Atom Economy and Yield of Synthesis Sequences

Abstract

To the memory of Marcus Ratzke Atom economy (AE) or atom utilization was one of the first defining terms in the sustainable chemistry movement. In contrast to the often-cited twelve (qualitative) principles of green chemistry, AE represents a metric for quantification purposes. The theoretical efficiency of a reaction expressed by its stoichiometric equation can be determined by AE Product [g/mol]/(Substrate 1 Substrate 2 ...) [g/mol] and compared with synthetic alternatives. Of course, the atom economy will be of limited use, if starting materials differ much in complexity, i.e., in the degree of refinement. In these cases, their syntheses have to be taken in consideration, too. But, the further the retrospect goes and the more preceding synthesis steps ramify, the more complex the calculation gets. To overcome this limitation, we introduce a stepwise approach that is enabled by a simple modification of the above formula (P product; S substrate; Syn. synthesis): AE P [g/mol]/((S1/AE(Syn. of S1)) (S2/AE(Syn. of S2)) ...) [g/mol]. To illustrate this equation, which is derived mathematically, the convergent multistep synthesis of the natural product trans-chrysanthemic acid is subjected to a stepwise method of calculation. The equation can be understood as a general expression for related ratios, i.e., there are corresponding modified equations for yield, selectivity, etc. In terms of the yield, it is no longer necessary to decide between the chains of the convergent synthesis, when possibly forced to ignore significant parts of the sequence. For demonstration purposes, the yield of the convergent synthesis of the natural product peridinin has been determined with a correspondingly modified equation.

The E Factor and Process Mass Intensity

“…In the context of driving a green chemistry agenda, Federsel described the contributions of PMI for the pharmaceutical industry in a recent review [82]. Other reviews have emphasized the mathematical relationships between green metrics in more complex scenarios [7,[83][84][85].…”

Sustainable Chemistry Metrics

“…Eissen has developed a method that allows a successive procedure, [34] without including the complex sequence in its totality. In a single independent reaction of a complex sequence, the AE is calculated by: where the coefficients a and b denote the multiplicity with which a molecule enters or leaves the synthesis.…”

Comparison of Two Alternative Routes to an Enantiomerically Pure β‐Amino Acid

“…Therefore, the application of relatively easily available metrics in synthesis design receives increasing importance. The atom economy [3,4], e.g., demonstrates how efficiently the substrates are converted to the product and it is often used to compare alternative reactions. However, besides the substrates there are solvents, catalysts, auxiliary materials, etc.…”