On using tree analysis to quantify the material, input energy, and cost throughput efficiencies of simple and complex synthesis plans and networks: Towards a blueprint for quantitative total synthesis and green chemistry

Synthetic plans or networks may be depicted as trees in a graph-theoretical sense. When drawn in a systematic way according to a defined convention key "green" metrics relating to the efficiency of performance of a synthesis to a target molecule may be easily obtained by inspection, that is, by a "connect-the-dots" approach. Example metrics include the cumulative and overall reaction mass efficiency (RME), the overall raw materials cost (RMC), and the fraction of total energy input directed to product (FTE). Throughout this paper kernel metrics are used to determine and compare the intrinsic efficiencies of synthetic plans since these depend directly on the nature of the chemical transformations and not on ancillary variables such as solvent usage, etc. Histograms of these metrics versus reaction stage allow for the easy determination of the mass-, cost-, and input energy-determining steps for a given synthesis plan. Other useful parameters that can be determined from a synthesis tree include the degree of convergence, the degree of asymmetry, the optimum time to complete a synthesis, and the degree of building to target structure with respect to reaction stage (molecular weight first moment). All of these metrics allow for easy comparison and ranking of synthetic plans. It is demonstrated that the tree analysis is robust and is applicable to any synthetic plan or network of any degree of complexity. The concept of "overall reaction yield" is shown to be applicable only to linear synthesis plans or networks and is replaced by the more general overall RME metric for syntheses involving mixed linear and convergent segments. The synthesis of the antibacterial agent triclosan is used as a tutorial exercise to introduce key concepts. Further example synthetic plans analyzed by the present tree analysis illustrating various plan types include quinine (Woodward-Doering-Rabe, Stork, Jacobsen, and Acharya-Kobayashi methods), sildenafil (asymmetric convergent), absinthin (symmetric convergent), papaverine (convergent using common intermediates), bupleurynol (multicomponent convergent), and polypeptide syntheses (Fischer, Bergmann-Zervas, Merrifield, azide, anhydride, and segment doubling methods). Example synthetic networks examined include industrial syntheses of veronal (5,5-diethylbarbituric acid) (complex branching to target node) and feedstock products derived from phthalic anhydride (complex branching from source node).