Metrics for green syntheses

Marco Eissen; Giacomo Trapasso; James Clark; Fabio Aricò; John Andraos; Pietro Tundo

doi:10.1515/pac-2025-0553

Article Publicly Available

Metrics for green syntheses

Marco Eissen , Giacomo Trapasso , James Clark , Fabio Aricò , John Andraos and Pietro Tundo

Published/Copyright: September 15, 2025

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From the journal Pure and Applied Chemistry

Abstract

Despite being introduced approximately 30 years ago, green metrics are still not widely implemented in the practice of Green Chemistry. Nowadays, there is a general desire and fashion for Green Chemistry considering the modern global concerns of climate change and resource scarcity. However, the scientific literature reveals a confusing array of definitions and methodologies related to green metrics, particularly in both organic and inorganic chemistry. In this review we want to focus on organic synthesis, namely new reaction pathways that employ organic and inorganic catalysts, grounded in fundamental chemistry. The application of rigorous green metrics must go along with the experimental validation of synthetic procedures. This is essential to establish clear guidelines for defining truly green synthetic approaches, and to prevent misunderstandings or overreaching claims that are based on subjective rather than objective assessments. This work originated from an IUPAC project aimed at providing standardized guidance for the use of green metrics. Accordingly, we present a list of green metrics and related terminology currently employed to assess material usage, energy efficiency, and environmental impact in individual reactions and synthetic strategies.

Keywords: Algorithm database; green chemistry; green metrics; metric glossary

Introduction

This work collects a selection of green metrics including both their mathematical formula as well as definitions and specific information (Fig. 1). In its current version, this selection is limited to mass-based metrics as they are clearly measurable, unlike qualitative factors such as environment and safety. A number of different and quite suitable methods for their potential quantification have been proposed in the literature. ¹ ^, ² As not all of these can be included here, the authors of this report do not consider it appropriate to present an arbitrary selection.

Fig. 1:

Green metrics.

Chemists have already adopted the 12 green chemistry principles; ³ ^, ⁴ however, we need now to be more precise before claiming to have developed a green reaction or process. In his Le Discours de la Méthode, Descartes observed “Le bon sens est la chose du monde la mieux partagée, car chacun pense en être bien pourvu” [Common sense is the most widely shared commodity in the world, for every man is convinced that he is well supplied with it.] ⁵ ^, ⁶ ^, ⁷ ^, ⁸ ^, ⁹ ^, ¹⁰ In this view, there is a fundamental problem with the thoroughness with which evidence for greenness is presented when it is used as a positive argument for published scientific results. Accurate documentation of the true content of a synthetic protocol is not a trivial matter. Procedures reported by academic researchers often fall short in accurately determining the true material and energy efficiency of chemical reactions. A common issue in scientific publications is the omission of crucial details, such as the quantities of materials used for work-up and purification. Additionally, key experimental parameters – including the order of reagent addition, control of temperature and pressure, reaction time, and the specific methods used for work-up and product isolation – are frequently underreported or inadequately described. These details are essential for ensuring the reproducibility of a reaction as originally reported.

Procedures in the chemistry literature that cannot be replicated not only casts doubt on the chemistry, but also corrodes the reputation of chemistry as a proper scientific discipline since the characteristic of reproducible experimental outcomes is a fundamental defining feature of a subject to be called a science. These shortcomings have been highlighted and discussed in the past ¹¹ ^, ¹² ^, ¹³ ^, ¹⁴ ^, ¹⁵ and recently prominent chemists and editors of journals have begun to change editorial policies to address them, especially in the context of ethics demanded by green chemistry in its application to process chemistry, the pharmaceutical industry, and new technologies. ¹⁶ ^, ¹⁷ ^, ¹⁸ ^, ¹⁹ ^, ²⁰ ^, ²¹ ^, ²² ^, ²³ ^, ²⁴ ^, ²⁵ ^, ²⁶ ^, ²⁷

Many experimental procedures reported in scientific journals as “green” do not withstand scrutiny when subjected to a comprehensive green metrics analysis. The current trend of casually labeling processes as green based on just one or two isolated criteria contributes to a misleading and often unscientific portrayal of sustainability. Furthermore, the proliferation of green metrics – frequently introduced under different names by their original authors despite representing similar or identical concepts – creates a confusing landscape. This inconsistency poses a significant challenge, particularly for chemists who are genuinely committed to understanding, practicing, and implementing the principles of green chemistry in their research.

What we currently need is to set aside priority pretensions and personal expectations from “green and sustainable chemistry”, advertised citations of authors’ publications in the scientific literature, and go beyond making fashionable, yet unsubstantiated, “green claims”. Therefore, green metrics are a necessary tool, as they serve to quantify in an unbiased way the efficiency or environmental performance of chemical processes and allow practical and effective changes in chemical manufacture to be measured moving forward from rough and casual estimation to precision and accuracy. They are the basis of clear, rational, and directed optimization of reaction and synthesis performance. The field of green chemistry, by its very nature, is a comparative science which gauges the material, energy, environmental impact, and safety-hazard impact performance of any given new procedure to a given target chemical with all prior experimental procedures to that compound. A verifiable and credible claim of greenness of any procedure is therefore one that is not absolute, but rather is one that is comparable by metrics analysis to all prior procedures. This necessarily means that metrics analysis applied on a set of synthesis plans leads to their ranking. A true claim of greenness for a procedure means it scores high in many categories of efficiency criteria: material consumption, energy consumption, environmental impact, safety-hazard impact.

All of these aspects can be made more transparent through life cycle assessment (LCA) and safety assessment. However, the time and effort required to conduct such evaluations are substantial. As a result, during the early stages of synthesis planning – when multiple implementation options are still under consideration – conducting full assessments is often not feasible or proportionate. Nevertheless, efforts are increasingly being made to incorporate these evaluations as early as possible in the decision-making process. ²⁸ ^, ²⁹ ^, ³⁰ ^, ³¹ In this regard, the quality of metrics, which are relatively easy to determine, is equally important. All laboratory scale information is included in E-factor and in the process mass intensity (PMI) ³² and it correlates to some extent with LCA impacts (see some examples ³³ ). ³² ^, ³⁴ This metric is used conceptually, see e.g., ³⁵ ^, ³⁶ ^, ³⁷ ^, ³⁸ although it is advisable to also keep an eye on the yield. ³⁹ In terms of size, PMI and the E factor are two sides of the same coin ⁴⁰ due to the relationship E = PMI – 1. However, as the PMI does not focus on waste like the E factor, but rather on the use of raw materials in line with the glass-half-full philosophy, ⁴⁰ it is better suited to the perspective of footprint calculations, ³² namely when the life cycle impact intensity (impact per mass) of a substance is multiplied ³⁰ by its mass per kilogram of product. On the other hand, metrics that include less information from the synthesis design are less meaningful. This applies, for example, to the atom economy AE. ⁴¹

Since chemistry is a science of compromise, only a subset of these is achievable. Moreover, all optimizations are continuously ongoing as the task of improvement to the ideal goal is an evolutionary process and depends on the discovery of new reactions (e.g., multi-component, catalytic, etc.), new energy favorable profiles for organic reactions (e.g. organic carbonates), and new methodologies to carry out existing reactions (e.g., continuous flow, microwave, etc.). Any claim of greenness must therefore be proven by using green metrics.

The motivation for using metrics is the expectation that by quantifying technical and environmental improvements, the benefits of new technologies will become more tangible, perceptible, or understandable by the public. In this view the term (green) metric is herein considered as a quantitative measure of some property using a scaled parameter. The use of green metrics will help the communication of research and facilitate the wider adoption of green chemistry technologies in industry, in order to verify and prove if they are sustainable from an industrial point of view. In fact, there is an expressed need and desire by both academia and industry to incorporate metrics to rigorously define efficiency and sustainability of chemical syntheses.

For these reasons, IUPAC took the initiative in helping to regulate this pivotal field for chemistry to avoid the creation of misconceptions, fallacies, and abusive advertisements of “greenness” that threaten to discredit this important field of chemistry. The aim of the IUPAC Project “Metrics for Green Syntheses” is to evaluate by rigorous metrics the greenness of chemical synthesis proposed, which has not been covered so far. As Descartes suggested, we should try to move forward from the generic and spontaneous intention to rigorous measures, from rough and casual estimation to precision.

In particular, one of the fields which deserves attention is organic synthesis in connection with environmental protection and sustainability. This includes the design of new reaction pathways and the use of both organic and inorganic catalysts grounded in fundamental chemistry – key aspects that any future development in Green Chemistry must consider, as they represent a true modern scientific challenge. It is necessary to give precise guidelines on synthetic green metrics to avoid misunderstanding and pretentious claims, due to subjective rather than objective evaluations. This should be particularly helpful if artificial intelligence is increasingly used in the planning of both individual technical-chemical processes and multi-stage synthesis sequences.

From these premises, this review will focus on establishing a list of metrics and related terms taken from papers published in the literature on the subject including formal definition for each term.

Symbols

(AE)_N = atom economy of final step

C = number of chiral centres

C_aromatic = number of carbon atoms in aromatic rings

C_total = total number of carbon atoms

E_MW = molecular weight ratio of reaction by-products to target product

ε = Yield

F _VI = mass fraction of valorized inputs

F _VO = mass fraction of valorized waste outputs

F _VP = mass fraction of valorized target product

F _RE = input enthalpic energy fraction arising from renewable energy sources

g_j = the number of green cells accrued for each substance j

H = number of heteroatoms

H_aromatic = number of heteroatoms (N, S, O) in aromatic rings

H_total = total number of heteroatoms

(IEE)_renewable = the input enthalpy energy arising from renewable resources

(IEE)_total = the total input enthalpy energy

j = dummy variable referring to jth reaction step

(LN)_N = Lavoisier of final step

(LN)_j = step Lavoisier numbers

m = mass

M _product = mass of target product

M ^* _product = mass of target product that is destined to be wasted

m _input = mass of input materials

M _NVI = mass of non-valorized inputs

m _product = mass of final target product

m _P = mass of final product

m _Yj = mass of intermediate products

M _VI = mass of valorized inputs

(MW)_Yj = molecular weights of intermediate products

(MW)_P = molecular weight of final product

N = total number of steps in linear sequence

n _j = amount of substance of the jth reactant in mole

n _k = amount of substance of the key reactant in mole, i.e. limiting reactant

P = the target product

P_j = a risk potential

q = by-product

Q = unfriendliness quotient

R = Reactant

(RME)_j = reaction mass efficiency of step j

(RME)_N = RME of final step

RME_T = total reaction mass efficiency

S₁, S₂ = reagents

S⁻¹ = inverse selectivity (called mass index) = PMI (PMI is the scientifically accepted term)

T = total (consideration of all syntheses of a synthesis sequence)

ϕ _j = the fractional mass contribution of waste substance j to the total waste

r_j = the number of red cells accrued for each substance j

ν_j = stoichiometric coefficient of the jth reactant

ν_p = stoichiometric coefficient of the product

ω₁ = Σ (MW_{intermediates} + MW_{starting material at beginning of each branch})

ω₂ = (total number of intermediate nodes + starting material nodes at beginning of each branch)(MW)_product

W _VO = waste mass of valorized outputs

W _NVO = waste mass of non-valorized outputs

X_j = standard environmental impact parameter value

X_ref = value for an arbitrarily chosen reference compound

y_j = the number of yellow cells accrued for each substance j

Abbreviations

A = fraction of aromatic atoms,

AAE = Actual Atom Economy

AE = atom economy

AP = acidification potential

ARDP = abiotic resource depletion potential

aux = auxiliary material

CCOHS = Canadian Centre for Occupational Health and Safety

E = Environmental factor

EAE = Experimental Atom Economy

E-factor = Environmental Factor

est = estimated

FLASC = Fast Life Cycle Assessment of Synthetic Chemistry

gAE (or AET) = global Atom Economy

gE (or ET) = global E-factor

GHS = Global harmonized system

GHSV = Gas Hourly Space Velocity

gPMI (or PMIT) = Global Process Mass Intensity

gRME = Global Reaction Mass Efficiency

GWP = Global Warming Potential

INGTP = Human Toxicity by Ingestion

INHTP = Human Toxicity by Inhalation

MCM = Multicompartment model

MRP = Material recovery parameter

MSDS = Materials Safety Data Sheets (MSDS)

MW = Molecular Weight

NFPA = National Fire Protection Association

NIOSH = National Institute for Occupational Safety and Health

ODP = Ozone Depletion Potential

PMI = Process Mass Intensity

REACH = Registration Evaluation Authorization and Restriction of Chemicals

RME = Reaction Mass Efficiency

RTECS = Registry of Toxic Effects of Chemical Substances

SF = Stoichiometric Factor

SFP = Smog Formation Potential

SI = Sustainability Index

SP = Side-Products

STY = Space Time Yield

TOF = Turnover frequency

TON = Turnover Number

UT-GCI = U Toronto Green Chemistry Initiative algorithm

Green metrics

In this section it is reported a selection of green metrics including their mathematical formula, definitions and specific information. Symbols are also indicated for simplicity although they are also all listed in Section “Abbreviations”. It is worth recalling the introduction, where it was pointed out that the metrics are almost all mass-based.

The following Table 1 represents a useful glossary for metrics and related guideterminology. ⁴² ^, ⁴³ ^, ⁴⁴ ^, ⁴⁵ ^, ⁴⁶ ^, ⁴⁷ ^, ⁴⁸ ^, ⁴⁹ ^, ⁵⁰

Table 1:

Glossary related to green metrics.

Name	Definition
Additive	A substance added to a reaction mixture that improves reaction performance toward a desired product. Additives are also added to products to achieve or improve certain properties. The role of an additive is not always well defined. ⁴²
Auxiliary	A substance or material used in the processing and especially in the post-processing of a chemical reaction typically in work-up procedures involving washing or extraction and in purification procedures involving chromatography or recrystallization.
Balanced chemical equation See reactant; reagent; by-product, coupled product; target product	A chemical equation written with reactants on the left-hand side and all products (target product plus all consequential by-products) on the right-hand side such that the number of each kind of atom appearing on the left is equal to the number of each kind of atom appearing on the right. The concept was introduced by Antoine Lavoisier in 1775 and is a practical consequence of the law of conservation of mass. A balanced chemical equation is the starting point of all metrics analyses. ⁴³
By-product See coupled product; side product.	A by-product is a secondary product derived from a production process, manufacturing process or chemical reaction; it is not the primary product. By-products and the target product appear on the right-hand side of a balanced chemical equation. ⁴⁴ ^, ⁴⁵
Catalyst	A substance added to a chemical reaction that accelerates the reaction. It participates in the reaction, but its structure remains unchanged at the end of the reaction. The consequences of its use are milder reaction conditions such as reduced temperature, shorter reaction times, higher product yield, and higher product selectivity. ⁴²
Catalyst loading	A term describing the mass of catalyst relative to the mass of substrate (usually the limiting reagent) in a given reaction. The usual units used are mol, mol%, weight and weight%.
Construction step See target bond forming step.	A reaction step in a synthesis plan that results in the formation of a target bond that appears in the final target structure of the plan. Well-strategized synthesis plans have a high proportion of construction steps, often containing construction steps that produce more than one target bond in the same reaction.
Coupled product(s)	Coupled products arise as a mechanistic consequence of producing the desired target product in a chemical reaction. The term is synonymous with by-products.
Extraction solvent	A solvent used in the workup operation in carrying out a chemical reaction. The mass of this solvent is counted in the E_aux contribution to E_total (E_T).
Fast life cycle assessment of synthetic chemistry (FLASC)^TM	FLASC is a trademark name of a life cycle assessment algorithm developed by GlaxoSmithKline (GSK) for the analysis of syntheses of pharmaceutical products. ⁴⁶
Molecular weight first-moment or building-up parameter See synthesis tree	This metric belongs to the set of essential synthesis strategy parameters that describes the net building up of a structure from the set of initial input and intermediate structures toward the final target product. The molecular weight first moment per reaction stage about the target product molecular weight in units of grams per mole is given by μ = ω 1 − ω 2 N + 1 where ω₁ = Σ (MW_{intermediates} + MW_{starting material at beginning of each branch}) ω₂ = (total number of intermediate nodes + starting material nodes at beginning of each branch)(MW)_product N is the number of reaction stages in a synthesis plan. The starting materials correspond to those inputs at the beginning stage of each branch that get incorporated in the subsequent intermediate product. The zeroth stage representing the starting substrates for the longest branch or root of the synthesis tree is accounted for by the extra stage in the denominator. If a reaction stage has parallel reactions and therefore consists of more than one intermediate product being formed in that stage, then each of their respective molecular weights are included in the first summed term, ω₁. The second term in ω₁ accounts for molecular weights of input starting materials at the beginning of each branch provided they contribute to the structure of the immediately resulting product. A positive value for μ indicates an overall net loss in MW per reaction stage (net degradation) and a negative value indicates an overall net gain in MW per reaction stage (net building up). The larger the magnitude of the first moment the greater is the effect of degradation or building up. Good synthesis plans are characterized by fewer reaction stages, the frequent occurrence of convergent reaction stages (i.e., parallel reactions), and large negative molecular weight first moments per reaction stage. ⁴⁷
Green metric(s) See metric	Green metrics are used to gauge the material efficiency, energy efficiency, environmental impact, safety-hazard impact, or synthesis strategy performance of a chemical reaction or synthesis plan against others for the same target molecule.
Hub intermediate	An intermediate that appears more than once in a synthesis tree diagram signifying that such an intermediate is common to several reaction pathways and therefore has a prominent status. A material efficient synthesis of a hub intermediate is central to achieve material efficient syntheses of other products that originate from it. The chemical structure of a hub intermediate is usually a common substructure of other more advanced products appearing in a reaction network.
Kernel	A descriptor that refers to the core material efficiency performance of a reaction based only on its by-product formation. All auxiliary materials such as excess reagents, catalysts, reaction solvents, work-up materials, and purification materials are ignored so that the focus is entirely on the inherent or intrinsic material performance of the reaction based on the design aspect of constructing the target molecule from a set of reactants. It represents the first stage of optimization with respect to material efficiency for any given chemical reaction.
Limiting reagent	In a chemical reaction the reagent that has the least number of moles associated with it corrected for its associated stoichiometric coefficient in a balanced chemical equation. For a balanced chemical equation given by: ν₁S₁+ ν₂S₂→ P + ν₃q where S₁ and S₂ are reagents, P is the target product, and q is the by-product; and the ν parameters are the respective stoichiometric coefficients, the limiting reagent is one that satisfies the criterion n S 1 ν 1 , n S 2 ν 2 = m S 1 MW S 1 ν 1 , m S 2 MW S 2 ν 2 where the m parameters refer to the respective masses and the MW parameters refer to the respective molecular weights of reagents. Hence, if n S 1 ν 1 < n S 2 ν 2 , then S₁ is the limiting reagent; otherwise, it is the reagent S₂.
Mass balance	The condition that the total sum of input materials used in a chemical reaction or synthesis plan is equal to the total sum of waste materials plus the mass of target product. Essentially it is the statement of the law of conservation of mass where the total mass of inputs is equal to the total mass of outputs. ⁴²
Mass of target product	The mass of target product collected from a chemical reaction or a synthesis plan. This quantity is used in the determination of reaction yield, E-factor, reaction mass efficiency, and process mass intensity.
Mass of waste	The difference in mass between the total mass of input materials used in a chemical reaction or synthesis plan and the mass of target product collected. Although recycling or the utilisation of byproducts and side products lead to a reduction in mass of waste, this is offset by additional energy and technical costs.
Metric	A quantitative measure of some property using a scaled parameter.
Molecular weight	Molecular weight is the mass of 1 mol of a pure chemical substance. Unit: g/mol.
Number of reaction steps	The count of reaction steps in a synthesis plan where a step constitutes isolation of the intermediate product along the way.
Process time	The length of time elapsed to carry out a chemical reaction from the point of adding all materials to the reaction vessel to isolating the purified target product. In batch operations, process time = residence time (reaction time) + workup time + purification time. Process time does not depend on reaction scale. In continuous flow operations using a single tube, process time = total reaction volume/ flow rate. The reaction volume is composed of the volume of reactants and the volume of reaction solvents. Process time depends on reaction scale. In continuous flow operations using multiple tubes in parallel, process time = (total reaction volume/flow rate)*(1/number of parallel tubes). This operation is called numbering up or scaling out.
Process water mass intensity	Process water mass intensity is the mass difference between freshwater usage and recycled water usage per mass of product made.
Process water use	Process water use is the total mass of water used in a process per mass of product made
Radial pentagon	A radial diagram with five axes pertaining to the following green metrics: atom economy, reaction yield, stoichiometric factor, material recovery parameter, and global reaction mass efficiency. This diagram is a useful visual aid to gauge any bottlenecks and strengths in the material efficiency performances of individual reactions. ⁴⁸
Raw material use see process mass intensity	Raw material use is the ratio of mass of total raw materials used to mass of product made. This quantity is essentially the same as process mass intensity.
Reactant or reagent	A reactant or reagent is a chemical substance that appears on the left-hand side of a balanced chemical equation. The word substrate is also used to designate that reagent or reactant whose structure appears in highest proportion in the target product of the reaction. Chemists use the three words interchangeably in the literature. ⁴⁹
Reaction solvent	A liquid selected for a conducting a reaction that satisfies the condition that its boiling point matches the desired reaction temperature and that it can dissolve the reactants, catalysts, and any other additives. Reaction solvents may or may not act as reagents. Examples of reactions where the reaction solvent is also a reagent are the Fisher esterification of carboxylic acids in alcohols, and the synthesis of acyl chlorides in thionyl chloride.
Reaction stage See reaction step; synthesis tree	In a linear synthesis plan, the number of reaction stages is equal to the number of reaction steps. In a convergent plan, the number of reaction stages is less than the number of reaction steps. In a convergent plan, a reaction stage can contain at least two reaction steps run in parallel as determined by its synthesis tree diagram.
Reaction step See synthesis tree.	A reaction step is defined as a chemical transformation that begins with an isolated set of starting materials and ends up with an isolated reaction product.
Residence time	The length of time a set of reactant spends in a reaction vessel or chamber. In batch operations, residence time = reaction time and does not change with reaction scale. In continuous flow operations, residence time = reactor volume / flow rate and does not change with reaction scale. The reactor volume is determined from the geometry of the reaction vessel, usually cylindrical.
Scale of reaction	For a balanced chemical equation, the associated scale of that reaction corresponds to the number of moles of limiting reagent.
Selectivity	A term used to describe reactivity according to a specific region or group or structural motif in a given molecular structure. There are three types of selectivity: (a) chemoselectivity: A general term used to describe desired selectivity in carrying out a reaction according to some specific chemical group over all others in a given molecule; (b) regioselectivity: Desired selectivity in carrying out a reaction according to a specific region or group over all others in a given molecule; (c) stereoselectivity: Desired selectivity in carrying out a reaction according to a specific stereochemical group over all others in a given molecule. ⁴²
Side product	A side product is a product formed in a reaction between reagents, usually undesired, that arises from a competing reaction pathway other than the one that produces the intended target product and its associated by-products. ⁴⁴
Side reaction See side product	A side reaction is a competing, often unwanted, reaction other than the intended reaction between a set of reactants. A side reaction produces side products via a different mechanism than the intended reaction.
Starting material	In a balanced chemical equation, the starting materials refer to reagents or reactants. When analyzed at the global level, starting materials also include catalysts, other additives, and reaction solvents.
Stoichiometric coefficient	In a balanced chemical equation, stoichiometric coefficients are the integer coefficients appearing before the chemical species. If the stoichiometric coefficient is 1 for a given species it is customarily not written.
Synthesis efficiency	A general term used by classically trained synthetic organic chemists to describe the material efficiency of a synthesis plan usually according to the number of reaction steps and the overall yield only. In reality, the parameterization of synthesis efficiency involves the following suite of green metrics applied to each step and to the whole plan: atom economy, yield, excess reagent consumption, E-factor, reaction mass efficiency, and process mass intensity.
Synthesis strategy	A general term used by classically trained synthetic organic chemists to describe the sequence of strategic steps employed in the total synthesis of a given target molecule. This entails (a) the type of reactions employed which can be in any one of the following broad categories: additions, substitutions, eliminations, rearrangements, redox reactions, or multi-component; (b) the number of those reactions that are target bond forming (construction steps) and those that are sacrificial steps (concession steps); and (c) whether the synthesis plan follows a linear or convergent trajectory. Tools often used to strategize how a given target molecule can be assembled from smaller molecules are retrosynthetic analysis and the large database of known named organic reactions.
Synthesis tree See first moment building up parameter	A diagram that facilitates the tracking of input reagents, intermediates, and the counting of reaction steps, branches, and points of convergence for a synthesis plan. It is also used to track the mole scales of each reaction from final target product to any intermediate or input material along the various branches. The shape of the diagram also is used to determine the degree of convergence, the degree of asymmetry parameters, and the first moment building up parameter. ⁵⁰
Synthesis: convergent	A synthesis plan that contains at least two independent branches made up of parallel consecutive sequences of reaction steps leading to intermediates that are used in convergent reaction steps. Such plans are made up of B branches and B – 1 points of convergence. The branch with the longest number of reaction steps is the main branch and is the one used to determine the overall yield of the plan.
Synthesis: divergent	A synthesis plan that contains one branch made up of a consecutive sequence of reaction steps leading to a common hub intermediate which is then used to make different target products via divergent branches in subsequent steps along parallel but independent paths.
Synthesis: linear	A synthesis plan that contains one branch made up of a consecutive sequence of reaction steps.
Target bond forming Step See construction step	A target bond forming reaction is a reaction step in a synthesis plan that involves forming a target bond that is found in the final product structure. ⁵⁰
Target product	The final desired product in a chemical reaction or synthesis plan.
Waste	Waste is the difference between the mass of all input materials and the mass of desired product collected. Although recycling or the utilisation of byproducts and side products lead to a reduction in mass of waste, this is offset by additional energy and technical costs.
Waste material	In a chemical reaction a waste material is either a reaction by-product, a reaction side product, unreacted reagents, a reaction solvent, a catalyst or other additive, a workup material, or a purification material.

Actual atom economy (AAE)

The actual atom economy is the ratio of the product mass to the mass of all reactants, or, in other words, is the product of the experimental atom economy and the yield. In the original literature ³² and also in an often quoted monograph, ⁵¹ the term actual atom economy cannot be found. It probably stems from the fact that M. Cann has not introduced a special term for “Percentage Yield x Experimental Atom Economy (ε·EAE)”, but repeatedly uses the term “actual”. In this respect, actual atom economy is a meaningful abbreviating term. It is expressly pointed out that this is the multiplication of the yield (ε) by the experimental atom economy (EAE) and not the multiplication by the atom economy (AE), as is often wrongly found in review literature. ⁵² ^, ⁵³

AAE = ε · EAE = RME

ε = yield

EAE = experimental atom economy

RME = reaction mass efficiency

unit: dimensionless

Atom economy (AE)

In a balanced chemical reaction, the atom economy (AE) is the molecular weight ratio of the target product to the sum of all reactants. Some synonyms of AE are global Atom Economy (gAE, GAE) overall Atom Economy and AE_total (AET). Essentially it measures the molecular weight fraction of reactants that end up in the desired product. The concept was introduced in 1991 by Barry Trost at Stanford University. ⁵⁴ ^, ⁵⁵ ^, ⁵⁶

A stepwise and thus programmable calculation of the atom economy of synthesis sequences can be done by dividing the molecular weight (MW) of the reactant by the atomic economy of its synthesis. Alternatively, the molecular weights of all reactants must be considered in the denominator.

Normally one or more reactants are used in excess. The experimental masses of the reactants are considered in the experimental atom economy. If the yield is also taken into account, then the related green metric is called reaction mass efficiency (RME_reaction) or the actual atom economy (AAE).

AE = ν p MW product ∑ j ν j MW reactant , j

MW = molecular weight

ν_j = stoichiometric coefficient of the jth reactant

ν_p = stoichiometric coefficient of the product

unit: dimensionless

Cumulative material efficiency metrics

There are several cumulative material efficiency metrics. ¹ ^, ⁵⁷ ^, ⁵⁸ ^, ⁵⁹ ^, ⁶⁰ ^, ⁶¹ ^, ⁶² Within the scope of this review, we want to focus on the most important ones such as:

Cumulative (overall) yield over N-steps is the multiplicative product of the step reaction yields; step reaction yields are expressed as fractions between 0 and 1. ⁶³ The unit is dimensionless (see also reaction yield)

overall yield : ε T = ∏ j = 1 N ε j

T = total (consideration of all syntheses of a synthesis sequence; sometimes the prefix ‘g’ for ‘global’ is used instead of the index T, e.g. gRME instead of RME_T)

N = total number of steps in linear sequence

j = dummy variable referring to jth reaction step

ε_j = yield of the jth reaction step

Cumulative atom economy relationship as a function of step atom economies (AE)_j, atom economy of final step (AE)_N, molecular weights of intermediate products (MW)_Yj, and molecular weight of final product (MW)_P. The unit is dimensionless. ⁶³

AE T = 1 1 AE N + 1 MW P ∑ j = 1 N − 1 MW Y j 1 AE j − 1

Cumulative E-factor relationship as a function of step E-factors (E_j), E-factor of final step (EN), masses of intermediate products (m _Yj), and mass of final product (m _P). ⁶³ ^, ⁶⁴

E T = E N + 1 m P ∑ j = 1 N − 1 m Y j E j or

E T = ∑ J = 1 N E j + ∑ J = 1 N − 1 E j m Y j m p − 1

Cumulative process mass intensity (PMI)_T as a function of cumulative E-factor, and as a function of step PMI (PMI)_j, PMI of final step, masses of intermediate products (m _Yj), and mass of final product (m _P). It should be noted that this formula indicates that the cumulative E-factor is not the sum of the reaction step E-factors as sometimes erroneously cited. ⁶² The unit is dimensionless.

PMI T = E T + 1 = PMI N + 1 m P ∑ j = 1 N − 1 m Y j PMI j − 1

Total / global reaction mass efficiency (RME_T = gRME) as a function of cumulative process mass intensity, and as a function of step reaction mass efficiency (RME)_j, RME of final step (RME)_N, masses of intermediate products (m _Yj), and mass of final product (m _P). ⁶³ Unit is dimensionless.

RME T = 1 PMI T = 1 1 RME T , N + 1 m P ∑ j = 1 N − 1 m Y j 1 RME j − 1

Cumulative Lavoisier number relationship as a function of step Lavoisier numbers (LN)_j, Lavoisier of final step (LN)_N, molecular weights of intermediate products (MW)_Yj, and molecular weight of final product (MW)_P. ⁶³ Unit is dimensionless.

LN T = LN N + 1 MW P ∑ j = 1 N − 1 MW Y j LN j − 1

Cumulative yield

The cumulative yield (see also overall yield in Cumulative material efficiency metrics Section “Cumulative material efficiency metrics, Introduction”) is the multiplicative product of reaction step yields along a linear synthesis sequence from step 1 to any step j > 1 downstream along that pathway. If the multiplication is taken along an entire N-step linear sequence, then the cumulative yield corresponds to the overall yield of the linear synthesis. The unit is dimensionless.

For convergent syntheses the cumulative yield can be determined along any point on a given linear branch from the beginning of that branch up to the end product of that branch which corresponds to an intermediate used as input material in a convergent step. Hence, for a convergent synthesis plan containing M branches there are in principle M cumulative yields that can be determined, one for each branch. One of these M branches corresponds to the main branch having the longest linear sequence from starting materials to the final desired product at the terminus of the convergent synthesis. If desired, several branches of a convergent synthesis can be considered. ⁵⁶

E_aux

This green metric represents the contribution to the total E-factor of a reaction from auxiliary materials where m is the mass of reaction solvent, catalyst, work-up materials, purification materials, and target product. E_aux can also be split up, for example by displaying E_workup.

E aux = m solvent + m catalyst + m workup + m purification m product

aux = auxiliary material

E_excess

This green metric represents the contribution to the total E-factor of a reaction from excess reagents where m is the mass of excess reagents and target product. The unit is dimensionless.

E excess = m excess reagents m product

Environmental factor (E-factor or E)

This green metric measures the mass ratio of waste produced in a chemical reaction to the mass of the target product collected. Synonyms used include global Environmental factor (gE), overall Environmental factor and E_total (E_T).

In an ideal reaction producing no waste of any kind E = 0. The total E-factor takes into account waste from all sources including reaction by-products and side products, reaction solvent, catalysts and other additives, workup materials, and purification materials. Process chemists sometimes, but not always, include any solvents used for cleaning equipment. The concept was introduced in 1994 by Roger Sheldon. ⁶⁵ He also proposed to consider an arbitrarily assigned unfriendliness quotient Q, by which the E factor could be multiplied in order to obtain an environmental quotient EQ. Q could consider different categories, e.g. toxicity, photochemical ozone creation potential, environmental degradation etc.

The unit is dimensionless although sometimes kg kg⁻¹ is used to express the waste as kg per kg of product.

Regarding synthesis plans (linear or convergent) composed of sets of appropriately scaled balanced chemical equations: Masses of intermediates formed as products in step 1 to step N–1 are not included since they are made and consumed in consecutive steps in an appropriately scaled synthesis plan.

Congeneric: the step E-factor pertains to a particular reaction step in a synthesis plan. The kernel E-factor (=E_kernel) bases only on the mass of waste due to reaction by-products and unreacted reagents in a given chemical reaction or a synthesis plan. E_excess (-kernel, -solvent, etc.) is the contribution to the E-factor of a reaction from excess unreacted reagents (by-products + side products + unreacted reagents, solvents, etc.).

E = m waste m product = PMI − 1 = 1 RME − 1

m = masses of substances

PMI = process mass intensity

RME = reaction mass efficiency

E_MW

Environmental factor based on molecular weight (E_MW) defined as the sum of the molecular weights of reaction byproducts as determined from a balanced chemical equation divided by the molecular weight of the target product. Thus, E_MW deviates from E_kernel in that neither yield nor excess reactant are taken into account. An E_MW equal to 0 corresponds to a chemical reaction producing no by-products with an AE = 1, or 100 %. An example is the [4 + 2] Diels-Alder cycloaddition of a dienophile and a diene. This metric is dimensionless.

The connecting relationship between E_MW and atom economy (AE) is given by the following equation:

E MW = 1 AE − 1

E_kernel

The metric is the contribution to the total E-factor of a reaction coming from by-products and stoichiometric unreacted reagents where the where m is the mass of by-products, stoichiometric unreacted reagents, and target product. This metric is dimensionless.

E kernel = m by ‐ products + m stoichiometric unreacted reagents m product

E_solvent

This metric represents the contribution to the total E-factor of a reaction from solvents where m is the mass of the reaction solvent and target product. Also, in this case the metric is dimensionless. Solvents used during work-up can be expressed as E_workup.

E solvent = m reaction solvent m product

Experimental atom economy (EAE)

In a balanced chemical reaction, the mass weight ratio of the target product, if this is assumed to be produced with 100 % yield, to the sum of all reactants. ³² Essentially it measures the theoretical mass fraction of reactants that potentially end up in the desired product. See a further example in the literature. ³³ ^, ⁶⁶ Thus the experimental atom economy differs from the atom economy by the additional consideration of reactant excess. The following applies: EAE is less than or equal to AE. Another term in connection with the atom economy is the reaction mass efficiency.

EAE = m product if 100 % yield ∑ j m reactant , j = n k · υ p υ k · MW product ∑ j n j MW reactant , j

n _j = amount of substance of the jth reactant in mole

n _k = amount of substance of the key reactant in mole, i.e. limiting reactant

m = masses of substances

MW = molecular weight

ν_k = stoichiometric coefficient of the key reactant

ν_p = stoichiometric coefficient of the product

If the stoichiometric coefficients ν_k and ν_p are identical, which is often the case, the quotient υ p υ k will have the value 1.

Gas hourly space velocity (GHSV)

The gas hourly space velocity ⁶⁷ is applicable to catalytic gas phase reactions and is given by the following equation:

HSV = total flow rate of gaseous reagents , c m 3 min − 1 catalyst volume , c m 3 · 60 min h − 1

The unit of the metric is h⁻¹.

Global process mass intensity (gPMI, PMI_T)

This metric - synonymous to overall process mass intensity - is applicable to single balanced chemical reactions and to synthesis plans (linear or convergent) composed of sets of appropriately scaled balanced chemical equations. The metric is dimensionless.

PMI T = gPMI = ∑ j m input , j m product = 1 gRME = 1 RME T

g = global

T = total (consideration of all syntheses of a synthesis sequence)

RME = reaction mass efficiency.

The m terms refer to the masses of the final target product and all input materials including reagents, catalysts, reaction solvents, workup materials, and purification materials. Masses of intermediates formed as products in step 1 to step N – 1 are not included since they are made and consumed in consecutive steps in an appropriately scaled synthesis plan.

For a formula for synthesis plans, see chapter 2.3 Cumulative material efficiency metrics

Global reaction mass efficiency (gRME, RME_T)

This metric - synonymous to overall reaction mass efficiency - is applicable to single balanced chemical reactions and to synthesis plans (linear or convergent) composed of sets of appropriately scaled balanced chemical equations. This metric is dimensionless.

RME T = gRME = m product ∑ j m input , j = 1 gPMI = 1 PMI T

where the m terms refer to the masses of the final target product and all input materials including reagents, catalysts, reaction solvents, workup materials, and purification materials. The terms T and g mean total and global because all syntheses of a synthesis sequence are considered. Masses of intermediates formed as products in step 1 to step N – 1 are not included since they are made and consumed in consecutive steps in an appropriately scaled synthesis plan. ⁴⁷

For a formula for synthesis plans, see chapter 2.3 Cumulative material efficiency metrics

Global atom economy (gAE, AE_T)

This metric pertains to the overall atom economy for a synthesis plan containing at least two reaction steps.

AE T = gAE = AE overall = ν p MW product ∑ j ν j MW input , j

where v _j is the stoichiometric coefficient of the jth input material, v_p is the stoichiometric coefficient of the product, and MW parameters refer to the respective molecular weights. The terms T and g mean total and global because all syntheses of a synthesis sequence are considered. Molecular weights of intermediates generated as products from step 1 to step N – 1 are not counted. See also Atom Economy for an example; see formula (2) under cumulative material efficiency metrics (entry 3). Sometimes, GAE is used instead of gAE in literature.

For a formula for synthesis plans, see chapter 2.3 Cumulative material efficiency metrics.

Global E-factor (gE, E_T)

This metric synonymous to overall E-factor is applicable to single balanced chemical reactions and to synthesis plans (linear or convergent) composed of sets of appropriately scaled balanced chemical equations.

E T = gE = E overall = ∑ j m waste , j m product = ∑ j m input , j − m product m product = gPM I − 1 = PMI T − 1

For a formula for synthesis plans, see chapter 2.3 Cumulative material efficiency metrics.

Lavoisier number

The Lavoisier number is defined as the reciprocal of atom economy and is related to the E-factor based on molecular weight according to formula reported. ⁶³

LN = 1 AE = E MW + 1

This expression is analogous to the connecting relationship between process mass intensity and reaction mass efficiency based on mass given by

PMI = 1 RME = E + 1

An ideally designed reaction produces no by-products at the kernel level and so its atom economy and Lavoisier numbers are both equal to 1, or 100 %. Lavoisier numbers for reactions suggest a convenient scale that measures how far away from ideality they are at the kernel level. For example, a reaction producing a target molecule with a Lavoisier number of 2 (i.e., with an atom economy equal to 0.5 or 50 %) means that it is two times further away from ideality than another reaction producing the same target molecule with no by-products. Reactions having high Lavoisier numbers much larger than 1 produce significant by-products and have low atom economies.

For a formula for synthesis plans, see chapter 2.3 Cumulative material efficiency metrics.

Material recovery parameter (MRP)

This metric takes into account auxiliary materials used in the reaction and post-reaction phases (work-up and purification) such as reaction solvents, catalysts, solvents and washings for extractions, and solvents for chromatography and recrystallization. ⁴⁸ This metric is dimensionless.

MRP = 1 1 + ε AE m solvent + m catalyst + m workup + m purification SF m product

SF = stoichiometric factor

AE = atom economy

ε = yield

The notion of recovery is used in the name since reaction and extraction solvents constitute the bulk of material used in a given chemical reaction and are consequently the first things that are easily recoverable for re-use or recycling.

Process mass intensity (PMI)

This metric was adopted by the pharmaceutical industry as the standard metric for material performance of a chemical reaction or synthesis plan. ⁶⁸ It was also called mass intensity product or mass index. ⁴¹ When PMI is applied to a synthesis plan it is called global process mass intensity and the masses of input materials are appropriately scaled to a common basis mole scale of target product.

Congeneric: Process solvent mass intensity is the total mass of solvent used (excluding water) per mass of product. Process water use is the total mass of water used in a process per mass of product made, whereas process water mass intensity is the mass difference between freshwater usage and recycled water usage per mass of product made. Also see Process mass intensity complexity model.

PMI = ∑ m input m product = E + 1 = 1 RME

m _input = masses of input materials

m _product = mass of final target product

E = environmental factor

RME = reaction mass efficiency

This metric is dimensionless; sometimes kg kg⁻¹ (or kg mol⁻¹ is used to express the material input as kg per kg of product (or as kg per mol of product). ⁶⁹ ^, ⁷⁰ ^, ⁷¹

For a formula for synthesis plans, see chapter 2.3 Cumulative material efficiency metrics.

Process mass intensity complexity model

This metric estimates PMI for a synthesis of a given compound on the basis of its structural attributes without having to go through the tedious task of working through the experimental procedure for each reaction step-by-step. ⁷² This metric is dimensionless.

PM I est = 131 + 26 C + 40 H − 515 A + 57 C − 1.5 H − 8

C = number of chiral centres

H = number of heteroatoms

A = fraction of aromatic atoms

est = estimated

A = c aromatic + H aromatic c total + H total

C_aromatic = number of carbon atoms in aromatic rings;

H_aromatic = number of heteroatoms (N, S, O) in aromatic rings;

C_total = total number of carbon atoms;

H_total = total number of heteroatoms

Process solvent mass intensity

Process solvent mass intensity is the total mass of solvent used (excluding water) per mass of product. ⁴¹

Process water mass intensity

Process water mass intensity is the mass difference between freshwater usage and recycled water usage per mass of product made. ⁴¹

Process water use

Process water use is the total mass of water used in a process per mass of product made. ⁴¹

Reaction mass efficiency (RME)

The RME is the ratio of the product mass to the mass of all reactants ⁴¹ ^, ⁶⁹ or to the mass of only stoichiometric amounts ⁴⁶ of the reactants, i.e. without excess of reactants, or to the mass of all substances, i.e. additionally also auxiliary substances, solvents, etc. Thus, the RME_reaction differs from the EAE only in that it is the actually isolated amount of product that is in the numerator and not the theoretically possible amount. The RME is the reciprocal of the PMI.

There are three definitions of RME. Two refer only to the reactants (RME_kernel and RME_reaction), while the third (RME) also considers other substances (auxiliaries, solvents, catalysts, etc.).

For a formula for synthesis plans, see chapter 2.3 Cumulative material efficiency metrics.

RME kernel = m product ∑ j n k v j v k MW reactant , j = AE · ε

RME reaction = m product ∑ j m reactant , j = n p MW product ∑ j n j MW reactant , j = EAE · ε

RME = m product ∑ j m input , j = 1 PMI

n _j = amount of substance of the jth reactant in mole

n _p = amount of the product in mole

n _k = amount of substance of the key reactant in mole, i.e. limiting reactant

v_j = stoichiometric coefficient of the jth reactant

v_k = stoichiometric coefficient of the key reactant

The factor v_j·v_k ⁻¹ takes into account differing stoichiometric coefficients of reactants and key reactant. Normally, the value is simply 1/1 = 1, if one molecule of A reacts with one molecule of B. However, in e.g. A + 2 B → P + q the value is 2/1 = 2.

m = masses of substances

MW = molecular weight

ε = yield

EAE = experimental atom economy

PMI = process mass intensity

AE = atom economy

Reaction yield or stoichiometric yield (ε)

The reaction yield is defined according to the following equation:

ε = n product n limiting reagent ν limiting reagent ν product

for a balanced chemical equation where ν refers to the respective stoichiometric coefficients and n refers to the amount of substances in moles. Reaction yields are customarily expressed as percentages.

Space time yield (STY)

This metric is often used by process chemists to measure synthesis production efficiency is space-time-yield, STY, given by the formula reported.

STY = mass of product total process time total volume of input materials

It can be applied to single chemical reactions or synthesis plans. The units are kg/m³/h, kg/m³/s, kg/L/h, kg/L/s. Sometimes the volume of the reactor is used instead of the volume of input materials.

Stoichiometric factor (SF)

For a balanced chemical equation, the stoichiometric factor is given by

SF = m actual reagents used m stoichiometric reagents = 1 + m excess reagents m stoichiometric reagents

where the m parameters refer to the respective masses. An SF value of 1 means that no excess reagents are used; an SF value greater than 1 means that excess reagents are used. ⁴⁷

Sustainability index (SI)

The sustainability index tracks the provenance of input materials, provenance of energy sources, and fate of output materials. A valorized input material is defined as one arising from renewable or recycled sources such as biomass, scrap metals, or retrieved by-products from other processes. ⁷³ A non-valorized input material is derived from non-renewable sources such as fossil fuels and virgin mineral ores. A valorized output material is defined as one destined to be recycled, reclaimed, or used in other processes. A non-valorized output material is defined as one that will end up as “dead waste” whether or not it undergoes treatment before release into the four main environ-mental compartments of air, water, soil, and sediment. The following energy sources are considered as renewable: hydroelectric, solar, wind, geothermal, and biofuels; and the following energy sources are considered as non-renewable: coal, other fossil-fuels such as petroleum and natural gas, and nuclear. An SI value equal to 1 means that all four fractions are each equal to 1 and hence a synthesis plan would be characterized as completely sustainable according to the limitations of SI. At the other extreme, an SI value equal to 0 means that a synthesis plan is characterized as completely unsustainable.

The sustainability index (SI) for a synthesis plan is defined as the root-mean square of four fractional quantities given by

S I = 1 2 F VI 2 + F VO 2 + F VP 2 + F RE 2

where F _VI, F _VO, F _VP, and F _RE are the mass fraction of valorized inputs, mass fraction of valorized waste outputs, mass fraction of valorized target product, and input enthalpic energy fraction arising from renewable energy sources, respectively.

Specifically, these four fractions are given by

F VI = M VI M totalinputs = M VI M VI + M NVI

F VO = W VO W VO + W NVO

F VP = M product − M product * M product

F RE = I E E renewable I E E total

where M _VI is mass of valorized inputs, M _NVI is mass of non-valorized inputs, W _VO is waste mass of valorized outputs, W _NVO is waste mass of non-valorized outputs, M _product is mass of target product, M ^* _product is mass of target product that is destined to be wasted, (IEE)_renewable is the input enthalpy energy arising from renewable resources, and (IEE)_total is the total input enthalpy energy obtained as a sum of all energy consumption as a result of heating and cooling over all input materials used in a synthesis plan above or below a reference state representing the ambient temperature and pressure conditions of 298 K and 1 atm, respectively.

Turnover frequency (TOF)

In a chemical reaction employing a catalyst, the turnover frequency is given by the following equation.

TOF = n product n catalyst 1 reaction time

n = amount of substance in moles

This green metric has h⁻¹ as unit.

Turnover number (TON)

In a chemical reaction employing a catalyst, the turnover number is given by the following equation. This green metric is dimensionless.

TON = n product n catalyst

n = amount of substance in moles

Algorithm database list

This section focuses on algorithm Database useful for the calculation of Green Metrics; specifications, websites and information on their use and applications are discussed in detail.

ACS green chemistry institute Pharmaceutical Roundtable PMI app

Within this app is possible to access several calculators of Green Metrics

Process Mass Intensity Prediction Calculator: “The Process Mass Intensity (PMI) Prediction Calculator was created by the ACS GCI Pharmaceutical Roundtable member companies, with leadership from Bristol-Myers Squibb, to predict a range of probable process efficiencies of proposed synthetic routes at various phases of drug development. The tool uses historical PMI data from multiple pharmaceutical companies and predictive analytics (Monte Carlo simulations) to estimate the probable PMI ranges. The tool can be used to predict PMI prior to any laboratory evaluation of the route; i.e., as an in-silico modelling effort, or at any other stage of a molecule’s development to assess and compare potential route changes.” ⁷⁴ ^, ⁷⁵ It should be noted that this calculator works for linear synthesis plans, but for convergent plans has the limitation that it is does not account for excess reagent consumption in convergent steps when two or more branches meet in the same reaction step.

Convergent Process Mass Intensity Calculator: “The original PMI calculator was enhanced to accommodate convergent synthesis in this second ACS GCI Pharmaceutical Roundtable PMI calculator. The Convergent PMI Calculator uses the same calculations, but allows multiple branches for single step or convergent synthesis.” ⁷⁵

Process Mass Intensity Calculator: “Decreasing the overall quantity of materials used to manufacture a final product is a significant challenge for pharmaceutical companies. Because of the large amount of solvent used in typical manufacturing processes, decreasing materials used saves companies money (less purchased and less energy used in workup and isolation). The Process Mass Intensity (PMI) metric was developed as a way to benchmark and quantify improvements towards greener manufacturing processes. The PMI Calculator enables you to quickly determine the PMI value by accounting for the raw material inputs on the basis of the bulk API output.” This calculator works for linear synthesis plans only. ⁷⁶

ChemSpider

This is a free online database of chemical substances sponsored by the Royal Society of Chemistry that includes various experimental and calculated physical and environmental property data that is important for carrying out life cycle assessments. It is useful since it incorporates the results of the EPA suite algorithm for predicting properties such as octanol-water partition coefficient, Henry law constant, water solubility, and persistence parameters in air, water, soil, and sediment. ⁷⁷

Classification, labelling and packaging regulation (CLP)

A European Union set of rules that came into effect in 2009 that governs classification and labelling regulations to protect workers, consumers, and the environment by providing appropriate labelling that reflects a chemical’s possible hazards (See also Globally Harmonizing System (GHS); Registration, Evaluation, Authorization, and Restriction of Chemicals (REACH)). Companies in Europe are required to appropriately classify, label and package their substances and mixtures before placing them on the market.

Regulation (EC) No 1272/2008 of the European Parliament and of the Council of 16 December 2008 on classification, labelling and packaging of substances and mixtures, amending and repealing Directives 67/548/EEC and 1999/45/EC, and amending Regulation (EC) No 1907/2006. ⁷⁸ ^, ⁷⁹ ^, ⁸⁰ ^, ⁸¹

Dangerous substances classification and labelling (DSCL) (Europe)

This system is part of the Dangerous Substances Directive law concerning chemical safety that has jurisdiction in the European Union (See also Life Cycle Assessment; material safety data sheet; potential: risk phrase).

Annex III of the directive defines standard phrases relating to the Nature of special risks attributed to dangerous substances and preparations, often referred to as R-phrases. The appropriate standard phrases must appear on the packaging and label of the product and on its MSDS. The R-phrases are the basis of the risk phrase potential used in life cycle assessment. In 2015 these warning phrases disappeared, being replaced by new hazard statements (or H-phrases). ⁸² ^, ⁸³ ^, ⁸⁴

Design institute for physical property data (DIPPR 801)

The DIPPR 801 project is affiliated with the American Institute of Chemical Engineers (AIChE). The database collates reliable thermophysical property data on 2424 industrial chemicals including 34 constant and 15 temperature dependent properties. Among these the following are important in estimating input energy consumption in carrying out chemical reactions: acentric factor, normal boiling point, critical pressure, critical temperature, heat capacity of ideal gas, heat capacity of liquid, heat capacity of solid, heat of vaporization, liquid density, solid density, and vapor pressure of liquid. ⁸⁵

EATOS

EATOS (Environmental Assessment Tool for Organic Syntheses) is a program first made available in 2001 and is the pioneering work on automated material efficiency green metrics calculations for individual reactions and synthesis plans. ⁸⁶ ^, ⁸⁷ ^, ⁸⁸ ^, ⁸⁹ ^, ⁹⁰ It 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. This software has not been updated since its launch. Features of the program include:

calculation of global PMIs and global E-factors for individual reactions and entire synthesis plans including environmental impact corrections;
breakdown of the above metrics into their constituent contributions according to substrates, catalysts, solvents, auxiliary materials, coupled products, and byproducts;
use of a 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 toward the last step in a plan; single syntheses can also be combined to a synthesis sequence after their entry.
visual 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.

The program uses the following terminologies:

“atom selectivity” means “atom economy”,
“mass index (S⁻¹)” means “process mass intensity”,
“mass efficiency” means “global reaction mass efficiency”,
“by-products” refers to products arising from competing reactions other than the entered balanced chemical equation (see “side products”),
“coupled products” refers to products arising as a consequence of producing the desired product according to the balanced chemical equation (see “by-products”).

EcoScale

EcoScale is a semi-quantitative tool suitable for introductory undergraduate education on green chemistry that is used to assess environmental and hazard impacts of chemicals used in a chemical reaction. It uses an arbitrary penalty point system out of an ideal value of 100 covering the following 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 and reaction time, and workup and purification components. Greener procedures have high EcoScale values. The algorithm applies only to single reactions, not synthesis plans, and only to reaction input materi-als. It has limited coverage of actual toxicity and hazard parameters and is heavily weighted toward simplified WHMIS and NFPA-704 labeling systems and qualitative information found in MSDS sheets. There is no visual display, and the EcoScale does not account for relative masses of input or waste materials in the assignment of penalty points. For example, 1.0 g of mercury used as reagent is assigned the same penalty points as if 100 g were used. The algorithm also does not consider waste reaction by-products. EcoScale is not recommended for work beyond teaching purposes at the introductory level. ⁹¹ ^, ⁹² ^, ⁹³

Fast Life Cycle Assessment of Synthetic Chemistry (FLASC)

FLASC is a trademark name of a life cycle assessment algorithm developed by GlaxoSmithKline (GSK) for the analysis of syntheses of pharmaceutical products. ⁴⁶

Global harmonized system (GHS)

GHS is an internationally agreed upon system of labeling chemical hazards managed by the United Nations that harmonizes descriptions and pictograms used by the European Union Classification, Labelling, and Packaging (CLP) Regulation and the United States Occupational Safety and Health and Administration (OSHA) standards into a single unified standard. Three broad categories of hazard are considered: physical, health, and environmental. Among physical hazards are the following 9 sub-categories: explosives, gases, flammable liquids, flammable solids, oxidizing substances and organic peroxides, toxic and infectious substances, radioactive substances, substances corrosive to metals, and miscellaneous. Among the health hazards are the following 12 sub-categories: acute toxicity, skin corrosion, skin irritation, serious eye damage, eye irritation, respiratory sensitizer, skin sensitizer, germ cell mutagenicity, carcinogenicity, reproductive toxicity, specific target organ toxicity, and aspiration hazard. Among the environmental hazards are the following 2 sub-categories: acute aquatic toxicity and chronic aquatic toxicity. GHS label components include hazard pictograms, signal words such as “danger” or “warning”, hazard statements, precautionary statements, product identifier (ingredient disclosure), supplier identification, and supplemental information. ⁹⁴ ^, ⁹⁵ ^, ⁹⁶ ^, ⁹⁷ ^, ⁹⁸

Green star

Green Star is a more advanced point-based system to ascertain the degree of greenness of a chemical process as compared to the EcoScale because it attempts to include all 12 principles of green chemistry in a semiquantitative manner. Hence, it has been advertised as a “holistic approach” to assess the degree of greenness of a chemical reaction, however it excludes green 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 non-green 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 based on relative areas of radial dodecagons pertaining to the scores accumulated based on the 10 green principles considered. ⁹⁹

Materials Safety Data Sheets (MSDS)

These are documents that describe occupational safety and health information, and spill handling procedures for chemical products. ¹⁰⁰ ^, ¹⁰¹ MSDS sheets are divided into the following 16 sections:

Identification of the substance/mixture and of the chemical supplier
Hazards identification
Composition/information on ingredients
First aid measures
Firefighting measures
Accidental release measure
Handling and storage
Exposure controls/personal protection
Physical and chemical properties
Stability and reactivity
Toxicological information
Ecological information
Disposal considerations
Transport information
Regulatory information
Other information

The following information important for life cycle assessment is found in MSDS sheets:

LD50 (oral), LD50 (dermal), LC50 (inhalation), flash point, lower explosion limit, occupational exposure limits, boiling point, log Kow, water solubility, and risk or hazard phrases.

Multicompartment model (MCM)

The multicompartment model (Level I) was developed by Donald Mackay at the University of Toronto and Trent University. This model determines the fate concentrations of a given mass of a chemical released into four environmental compartments: air, water, soil, and sediment. ¹⁰² ^, ¹⁰³ ^, ¹⁰⁴ ^, ¹⁰⁵ ^, ¹⁰⁶ ^, ¹⁰⁷

Multivariate method

The multivariate metric exercise developed at Queen’s University is a truncated life cycle assessment (LCA) method based on the concept of defining a risk potential, P_j, for substance j as the ratio of a standard environmental impact parameter value, X_j, based on some property of the substance, to its value for an arbitrarily chosen reference compound, X_ref, according to the expression

P j = X j X ref .

The exercise used the following seven potentials: acidification (AP), ozone depletion (ODP), smog formation (SFP), global warming (GWP), human toxicity by ingestion (INGTP), human toxicity by inhalation (INHTP), and abiotic resource depletion (ARDP). The global warming potential also incorporated a contribution from energy consumption in the form of CO₂ equivalents from heating, distillation, and refluxing operations. Energy consumptions from cooling and pressurization procedures were neglected. In addition, the degrees of bioaccumulation and persistence were estimated using octanol−water partition coefficients and the Boethling index_.

For a given reaction, the above seven potentials are determined for each substance that contributes to overall waste, namely, byproducts, and all auxiliary materials (reaction solvents, catalysts, workup materials, and purification). Waste contributions from unreacted reagents are not considered in the analysis.

When comparing results for different reactions leading to the same target compound at a common basis scale (usually 1 kg), tables are constructed showing these summed risk indices in a head-to-head fashion, and a red−yellow−green color-coding scheme is used to make decisions on which reaction is relatively greener. For each risk index category, red is assigned to the highest value, green is assigned to the lowest value, and yellow is assigned to intermediate values. Relatively greener plans are associated with a higher frequency of green-colored risk indices. ¹⁰⁸ ^, ¹⁰⁹ ^, ¹¹⁰

National fire protection association (NFPA) 704 labeling system

The National Fire Protection Association (NFPA) is a United States trade association, that creates and maintains private, copyrighted standards and codes pertaining to fire protection for usage and adoption by local governments. The 704 labelling system refers to the Standard System for the Identification of the Hazards of Materials for Emergency Response (four-color hazard diamond symbol). NFPA 704: Standard System for the Identification of the Hazards of Materials for Emergency Response; National Fire Prevention Association: Quincy, MA, 2007. ¹¹⁰

National Institute for occupational safety and health (NIOSH)

The National Institute for Occupational Safety and Health (NIOSH), established in 1970, is the United States federal agency responsible for conducting research and making recommendations for the prevention of work-related injury and illness. It compiles lists of occupational exposure limits for various industrial chemicals. ¹¹¹

Registration evaluation authorization and restriction of chemicals (REACH)

Registration, Evaluation, Authorisation and Restriction of Chemicals (REACH) is a European Union regulation dated 18 December 2006 and came into force on 1 June 2007. REACH addresses the production and use of chemical substances, and their potential impacts on both human health and the environment. ¹¹²

Registry of toxic effects of chemical substances (RTECS)

Registry of Toxic Effects of Chemical Substances (RTECS) is a database of toxicity information compiled from the open scientific literature without reference to the validity or usefulness of the studies reported. Until 2001 it was maintained by US National Institute for Occupational Safety and Health (NIOSH) as a freely available publication. It is now maintained by the private company Symyx Technologies and is available only for a fee or by subscription. The RTECS database is also available by subscription via the Canadian Centre for Occupational Health and Safety (CCOHS). RTECS contains LD50 (oral), LD50 (dermal), and LD50 (inhal) data. ¹¹³

Solvent selection tool

This tool allows for selection of greener solvent options based on physical, toxicological, and safety-hazard properties. ¹¹⁴ ^, ¹¹⁵ ^, ¹¹⁶

U Toronto green chemistry initiative algorithm (UT-GCI)

An algorithm developed by the University of Toronto Green Chemistry Initiative (GCI) for accessing the degree of greenness of a chemical reaction according to material efficiency, environmental impact, and safety-hazard impact that is a hybridized method that combined the easy-to-understand attributes of the EcoScale and Green Star methods with the ideas of mass weighted parameters and uncertainties advanced in the BI and SHI method. ¹¹⁷

For a given chemical reaction, the following parameters were considered for assessing greenness: reaction temperature, reaction pressure, LD50 (oral), LD50 (dermal), LC50 (inhalation), OEL, log K_ow, GWP, acidification potential, LEL, flammability, corrosivity, explosiveness, reaction with water, oxidizing potential, and pyrophoricity. A red−yellow−green−gray color-coding scheme was implemented where each color was associated with a particular range of values for each parameter. Red indicated a notable hazard, yellow an intermediate hazard, green a mild hazard, and gray an uncertain hazard. Instead of simply counting the number of each kind of color for each waste substance, mass weighted color scores were determined according to:

red score = ∑ j ϕ j r j ∑ j r j , yellow score = ∑ j ϕ j y j ∑ j y j , green score = ∑ j ϕ j g j ∑ j g j , gray score = ∑ j ϕ j u j ∑ j u j .

where ϕ _j represents the fractional mass contribution of waste substance j to the total waste and r_j, y_j, and g_j represent the number of red, yellow, and green cells accrued for each substance j, respectively.

The scores can be applied to input materials only and to waste materials only.

Workplace hazardous materials information system (WHMIS)

The Workplace Hazardous Materials Information System (WHMIS) (known as SIMDUT, Système d’information sur les matières dangereuses utilisées au travail in French) is Canada’s national workplace hazard communication standard. The key elements of the system, which came into effect on October 31, 1988, are cautionary labelling of containers of WHMIS controlled products, the provision of material safety data sheets (MSDSs) and worker education and site-specific training programs. ² ^, ¹¹⁷ ^, ¹¹⁸ ^, ¹¹⁹ ^, ¹²⁰

Conclusions

This work provides guidelines for quantifying the greenness of a synthetic approach. It highlights various tools that utilize rigorous green metrics to assess the material, energy, and environmental impacts of individual reactions and synthesis processes. A section is also dedicated to algorithm databases that support the calculation of green metrics. By using these metrics, the scientific community can quantify both the technical and environmental improvements of new technologies, making their benefits more accessible to the public. Ultimately, a quantitative tool for assessing the greenness of chemical processes will aid in communicating research findings and promote the broader adoption of green chemistry technologies in industry.

Corresponding authors: Fabio Aricò, Environmental Science, Informatics and Statistics, Cà Foscari University, Venice, Italy, e-mail: fabio.arico@unive.it; John Andraos, CareerChem, Toronto, ON, Canada, e-mail: c1000@careerchem.com; and Pietro Tundo, University of Venice, Venice, Italy, e-mail: tundop@unive.it

Funding source: Ministero dellâ€™Istruzione, dellâ€™UniversitÃ e della Ricerca

Award Identifier / Grant number: DoE 2023-2027 (MUR, AIS.DIP.ECCELLENZA2023_27.FF p

Acknowledgments

This work was supported by the DoE 2023–2027 (MUR,AIS.DIP.ECCELLENZA2023_27.FF project).

Research ethics: Not applicable.
Informed consent: Not applicable.
Author contributions: Conceptualization, writing and supervision: John Andraos, Pietro Tundo, Marco Eissen and Fabio Aricò; Data curation and Writing – original draft: Marco Eissen and Fabio Aricò; Revision and wring: Giacomo Trapasso, James Clark.
Use of Large Language Models, AI and Machine Learning Tools: None declared.
Conflict of interest: The author states no conflict of interest.
Research funding: IUPAC Project No.: 2017-030-2-041.
Data availability: Not applicable.

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Received: 2025-08-14

Accepted: 2025-09-08

Published Online: 2025-09-15

https://doi.org/10.1515/pac-2025-0553

Keywords for this article

Algorithm database; green chemistry; green metrics; metric glossary

Metrics for green syntheses

Article

Abstract

Introduction

Symbols

Abbreviations

Green metrics

Actual atom economy (AAE)

Atom economy (AE)

Cumulative material efficiency metrics

Cumulative yield

Eaux

Eexcess

Environmental factor (E-factor or E)

EMW

Ekernel

Esolvent

Experimental atom economy (EAE)

Gas hourly space velocity (GHSV)

Global process mass intensity (gPMI, PMIT)

Global reaction mass efficiency (gRME, RMET)

Global atom economy (gAE, AET)

Global E-factor (gE, ET)

Lavoisier number

Material recovery parameter (MRP)

Process mass intensity (PMI)

Process mass intensity complexity model

Process solvent mass intensity

Process water mass intensity

Process water use

Reaction mass efficiency (RME)

Reaction yield or stoichiometric yield (ε)

Space time yield (STY)

Stoichiometric factor (SF)

Sustainability index (SI)

Turnover frequency (TOF)

Turnover number (TON)

Algorithm database list

ACS green chemistry institute Pharmaceutical Roundtable PMI app

ChemSpider

Classification, labelling and packaging regulation (CLP)

Dangerous substances classification and labelling (DSCL) (Europe)

Design institute for physical property data (DIPPR 801)

EATOS

EcoScale

Fast Life Cycle Assessment of Synthetic Chemistry (FLASC)

Global harmonized system (GHS)

Green star

Materials Safety Data Sheets (MSDS)

Multicompartment model (MCM)

Multivariate method

National fire protection association (NFPA) 704 labeling system

National Institute for occupational safety and health (NIOSH)

Registration evaluation authorization and restriction of chemicals (REACH)

Registry of toxic effects of chemical substances (RTECS)

Solvent selection tool

U Toronto green chemistry initiative algorithm (UT-GCI)

Workplace hazardous materials information system (WHMIS)

Conclusions

Acknowledgments

References

E_aux

E_excess

E_MW

E_kernel

E_solvent

Global process mass intensity (gPMI, PMI_T)

Global reaction mass efficiency (gRME, RME_T)

Global atom economy (gAE, AE_T)

Global E-factor (gE, E_T)