Universal characteristics of chemical synthesis and property optimization

Abstract

A common goal in chemistry is to optimize a synthesis yield or the properties of a synthesis product by searching over a suitable set of variables (e.g., reagents, solvents, reaction temperature, etc.). Synthesis and property optimizations are regularly performed, yet simple reasoning implies that meeting these goals should be exceedingly difficult due to the large numbers of possible variable combinations that may be tested. This paper resolves this conundrum by showing that the explanation lies in the inherent attractive topology of the fitness landscape specifying the synthesis yield or property value as a function of the variables. Under simple physical assumptions, the landscape is shown to contain no suboptimal local extrema that could act as traps on the way to the optimal outcome. The literature contains broad evidence supporting this ''OptiChem'' theory. OptiChem theory implies that increasing the number of variables employed should result in more efficient and effective optimization, contrary to intuition.

Fundamental Principles of Control Landscapes with Applications to Quantum Mechanics, Chemistry and Evolution

“…Satisfaction of the assumptions implies that maximization of J is possible and that any desired set {K} may be generated by some choice of c. Combining the convex property of the set {K} with the inherent linear dependence of J(K) upon K (i.e., from Equation (2.20)) shows that the resulting landscape J contains no local minima or maxima (i.e., traps) and that connected optimal solutions of J (i.e., level sets) may exist on the landscape [37]. This result arises naturally from considering unconstrained convex optimization theory [6].…”

“…The degree to which the predictions (a) through (c) of OptiChem theory hold in laboratory investigations has recently been assessed through examination of the extensive literature reporting chemical control landscapes, with the overwhelming finding that reported control landscapes are almost all trap-free [37,38]. Although these studies cannot claim to have performed an exhaustive search of the literature, overall 142 separate control landscapes were identified, with 123 appearing trapfree and with 19 containing traps (i.e., a clear sub-optimal maximum).…”

“…Energy landscapes constitute a specific sub-class drawn from the general family of control landscapes in chemistry because the variables are often highly constrained, for instance, the only significant variable freedom for protein folding is torsional motion. While energy landscapes typically have a rugged topology [58], recent studies [37,38] demonstrate that control landscapes in chemistry possess a "regular" trap-free topology, upon satisfaction of Assumptions (1), (2) and (3).…”

“…The topological analysis of the resulting control landscape and its practical implications have recently been termed "OptiChem" theory [37,38]. The presence of a trap-free control landscape provides an organizing principle for explaining why synthesis and property discovery is far easier than the apparent complexity of such problems would suggest.…”

“…For instance, the application of genetic algorithms (GA) [20] and other optimal search procedures shows that optimization of both synthesis yield and properties typically may be achieved by carefully screening a small number of potential combinations of variables, even for nominally highly complex systems. An extensive review of practical synthesis and property optimizations beating the curse of dimensionality is given in [37,38]. The origin of these mounting successes is the key topic addressed in this section.…”