Thermodynamic properties, of molecules

Investigations to find such additive constituent properties of molecules go back to the 1920s and 1930s with work by Fajans [6] and others. In the 1940s and 1950s lhe focus had shifted to the estimation of thermodynamic properties of molecules such as heat of formation, AHf, entropy S°, and heat capacity, C°. 

The excitation of molecular vibrations by light produces the phenomena of infrared and Raman spectra. Measurements of these spectra have become standard techniques for analysis of chemical structures and, through the measurements of force constants, for calculahon of the thermodynamic properties of molecules. 

Since then, groups have been derived for heats of formation of solid nitroaromatics (Ref 20) and for solid and liquid nitroalkanes (Ref 22) Group Additivity. The basic idea behind Group Additivity is that chemical thermodynamic properties of molecules consist of contributions from the individual groups that make up the molecule. Group Additivity is therefore an extension of the series atom additivity, bond additivity,. . . , and turns out to be an excellent compromise between simplicity and accuracy... 

The combination of the electronic and topological factors within this approach yields high correlations with thermodynamic properties of molecules. 

Statistical mechanics is often thought of as a way to predict the thermodynamic properties of molecules from their microscopic properties, but statistical mechnics is more than that because it provides a complementary way of looking at thermodynamics. The transformed Gibbs energy G for a biochemical reaction system at specified pH is given by... 

Given a source of organic precursors, the question remains, Which reactions might have occurred with and between the precursors on early Earth, and in what quantities would they have been found To address that question, the committee looked at the thermodynamic properties of molecules. 

Historically, the field of molecular dynamics (MD) evolved as a means of simulating the behavior of molecules in an attempt to reproduce and, hopefully, to predict structural, dynamic, and thermodynamic properties of molecules.78-80 In recent years, however, it has become popular as a means for refining molecular structures with respect to experimental data.81 This relies on the fact that if any system is simulated, it will tend to run downhill energetically... 

These results show that Raman spectroscopy may be used to quantify the thermodynamic properties of molecules with at least the same accuracy as IR spectroscopy. However, the main advantage of Raman spectroscopy lies in the possibility of determining the sample temperature of precisely those molecules which are excited by the laser beam from Stokes/anti-Stokes intensity ratios. Furthermore, investigations of aqueous solutions (such as biological samples) are expected to create less technical problems than IR window materials. 

One theoretical approach for the calculation of certain thermodynamic properties of molecules is the use of semiempirical (MO) calculations. As an example, the heat of... 

Mekenyan, Q., Bonchev, D. and Trinajstic, N. (1980). Chemical Graph Theory Modeling the Thermodynamic Properties of Molecules. Int.J.QuaniChem., 28,369-380. 

Because of the time-consuming nature of full dynamical (or Monte Carlo) treatments of the thermodynamic properties of molecules as large as proteins, simplified approaches have been used to obtain approximate results. In what follows, a series of methods is described in increasing order of sophistication. The first section treats classical vacuum calculations, which are concerned with the evaluation of the system energy. Next, methods that take into account internal flexibility and harmonic fluctuations are outlined. Finally, techniques for calculating the free energies in condensed phases are presented. 

The stable isotopic compositions of elements having low atomic numbers (e. g. H, C, N, O, S) vary considerably in nature as a consequence of the fact that certain thermodynamic properties of molecules depend on the masses of the atoms of which they are composed. The partitioning of isotopes between two substances or two phases of the same substance with different isotope ratios is called isotopic fractionation. In general, isotopic fractionation occurs during several kinds of physical processes and chemical reactions ... 

Tables 1.1 and 1.2 contain the data necessary to calculate the thermodynamic properties of molecules in the gas phase by BENSON s methods.

Even a property as sensitive as the energy can exhibit additive group contributions as was once again first demonstrated in the experimentally determined heats of formation of the normal hydrocarbons . Benson has demonstrated how this and other thermodynamic properties of molecules and the changes in these properties upon chemical reaction can be usefully tabulated and predicted in terms of group contributions. 

High-level benchmarked quantum chemical calculation results have been reached or are now more accurate than experimental accuracy, and spectroscopic and thermodynamic properties of molecules, such as radicals, which are otherwise very hard to measure experimentally, can be predicted. 

Asymmetric Tops attached to a Rigid Frame.— The calculation of thermodynamic properties of molecules containing asymmetric tops attached to a rigid frame is in general complicated by the change of molecular moments of inertia on internal rotation. Furthermore, the restricting potential for an asymmetric top is likely to be more complex than for a symmetric top. 

Many applications of Kilpatrick and Pitzer s procedure for calculating thermodynamic properties of molecules with compound rotation have been reported. In all cases possible potential energy cross-terms between rotating tops have been neglected. Contributions from internal rotation of symmetric tops have been calculated using the appropriate tables." These tables have also been used in calculations for the internal rotation of asymmetric tops hindered by a simple -fold cosine potential. 3-Fold potential barriers have been assumed in calculations for the —OH rotations in propanol and 1-methylpropanol, the —SH rotations in propane-1-thiol, butane-2-thiol, 2-methylpropane-l-thiol, and 2-methylbutane-2-thiol, the C—S skeletal rotations in ethyl methyl sulphide, diethyl sulphide, isopropyl methyl sulphide, and t-butyl methyl sulphide, and the C—C skeletal rotations in 2,3-dimethylbutane, and 2-methylpropane-l-thiol. 2-Fold cosine potential barriers have been assumed in calculations in the S—S skeletal rotations in dimethyl disulphide and diethyl disulphide. ... 

This is another example of the equipartition principle, and its implications about the thermodynamic properties of molecules are also verifiable experimentally. 

There are two points to consider in light of equation 18.21 or 18.22. First, the more atoms a molecule has, the more terms will be in the product (because as N increases, 3N — 6 increases). Second, because we should suspect that will have some effect on the thermodynamic properties of the gas, we might also think that as the number of atoms in the molecule increases, the thermodynamic functions will deviate more from monatomic gas thermodynamic values. This is indeed the case, as we will see in a few sections. This is one reason why we confined ourselves to monatomic gases as examples in our earlier treatments. This is also a reason why it was difficult to classically predict thermodynamic properties of molecules Molecules have other ways to distribute energy. This can have a major impact on their thermodynamic properties. 

The point of this section is that statistical thermodynamics can derive expressions for thermodynamic properties of molecules. Many computer programs are available that use the expressions in Table 18.5 to calculate thermodynamic properties of molecules, given their energy levels (which can be determined spectroscopically or theoretically). Application of these equations gives the physical chemist a powerful tool for understanding the thermodynamic properties of molecules. 

We have seen how statistical thermodynamics can be applied to systems composed of particles that are more than just a single atom. By applying the partition function concept to electronic, nuclear, vibrational, and rotational energy levels, we were able to determine expressions for the thermodynamic properties of molecules in the gas phase. We were also able to see how statistical thermodynamics applies to chemical reactions, and we found that the concept of an equilibrium constant presents itself in a natural way. Finally, we saw how some statistical thermodynamics is applied to solid systems. Two similar applications of statistical thermodynamics to crystals were presented. Of the two, Einstein s might be easier to follow and introduced some new concepts (like the law of corresponding states), but Debye s agrees better with experimental data. 

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