Unification of reaction metrics for green chemistry: Applications to reaction analysis

A formalism is presented which unifies key reaction metrics associated with greenness in chemical reactions with respect to raw materials usage. The fundamental basis of this treatment begins with balanced chemical reactions in which byproducts are identified. The primary or kernel metrics are reaction yield, scale of reaction, stoichiometric factor (SF), and Trost's atom economy (AE). The stoichiometric factor is a new metric that is defined to account for reactions run under nonstoichiometric conditions, that is, with one or more reagents in excess. A general relation for reaction mass efficiency (RME) is derived which shows that this metric is a composite of the aforementioned primary metrics and takes into account solvent usage in the reaction and postreaction phases (workup and purification). The Sheldon environmental impact factor E is treated at various levels of complexity according to what is constituted as waste and is shown to be related to RME by a simple inverse expression. A flowchart is presented which shows other simple relationships connecting all metrics. Raw material costs, optimum conditions for recycling or reclaiming catalysts and reaction and postreaction solvents, and the handling of reactions giving isomeric products are also assessed. General algorithms are proposed for determining kernel reaction metrics for linear and convergent sequences that can be used to compare the intrinsic, or best-case scenario, green performances of synthetic plans to a common target structure. All key relationships can be implemented in a spreadsheet format from which reaction histograms or maps can be generated. Individual reaction RME performances can be gauged, ranked, and decomposed according to AE, SF, and reaction yield kernel metrics. This allows for the easy identification of best and worst reactions in a process or sequence. Example applications of the present methodology include the following: (a) a comparative analysis of the synthesis of quinine by the classic Woodward-Rabe and the modern greener Stork methods; (b) the analysis of the industrial synthesis of sildenafil (Viagra) by a convergent strategy; and (c) the analysis of kinetic resolution of racemic alcohols by a successive oxidation and recycling reduction cycle.