Society Process Mass Intensity (PMI) Calculator 20, Green Aspiration Level (GAL) 21, EcoScale 22, and Green Star 23-27. We briefly describe how each method handles calculations of material efficiency metrics for single reactions, linear plans, and convergent plans. To streamline the flow of the paper we highlight only key features of worked out results of each algorithm applied to the same set of chemical examples taken from Organic Syntheses and those selected by authors when they first introduced their methods in the literature. This gives, for the first time, direct head-to-head comparisons of each algorithm with respect to material efficiency so users can readily see their respective merits and limitations. For brevity, the Supporting Information contains extensive instructional notes and calculation outputs for



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4 each example. Wherever possible we also supply missing information not given in the original publications so that prospective users can fully understand how a given algorithm is implemented. In the subsequent paper 28 we describe in detail how each method handles calculations of environmental impact metrics, again using the same set of chemical examples. Based on our experience, we conclude with discussions on pitfalls in using material efficiency metrics and recommendations on best practice applications of certain algorithms as appropriate. We also suggest possible further refinements to improve the content and presentation of the algorithms. The chemical examples fall into three categories of analysis: individual reactions, linear plans, and convergent plans. For stand-alone reactions, the synthesis of 2,2-diethoxy-1isocyanoethane 29 was selected. For linear plans, the syntheses of thiete- 1,1-dioxide (3 steps) 30, and 2-methyl-4-nitro-5-propyl-2H-pyrazole-3-carboxylic acid (5 steps) 21, a key intermediate in the synthesis of sildenafil, were selected. For convergent plans, ethyl phenylcyanopyruvate (3 steps, 2 branches) 31-33, sildenafil (7 steps, 2 branches) 21, and a PEG-based polyol (10 steps, 3 branches) 19, were selected. Part 2.7 of the Supporting Information also contains an advanced convergent plan example for coenzyme A (22 steps, 6 branches) 34. Schemes 1, 2, and 3 show the synthesis strategies for each of these target molecules. The subsequent paper applies these algorithms to three different synthesis routes to aniline and four reaction procedures to iron(II)oxalate dihydrate. In that paper, both material efficiency performance and environmental and safety-hazard impacts are evaluated and compared for those examples. The interplay between these groups of metrics in deciding the overall greenness of competing routes to the same target products is illustrated.


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5

Scheme 1. Synthesis plans for 2,2-diethoxy-1-isocyanoethane, thiete 1,1-dioxide, and 2-methyl4-nitro-5-propyl-2H-pyrazole-3-carboxylic acid.



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8

Scheme 2. Synthesis plans for ethyl phenylcyanopyruvate, sildenafil, and a PEG-based polyol.


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9

Scheme 3. Synthesis plan for coenzyme A (see Part 2.7 in Supporting Information).



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10 Material Efficiency Metrics The metrics focused on in this work are reaction yield (RY), atom economy (AE), Efactor (E), reaction mass efficiency (RME), and process mass intensity (PMI) applied to both individual reactions (designated with the term “step”, as in step PMI) and overall synthesis plans (designated with the term “global”, as in global PMI). We also use the term “kernel” on E, RME, and PMI to refer to the fundamental stoichiometric case when no excess reagent or auxiliary material contributions are counted in the computation of both step and global metrics parameters. Table 1 summarizes the essential features of each algorithm, listed in chronological order, with respect to metrics parameters calculated, visual aids presented, ease of use, and limitations. Tables 2 to 4 summarize the material metrics calculated for 2,2-diethoxy-1isocyanoethane (single reaction), thiete 1,1-dioxide (linear plan, 3 steps), and ethyl phenylcyanopyruvate (convergent plan, 3 steps, 2 branches) according to the sequences shown in Schemes 1 and 2 using the seven algorithms. Tables S1 to S4 given in Part 1 of the Supporting Information summarize the same parameter outputs for the syntheses of 2-methyl-4-nitro-5-propyl-2H-pyrazole-3-carboxylic acid, sildenafil citrate, a PEG-based polyol, and coenzyme A based on Schemes 2 and 3.

Table 1. Summary of material efficiency features for all seven algorithms. Algorithm

Chemical

Green

systems

metrics

handled EATOS

S, L, C

1

(2005)

S, L, C

Ease of use

Limitations

Histograms

Requires

No complete

for E and

separate Java

report of

PMI

script

calculations

performance

program to

via single

run

command

parameters AE, E, PMI

(2001)

Andraos

Visual aids

AE, E,

radial

Uses

Prone to user

RME, PMI

polygons,

template

transcription

histograms,

Excel

errors when

pie charts

REACTION

entering the

and

same data in


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11

EcoScale

S

AE only

none

(2006)

SYNTHESIS

different

spreadsheets

worksheets

Very easy to

Based on

implement

arbitrarily chosen penalty score; not able to handle synthesis plans

Augé

S, L, C

(2008)

AE, RME,

none

PMI

Provides a

Requires co-

fast method

verification by

of

other methods

determining

to avoid errors

overall PMI

in convergent

for a

plan analysis;

synthesis

no automated

plan

template calculator available

Green Star

S

AE only

(2010)

radial

Attempts to

Based on

polygons

quantify all

arbitrarily

12 principles

chosen merit

of green

score ranging

chemistry

from 1 (non-

using a merit

green) to 3

point system

(green); no automated template available

ACS PMI

S, L, C

PMI only

None

Uses


Assumes


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12 Calculator

template

scaling factor

(2012)

Excel

of 1 in all

spreadsheets

reactions; limited only to PMI determinations

GAL

S, L, C

AE, E, PMI

pie charts

(2015)

Allows

Assumes

determination scaling factor of step E-

of 1 in all

factor and

reactions; no

step PMI

automated

contributions

calculator template available

1

S = single reactions; L = linear plans; C = convergent plans.

Table 2. Summary of global material metrics calculated for the synthesis of 2,2-diethoxy-1isocyanoethane.1 Algorithm

RY (%)

AE (%)

E-factor

RME (%)

(kg/kg)

PMI (kg/kg)

EATOS

NC

21.1

37.2

NC

38.2

Andraos

62.8

21.1

37.2

2.6

38.2

Augé

62.8

21.1

37.2

2.6

38.2

ACS PMI

NC

NC

NC

NC

38.2

GAL

62.8

21.1

37.2

NC

38.2

EcoScale

62.8 (19

NC

NC

NC

NC

21.1

37.2

NC

38.2

penalty points) Green Star 1

62.8

NC = not calculated.

Table 3. Summary of global material metrics calculated for the synthesis of thiete 1,1-dioxide.1


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13 Algorithm

RY (%)

AE (%)

E-factor

RME (%)

(kg/kg)

PMI (kg/kg)

EATOS

NC

33.1

357.8

NC

358.8

Andraos

19.6

33.1

357.8

0.3

358.8

Augé

19.6

33.1

357.7

0.3

358.7

ACS PMI

NC

NC

NC

NC

358.8

GAL

19.6

33.1

357.8

NC

358.8

EcoScale

NA

NA

NA

NA

NA

Green Star

NA

NA

NA

NA

NA

1

NC = not calculated; NA = not applicable.

Table 4. Summary of global material metrics calculated for the synthesis of ethyl phenylcyanopyruvate.1 Algorithm

RY (%)

AE (%)

E-factor

RME (%)

(kg/kg)

PMI (kg/kg)

EATOS

NC

47.9

10.7

NC

11.7

Andraos

54.9

47.9

10.7

8.5

11.7

47.9

10.7

8.5

11.7

(steps 1 and 2), 55.3 (steps 1* and 2) Augé

54.9 (steps 1 and 2)

ACS PMI

NC

NC

NC

NC

11.7

GAL

54.9 (steps 1

47.9

10.7

NC

11.7

and 2) EcoScale

NA

NA

NA

NA

NA

Green Star

NA

NA

NA

NA

NA

1

NC = not calculated; NA = not applicable.

Environmental Assessment Tool for Organic Synthesis (EATOS)



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14 The EATOS program was first made available in 2001 and is the pioneering work on automated material efficiency green metrics calculations for individual reactions and synthesis plans 4,10. This program runs on various Windows operating systems and is freely available online through registration, however it requires a separate Javascript program (Java Run Time Environment (version 1.4)) to run it. Since 2001 no newer versions have been published. EATOS calculations are correct and agree entirely with results from recent REACTION and SYNTHESIS spreadsheets given by Andraos as shown by comparison of the results given in Tables 2 to 4. Although the program is easy to use and reliable, the user needs to be made aware of terminologies used by the author and caveats about using the program properly which are not described in the accompanying manual 3. Hence, in the EATOS folder of the Supporting Information we included simplified and step-by-step instructions on how to implement EATOS using the worked examples summarized in Tables 2 to 4. The program works out global PMIs and global E-factors for individual reactions and entire synthesis plans, and it breaks them down into their constituent contributions according to substrates, catalysts, solvents, auxiliary materials, coupled products, and by-products. In terms of terminologies, EATOS uses “atom selectivity” to mean “atom economy”, “mass index (S-1)” to mean “process mass intensity”, and “mass efficiency” to mean “global reaction mass efficiency”. The phrase “by-products” refers to products arising from competing reactions other than the entered balanced chemical equation, what we call “side products” 36; and the phrase “coupled products” refers to products arising as a consequence of producing the desired product according to the balanced chemical equation, what we call “byproducts” 36. The program performs more reliably if masses of isolated intermediate products in each step are entered rather than reaction yields, which have to be worked out independently by the user. It does not calculate overall reaction yields for synthesis sequences. For analyses of syntheses the program uses a nested chain method of importing data sheets containing masses of intermediate products and input materials in the forward sense beginning from the first step and working towards the last step in a plan. This works fine for keeping track of step numbers in linear plans, but does not work effectively for convergent plans. The output histogram for convergent plan performance does not display information about individual steps in convergent branches even though they are definitely taken into account numerically in the calculations of global E-factor and global PMI. The program appears to compress all steps in a convergent branch leading up to a convergence point as a single step and determines the overall


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15 step count as the difference between the number of steps along the longest branch and the number of convergence points along it. As an example, the EATOS step performance histogram for the entire synthesis of coenzyme A shows only 8 steps; however, the synthesis plan is composed of 22 individual reaction steps in total with 11 steps along its longest chain and has 5 convergent branches (i.e., 5 convergence points) in turn composed of 2, 1, 6, 1, and 1 steps, respectively. Three of the five convergence points lie along the main branch of 11 steps; hence, EATOS counts the overall number of steps in the synthesis plan as 11 – 3 = 8. Mole scales are continuously adjusted along the way as subsequent steps are linked together in the chain; however, the user is blind to these calculations and the scaling factors are not included in the program output yet it is clear that they are used in the calculation otherwise the program would not yield results that are consistent with other algorithms (see Tables 2 to 4). Since the program operates in the forward sense, an arbitrarily chosen target basis scale for the final product in a plan cannot be chosen and therefore the corresponding adjusted masses of all input materials in an entire plan cannot be worked out accordingly in a backwards fashion. This is a problem for practical reasons when wanting to purchase correct quantities of ingredients for the production of a chosen mass of final product. Curiously, the number of moles of reagents or products is not calculated in the data sheets. This is problematic in designating which reagent is the limiting reagent, especially when dealing with convergent steps that begin with substrates from different branches. One needs to do separate calculations outside the program to determine the number of moles of each imported substrate to ensure proper assignment of limiting reagents for entry in the “Substrate 1” field in the substrate-product-coupled products sheet. Entering a reagent used in excess in the “Substrate 1” field results in an error message later in the program, when the user attempts to calculate the E-factor and PMI parameters, telling the user that insufficient input material was used in the reaction. Essentially the calculation of the metrics parameters aborts. Since there is only one opportunity to correctly import and enter data pertaining to molecular formulas and stoichiometric coefficients for substrates, products, and coupled products with respect to limiting reagent and excess reagent designations, rectification of this kind of error in this data sheet can only be done by deleting it and starting again. Despite this restriction, it has a useful alert feature that informs the user to make necessary adjustments if an entered equation is improperly balanced. However, changes can be made to masses of all entered materials in the subsequent second seven-sheet window for substrates-catalysts-solvents- auxiliary materials-



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16 product-coupled products-by-products. Auxiliary materials for work-up and purification are lumped together so it is tedious to work out separate E-workup (PMI-workup) and E-purification (PMI-purification) contributions. The only output of the program is a histogram of four bars pertaining to global E-factor and global PMI outputs with and without environmental impact factor corrections. A full numerical report of step and global E-factor and PMI outputs is not possible with one keystroke or menu selection. Instead, the cursor needs to be brought over a particular section of any of the four histogram bars followed by a mouse click in order to view its corresponding partial numerical report, which can then be cut and paste into a word processing program. The procedure is awkward since it is repetitive to export several entries in a long plan of many steps, especially when sections of the histogram are too small to display on the scale shown. The histogram scale unfortunately cannot be expanded or shrunk using zoom in or zoom out functions in order to circumvent the cursor problem when obtaining numerical results for small (less than 1%) contributions to S-1 (PMI) or E-factor bars; for example, from catalysts and excess reagents. This is problematic when the contribution by auxiliary materials usually overwhelms other contributions.

Andraos Algorithm The Andraos algorithm first described in 2005 2 makes use of REACTION and SYNTHESIS Microsoft Excel spreadsheets to automate material efficiency green metrics analysis for any reaction or synthesis plan. The main features of the algorithm are the use of a ubiquitous software package with embedded formulas in template workbook sheets and the extensive use of visual diagrams such as radial polygons and histograms to help the user pinpoint strengths and weaknesses in reaction performance so that appropriate optimization can be made. Overall reaction performance with respect to material efficiency is determined by the vector magnitude ratio (VMR) 35, a convenient parameter for ranking different reactions to the same target product, that is based on the mathematical relationship that connects RME or PMI to RY, AE, excess reagent contribution, and auxiliary material contribution 9,13 (see equation (1)). An analogous pseudo-VMR parameter based on the same principle may also be defined for ranking different synthesis plans to the same target product. Here, it should be noted that the radial pentagon for overall synthesis plan performance is composed of global AE, overall yield (with respect to the longest branch), global excess reagent consumption, and global material recovery


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17 parameter. Unlike the case of single reactions, the multiplication of these four parameters does not formally equal global RME for a plan; however, the radial diagram is useful in describing which of the four parameters may be responsible for high or low values of global RME. The main features of the spreadsheet program have already been discussed in detail elsewhere 1. Here, we only mention limitations and caveats on its use. Though the handling of linear plans is simple, the application of the algorithm to convergent plans requires care but is made easier using synthesis tree diagrams which help the user better keep track of branches, points of convergence, and reaction steps. Synthesis tree diagrams 9,36 are constructed using ChemDraw (a software component of ChemBioOffice Suite) and illustrations may be imported directly into Excel. The first limitation in using the REACTION and SYNTHESIS spreadsheets is ensuring the fidelity of data entries copied from REACTION spreadsheets for individual reactions (masses of materials and scaling factors) to the master SYNTHESIS spreadsheet that determines the performance of an entire plan. The second limitation is the entry of the correct number of reaction blocks in the SYNTHESIS spreadsheet that correspond to individual reaction steps in a manner that preserves all embedded formulas. These added blocks involve inserting extra rows in the spreadsheet, which necessarily requires adjustments in the cells corresponding to sums of quantities in appropriate columns. Mastery in the use of Excel is paramount in implementing the Andraos algorithm confidently. Transcription errors and adjustments of rows with embedded formulas can be eliminated if all spreadsheets and synthesis tree diagrams are integrated into one seamless software interface that requires only one set of data to be entered once as is done in the EATOS software package.

Modified Augé Algorithm The Augé algorithm 11 was introduced in 2008 with the aim of establishing a universal mathematical relationship between the global material economy (GME), equivalent to global PMI, of a generalized synthesis plan – linear or convergent – and its global atom economy (GAE). For the sake of clarity of definitions, Augé used the term “mass intensity” (MI) to mean PMI and used the relation MI = E + 1 which is identical to PMI = E + 1. GME was defined as 1/MI, exactly as the Andraos definition of RME was defined, namely, RME = 1/PMI. GAE is identical to the term “overall AE” used by Andraos and EATOS. GAE represents the hypothetical maximum value of GME, when all reaction yields are equal to 100 %, and no



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18 excess reagents or auxiliary materials are used. Hence, the following relationships hold: gPMI =

1 1 1 1 1 = = E + 1 and gPMI min = = = = Emin + 1 , gRME GME gRMEmax GMEmax GAE

where it is understood that Emin = 0 is the ideal lowest E-factor value and GAE = 1 is the ideal highest atom economy value when no byproducts are produced in any reaction in a synthesis plan and all other materials are excluded. The algorithm was first derived for a single step reaction and extended to multi-step sequences and then applied to the Novartis synthesis of discodermolide 18 and the author’s synthesis of PEG-based dendrimer polyols 19. No accompanying visual aids of the calculation results were included and no template calculator was given to facilitate computation. To make it user friendly and practical, we recast the complex algorithm in simplified notation and connect it to parameters already defined in the EATOS and Andraos algorithms. We call this a modified Augé algorithm. In the Supporting Information we also supply a simple user-friendly Excel template (modified-Auge-algorithm.xls) with graphical display of step PMI contributions that is applicable to linear and convergent plans. For a single reaction, the Andraos relation for global PMI is given by equation (1)

gPMI =

SF ε ( AE )( MRP )

(1)

where, SF and MRP are the stoichiometric factor and the material recovery parameter respectively and are given by equations (2) and (3).

SF =

actual mass of reagents excess mass of reagents = 1+ stoichiometric mass of reagents stoichiometric mass of reagents

MRP =

( SF )( mass of target product ) ( SF )( mass of target product ) + ε ( AE )( mass of auxiliaries )

(2)

(3)

The Augé algorithm rewrites equation (1) as shown in equation (4) (see derivation in Part 2 of the Supporting Information).

gPMI =

1+ b + s ε ( AE )

(4)

where, the parameters b and s are given by equations (5) and (6). b=

mass of excess reagents stoichiometric mass of reagents

(5)


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19

s=

mass of auxiliaries stoichiometric mass of reagents

(6)

The simple connecting relationships between the Andraos SF and MRP parameters and the Augé b and s parameters are given in equations (7a) and (7b) (see derivation in Part 2 of the Supporting Information). SF = 1 + b

MRP =

(7a)

1+ b 1+ b + s

(7b)

The kernel PMI is found when SF = 1, MRP = 1, b = 0, and s = 0 implying no excess reagents and auxiliary materials are used. Application of our modified Augé algorithm to synthesis plans differs significantly in form and structure from the original. For a linear plan of N steps, the expression for global PMI is given by equation (8) (see derivation in Part 2 of the Supporting Information).

gPMI =

 N    Term 1 − Term 2 ( ) ( ) ∑  k k  MP  N k =1  1

 1  N  1 = ∑ MP  ε ε ε ...ε N k =1  k k +1 k + 2 N

 1 + B + s k k    ( AE ) k 

      MP − MP k k −1       

(8)

where M P is the molecular weight of the final target product, M P is the molecular weight of N k intermediate product in step k, ( AE )k is the atom economy of step k, and Bk = ∑ bk , j is the j sum of all excess reagent contributions in step k from j reagents. When dealing with convergent plans involving multiple ancillary branches in addition to the main branch, as expected, the analysis increases in complexity. There are two tasks to perform which are greatly facilitated by the use of synthesis tree diagrams discussed in our previous work 36. The first task is to locate the convergent steps in the plan. The second task is to identify in each convergent step which substrate is used in excess, i.e. either the intermediate product of the preceding step along the main branch, or the terminal intermediate product of the convergent branch. This second task is extremely important because it will determine how the φ scaling factors for each convergent step are to be entered in the formula for global PMI. The φ scaling factor is defined as the ratio of actual moles of a substrate used in excess and the stoichiometric moles of that substrate. The



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20 range of φ is therefore φ ≥ 1 . For a convergent plan consisting of a long branch of N steps and two shorter branches composed of M and Q steps respectively, the global PMI expression takes on the form given in equation (9). Here it is assumed that in each convergent step, the excess reagents arise from the terminal intermediate products of each convergent branch (see derivation in Part 2 of the Supporting Information). This means that the φ scaling parameter for each convergent step is multiplied across all input materials contained in its corresponding convergent branch. For the main branch, φ is defaulted to 1.

 N      1 + Bk + sk  1    MP − MP    ∑  ε ε  k k − 1  → ε N    ( AE )   k =1 k k +1 k      branch 1, N steps       M     1 + Bk ' + sk '  1  1        gPMI = ' M M + − φ   ∑  ε ε → ε ε    ( AE )  Pk ' Pk '−1   MP   M r   k'  N   branch 2, M steps   k '=1 k ' k '+1      Q      1 + B + s  1 +φ "   k '' k '' ∑  ε ε → ε ε '    ( AE )  M Pk '' − M Pk ''−1     Q r   k ''    branch 3, Q steps    k ''=1 k '' k ''+1  −

φ "M P φ ' M P Q M +  εr ' M P  εr N  1

  

(9) where, M P is the molecular weight of the final product in the synthesis plan N Bk = ∑ bk , j , Bk ' = ∑ bk ', j , Bk '' = ∑ bk '', j contributions from excess reagents j j j

sk , sk ' , sk '' contributions from auxiliary materials M P , M P M P molecular weights of isolated intermediates k

k'

k ''

( AE )k , ( AE )k ' , ( AE )k '' , step atom economy terms ε r , chain of yields from convergent step in branch 2 to end of synthesis along main branch to final product ε r ' , chain of yields from convergent step in branch 3 to end of synthesis along main branch to final product φ ' , actual moles of terminal product in branch 2/stoichiometric moles of terminal product in branch 2


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21

φ " , actual moles of terminal product in branch 3/stoichiometric moles of terminal product in branch 3 Comparing the form of equation (9) with that in equation (8) for a linear plan, we observe that the symbolism of the summed terms in square brackets for each branch is preserved. The additional terms referring to the masses of terminal products in each convergent step need to be subtracted off since they are not considered net input materials – they are made in preceding steps and then are committed as reagents in the following steps. We also note that the φ parameters appear as multiplying factors outside of the terms referring to the convergent branches only. For the case when in a convergent step the excess reagent is the intermediate product in the main branch, rather than the terminal product of the convergent branch as mentioned above, the φ parameter for that product is multiplied across the chain of input materials along the main branch that precede that convergent step but only up to the first preceding convergent step. This situation is encountered in the example of the PEG-based polyol synthesis and is described in detail in Part 2.6 of the Supporting Information. More complicated situations may be encountered when both kinds of cases arise in the same plan, particularly if the plan has many convergent branches. The modified Augé algorithm applied to convergent plans is therefore tricky since correct implementation of the φ multipliers to each branch at the junction of converging branches requires great care. We emphasize that the synthesis tree diagram facilitates identifying those convergent steps and annotating which intermediate products are used in excess to ensure correct implementation of the φ parameters. It is advisable in our experience to independently check the results of the modified Augé algorithm using either the Andraos or EATOS algorithms. The example of coenzyme A given in Part 2.7 of the Supporting Information involving 6 branches is an excellent exercise to test the consistency of results of all three algorithms. The results shown in Tables 2 to 4 and S1 to S4 indicate complete agreement between algorithms for the examples selected. Furthermore, the formalism of the expressions given in equations (8) and (9) for linear and convergent plans is much simpler to follow than the original Augé formalism and avoids the problem of nonintuitive negative-valued b coefficients that are defined differently in the original work. Recall that in the present modified formalism the definition of b for excess reagent consumption given by equation (5) for a single reaction is always a positive quantity as are the related B parameters appearing in equations (8) and (9) for synthesis plans, so there is no loss in meaning. It should be



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22 noted that the complex form of equations (8) and (9) does not allow complete factorization or separation of global PMI into terms exclusively representing global atom economy and overall yield as is done in equation (4) for a single reaction as shown in the Appendix (Part 2). Part 3 of the Appendix also shows a simple proof that equation (8) preserves the inverse relationship between PMI and GAE for a two-step linear sequence. A similar proof can be written using equation (9) for convergent sequences. ACS PMI Calculator The American Chemical Society PMI calculator 20 came about from various workshops of the Pharmaceutical Roundtable sponsored by the Green Chemistry Institute based in the United States. Following the consensus reached by process chemists in the pharmaceutical industry that PMI is the go-to parameter to describe material efficiencies for reactions and synthesis plans 6,37, the calculator is focused exclusively on this parameter since it is very easy to calculate. PMI also has a psychological advantage in that it is a quantity determined from a positive point of view, rather than the negative waste point of view advanced by the E-factor. This is akin to viewing a glass as half-full versus as half-empty, though both views are equally valid. The calculator is set up using a Microsoft Excel template spreadsheet and is freely downloadable 20. Nevertheless, currently the website contains only one example pertaining to a simple two-step reaction sequence; no examples are available for convergent plans, though a template file is available to carry out such a calculation. There are no accompanying visual aids, though these can be created through the use of histograms that showcase step PMI contributions. These contributions could be further dissected into reaction solvent usage, workup material consumption, and purification material consumption. From the connecting relationship, PMI = E + 1, a histogram of step E-factor contributions could also be constructed. This simple relationship is powerful since it allows the determination of E without having to itemize each material that contributes to the global waste produced in a reaction or synthesis plan. It is not always the case that the identities of each waste material are known. In fact, it is computationally very simple to determine PMI by summing all masses of well defined input materials and dividing by the mass of isolated product. The mass of global waste is determined by taking the difference between the overall sum of input materials and the mass of isolated product. Both arithmetic computations do not require knowledge of chemistry or balancing


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23 chemical equations. For industrial reactions, like biotransformations, that cannot be written as properly balanced equations, it is still possible to determine PMI and E. Such E-factor histograms would allow the pinpointing of which steps contribute the most and least to the overall waste generated in a plan. The main restriction in the calculator’s use is that the output mass of product from one reaction step is inputted directly as a reagent mass in the following step. This means that the scaling factor from step to step is fixed at 1. If one wishes to work out the material efficiency of a synthesis plan composed of separate reaction steps carried out at different mole scales, as is commonly encountered in the chemistry literature, the calculator is unusable until all the scaling factors are worked out beforehand. In fact, from the way it is set up, no knowledge of a balanced chemical equation is actually required, only the recipe of amounts of ingredients from step to step are needed with the assumption that the entire product output of the previous step is committed as input in the next step. From a green chemistry perspective this tool is currently oversimplified and limited in scope, but is also easily improvable.

Green Aspiration Level (GAL) The green aspiration level (GAL) concept 21 introduced by process chemists in the pharmaceutical industry adjusts calculated E-factors by correcting them for reaction complexity. The authors defined complexity as the difference between the total number of steps in a synthesis plan and the number of steps that are concession reactions; that is, reactions that are sacrificial and do not produce target bonds in the final product structure. Andraos has previously compiled an extensive database of sacrificial and target bond forming reactions (construction reactions) in a survey of over 1000 academic and industrial synthesis plans in the literature covering 12,000 reactions and over 200 target products including pharmaceuticals, agrichemicals, natural products, dyestuffs, fragrances, high value industrial chemicals, and molecules of theoretical interest 35,38. Equations (10a) and (10b) define minimum and maximum values of GAL depending on whether minimum and maximum values of E-factor are used in the computation, respectively. The authors used the terms “simplified E-factor” to refer to an E-factor that excludes solvent and water consumption (Emin), and “complete E-factor” to refer to an E-factor that includes them (Emax). The latter term is consistent with the traditional definition of E-factor.



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24

E GALmin = min ( complexity ) 9

(10a)

E GALmax = max ( complexity ) 9

(10b)

Both the minimum and maximum values of GAL are referenced to an arbitrarily chosen complexity value of 9. This number was determined under the assumption that the average number of synthesis steps (i.e., isolations) in a plan to a drug target is 7 and that each step involves on average of 1.3 chemical transformations excluding any sacrificial/concession transformations. Hence, the multiplication of 7 and 1.3 leads to 9.1. The computation of all Efactors for synthesis plans was done using the ACS PMI calculator using a step scaling factor of 1 throughout. The authors used the linear synthesis of 2-methyl-4-nitro-5-propyl-2H-pyrazole-3carboxylic acid and the convergent synthesis of sildenafil citrate as illustrations of their method. The authors did not disclose how they transformed the virgin experimental data for all amounts of materials used in each reaction step into the adjusted mass scales needed to implement the ACS PMI calculator. Clearly, this had to be done prior to using the PMI calculator since, as discussed in the previous section, it has no provision for implementing scaling factors. Step and global PMIs were computed and these were converted to step and global E-factors. The step Efactor contributions to the global E-factors were also calculated and shown to be additive. However, the authors erroneously concluded that step PMI contributions to the global PMIs were not additive. Part 3 of the Supporting Information gives a simple proof that both step E-factor contributions and step PMI contributions are indeed additive. The respective sums correspond to global E-factor and global PMI, which are entirely consistent with the results of the EATOS program where complete breakdowns of these parameters are itemized in an additive sense. As shown in Tables 2 to 4, the percent reaction mass efficiency (RME) was the only parameter not calculated.

EcoScale The EcoScale algorithm 22 is applicable to single reactions only, i.e. synthesis plans are excluded. It uses an arbitrary penalty point system based on the following reaction categories: reaction yield, cost of reaction components (based on producing 10 mmol of final product), safety of reaction components, technical setup (type of equipment used), reaction temperature


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25 and reaction time, and workup and purification components. Demerit points are tallied up and subtracted from 100 to obtain the final EcoScale parameter. Greener reactions are characterized with high EcoScale scores. There are no visual aids that accompany the determination of this parameter. Penalty points increase with increasing health hazard, environmental impact, deviation from ambient reaction conditions, cost of materials used, and complexity of equipment used. The authors did not provide a universal template that can be automated to any reaction. In this work, we provide such a user-friendly Excel template that determines reaction AE and yield and all penalty points based on the required entered data (see EcoScale-template.xls in Supporting Information). The only material efficiency metric that EcoScale considers is reaction yield. No analogous thresholds on atom economy are set on which scaled penalty points are assigned. This method is very appealing for instructional purposes because it is intuitive, making it easy to convey concepts about green chemistry principles to novices introduced to the subject for the first time, and because it is based on simple tallying up of demerit points. However, apart from the intrinsic problem of penalty scores being arbitrary, the penalty points are given only with respect to input materials used , thus ignoring waste products formed as a consequence of carrying out the reaction. This means that semi-quantitative analysis of hazardous waste is not possible with the EcoScale. Furthermore, penalty points are uncorrected for the actual amounts of materials used. For example, if 1 g of highly flammable solvent is used, it is given the same penalty score of 5 as when 1 ton of it is used. Given these limitations, particularly the restriction on reaction yield as the only material efficiency metric, we recommend that its utility may be justified for instruction to chemistry and non-chemistry professionals introduced to green chemistry principles for the first time. Serious practioners of green chemistry, however, would have to graduate to the more advanced algorithms mentioned in previous sections to better appreciate the determination and implementation of all material efficiency green metrics in decision making analyses. This is particularly true when dealing with synthesis plans which the EcoScale cannot handle.

Green Star Green Star 23 is a more advanced point-based system as compared to the EcoScale since it attempts to include all 12 principles of green chemistry in a semi-quantitative manner. Hence, it has been advertised as a “holistic approach” to assess the degree of greenness of a chemical



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26 reaction, though it excludes principles 4 and 11, which refer to designing benign products and real-time monitoring of reactions to prevent pollution, respectively. Like the EcoScale, Green Star is exclusively applied to individual reactions and not to synthesis plans. The main differences are that Green Star is based on a positive merit point system as opposed to a negative demerit point system and that it takes into account reaction waste products; namely, reaction byproducts. Nevertheless, the point system arbitrarily assigns a minimum value of 1 for nongreen performance and a maximum value of 3 for benign performance to each green principle selected. The criteria scores for health, environmental impact, flammability, reactivity, degradability, and renewability characteristics, assigned to each chemical are summed in order to determine the green principle scores. The set of green principle scores in turn allows determination of the green star area index (GSAI) parameter. One important caveat for users to be aware of is that the authors’ original criteria scorings used a demerit point scale, where 1 was associated with benign performance and 3 was used for non-green performance, yet the green principle scorings on which GSAIs were determined were based on the reverse merit point scale. To be logically self-consistent, in this work we maintained the same order of merit points for both criteria and green principle scores. In addition, for determination of GSAI, Green Star also utilizes the following material efficiency metrics: RY, AE, RME, and PMI. However, authors of this algorithm do not count aqueous based waste materials as part of the E-factor calculation. The Supporting Information contains an Excel template file (GreenStar-template.xls) that blends the beginning of the Andraos SYNTHESIS spreadsheet, where RY, AE, RME, and PMI are determined, and the GSAI parameter. The accompanying radial polygon visual aid based on 10 of the 12 green chemistry principles resembles the concept of the Andraos radial pentagon, except that areas are determined instead of vector lengths (see VMR parameter discussed in previous sections). Relatively greener reaction procedures will have larger GSAI scores as well as larger VMR scores. The “greener” GSAI polygons will cover larger areas between the outer perimeter (bounded by the edge assigned with a score of 3) and the inner perimeter (bounded by the edge assigned with a score of 1). This is analogous to the outer edge of 1 for ideal green performance and the centre point for non-green performance in the Andraos radial pentagon. It should be noted, however, that comparison of areas from different radial polygon diagrams is valid so long as the order of polygon parameters (i.e., order of green chemistry principles) are preserved from diagram to diagram. The use of vector lengths avoids the order of parameters


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27 problem since the length magnitude does not depend on it. Similarly to EcoScale, Green Star does not correct its scores for relative amounts of input materials used or waste products made. From an instructional point of view, Green Star has the same attributes as EcoScale except that it addresses some of the latter’s shortcomings. Recent evolutions of the Green Star radial diagram 24-27 indicate that it has changed its appearance from the one first published in 2010, yet the determination of the GSAI parameter remains the same. Users need to be made aware that the areas of green coloured wedges shown in the most recent star-like diagrams do not correspond to the polygon areas required for the computation of the GSAI parameter. In fact, the computation of areas of the green coloured wedges in the modern diagrams is far more complex than that for the first generation diagram, which is best described as an irregular cyclic decagon than an actual star. This occurrence is an example of the problem of attempting to achieve aesthetically pleasing diagrams at the risk of losing computational meaning. The authors have also presented the Green Star tool as a means to survey various published synthesis procedures for any given compound with respect to how they perform with respect to the 12 principles of green chemistry. The authors’ idea to use this tool in advance of carrying out laboratory work by dissecting procedures into reaction, isolation, and purification steps is a useful back-of-the-envelope exercise 27. The application of picking out the best performing stages in order to put together a complete sequence of operational steps for a synthesis procedure is a direct method to come up with an overall optimized best green procedure and is worthy of merit. However, the results of such an analysis must be checked experimentally, since in practice the reaction, isolation, and purification stages in a procedure are generally not mutually exclusive as suggested by the back-of-the-envelope exercise. For example, a set of reagents to make compound A using solvent B will work because those reagents are soluble in solvent B. If it is found that another set of reagents is used to make the same compound more efficiently in solvent C which is more toxic than solvent B, then the suggestion of using solvent B instead for this combination of reagents may not work simply because they may be insoluble in solvent B. In other words, the so-called best combination satisfying the Green Star analyses for the three stages must be checked by experimental work before it can be pronounced as the “greenest” option. These caveats about recent usages of Green Star need to be emphasized upfront to avoid propagating any misconceptions.



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28

Misconceptions and Misrepresentations In this section we discuss various problems that have appeared in the literature where usage of material efficiency metrics has lead to significant misinterpretations or limitations about concluding or declaring reaction or synthesis greenness. The first point to recognize is that the determination of synthesis plan greenness is a comparative analysis not an absolute one. Hence, the declaration of greenness is based on comparing various metrics attributes for a set of competing plans to the same target product. As we mentioned in the Introduction, true synergistic optimization is achieved when optimization of a suite of metrics is carried out in an orchestrated manner. So the goal is to have a plan among the competing set that possesses all attributes as far as possible, highest overall yield, lowest step count, highest atom economy, and lowest PMI. If there is a scattering of good performances across several plans to a given target molecule, then such a scenario is unorchestrated; e.g., plan A has the highest overall yield, plan B has highest overall atom economy, and plan C has lowest PMI. Secondly, claims of “conciseness,” “efficiency,” or “greenness” made on the basis of one or two criteria like overall yield, or step count, or one of the 12 green principles would not constitute genuine claims of “greenness”. Thirdly, claiming greenness of an entire plan on the basis of one key reaction in a plan that showcases novel chemistry while ignoring the rest of the plan which usually involves steps utilizing routine chemistry, also is not a genuine claim of “greenness”. The final point to recognize is that even if the “greennest” plan is achieved today with the current available technology, there will always be newer opportunities to make further improvements as new chemical transformations are discovered. Hence, the quest for optimization is never truly complete and this gives chemists limitless opportunities to revisit and test new ideas. (i) Experimental procedure reporting Experimental procedures are often lacking any one or more of the following items: • Masses of drying agents used (magnesium or sodium sulfate) • Masses of silica gel or alumina used in flash chromatography • Masses of chromatographic solvents used as eluents • Masses of catalysts used • Masses of reaction solvents • Masses of wash solvents • Masses of recrystallization solvents


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29 • Masses of extraction solvents • Masses of decolorizing charcoal • Masses of celite • Mass of dihydrogen used in hydrogenation reactions • Mass of dioxygen used in oxidation reactions • Mass of any gaseous reagent Clearly, missing information obviously compromises accurate and reliable estimates of E and PMI for a reaction or synthesis plan and is the greatest impediment to carrying out any materials metrics analysis regardless of sophistication. It also plays havoc with respect to ranking competing synthesis plans to the same target molecule. When such information is lacking assumptions need to be made and therefore estimates of E and PMI are to be interpreted as lower limits. Extreme caution is needed when ranking such plans, especially if these lower limits are numerically similar to other competing plans whose mass utilization data are complete. The EATOS program was the first algorithm to introduce the following assumptions when masses of auxiliary materials are not reported in experimental procedures: 1. Extraction from aqueous media using an organic solvent: 300 mL solvent per L aqueous medium (multiplying factor = 0.3) 2. Aqueous washes of organic solvent: 300 mL water per L organic solvent (multiplying factor = 0.3) 3. Brine: 100 mL brine per L organic solvent (multiplying factor = 0.1) 4. Drying agents: 20 g per L organic solvent (multiplying factor = 0.02) Unfortunately, these assumptions are limiting as they do not cover all of the items listed earlier, especially chromatographic solvent consumption which is very difficult to estimate since this is highly dependent on the specific separation properties of the reaction products, and yet it clearly constitutes the bulk of the mass of input materials used in a given reaction procedure if this purification technique is used. (ii) Reaction yield issues This category constitutes several elements. Firstly, it needs to be stated that reaction yield performance depends on reaction scale and must be determined experimentally. There is no way to make predictions by any theoretical means. Nondisclosure of reaction yields for all reaction steps in a synthesis plan results in gaps which forces assumptions to be made about individual



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30 reaction performance. One may use literature data from analogous reactions to interpolate yield estimates. Reporting of yields after a stretch of two or more sequential reactions thus avoiding intermediate isolations poses a computational challenge. Individual reaction performance within that sequence of steps may be taken as the geometric mean. In both scenarios, estimates of lower limits on E-factor or PMI (or upper limits on RME) are the only reasonable results that can be obtained for such plans. Sometimes authors may use tactics to artificially amplify reaction yield performance when yields are below 50%. For example, percent conversion and percent selectivity are reported instead of percent yield. Of course, the multiplicative product of these fractions is equal to the percent yield. As an example, if the percent conversion is 60 % and the percent selectivity to a given product is 80 %, the overall yield performance to that product is 0.6 X 0.8 = 0.48 or 48 %. Rather than revealing this low figure, only the former two percentages may be stated in a publication. Another way to “amplify” reaction yield data is to report the yield based on recovered starting material. In this case, the “yield” includes the desired target product plus unreacted starting material, thereby augmenting the numerator of the fraction relative to its denominator (representing moles of limiting reagent). Another form of yield exaggeration is the reporting of yields in classical resolution steps as exceeding 50%. In this instance, the percent yield reported is not with respect to the starting mass of racemic mixture as is required in proper determinations of E and PMI, but with respect to half its mass, that is, the half corresponding to the desired enantiomer assuming no losses along the way. The following synthesis plans taken from Organic Syntheses apply this practice: (+)-2-octanol42, (+)-αphenylethylamine43, (S)(−)-1-phenylethylamine44 , (+)-α-(isopropylideneaminooxy)propionic acid45, (S)-(−)-α-(1-naphthyl)ethylamine46, (S) (+)-binaphthylphosphoric acid47, (1S,2S)-(−)-1,2-diphenyl-1,2-ethylenediamine48, (R)(+)BINAP49, and (R,R)(−)-N,N′-dimethyl-1,2-diphenylethane-1,2-diamine50. (iii) Biotransformation reactions Biotransformation reactions appearing in synthesis plans pose a significant challenge to carrying out material metrics calculations for two main reasons: (1) a balanced chemical equation may not be known, and (2) reaction yields are not reported using the usual definition that a chemist would use. As a consequence of not knowing what the balanced chemical equation is with appropriate stoichiometric coefficients, the concept of a limiting reagent is inapplicable. Molar product yield is reported which is obtained by dividing the number of moles of product collected


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31 by the number of moles of substrate of interest. Consequently, there are unfortunately few opportunities to showcase the performances of such plans against conventional chemical methods in head-to-head comparisons. (iv) Which is more efficient - convergent versus linear plans?This often debated question has no definite answer as we have demonstrated recently.9 As an example, here we note the results for two total syntheses of the alkaloid papaverine: (a) Redel–Bouteville 1949 synthesis of papaverine51 - linear; 8 steps; E-factor = 24 (b) Pictet-Gams 1909 synthesis of papaverine52,53 - convergent; 11 total steps; E-factor = 128 The bottom line is that each candidate synthesis plan to a given target product, regardless of whether it is linear or convergent, needs to be evaluated thoroughly by the algorithms described without imposing any prejudgement about performance. (v) Which is more efficient – shorter versus longer step count plans? This related question also has no definite answer as one can find apparent counter-intuitive examples where a plan with fewer steps is less material efficient than one with more steps for the same target compound. This is commonly the result of a poor performing reaction yield for a reaction in a plan, usually occurring at an early stage in the plan where the mole scale is high, that has catastrophic effects on the overall PMI. As an illustrative example, the third generation 1999 Roche synthesis of oseltamivir phosphate54,55 has the following performance profile: 13 steps; 39 % overall yield; and 94.7 kg waste produced per mole of product. On the other hand, the fourth generation 2000 synthesis of the same pharmaceutical has the following profile: 9 steps; 1 % overall yield; and 2092.4 kg waste produced per mole of product.56 In the latter shorter synthesis, the second step had a reaction yield of only 21 % whereas, in the former synthesis, though 4 steps longer, no step had a reaction yield below 88 %. Again, as in the case of convergent versus linear plans, no prejudgements about plan material efficiency can be made based on step count alone. (vi) Where to begin a metrics analysis (starting materials)? When one analyzes a plan from a so-called “readily available starting material” it is usually a compound with a fairly advanced structure that is commercially available. If one begins the materials metrics analysis with such a starting material, then it artificially reduces the step count and ultimately gives an unfair advantage over other plans. Obviously, that starting material needs to be made from some other starting material via its own synthesis plan. From a



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32 computational point of view, the absolute fairest comparison between competing plans is when all plans begin from the same starting material and all routes lead to the same target product. Such comparisons are achievable for analyzing competing plans to simple product structures such as first, second, or third generation high volume chemical commodities from the petroleum industry. However, this criterion becomes less and less achievable as the complexity of the target structure increases. To illustrate the effect of changing the starting line on E-factor determinations we point out the following two examples. The Trost synthesis of oseltamivir phosphate57 is a 9-step linear plan that begins from 6-oxa-bicyclo[3.2.1]oct-3-en-7-one. The Efactor for that plan is 2685. That bicyclic compound can be made in three steps from butadiene and acrylic acid, both originating from petroleum chemical feedstocks. When the evaluation is carried out, now on a 12-step linear sequence, the E-factor increases by 6.5 % to 2859. Yet, the former plan was advertised as the shortest plan achieved for that pharmaceutical compared with the average 12-step count plans by Roche that began from shikimic acid. In a second example, where a convergent plan is compared to a linear one to the same target product, we illustrate the effect on E-factor determinations when one of the branches to an advanced intermediate is truncated from the computation. The 4-step linear Pfizer plan55 to sildenafil involving 2-methyl5-propyl-2H-pyrazole-3-carboxylic acid as an intermediate in step 3 in the plan has an E-factor of 69. That substrate in turn needs to be made from 2-pentanone in three steps. Inclusion of this extension changes the 4-step linear sequence to a convergent plan comprising 7 steps overall where the step involving 2-methyl-5-propyl-2H-pyrazole-3-carboxylic acid becomes a convergent step. The E-factor for this convergent synthesis involving two branches increases by 68 % to 116. (vii) Inclusion versus omission of metrics analysis of synthesis of specialized catalysts Here we illustrate such an effect using the synthesis of (-)-menthol as an example. The Takasago synthesis56-59 involves [Rh((S)-(–)-BINAP)(cod)]ClO4 catalyst in a stereoselective isomerization step. If the synthesis of this specialized catalyst is not counted, 48.4 kg of waste are generated per mole of (-)-menthol produced. If its synthesis is included57,60,61 under the condition that 0.002456 mol are required to make 1 mole of (-)-menthol, then an additional 1.76 kg of waste needs to be accounted for. (viii) “Solvent-less” reactions


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33 This term is often used to advertise achieving reaction greenness since it is well known that solvent usage contributes the bulk of overall material consumption when carrying out any chemical reaction. However, problems arise when authors making such claims omit solvent usage in post-reaction procedures, namely in purification steps. Hence, the term is really valid when reaction solvent is eliminated. As an example, the synthesis of 2,2,4-trimethyl-2,3dihydro-1H-benzo[b][1,4]diazepine from two equivalents of acetone and o-phenylenediamine was achieved under solventless conditions according to two claims in the literature. In one claim62, carried out under solvent free conditions where acetone was used in stoichiometric amounts and the reaction was conducted using microwave irradiation, the calculated E-factor was 0.26. In a second claim63 using the same language, where the reaction was also carried out using a stoichiometric amount of acetone under catalytic conditions, the calculated E-factor was over 2600 times larger at 679 when chromatographic solvents were counted in the computation. In the former case, no additional purification solvents were used. (ix) Relating step material efficiency metrics to overall plan material efficiency metrics A recent report64 has used the sum of reaction E-factors as a proxy for estimating the overall Efactor for a linear plan. As tempting as that may be, it is shown in Part 3.1 of the Supporting Information that the actual connecting relationship between step and overall E-factors for a linear plan of N steps is given by equation (11). This expression does, in fact, reduce to a simple sum of step E-factors only if all the mass terms in all reaction steps, including the final product, are equal to each other. Such a highly specialized mathematical condition suggests that the mass of each product obtained in every step along the linear sequence is constant, which is practically not achievable. Based on the form of equation (11), we can write analogous expressions for how overall PMI, overall RME, and overall AE are related to their corresponding step metrics. These are shown in equations (12) to (14).

mP ( E N + 1) + ET =

N −1

∑

j =1

( )

mY E j j

−1

mP N −1 m PMI + P N

PMIT = ET + 1 =

∑

(11)

(

)

mY PMI j − 1 j

j =1 mP

(12)



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34

gRME =

1 = PMIT

where mY j =

mP N −1 m PMI + ∑ mY PMI j − 1 P N j j =1

( MW )Y

(

j

ε j +1...ε N

(13)

)

, mYj and (MW)Yj represent the mass and molecular weight of intermediate

product Yj along the linear chain, respectively, and mP is the mass of the target product..

( AE )T

=

( MW )P

 N −1 ( MW )Y  ( MW ) j P ∑ − ( MW )Y  + j  j =1 ( AE ) j  ( AE ) N  

(14)

Concluding Remarks and Recommendations In this paper we have discussed and compared the performances of seven published algorithms on material efficiency green metrics with respect to calculation outputs, visual displays, and ease of use. For the first time their performances were compared head-to-head using the same set of chemical examples taken from Organic Syntheses and original literature that introduced the algorithms. Though all algorithms determine the essential material efficiency metrics there is variability in their level of rigor and robustness with respect to their analysis of individual chemical reactions and synthesis plans. The most thorough are the EATOS and Andraos algorithms. We recommend these for advanced practitioners of green chemistry. Both have useful visual displays of the computational data, though the EATOS program could be greatly improved with respect to ease of use in extracting numerical summaries from the outputted histogram. The main drawback with EATOS is that much of the calculation is done in the background and is hidden from the user. This takes away from its pedagogical value if one wants to understand the internal workings of the program. The modified Augé algorithm described in this work is only recommended as an optional method for advanced users as a fast procedure, however it is limited to determining global PMI and global AE. Though we have advanced a simpler modified version to the original formalism with an accompanying graphic to illustrate step PMI contributions, in certain cases the algorithm is still tricky to implement and users may perceive that it has limited value especially when other algorithms exist that are inherently less complex . We also emphasize that it must be checked with the results of either the Andraos or EATOS procedure to ensure proper application of the φ scaling parameters in all


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35 branches in a synthesis plan. The ACS PMI calculator and GAL algorithm, which uses the PMI calculator, are simplistic and limited to plans with step scaling factors of 1. Both of these were put forward by the pharmaceutical industry to be appealing to non-chemistry business professionals working in that industry so they could understand and better appreciate the principles of green chemistry. The EcoScale and Green Star algorithms attempt to broaden the scope of assessment of “greenness” by including environmental impact and health hazards in addition to material efficiency metrics. However, both of them are limited to analysis of individual chemical reactions and not to synthesis plans. Furthermore, they are less rigorous since their coverage of material efficiency metrics is limited to the fundamental metrics of RY and AE, and both use arbitrarily chosen demerit / merit point systems, respectively. These approaches are more appropriate for introductory instruction in green chemistry topics since they are very easy to implement and understand. Throughout this work we simplified and augmented algorithms with diagrams and automated template spreadsheets as appropriate so that they may be more accessible to professional chemists and chemical engineers in grasping their methodologies and for them to implement green chemistry practices in their work. We have also highlighted various misinterpretations and misconceptions in the use of materials metrics analysis when claims of greenness are made.

Appendix Part 1: For any given chemical reaction, the process mass efficiency can be written in terms of atom economy, reaction yield, stoichiometric factor accounting for excess reagent consumption, Curzon’s reaction mass efficiency, and mass of auxiliary materials as shown by the sequence of expressions given below in equations (A1a-Alg). Moreover, reaction yield is the multiplicative product of selectivity and conversion all expressed as proper fractions, and PMI and E-factor are related by the simple connecting relation PMI = E + 1 mentioned earlier in the text.



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36

1

PMI =

    1  1   ( AE )( yield )     mass of auxiliaries  SF   1 ∑  1 + ( AE )( yield )     SF  ( mass of product )   1 =     1   RMECurzons   mass of auxiliaries ∑  1 + RMECurzons ( mass of product )    ∑ mass of auxiliaries   1 + RMECurzons RMECurzons  ( mass of product )  mass of auxiliaries 1 = +∑ RMECurzons ( mass of product )

=

=

1

1

( AE )( yield ) 

1    SF 

+

∑ mass of auxiliaries ( mass of product )

=

∑ mass of reactants + ∑ mass of auxiliaries

=

∑ mass of all materials used

( mass of product )

( mass of product )

( mass of product )

Part 2: For an N-step sequence (N > 2) given by

S1 + S2 P1 + Q1 (step 1) P1 + S3 P2 + Q2 (step 2) P2 + S4 P3 + Q3 (step 3) … PN-1 + SN+1 PN + QN (step N)


(A1a-Alg)

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37 where no excess reagents or auxiliary materials are used and step atom economies given by equations (A2a to A2d), the expression for the global process mass intensity is given by equation (A3). MP 1 MS + MS 1 2 MP 2 ( AE )2 = MP + MS 1 3

( AE )1 =

( AE )3 =

MP 3 MP + MS 2 4

(A2a – A2d)

...

( AE ) N

=

MP N MP + MS N −1 N +1

N  1  gPMI = ∑  MP  ε ε ε ...ε N k =1  k k +1 k + 2 N 1

 1       M − M Pk −1      ( AE )  Pk  k    

  1   1 1    M P1 − M P0  +  ε ...ε ε ε ...ε  ( AE )1  1  1 2 N    2 N =  MP   N 1  1    M PN − M PN −1  ... +  ε N   ( AE ) N    

(

)

 1      M P2 − M P1  +   ( AE )    2        

(

)

1 1   M M M P + M S − M P + + + S S  1 2 1 3 1 ε 2 ...ε N 1  ε1ε 2 ...ε N  =   1 MP   N ... + MP + MS − MP N −1 N N −1   εN

(

 1 =  MP N 

)

  1  M + M S + ε1M S + ε1ε 2 M S + ... + ε1ε 2 ...ε N −1M S 2 3 4 N   ε1ε 2 ...ε N  S1 

(

(A3) where M P = 0 since there is no intermediate product that precedes P1. 0 Since the global atom economy is given by equation (A4) GAE =

MP N M S + M S + M S + M S + ... + M S 1 2 3 4 N

(A4)


)


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Page 38 of 46

38 we can rewrite equation (A3) as shown in equation (A5).

1  1  gPMI =    GAE   ε1ε 2 ...ε N

  M S1 + M S2 + ε1M S3 + ε1ε 2 M S4 + ... + ε1ε 2 ...ε N −1M S N +1     M S + M S + M S + M S + ... + M S   1 2 3 4 N 

   1  1 =   GAE   N  ∏ ε k  k =1

    1 + ε X + ε ε X + ... + ε ε ...ε 1 1 1 2 2 1 2 N −1 X N −1    1 + X1 + X 2 + ... + X N −1     N −1       1 + ∑ ε1ε 2 ...ε k X k    1  1  k =1 =    N N −1  GAE     1+ ∑ Xk  ∏ ε k    k =1  k =1   

(A5) where X k =

MS

k + 2 . The corresponding global material efficiency is given by equation MS + MS 1 2

(A6). N −1   1+ ∑ Xk  N  1 k =1 GME = = ( GAE )  ∏ ε k   N −1 gPMI    k =1  1 + ∑ ε1ε 2...ε k X k  k =1 

      

(A6)

We note that equation (A6) is composed of three terms: overall global atom economy (GAE), overall yield, and a third term that also includes reaction yields and molecular weights of reagents. Such a third term does not appear in equation (4) for a single reaction. Furthermore, when all the reaction yields are equal to 1 the second and third terms each become 1 and GME reaches its maximum value equal to GAE. Part 3: For a two-step sequence given by

S1 + S2 P1 + Q1 (step 1)


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39 P1 + S3 P2 + Q2 (step 2) where no excess reagents or auxiliary materials are used, equation (8) reduces to equation (A7) since all the B and s terms are zero.

gPMI min =

1 MP 2

  1    1   M P1 − M P0 +   M P2 − M P1    ( AE )2    ( AE )1  

(A7)

Substitution of the definitions for AE for each step given by equations (A2a and A2b), into equation (A7) yields equation (A8).

{

1 MS + MS − MP + MP + MS − MP 1 2 0 1 3 1 MP 2 MS + MS + MS 1 2 3 = MP 2

gPMI min =

=

1 MP 2 MS + MS + MS 1 2 3

=

1 GAE

} (A8)

where M P = 0 since there is no intermediate product that precedes P1. Hence, the minimum 0 value of gPMI is equal to the maximum value of gRME (GME) which, in turn, is equal to global atom economy (GAE).

Supporting Information Part 1: Tables S1 to S4. Part 2: Microsoft Excel template spreadsheets for modified Augé, EcoScale, and Green Star algorithms (modified-Auge-template.xls, EcoScale-template.xls, GreenStar-template.xls). Part 3: Workbook Excel spreadsheets for syntheses of 2,2-diethoxy-1-isocyanoethane, thiete 1,1-dioxide, ethyl phenylcyanopyruvate, 2-methyl-4-nitro-5-propyl-2H-pyrazole-3carboxylic acid, sildenafil citrate, a PEG-based polyol, and coenzyme A (Excel-workbooks folder).



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40 Part 4: Instructions for using EATOS and EATOS file outputs. Part 5: Derivation of formulas for modified Augé algorithm. Part 6: Proof of additive step E-factor contributions and step PMI contributions. This material is available via the Internet at http://pubs.acs.org.

Acknowledgements Andrei Hent and the reviewers are thanked for useful commentary in helping to improve the manuscript.

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46 For Table of Contents Use Only: TOC Graphic

Critical Evaluation of Published Algorithms for Determining Material Efficiency Green Metrics of Chemical Reactions and Synthesis Plans John Andraos*, CareerChem, 504-1129 Don Mills Road, Toronto, ON M3B 2W4 Canada ([email protected]) Synopsis: A detailed comparison is made of several material efficiency green metrics algorithms on the same set of chemical examples to ascertain their practical application in determining sustainable solutions to chemical processes.


Critical Evaluation of Published Algorithms for Determining Material

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