**1. Introduction**

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This chapter aims at understanding what is at stake when thermodynamics is used in chemical quantum calculations. Quantum chemistry and thermodynamics seem to be two incommensurable scientific worlds the assumptions and the statements of which are thoroughly different. So my questions are: How was thermodynamics been integrated into the chemical quantum background at the very beginning of quantum chemistry? What are its role and status in current *Density Functional Theory* and others quantum methods used in chemistry?

I refer both to history and epistemology to grasp this entanglement of scientific approaches. First of all, I propose to analyze how thermodynamics became involved in chemistry. In this respect, I will point out how the concept of energy provides the old chemical affinity with a quantitative tool to understand chemical transformations. The birth of thermochemistry aroused opposition between two old rival conceptions of matter that framed the history of chemistry, that is to say the aggregate and the 'mixt' stances1.

I will then highlight that this duality of conceptions was still at stake when Mulliken and Pauling created two different quantum chemical approaches. In this context, thermodynamics was not just used as a mere tool to calibrate methods; it also guided the contrivance of new quantum concepts or parameters from the outset. Following this line of reasoning, I will query how the concept of 'state', be it electronic or thermodynamic, allows us to bridge thermodynamics to quantum chemistry in a different way. I will indicate why and how the second law of thermodynamics is reflexively of importance to understand molecular calculations and to better grasp the relation between a molecular "whole" and its respective parts.

These investigations are widened by a global overview of the ways thermodynamic parameters are currently involved in workaday quantum methods in order to describe molecular reactivity.

To conclude, the paper will query the status of thermodynamics in predictive quantum methods. I will insist on the status of the concept of energy and the heuristic power of the second law of thermodynamics on quantum grounds.

<sup>1</sup> A 'mixt' is a chemical combination composed of elements but not bearing the same properties as the constitutive elements. Conversely, an aggregate is a mere additive combinations of elements and their properties.

The Role and the Status of Thermodynamics in Quantum Chemistry Calculations 471

(Daumas, 1946). After many attempts, Maximilian Güldberg and Peter Waage asserted in 1861 that they were able to "find for each element and each chemical combination, numbers which express their relative affinity"4 (Güldberg & Waage, 1867). Güldberg and Waage quickly connected the emerging concept of chemical equilibrium with the notion of affinity so as to designate the chemical force which was supposed to lead to the equilibrium. They then established the crucial chemical law of mass action while studying reaction rates, and

The development of the energy approach in chemistry was the result of a fortuitous combination of independent works proposed by Wilhelm Hortsmann in Germany, by Josiah Willard Gibbs in America and by Bakhuis Roozeboom and J.H. Van't Hoff in Holland. Hortsmann integrated Rudolf Clausius' considerations on isolated systems into chemistry. In so doing, he rediscovered in 1873 the law of mass action by means of calculation without having any idea that it had already been found on other grounds. The same year, Gibbs, published a paper entitled '*On the equilibrium of heterogeneous substances'*, within which he proposed a mathematical description of chemical equilibrium. This work remained mostly unknown by chemists because they didn't have the necessary basic mathematical knowledge to grasp it. In 1882, Hermann von Helmholz rediscovered Gibbs' results -which he totally ignored- using the theory of heat published by J. Clark Maxwell in 1871. All these publications gave rise to new chemical concepts which dealt with energy changes in a chemical system submitted to the action of the various forces that led to an equilibrium. One must have distinguished, according to Helmholtz, between the part of energy which appeared only as heat and the part which could be freely converted into other kinds of work, i.e. the "free energy". Subsequently, the production of a decrease in free energy enabled chemists to explain chemical stability (Kondepudi & Prigogine, 1998). In 1884, Pierre Duhem introduced the notion of internal thermodynamic potential by analogy with

Applications to experimental chemistry by the Dutch school, for example, Roozeboom had to cope with difficulties in interpreting hydrobromic acid decomposition in the presence of water in the gas phase. His colleague physicist J.D. Van der Waals suggested to him to use Gibbs's work and helped him to put forward the so-called *phases rule*. Van't Hoff established the law of equilibrium variation depending on temperature and gave to the measure of the affinity as the expression of the maximum work that the system must be able to provide under defined conditions. According to Van't Hoff, affinity was the leading force which produced chemical transformation. The change of affinity sign accompanied the change in the direction of the reaction which occurred at the transition point (Kragh & Weininger, 1996). From that time onwards, researchers gradually moved their attention to other factors of equilibrium. In 1888, Henry Le Chatelier proposed a way to predict how a chemical equilibrium moved according to the variation of the factors on which it depended. Chemical affinity became therefore one of the many aspects of the chemical act allowing improved

At the beginning of the twentieth century, chemists attempted to know not loner why, but how matter is transformed. Chemical kinetics studied the process of transformation of matter. Swante Arrhenius introduced the concept of energy activation, researches gradually

4 The French original sentence is : " (…) *trouver pour chaque élément et pour chaque combinaison chimique,* 

the effects of time, temperature and mass factors.

classical mechanics (Duhem, 1902).

forecasts and performances.

*des nombres qui expriment leur affinité relative"*
