Rotation internal, thermodynamic properties

We are interested in understanding how this relative motion of two parts of the molecule contributes to its thermodynamic properties. It turns out that the thermodynamic treatment of this internal rotation depends upon the relative... 

So far, we have used the statistical approach to calculate the thermodynamic properties of an ideal gas. Translational, rotational, vibrational, and electronic contributions were included, along with internal rotations where applicable. 

Table A4.1 summarizes the equations needed to calculate the contributions to the thermodynamic functions of an ideal gas arising from the various degrees of freedom, including translation, rotation, and vibration (see Section 10.7). For most monatomic gases, only the translational contribution is used. For molecules, the contributions from rotations and vibrations must be included. If unpaired electrons are present in either the atomic or molecular species, so that degenerate electronic energy levels occur, electronic contributions may also be significant see Example 10.2. In molecules where internal rotation is present, such as those containing a methyl group, the internal rotation contribution replaces a vibrational contribution. The internal rotation contributions to the thermodynamic properties are summarized in Table A4.6.

Table A4.6 Contributions to the thermodynamic properties due to internal rotation as a function of V, the rotational barrier, and... 

It was shown in the previous section that different relatively stable conformations of a given molecule can result from internal rotation of a particular functional group. The possibility of the existence of various conformers is of extreme importance in many applications. It should be noted, for example, that the biological activity of an organic molecule often depends on its confonfia-tion - in particular the relative orientation of a specific functional grtmp. As another example, the thermodynamic properties of, say, an alkane are directly related to the conformation of its carbon skeleton. In this context the industrial importance of /sooctane is well-known. 

In the calculation of the thermodynamic properties of the ideal gas, the approximation is made that the energies can be separated into independent contributions from the various degrees of freedom. Translational and electronic energy levels are present in the ideal monatomic gas.ww For the molecular gas, rotational and vibrational energy levels are added. For some molecules, internal rotational energy levels are also present. The equations that relate these energy levels to the mass, moments of inertia, and vibrational frequencies are summarized in Appendix 6. 

The thermodynamic properties of a substance in the state of ideal gas are calculated as the sums of contributions from translation and rotation of a molecule as a whole, vibrations and internal rotation in the molecule, and electronic excitation. For example, for entropy and heat capacity the following equations hold ... 

Equations 4.2 and 4.3 are simplified for C60H2n because internal rotation does not occur in these molecules. As it was demonstrated for the C60 fullerene, the electronic contributions to its thermodynamic properties may be neglected at T < 1,000 K (Diky and Kabo 2000). The same is expected for fullerene hydrides. 

Li, J.C.M., Pitzer, K.S. (1956) The thermodynamic properties of 1,1-dichloroethane heat capacities from 14 to 294 K, heats of fusion and vaporization, vapor pressure and entropy of the ideal gas. The barrier to internal rotation. J. Am. Chem. Soc. 78, 1077-1080. 

Scott, D.W., Good, W.D., Gurthrie, G.B., Todd, S.S., Hossenlopp, IA., Douslin, D.R., McCullough, J.P. (1963b) Chemical thermodynamic properties and internal rotation of methylpyrines. II. 3-Methylpyridine. J. Phys. Chem. 67, 685-689. 

Thermodynamic Properties S(298), Cp(T)), Internal Rotations and Group Additivity Parameters in Vinyl and Phenyl Hydroperoxides ... 

Quantum chemistry applies quantum mechanics to problems in chemistry. The influence of quantum chemistry is evident in all branches of chemistry. Physical chemists use quantum mechanics to calculate (with the aid of statistical mechanics) thermodynamic properties (for example, entropy, heat capacity) of gases to interpret molecular spectra, thereby allowing experimental determination of molecular properties (for example, bond lengths and bond angles, dipole moments, barriers to internal rotation, energy differences between conformational isomers) to calculate molecular properties theoretically to calculate properties of transition states in chemical reactions, thereby allowing estimation of rate constants to understand intermolecular forces and to deal with bonding in solids. 

J. Chao, R. C. Wilhoit and B. J. Zwolinski, Ideal gas thermodynamic properties of ethane and propane , J. Phys. Chem. Ref. Data, 2, 427 (1973). Review and evaluation of structural parameters (including vibrational frequencies and internal rotation properties) tabulation of thermodynamic properties [C°, S°, H° — H°), (H° — H )/T, - G°-Hl)/T, AfG°,AfH°, logK ] for 0< T (K)< l500 calculated by statistical thermodynamic methods [rigid-rotor harmonic oscillator (RRHO) approximation]. 

In most quantum chemical program packages, these equations are used only to calculate the temperamre dependence of thermodynamic properties. Internal free and hindered rotation contributions to the partition functions are normally neglected or implicitly use the pseudo-vibration approach for the internal rotor. 

Thermodynamic contributions from the internal rotation of several symmetric tops may be readily calculated by appropriate summation of terms in Table 4. Few reliable calculations, however, have been reported. Thermodynamic properties of propane and several methyl-substituted benzenes have been reported, for example, but subsequent more accurate work has shown the necessity for considering that the internal rotation may be restricted. " Although the subsequent calculations for m-xylene and p-xylene used 6-fold internal rotation barriers of 2.1 to 3.1 kJ mol", more recent statistical calculations for toluene employing the presence of free rotation suggest that internal rotation in the two xylenes may be effectively unrestricted. 

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