Structure, shape, topology: entangled concepts in molecular chemistry

Abstract

The concepts of molecular structure and molecular shape are ubiquitous in the chemical literature, where they are often taken as synonyms, with unavoidable drawbacks in chemistry teaching. A third concept, molecular topology, is less frequent but it is a reference term in molecular research domains such as Quantitative Structure–Activity Relationships. The present paper proposes an epistemological analysis of these three notions, aimed at clarifying the nature of their relationship, as well as the contiguities and differences between them. At first, we discuss the various acceptations of the terms molecular structure and molecular shape. Then, we examine some crucial milestones in the history of these concepts and we analyse the relationship between structure, shape and topology from an epistemological viewpoint. We point out the distinguishing features of each concept and we show that their semantic openness, that may be fruitful in a specialized context, turns into a source of incoherence and inaccuracy in the teaching context, fostered by the misleading use of these terms made by textbooks. Eventually, we propose a criterion fit to discriminate between the conceptual domains of molecular shape, molecular structure and molecular topology.

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Fig. 1
Fig. 2
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(Lewis 1916)

Fig. 6
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Scheme 1
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(Meyer 1890)

Fig. 9
Scheme 2

Notes

  1. 1.

    Here, we use this term in the acceptation of Systemic Science.

  2. 2.

    This is especially relevant at the teaching level, as the symbolic language may induce misconceptions in pupils. For a discussion on this educational topic see Jensen (1998).

  3. 3.

    In the following paragraph, we will discuss two cases (H5O2+ and the base pairs of DNA) where this model does not hold, as the skeleton may change or break without any considerable energy expense, giving rise to different structures. The existence of such systems marks the limits of the skeleton model (Cerro and Merino 2009).

  4. 4.

    Theoretical analysis always implies models. In molecular quantum calculations, the model focuses on the isolated molecule, with the assumption that the description of complex experimental situations may rely exclusively on the intrinsic properties of such molecule. The model may be further developed by adding other entities in interaction with the original single molecule. For example, the theoretical investigation of DNA base pairs coupling was carried out by adding solvation to the PCM (Polarizable Continuum Model) modelisation (Villani 2012, 2013a); the system was expanded to include dimers of base-pairs and the stacking interaction between them (Villani 2013b, c).

  5. 5.

    The main reason for adopting the BO approximation is practical: the mass disparity between nuclei and electrons allows disentangling their respective motions and simplifies calculation tremendously. The BO approximation applies to most chemically relevant cases, although the calculation carried out without approximation would end up almost to the same result. The BO approximation is not applicable whenever two or more electronic states are quasi- or completely degenerate. In this case one must rely on conical intersections. This kind of systems has been investigated either through model systems (Ferretti et al. 1996; Lami and Villani 2004) or biologically relevant system, like rhodopsin (Andruniów et al. 2004).

  6. 6.

    Besides, linking a foundational chemical concept, such as molecular structure, to an approximation has always raised philosophical problems.

  7. 7.

    The widely used Gaussian software (Gaussian 2016) encompasses three possibilities: Mulliken’s charges, Hirshfeld’s charges and NBO (Natural Bond Orbital).

  8. 8.

    URL: https://en.oxforddictionaries.com/definition/shape.

  9. 9.

    At least, this is true with objects whose dimensional scale is directly accessible to humans. In all other cases, the problem is complex (e.g. how a coastal profile can be defined?).

  10. 10.

    For a formal use of the notion of parametric shape it is possible to refer to the literature of research fields related with space, as architecture and territorial planning, or to research field related with the graphical representation of shapes (Grasl and Economou 2013).

  11. 11.

    The overall development of stereochemistry is described by important historiographic works (Ramsay 1981; Ramberg 2017).

  12. 12.

    The term 'affinity' wold be subsequently replaced by 'valence'; here we report the original terms employed by the authors.

  13. 13.

    The Zeitschrift für Chemie was published in German; the Zeitschrift was managed by German and Russian chemists.

  14. 14.

    The page of van’t Hoff (1874b) where the icons are displayed is available at URL: http://sciencepenguin.com/jacobus-henricus-van-t-hoff/.

  15. 15.

    In other two passages of the text, van't Hoff refers to his molecular models as forme du tétrahèdre (van’t Hoff 1875, p. 15, 16).

  16. 16.

    The cognitive pathway followed by van’t Hoff in devising his material models is effectively retraced in (Friedman 2016).

  17. 17.

    We use the double index (Mi,M) to distinguish this model from Fischer iconic model, designated as (Mi,F), that is mentioned further on.

  18. 18.

    According to Leslie Glasser: “Being an essentially geometrical concept, symmetry is especially suitable for study by means of diagrams and models, the use of which can enhance that ability to visualize in three dimensions” (Glasser 1967).

  19. 19.

    An official site of the US Government collects several papers on this issue, under the common title "Sample records for molecular shape amphiphiles". The abstract reports expressions like: “wedge-shaped amphiphilic molecules”, “H-shaped supra-amphiphiles”, “dumbbell-shaped giant hybrid molecule”, “Y-shaped amphiphilic block polyurethane (PUG) copolymers”, “Gear-shaped amphiphile molecules”, “Amphiphilic crescent-moon-shaped microparticles”, V-shaped polyaromatic amphiphiles.

    URL: https://www.science.gov/topicpages/m/molecular+shape+amphiphiles.html.

  20. 20.

    The principle is valid within the energetic scale of fundamental and excited states and in non-radioactive systems.

  21. 21.

    As regards the topological character of the notion of ‘functional group’ we may cite the Nobel Laureate Corey: “Modern synthetic chemistry is a multifaceted discipline that greatly benefits from the development of unifying concepts. One of the most useful of these is the idea of the “functional group,” generally considered to be a specific collection of connected atoms that occur frequently in organic structures and that exhibit well defined and characteristic chemical behavior.” (Corey 2007, p. vii).

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Ghibaudi, E., Cerruti, L. & Villani, G. Structure, shape, topology: entangled concepts in molecular chemistry. Found Chem 22, 279–307 (2020). https://doi.org/10.1007/s10698-019-09333-8

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Keywords

  • Molecular structure
  • Molecular shape
  • Molecular topology
  • Systemic approach
  • Chemical education