**3. The integration of thermodynamics into first quantum methods: The reviving of the aggregate/'mixt' duel**

## **3.1 Two conceptions of matter and the thermodynamics embodiment within chemical practices**

First and foremost, I would like to develop the opposition of conceptions of matter we previously stressed. Duhem's claim for an energy description of molecules that need not rely on any atomic assumption reminds us of other historical oppositions.

In the seventeenth century for instance, Nicolas Lemery in his famous *Cours de Chymie*, tried to account for chemical transformations by means of a multitude of corpuscles with different forms. Gabriel-François Venel argued that this reductive approach was unable to explain and predict chemical properties. Venel asserted that chemists studied 'mixt' whereas mere 'aggregates' came under mechanics. Venel used Georg Ernest Stahl's distinction between an aggregate which was defined as a mere sum of various substances that continued to exist in the whole compound, and a 'mixt' within which reactants disappeared to form an emergent new whole with specific properties. Two conceptions of matter were at odds in this context and became progressively more important within the debate. On the one hand, mechanics considered matter to be homogeneous, without qualities and necessarily informed by something from outside. This kind of matter representation solely

turned to focus on the question of the energy transfer and the direction of collisions between chemical bodies. Wilhelm Ostwald succeeded in describing chemical equilibrium without making any reference to atoms (Ostwald, 1919). Two antagonistic approaches of matter were at stake. Thermochemistry revolved around energy and denied any reality to atoms whereas chemical kinetics was based on the atomic assumption. Thomsen, for instance, used structural theory to assign heats of formation to specific bond types found in organic molecules. In this respect, he tried to reduce chemical properties to a mere juxtaposition of atomic properties. Others, like F.W. Clarke tried to connect the heat of formation with the one and only number of atomic linkages within the molecule. By doing so, he tried to connect valence with affinity (Weininger, 2001). All the attempts that tried to understand

To sum up this first part, I would like to emphasize that the integration of thermodynamics within the frameworks of chemistry was made possible because chemists were looking for a quantitative measure of affinity. The way thermodynamics became thermochemistry depended on the instrumentation and the practices that chemists contrived to tackle the challenge of affinity. As the philosopher Joseph Rouse points out: 'Practices are not just pattern of action, but the meaningful configurations of the world within which actions can take place intelligibly, and thus practices incorporate the objects that they are enacted with and on and the settings in which they are enacted'. (Rouse, 1996, p.135). Thermodynamics was thus integrated into chemical projects and then transformed by such integration because it made chemists goals achievable and intelligible within such new practical

I suggest we should take more distance and consider the whole history of chemistry to analyze the way this integration actually took place. Let us widen the circle to grasp what is at stake behind this integration and how the duel between different conceptions of matter will remain active at the very beginning of quantum chemistry. This study will enable us to

understand the role of thermodynamics in the first chemical quantum calculations.

**3. The integration of thermodynamics into first quantum methods: The** 

rely on any atomic assumption reminds us of other historical oppositions.

**3.1 Two conceptions of matter and the thermodynamics embodiment within chemical** 

First and foremost, I would like to develop the opposition of conceptions of matter we previously stressed. Duhem's claim for an energy description of molecules that need not

In the seventeenth century for instance, Nicolas Lemery in his famous *Cours de Chymie*, tried to account for chemical transformations by means of a multitude of corpuscles with different forms. Gabriel-François Venel argued that this reductive approach was unable to explain and predict chemical properties. Venel asserted that chemists studied 'mixt' whereas mere 'aggregates' came under mechanics. Venel used Georg Ernest Stahl's distinction between an aggregate which was defined as a mere sum of various substances that continued to exist in the whole compound, and a 'mixt' within which reactants disappeared to form an emergent new whole with specific properties. Two conceptions of matter were at odds in this context and became progressively more important within the debate. On the one hand, mechanics considered matter to be homogeneous, without qualities and necessarily informed by something from outside. This kind of matter representation solely

affinity thanks to additive and reductive descriptions failed.

**reviving of the aggregate/'mixt' duel** 

backgrounds.

**practices** 

described by its form and motion could not account for the world of chemical activities and diversity according to Venel. On the other hand, most chemists considered matter to be heterogeneous and able to act and react (Bensaude-Vincent & Simon, 2008). More often than not, chemists pragmatically used one description or the other according to their laboratory goals. As Bensaude-Vincent and Simon write: 'We prefer to see this duel between the two approaches as a characteristic feature of the history of chemistry. Chemists have always been confronted with this interpretative dichotomy, and, depending on the period, they have opted for a version of atomism or an elementary approach, or else have tried to reconcile the two.*'* (Bensaude-Vincent & Simon, 2008, p. 128).

Not only did thermodynamics enable chemists to construe a quantitative version of affinity but it also fitted very well into the cultural background that had been framing chemists' activities for a long time. Thermodynamics embodiment within chemical practices was thus at least twofold; it provided chemists with quantitative tools for understanding chemical reaction while recasting old oppositions of matter representations. Along with this perspective, thermodynamics could easily be integrated into the usual chemical way of thinking about matter while reconfiguring it. As Rouse claims (1996, p.157): 'In order to understand how scientific knowledge is situated within practices, we need to take account of how practices are connected to one another, for knowledge will be established only through these interconnections. Scientific knowing is not located in some privileged type of practice, whether it be experimental manipulation, theoretical modeling, or reasoning from evidence, but in the ways these practices and others become intelligible together.'

Duhem focused his work on the dichotomy between the 'mixt' and the aggregate referring to Aristotle's philosophy (Needham, 1996). Like Sainte-Claire Deville and Berthellot, but not because of the same positivist reasons, he rejected atomism then deeply rooted in structural organic chemistry. According to the structural molecular paradigm, the physical arrangement of the constituent elements accounted for the properties of the whole compound. Since Lavoisier, chemists have been explaining the properties of compounds by reference to the nature, the proportion and, more recently, the bonds of its constitutive parts, be they atoms or elements: a logic that runs from simple to complex frameworks in post-Lavoisian chemistry (Bensaude-Vincent & Simon, 2008). Conversely, the holistic energy approach used compounds to explain the properties of the elements. In this respect, atomism had a weak explanatory power because it could not completely illuminate chemical processes. According to Duhem, chemical formula could make chemists believe that substances remained unchanged when they entered into combinations whereas they only existed potentially within them (Duhem, 1902). Joseph Earley has recently proposed an argument on the same lines. He uses the example of sea water in which salt and water cease to exist in their actual states–because for instance of solvatation- but they can be reproduced by distillation (Earley, 2007). When the 'mixt' ceases to exist, it is made to reproduce its separate constituents as Venel might have asserted. In this respect, water and salt potentially exist in sea water but do not actually exist within it. Duhem then undertook to retranslate Aristotle's concept of power into that of the thermodynamic potential (Duhem, 1902). Measurable properties and mathematics allowed him to describe chemical reaction within the context of thermochemistry.

Duhem rejected both the idea of valence taken as an intrinsic atomic property and the concept of atomicity. According to him, the whole components could only give rise to valence information but not the contrary. The opposition between a holistic approach of

The Role and the Status of Thermodynamics in Quantum Chemistry Calculations 475

validity of this quantum mechanical treatment of chemical bonding; it was as not just a mere tool to calibrate methods. Empirical data really aroused Pauling's creativity and guided him to adapt his quantum work. By applying the rules for the electron-pair bond, Pauling removed the apparent incompatibility between chemistry and quantum theory (Gavroglu & Simões, 1994). Pauling answered more directly the concerns of the chemists by stressing the three-dimensional structure of molecules, the electrons being the bonding officers of the atoms. The valence bond approach which he developed with Slater was more quickly acknowledged by chemists because resonance corresponded to their usual representations

Mulliken proposed a very different quantum approach based on molecular spectroscopy. With regard to the concept of valence considered as an intrinsic property of the atom, Mulliken opposed the notion of 'energy state' deduced from molecular spectra on the basis of an *electronic configuration*, *i.e.*, of a distribution of the molecular electrons in different orbits. In this description, each orbit is delocalized over all the nuclei and can contribute, depending on each specific case, a stabilizing or destabilizing energy contribution to the total energy of the molecule (Llored, 2010). The sum of the energy contributions of each electron in its orbit determined whether the electronic configuration allowed for the existence of a stable molecule, *i.e.*, whether its energy was stabilizing overall. For Mulliken, the atom did not exist as a component in a molecule. His concept of molecular state suggested molecular variability of energy and geometry that could not even be considered within the approaches of Lewis and Irving Langmuir. Mulliken proved that the spectral states of the molecules could be obtained from that of their molecular ions by the mere addition of an electron without changing the quantum numbers and, thus, worked out his molecular *Aufbauprinzip* (Llored, 2010). This close connection between the quantum theory and the spectral studies gave birth to the correlation diagrams of 1932 (Mulliken, 1932b). Those diagrams made it possible to consider the degree of likeness between a molecule and its separated atoms or its united atom - a fictitious atom obtained by the coalescence of the two atoms such as helium He for two hydrogen H atoms - thanks, in particular, to empirical knowledge of the inter-nuclear distances, energy dissociation and of the charges of the nuclei. The molecule from then on was considered as a composite, *i.e.*, a new entity rather than a mere aggregate of individualized atoms. He wrote: 'In the 'molecular' point of view advanced here, the existence of the molecule as a distinct individual built up of nuclei and electrons is emphasized, whereas according to the usual atomic point of view the molecule is regarded as composed of atoms or of ions held together by valence bonds. From the molecular point of view, it is a matter of secondary importance to determine through what intermediate mechanism (union of atoms or ions) the finished molecule is most conveniently reached. It is really not necessary to think of valence bonds as existing in the molecule (Mulliken, 1931). Despite their irreducible differences, Duhem's thermodynamic potential echoed the electronic states developed by Mulliken insofar as both considered a molecule from an energy standpoint as a 'mixt' not as an 'aggregate'. The '*electronic state'*, the '*binding capacity'*, the '*promotion*' of an electron, '*the energy-bonding-power',* are among the many concepts Mulliken built to explain the capacity of the electrons to be linked to nuclei to form

The semantic shift from the concept of molecular *orbit* to that of molecular *orbital* –MOoccurred in 1932. The concept of orbital took all its significance from Max Born's probabilistic interpretation that the square of a molecular orbital corresponded to the

and structural formula (Llored & Bitbol, 2010).

a molecule seen as a whole (Harré & Llored, 2011).

chemical bodies on the one hand and the aggregative atomic description on the other hand will appear of primary importance at the very beginning of quantum chemistry. I propose to study how Linus Pauling and Robert Sanderson Mulliken created the first chemical quantum approaches in the context described before and how they integrated thermodynamics and quantum mechanics into chemistry.
