Divergence, Diagnostics, and a Dichotomy of Methods

Abstract

COMPUTATIONAL MODELING IN ORGANIC chemistry employs multiple methods of approximation and idealization. Coordinating and integrating methods can be challenging because even if a common theoretical basis is assumed, the computational result can depend on the choice of method. This can result in epistemic dissent as practitioners draw incompatible inferences about the mechanisms of organic reactions. These problems arose in the latter part of the twentieth century as quantum chemists attempted to extend their models and methods to the study of pericyclic reactions. The Woodward-Hoffmann rules were introduced in the mid-1960s to rationalize and predict the energetic requirements of a number of reactions of considerable synthetic significance. Soon after, quantitative quantum chemical approaches developed apace. But alternative methods of approximation yielded divergent quantitative predictions of transition state geometries and energies. This chapter explores the difficulties facing quantum chemists in the late twentieth century as they attempted to construct computational models of pericyclic reactions. Divergent model predictions resulted in the methods used to construct computational models becoming the focus of epistemic scrutiny and dissent. The failure to achieve robust quantitative results across quantitative methods prompted practitioners to scrutinize the consequences of pragmatic tradeoffs between computational manageability and predictive accuracy. I call the strategies employed to probe pragmatic tradeoffs diagnostics. Diagnostics provides the means to probe manageability—accuracy tradeoffs for sources of predictive divergence and to determine the reliability and applicability of approximation procedures, idealizations, and even techniques of parametrization. Furthermore, although technological developments in computing power continues to increase, and indeed that there is now a general consensus on the veracity of high level ab initio and density functional methods applied to pericyclic reactions, diagnostics imposes non-contingent pragmatic constraints on computational modelling. What counts as a “manageable” model is characterized by two dimensions: computational tractability and cognitive accessibility. While the former is a contingent feature of technological development the latter is not because cognitive skills are an ineliminable feature of computational modelling in organic chemistry.