Focusing on computational studies of pericyclic reactions from the late twentieth century into the twenty-first century, this paper argues that computational diagnostics is a key methodological development that characterize the management and coordination of plural approximation methods in computational organic chemistry. Predictive divergence between semi-empirical and ab initio approximation methods in the study of pericyclic reactions has issued in epistemic dissent. This has resulted in the use of diagnostics to unpack computational greyboxes in order to critically assess the effect of (...) specific misrepresentations on predictive accuracy given that approximations and idealizations must be made to render computational models tractable. Furthermore, benchmarking is used to determine the applicability of approximation methods depending on how accurate the results need to be in a given research context. The epistemology of benchmarking consists of the co-generation of data sets in a hybrid computational–experimental form used to standardize computational methods but does not determine a unique quantitative method to be used across computational organic chemistry. (shrink)