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Diagnostics in computational organic chemistry

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Abstract

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.

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Notes

  1. An important exception is the early quantum chemical treatment of the Diels–Alder reaction by Evans and Warhurst (1938) and Evans (1939). Michael Dewar (1971) provocatively argued that these treatments of the Diels–Alder reaction pre-empt later theoretical developments introduced by Woodward and Hoffmann and Fukui’s frontier molecular orbital theory (see “Polarization in the quantum chemistry of organic reactions” section). The significance of the earlier treatments and their relationship to the work of Woodward and Hoffmann, and Fukui, is itself a controversial issue. This is beyond the scope of the current article. For a response to Dewar, see Berson (1999).

  2. Doering was instrumental to chemists’ understanding of these reactions, for example his study of the Cope rearrangement that indicated a preference for a chair-like transition state (Doering and Roth 1962).

  3. Hoffmann and Fukui were awarded the 1981 Nobel Prize for chemistry (Woodward passed away in 1979).

  4. As Weisberg (2004, p. 1071) points out, Hoffmann’s ideas on what counts as “qualitative models” does not literally mean an absence of numbers. It instead concerns “degrees of approximation and idealization”.

  5. Some chemists consider the Pariser-Par-Pople semi-empirical approach and Dewar’s development of them as “as simplifications of the ab initio methods, since they use the SCF procedure […] to refine the Fock matrix, but do not refine these elements ab initio” (Lewars 2003, p. 340). For a debate on the role, methodological status, and distinction between semi-empirical and ab initio methods, see Ramsey (1997, 2000) and Scerri (2004a, b).

  6. For the relationship between Richard Levins’ (1966) idea of trade-offs and manageability-accuracy trade-offs in quantum chemistry, see Fisher (2015b).

  7. Portides (2007) treats “idealization” as an inclusive term referring to both distortion and abstraction. He argues that approximation “piggy-backs” on idealization in the sense that “scientific methodology requires that a process of de-idealization takes place before we can usefully and meaningfully talk of approximation” (ibid, p. 708). Portides point is that from a pragmatic perspective one must consider the extent of idealization because to talk of an approximation of a target system and hence for a simplified theoretical description to have reference, the system must be sufficiently de-idealized for it to count as an actual system. Below, I will talk of idealizations as counterfactuals, assuming that only aspects of genuine target systems are idealized.

  8. There is, of course, an extensive literature on this and related issues. See for example Cartwright (1983), Portides (2005), Suárez (1999), Suárez and Cartwright (2008).

  9. In many ways, computational models in quantum organic chemistry are similar to simulations. In particular, computational models in quantum organic chemistry share at least some similarities with simulations as described by Winsberg (2003, 2010). But this is not an issue I can pursue here.

  10. Another factor is ownership and access to propriety software. The history of quantum chemical software is distinguished by how much of the software was written by the quantum chemists themselves (Gavroglu and Simões 2012). But the rise of the commercial Gaussian software since 1970 raises additional issues concerning epistemic access to grey-boxed computational models. Perhaps the algorithms will always be partially epistemic opaque for reasons in addition to the automation of the computational processes. Furthermore, the use of Gaussian can result in a “technical sense” of standardization in computational chemistry: using the Gaussian program meant that practitioners “…geared their work towards cases and questions that fit the scope of the program” (Lenhard 2014a, p. 92).

  11. See Hendry (1998) where he argues that in quantum chemistry the improvements (de-idealizations) are driven not by quantum mechanics but by explanatorily autonomous chemical concepts, undermining Laymon’s idea of monotonic improvability from the perspective of quantum physics.

  12. Since the means of representation in this case is constituted by approximation methods, the means can be thought of as similar to what Humphreys calls a “computational templates” used to render an equation’s form computationally tractable (Humphreys 2004, pp. 60–61).

  13. See Lenhard (2014a) who argues that density functional theory is the central procedure in the turn to computational quantum chemistry in the early 1990s.

  14. Benchmarking is also of significance in other sciences. For example, Gelfert (2009) argues that “rigorous results”—exact mathematical relations between variables in mathematical modelling—are employed to benchmark simulations in many-body physics.

  15. This invites comparison to the idea that the use of computers in simulations is a form of experimentation (see for example Winsberg 2010). Critically evaluated data is, however, interactive thereby assuming a difference between “computation” and “experimentation”. Having said that, chemists like Dewar and colleagues were into doubt that computers offered the promise of new experimental instruments whose use would comparable to infrared or nuclear magnetic resonance spectroscopy (Bingham et al. 1975, p. 1285).

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Acknowledgments

I thank Buhm Soon Park for his helpful comments an earlier draft of this paper.

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    Grant Fisher

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Fisher, G. Diagnostics in computational organic chemistry. Found Chem 18, 241–262 (2016). https://doi.org/10.1007/s10698-016-9253-4

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