**4. The role and status of thermodynamics in modern quantum chemistry**

Kohn–Sham density functional theory has become one of the most popular tools in electronic-structure theory due to its excellent performance-cost ratio as compared with correlated wave function theory, WFT. Within this theory, the molecular space is divided

The Role and the Status of Thermodynamics in Quantum Chemistry Calculations 483

thermochemistry among others data; (2) 'DBH76' is database of 76 diverse barrier heights concerning for instance nucleophilic substitution and hydrogen transfer. Truhlar and Zhao then discuss the performance of new functionals for these databases, they conclude that functionals labeled 'MO6-2X' and 'MO5-2X' are the '*best performers*' for the main-group thermochemistry and barrier heights. They propose cases study to exemplify their statement. The isomerization energy of octane involves stereoelectronic effects; none of the previous functionals gives the right sign for the isomerization energy from 2,2,3,3 tetramethylbutane to *n*-octane. The functional 'B3LYP' gives an error of 10 kcal/mol while 'M05-2X' predicts the right sign because this later allows a better description of mediumrange XC energies, which are manifested here as attractive components of the non-covalent interaction of geminal methyl and methylene groups (Trulhar & Zhao, 2008a). On the basis of 496 data in 32 databases, they recommend different 'best functionals' designed to transition metal thermochemistry, main-group thermochemistry, kinetics, non-covalent

Choosing a functional of electron density depends upon: (1) the necessary accuracy; (2) the chemical system; (3) the time of calculation. It also requires choosing a set of functions called a basis to achieve calculations for each atom. The basis change according to the type of atoms and different effects such as diffusion, polarization, pseudo potentials for chore electrons, and the size of functions -double, triple zeta-. The functional and its relative basis set define a level of calculation, the process of which requires choosing a computer program such as Gaussian type or Turbomole to be processed. If calculations are not convergent, researchers can change the functional, the size of the grids and convergence thresholds in order to optimize geometry or to calculate molecular energy. Each step reveals know-how, chemical culture and pragmatic compromises. Notwithstanding their basic differences, the ways thermochemistry is involved within molecular orbital approximation or DFT approach are quite similar. Modeling includes thermochemistry as a tool for calibration but also as a heuristic guide for theoretical parameters adjustments inside functionals or wavefunctions or for the design of new quantum methods (Grimme et al., 2007). The structure, within which calculations are made, is well framed by the Variational Principle. We thus realize that thermodynamic quantities partly shape current quantum practices of optimization of geometry and calibration. Calculations help researchers to find out the energy surface associated with a particular chemical reaction. The knowledge of the minimum points on an energy surface makes it possible for a chemist to interpret thermodynamic data. Besides, thermodynamics can retroactively justify minimization of energy as we have already explained. Thermodynamics and energy surface are thus interconnected to determine transition structure and reaction pathways. Modelling structural configurations is of importance in this context and the quantum calculations of entropy play a leading role in

Before I conclude, I would like to focus on a last case study to widen and deepen my enquiry. Let us consider how thermodynamic quantities are used to model solvatation effects and to scrutinize a chemical reaction mechanism within the DFT calculation background. I will refer to a study about zinc-thiolate complexes reactivity depending on the zinc ligands (Picot et al., 2008). Some calculations are shaped by thermodynamic quantities especially designed for quantum context, that is to say that do not exist in classic thermodynamics. It is typically the case of the zero-point vibrational energy labeled 'ZPVE'. The molecular vibration energy is not equal to zero at absolute zero –O K-, it is a quantum

interactions.

such descriptions and predictions.

into grids of cubes; researchers define an electronic density for each point of this space. It is a holistic approach that enables quantum chemists to calculate molecular geometry or total energy exhaustively thanks to its electronic density – 'ρ(r)' -, provided that its Ground-State is not degenerate. The total energy is in consequence a *functional* of the electronic density that is to say a function the basic variable of which is the electronic density function (Kohn et al., 1996). Several authors have applied the Variational Principle to the total energy with the purpose of determining the exact electronic density that minimizes it. Approximations are required because the exact electronic density cannot be reached. The accuracy of a DFT calculation depends upon the quality of the exchange–correlation – XC - functional. This functional is used to account for the exchange-correlation energy term –EXC-. This energy contains not only the non-classical effects of self-interaction, exchange and correlation, which are contributions to the potential energy of the system, but also a portion belonging to the kinetic energy. The past two decades have seen remarkable progress in the development and validation of XC density functionals.

The first generation of functionals is called the local spin density approximation – LSDA -, in which density functionals depend only on local spin densities. Although LSDA gives accurate predictions for solid-state physics, it is not a useful model for chemistry due to its severe overbinding of chemical bonds and underestimation of barrier heights. The second generation of density functionals is called the generalized gradient approximation – GGA -, in which functionals depend both on the electronic density and its gradient. GGA functionals have been shown to give more accurate predictions for thermochemistry than LSDA ones, but they still underestimate barrier heights (Trulhar & Zhao, 2008a). In thirdgeneration functionals, a Laplacian term density is added in the functional form; such functionals are called meta-GGAs. LSDAs, GGAs, and meta-GGAs are "local" functionals because the electronic energy density at a single spatial point depends only on the behavior of the electronic density and kinetic energy at and near that point. Local functionals can be mixed with nonlocal Hartree–Fock – HF - exchange as justified by the adiabatic connection theory (Becke, 1993). Functionals containing HF exchange are usually called hybrid functionals, and they are often more accurate than local functionals for main group thermochemistry (Trulhar & Zhao, 2008a, 2008b). This field of research aims at creating new density functionals with broader applicability to chemistry by including, for instance, noncovalent interactions. The crucial step is the calibration of new functionals against benchmark databases or best theoretical estimates (Goerigk & Grimme, 2010). Let us consider a case study developed by Truhlar and Zhao in order to understand the role and the status of thermochemistry in such a current context.

The most popular density functional, 'B3LYP', an hybrid GGA, has some serious shortcomings among which is its underestimation of barrier heights by an average of 4.4 kcal/mol for a database of 76 barrier heights. This underestimation is usually ascribed to the self-interaction error (unphysical interaction of an electron with itself) in local DFT (Trulhar & Zhao, 2008a). Truhlar and Zhao change parameters and include new ones while shaping a new mathematical functional form that takes physical phenomena into account. In so doing, they design a new functional by trial and error. They then use databases to appraise the reliability of a new functional within a defined purpose. Two databases gather all the thermodynamic quantities: (1) the data base 'TC177' is a composite database consisting of 177 data for main-group thermochemistry including atomization energies, ionization potentials, electron affinities, proton affinities of conjugated polyenes, and hydrocarbon

into grids of cubes; researchers define an electronic density for each point of this space. It is a holistic approach that enables quantum chemists to calculate molecular geometry or total energy exhaustively thanks to its electronic density – 'ρ(r)' -, provided that its Ground-State is not degenerate. The total energy is in consequence a *functional* of the electronic density that is to say a function the basic variable of which is the electronic density function (Kohn et al., 1996). Several authors have applied the Variational Principle to the total energy with the purpose of determining the exact electronic density that minimizes it. Approximations are required because the exact electronic density cannot be reached. The accuracy of a DFT calculation depends upon the quality of the exchange–correlation – XC - functional. This functional is used to account for the exchange-correlation energy term –EXC-. This energy contains not only the non-classical effects of self-interaction, exchange and correlation, which are contributions to the potential energy of the system, but also a portion belonging to the kinetic energy. The past two decades have seen remarkable progress in the

The first generation of functionals is called the local spin density approximation – LSDA -, in which density functionals depend only on local spin densities. Although LSDA gives accurate predictions for solid-state physics, it is not a useful model for chemistry due to its severe overbinding of chemical bonds and underestimation of barrier heights. The second generation of density functionals is called the generalized gradient approximation – GGA -, in which functionals depend both on the electronic density and its gradient. GGA functionals have been shown to give more accurate predictions for thermochemistry than LSDA ones, but they still underestimate barrier heights (Trulhar & Zhao, 2008a). In thirdgeneration functionals, a Laplacian term density is added in the functional form; such functionals are called meta-GGAs. LSDAs, GGAs, and meta-GGAs are "local" functionals because the electronic energy density at a single spatial point depends only on the behavior of the electronic density and kinetic energy at and near that point. Local functionals can be mixed with nonlocal Hartree–Fock – HF - exchange as justified by the adiabatic connection theory (Becke, 1993). Functionals containing HF exchange are usually called hybrid functionals, and they are often more accurate than local functionals for main group thermochemistry (Trulhar & Zhao, 2008a, 2008b). This field of research aims at creating new density functionals with broader applicability to chemistry by including, for instance, noncovalent interactions. The crucial step is the calibration of new functionals against benchmark databases or best theoretical estimates (Goerigk & Grimme, 2010). Let us consider a case study developed by Truhlar and Zhao in order to understand the role and

The most popular density functional, 'B3LYP', an hybrid GGA, has some serious shortcomings among which is its underestimation of barrier heights by an average of 4.4 kcal/mol for a database of 76 barrier heights. This underestimation is usually ascribed to the self-interaction error (unphysical interaction of an electron with itself) in local DFT (Trulhar & Zhao, 2008a). Truhlar and Zhao change parameters and include new ones while shaping a new mathematical functional form that takes physical phenomena into account. In so doing, they design a new functional by trial and error. They then use databases to appraise the reliability of a new functional within a defined purpose. Two databases gather all the thermodynamic quantities: (1) the data base 'TC177' is a composite database consisting of 177 data for main-group thermochemistry including atomization energies, ionization potentials, electron affinities, proton affinities of conjugated polyenes, and hydrocarbon

development and validation of XC density functionals.

the status of thermochemistry in such a current context.

thermochemistry among others data; (2) 'DBH76' is database of 76 diverse barrier heights concerning for instance nucleophilic substitution and hydrogen transfer. Truhlar and Zhao then discuss the performance of new functionals for these databases, they conclude that functionals labeled 'MO6-2X' and 'MO5-2X' are the '*best performers*' for the main-group thermochemistry and barrier heights. They propose cases study to exemplify their statement. The isomerization energy of octane involves stereoelectronic effects; none of the previous functionals gives the right sign for the isomerization energy from 2,2,3,3 tetramethylbutane to *n*-octane. The functional 'B3LYP' gives an error of 10 kcal/mol while 'M05-2X' predicts the right sign because this later allows a better description of mediumrange XC energies, which are manifested here as attractive components of the non-covalent interaction of geminal methyl and methylene groups (Trulhar & Zhao, 2008a). On the basis of 496 data in 32 databases, they recommend different 'best functionals' designed to transition metal thermochemistry, main-group thermochemistry, kinetics, non-covalent interactions.

Choosing a functional of electron density depends upon: (1) the necessary accuracy; (2) the chemical system; (3) the time of calculation. It also requires choosing a set of functions called a basis to achieve calculations for each atom. The basis change according to the type of atoms and different effects such as diffusion, polarization, pseudo potentials for chore electrons, and the size of functions -double, triple zeta-. The functional and its relative basis set define a level of calculation, the process of which requires choosing a computer program such as Gaussian type or Turbomole to be processed. If calculations are not convergent, researchers can change the functional, the size of the grids and convergence thresholds in order to optimize geometry or to calculate molecular energy. Each step reveals know-how, chemical culture and pragmatic compromises. Notwithstanding their basic differences, the ways thermochemistry is involved within molecular orbital approximation or DFT approach are quite similar. Modeling includes thermochemistry as a tool for calibration but also as a heuristic guide for theoretical parameters adjustments inside functionals or wavefunctions or for the design of new quantum methods (Grimme et al., 2007). The structure, within which calculations are made, is well framed by the Variational Principle. We thus realize that thermodynamic quantities partly shape current quantum practices of optimization of geometry and calibration. Calculations help researchers to find out the energy surface associated with a particular chemical reaction. The knowledge of the minimum points on an energy surface makes it possible for a chemist to interpret thermodynamic data. Besides, thermodynamics can retroactively justify minimization of energy as we have already explained. Thermodynamics and energy surface are thus interconnected to determine transition structure and reaction pathways. Modelling structural configurations is of importance in this context and the quantum calculations of entropy play a leading role in such descriptions and predictions.

Before I conclude, I would like to focus on a last case study to widen and deepen my enquiry. Let us consider how thermodynamic quantities are used to model solvatation effects and to scrutinize a chemical reaction mechanism within the DFT calculation background. I will refer to a study about zinc-thiolate complexes reactivity depending on the zinc ligands (Picot et al., 2008). Some calculations are shaped by thermodynamic quantities especially designed for quantum context, that is to say that do not exist in classic thermodynamics. It is typically the case of the zero-point vibrational energy labeled 'ZPVE'. The molecular vibration energy is not equal to zero at absolute zero –O K-, it is a quantum

The Role and the Status of Thermodynamics in Quantum Chemistry Calculations 485

the interactions between the solute and the solvent is a challenge for current quantum chemists. In this context, thermodynamic quantities are the heuristic framework that shapes quantum investigations for achieving better models. The calculation of such thermodynamic quantities stir up: (1) new polarization descriptions and understanding; (2) the creation of new algorithms and cavity topological models (Barone et al., 2004); (3) the continuous recasting of levels of description and software to optimize geometry or to calculate energy quantities (Takano & Houk, 2005); (4) the modelling of the electronic density of the solute

It is then easy to express the free energy of chemical reaction in water using the following

ΔGwater = ΔGgas + ΔGsolv (P) - ΔGsolv (R) Let us analyze how those thermodynamic quantities guide Picot et al. during their investigation of zinc-thiolate complexes alkylation. This short study will allow us to grasp thermodynamics role and status in workaday chemical quantum practices of research. They first need biomimetic models that are appropriate for both structural and mechanistic studies. Based on the experimental data, they search for a consistent series of zinc complexes in which the ligands, the electric charge, and the availability of hydrogen bonding to the atom of sulfur can be varied. They choose the Gaussian 03 software and a level of calculation for the geometry optimizations using basis especially designed for each atom or physical contraction, diffusion or polarization. For each possible mechanistic pathway -see figure 1 below-, they scrutinize each stationary point by using frequency analysis. Each transition state –labeled TS1-3 in the mechanisms presented below- was verified by stepping

along the reaction coordinate and confirming that the transformation occurred.

They then calculate the gas phase Gibbs free energy, and use C-PCM model to calculate the solvatation free energy within a precise set of levels of calculations. They can finally work out the react free energy in aqueous phase. They assess the adequacy of the chemical modeling and of the level of computation against observed databases of zinc complexes. They thus propose all the necessary thermodynamic quantities to analyze the chemical

Those thermodynamic quantities guide the authors along their line of enquiry. They compared energy barriers required to reach transition states in order to elucidate all the influencing parameters such as the global charge of the complex, the hydrogen bond, the role of zinc ligands and that of the solvent. In doing so, they confirm that their

especially outside the cavity.

reaction - figure 2 below.

classic thermodynamic cycle (Picot et al., 2008):

This cycle in turn implied the following formula:

mechanical effect which is a consequence of the Uncertainty Principle. Once a stationary point is localized, be it an energy minimum or a transition state, its energy turns out to be less important than the experimental energy of the molecule. For comparison with experimentally obtained thermochemical data, zero‐point vibrational energy is required to convert total electronic energies obtained from *ab initio* quantum mechanical studies into 0 K enthalpies. The currently accepted practice is to employ self‐consistent‐field harmonic frequencies that have been scaled to reproduce experimentally observed fundamental frequencies (Grev et al., 1991). This procedure introduces systematic errors that result from a recognizable flaw in the method, namely that the correct ZPVE -G (0)- is not one half the sums of the fundamental vibrational frequencies. The use of scaling factors is therefore required (Grev et al., 1991); they depend upon the level of description and its computer data processing. It is then possible to calculate other thermodynamic quantities related to a chemical reaction such as the gas phase Gibbs's free energy from the equation:

$$
\Delta \mathbf{G}\_{\text{gas}} = \Delta \mathbf{E}\_{\text{elec}} + \Delta \mathbf{Z} \mathbf{P} \mathbf{V} \mathbf{E} + \Delta \mathbf{E}\_{\text{T}} - \mathbf{T} \Delta \mathbf{S}
$$

ΔEelec, ΔZPVE, ΔET and ΔS are the differences of electronic energy, zero-point vibrational energy, thermal energy and entropy between the products and the reactants, respectively (Picot et al., 2008).

The solvatation free energy of each compound is determined by calculations depending on a model. This quantity is always defined as the required amount of energy necessary to transfer a molecule of gaseous solute into the solvent. The crucial step is to appraise how the solvent gets involved in a chemical reaction. Its action can be direct if some molecules of solvent take part in the chemical process or indirect if the solvent –then labeled the 'bulk medium'- only modifies reactants reactivity compared with that of the same molecules in the gas phase. Whatever the context may be, the solvatation free energy is calculated from the equation (Leach, 2001):

$$
\Delta \mathbf{G}\_{\text{solv}} = \Delta \mathbf{G}\_{\text{elec}} + \Delta \mathbf{G}\_{\text{vdw}} + \Delta \mathbf{G}\_{\text{cav}},
$$

ΔGelec quantifies the interaction between the solvent and the solute, it is all the more important as the iconicity or polarity is great. ΔGvdw takes into account Van der Waals interactions between the two. To finish, ΔGcav quantifies the cavity occupied by the solute while counting solvent reorganization around the cavity and the necessary work to fight against solvent pressure when the cavity is created. It is possible to encompass the two last terms within the equation:

$$
\Delta \mathbf{G}\_{\text{vdw}} + \Delta \mathbf{G}\_{\text{cav}} = \mathbf{a} \cdot \mathbf{S} + \mathbf{b}
$$

a and b are constants, and S is the area of contact between the solute and the solvent. The different models that enable chemists to calculate ΔGsolv mostly differs by the way they appraise ΔGelec. From earlier models developed by Born (1920) and Onsager (1936) to the PCM model –Polarisable Continuum Method-, the form of the cavity and the study of polarization between the solvent and the solute were continuously modified and improved (Barone et al., 2004; Cossi et al., 2002). The surface of the cavity was divided into finegrained fragments labeled 'tesserae', the wavefunction of solute is determined by Self-Consistent Field iteration. Two others models were performed, the COSMO theory – Conductor-Like Screening Model- and C-PCM approach –Conductor-Like PCM-. Modeling

mechanical effect which is a consequence of the Uncertainty Principle. Once a stationary point is localized, be it an energy minimum or a transition state, its energy turns out to be less important than the experimental energy of the molecule. For comparison with experimentally obtained thermochemical data, zero‐point vibrational energy is required to convert total electronic energies obtained from *ab initio* quantum mechanical studies into 0 K enthalpies. The currently accepted practice is to employ self‐consistent‐field harmonic frequencies that have been scaled to reproduce experimentally observed fundamental frequencies (Grev et al., 1991). This procedure introduces systematic errors that result from a recognizable flaw in the method, namely that the correct ZPVE -G (0)- is not one half the sums of the fundamental vibrational frequencies. The use of scaling factors is therefore required (Grev et al., 1991); they depend upon the level of description and its computer data processing. It is then possible to calculate other thermodynamic quantities related to a

ΔGgas = ΔEelec + ΔZPVE + ΔET – TΔS ΔEelec, ΔZPVE, ΔET and ΔS are the differences of electronic energy, zero-point vibrational energy, thermal energy and entropy between the products and the reactants, respectively

The solvatation free energy of each compound is determined by calculations depending on a model. This quantity is always defined as the required amount of energy necessary to transfer a molecule of gaseous solute into the solvent. The crucial step is to appraise how the solvent gets involved in a chemical reaction. Its action can be direct if some molecules of solvent take part in the chemical process or indirect if the solvent –then labeled the 'bulk medium'- only modifies reactants reactivity compared with that of the same molecules in the gas phase. Whatever the context may be, the solvatation free energy is calculated from

ΔGsolv = ΔGelec + ΔGvdw + ΔGcav ΔGelec quantifies the interaction between the solvent and the solute, it is all the more important as the iconicity or polarity is great. ΔGvdw takes into account Van der Waals interactions between the two. To finish, ΔGcav quantifies the cavity occupied by the solute while counting solvent reorganization around the cavity and the necessary work to fight against solvent pressure when the cavity is created. It is possible to encompass the two last

ΔGvdw + ΔGcav = a S + b a and b are constants, and S is the area of contact between the solute and the solvent. The different models that enable chemists to calculate ΔGsolv mostly differs by the way they appraise ΔGelec. From earlier models developed by Born (1920) and Onsager (1936) to the PCM model –Polarisable Continuum Method-, the form of the cavity and the study of polarization between the solvent and the solute were continuously modified and improved (Barone et al., 2004; Cossi et al., 2002). The surface of the cavity was divided into finegrained fragments labeled 'tesserae', the wavefunction of solute is determined by Self-Consistent Field iteration. Two others models were performed, the COSMO theory – Conductor-Like Screening Model- and C-PCM approach –Conductor-Like PCM-. Modeling

chemical reaction such as the gas phase Gibbs's free energy from the equation:

(Picot et al., 2008).

the equation (Leach, 2001):

terms within the equation:

the interactions between the solute and the solvent is a challenge for current quantum chemists. In this context, thermodynamic quantities are the heuristic framework that shapes quantum investigations for achieving better models. The calculation of such thermodynamic quantities stir up: (1) new polarization descriptions and understanding; (2) the creation of new algorithms and cavity topological models (Barone et al., 2004); (3) the continuous recasting of levels of description and software to optimize geometry or to calculate energy quantities (Takano & Houk, 2005); (4) the modelling of the electronic density of the solute especially outside the cavity.

It is then easy to express the free energy of chemical reaction in water using the following classic thermodynamic cycle (Picot et al., 2008):

This cycle in turn implied the following formula:

$$
\Delta \mathbf{G}\_{\text{water}} = \Delta \mathbf{G}\_{\text{gas}} + \Delta \mathbf{G}\_{\text{solv}} \text{ (P) - } \Delta \mathbf{G}\_{\text{solv}} \text{ (R) }
$$

Let us analyze how those thermodynamic quantities guide Picot et al. during their investigation of zinc-thiolate complexes alkylation. This short study will allow us to grasp thermodynamics role and status in workaday chemical quantum practices of research.

They first need biomimetic models that are appropriate for both structural and mechanistic studies. Based on the experimental data, they search for a consistent series of zinc complexes in which the ligands, the electric charge, and the availability of hydrogen bonding to the atom of sulfur can be varied. They choose the Gaussian 03 software and a level of calculation for the geometry optimizations using basis especially designed for each atom or physical contraction, diffusion or polarization. For each possible mechanistic pathway -see figure 1 below-, they scrutinize each stationary point by using frequency analysis. Each transition state –labeled TS1-3 in the mechanisms presented below- was verified by stepping along the reaction coordinate and confirming that the transformation occurred.

They then calculate the gas phase Gibbs free energy, and use C-PCM model to calculate the solvatation free energy within a precise set of levels of calculations. They can finally work out the react free energy in aqueous phase. They assess the adequacy of the chemical modeling and of the level of computation against observed databases of zinc complexes. They thus propose all the necessary thermodynamic quantities to analyze the chemical reaction - figure 2 below.

Those thermodynamic quantities guide the authors along their line of enquiry. They compared energy barriers required to reach transition states in order to elucidate all the influencing parameters such as the global charge of the complex, the hydrogen bond, the role of zinc ligands and that of the solvent. In doing so, they confirm that their

The Role and the Status of Thermodynamics in Quantum Chemistry Calculations 487

computational outcomes are in agreement with several experimental studies. They for instance show that the net electronic charge of the complex plays a significant role not only on its reactivity, but especially on the mechanism of thiolate alkylation. They finally discuss the nature of the pathways depending on all those energy considerations. Once again, geometry and molecular configurations of the transition state are modeled and assumed to make those predictions become achievable. The entropic contribution is thus of primary

Thermodynamics is thus a tool for calibrating levels of computation (Curtis et al., 1997; Trulhar & Zhao, 2008b), but it also shapes solvatation modeling and the basic reasoning of mechanistic investigation (Takano & Houk, 2005). In a way, thermodynamics embeds a wide class of quantum activities of seeking and predicting. It provides quantum chemical methods with necessary conditions for reasoning and inventing new methods for

The study of both earlier and recent quantum chemical methods highlights the way that thermodynamics is intertwined with quantum methods within a large network of scientific practices that includes computation, chemistry, spectroscopy, crystallography, physics, and so on. As Rouse claims concerning scientific practices (1996, p. 177): 'What results is not a systematic unification of the achievements of different scientific disciplines but a complex and partial overlap and interaction among the ways those disciplines develop over time.' Chemists connect ways of doing science and transform them within ongoing open-ended processes of research. As we have pointed out, thermodynamics was transmuted into thermochemistry through chemical practices, and conversely chemical instrumentation and

The role of thermodynamics is undoubtedly to validate models and methods while stirring up techno scientific creativity. The status of thermodynamics within quantum chemical methods is that of a reference framework that enables chemists to carry out their semiempirical calculations or to create new *ab initio* predictions for thermodynamic data. This conclusion can be widened by considering other methods such as metadynamics, AIM –

This study also points out that alleged incommensurable scientific worlds such as thermodynamics and quantum mechanics, the assumptions, the formalisms and the natures – descriptive or predictive - of which are completely different, can constitutively interact to form the composite field of quantum chemistry. Epistemological queries thus arise concerning inter-levels description of what we call 'reality' and the way scientific fields and knowledge can be mutually stabilized. To this extent, this study also stresses the importance of an epistemology that focuses its attention on scientific practices while including historical

It is interesting to notice that chemical affinities reappear in the latest quantum chemical background. Truhlar and Zhao, among others, refer to affinities –electron affinities, proton affinities of different molecules- in their benchmark databases. Thermodynamics was first introduced in chemistry, we have shown, because it provided chemists with a notion of quantitative affinity. This concept went astray in earlier chemical quantum works and then reappeared from within databases or concepts that help current quantum chemists to shape

importance to query such chemical potential mechanisms.

ways of modeling were transformed by thermochemistry.

calculations (Grimme et al., 2010).

Atoms in Molecules - and so on.

insights.

**5. Conclusion** 

Fig. 1. Possible mechanistic pathways for the alkylation of a zinc-bound thiolate by methyl iodide. (Picot et al., 2008).


Fig. 2. Relative ΔGgas and ΔGwater in kcal.mol-1. (Picot et al., 2008).

computational outcomes are in agreement with several experimental studies. They for instance show that the net electronic charge of the complex plays a significant role not only on its reactivity, but especially on the mechanism of thiolate alkylation. They finally discuss the nature of the pathways depending on all those energy considerations. Once again, geometry and molecular configurations of the transition state are modeled and assumed to make those predictions become achievable. The entropic contribution is thus of primary importance to query such chemical potential mechanisms.

Thermodynamics is thus a tool for calibrating levels of computation (Curtis et al., 1997; Trulhar & Zhao, 2008b), but it also shapes solvatation modeling and the basic reasoning of mechanistic investigation (Takano & Houk, 2005). In a way, thermodynamics embeds a wide class of quantum activities of seeking and predicting. It provides quantum chemical methods with necessary conditions for reasoning and inventing new methods for calculations (Grimme et al., 2010).
