Free energies of dimerization

Schoonmaker and Porter ( ) analyzed the vapors in equilibrium with liquid CsOH and mixed KOH-CsOH condensed phases with a mass spectrometer and reported the presence of appreciable concentrations of dimer in the temperature range 650-700 K. By applying the method of relative equilibrium constants, these workers calculated the difference in the free energies of dimerization for KOH-CsOH. A 3rd law analysis of their free energy data for this pair leads to a difference in the enthalpies of dimerization of 4.9 kcal mol at 298.15 K for CsOH and KOH. Based upon the adopted value for KOH(g), AjH (dimerization, 298. 15 K) = -45.3 3.0 kcal mol" (2), we derive A H (dimerization, 298.15 K) -40.4 4.0 kcal mol" for 2 CsOH(g) = Cs2(0H)2(g). Combining this result with the enthalpy of formation for the gaseous monomer (3), that for the dimer is AjH (CS2(0H)2, g. 298.15 K) = -164.4+10.0 kcal mol" (-687.8+41.8 kJ mol" ). 

Regarding the first question, there was the vague and qualitative description of HcfO interaction as a tendency of nonpolar solutes to adhere to each other. This was later translated in terms of standard free energy of dimerization of some compounds such as carboxylic acids in water. That descriptive definition was not satisfactory and I felt a new and more precise definition was needed. The standard free energies of dimerization were known for molecules that dimerize. They dimerize because they form hydrogen bonds. Therefore, it was not clear which part of the standard free energy was due to the hydrogen... 

The first experimental quantity is the dimerization constant and the corresponding standard free energy of dimerization of carboxylic acids in various solvents (Schrier et ah, 1964 Schneider et al., 1965 Moon et al., 1965 Kunimitsu et al, 1968). Consider the dimerization constants for association of... 

Schrier et al. (1964) suggested the following method of extracting information on HcpO interactions from these data. Suppose that the standard free energy of dimerization (A/r = —RT In Ko) could be split into two contributions ... 

FIGURE 4.5 The free energy of dimerization of simple hydrocarbons in various solvents. The behavior in water is remarkably different. Reprinted from Ben-Naim (1971) with permission. 

The second experimental quantity that, in principle, is suitable for the study of HI, in the sense of attraction between a pair of particles, is the dimerization constant, or the corresponding standard free energy of dimerization of nonelectrolytes in various solvents. 

According to Israelachvili (1985), for two small molecules we would expect a free energy of dimerization of water of the order 0.04 kJ moP at 25 °C, a value too small to induce immiscibihty. This value is at least 100 times larger than the reported experimental values. The lack of agreement may be related to the breakdown of the simple model of the excess polarizability for highly polar molecules. 

Jorgensen W L, J K Buckner, S Boudon and J Tirado-Reeves 1988. Efficient Computation of Absoluti Free Energies of Binding by Computer Simulations - Applications to the Methane Dimer ir Water. Journal of Chemical Physics 89 3742-3746. 

WL Jorgensen, JK Buckner, S Boudon, J Tirado-Rives. Efficient computation of absolute free energies of binding by computer simulations. Application to the methane dimer m water. J Chem Phys 89 3742-3746, 1988. 

IkSnin, I. Pohorille, A. Chipot, C., Insights into the recognition and association of transmembrane a-helices. The free energy of a-helix dimerization in glycophorin A., J. Am. Chem. Soc. 2005,127, 8478-8484... 

The 2-substituted system has proven especially attractive to modelers because the experimental equilibrium constants are known both in the gas phase and in many different solutions. As a result, the focus of the modeling study can be on the straightforward calculation of the differential solvation free energy of the two tautomers, without any requirement to first accurately calculate the relative tautomeric free energies in the gas phase. However, in 1992 Les et al. [290] suggested that prior experimental data [240,266,288], primarily in the form of ultraviolet spectra in the gas phase and in low-temperature matrices, had been misinterpreted and that the reported equilibrium constants referred to homomeric dimers of tautomers (i.e., (42)2 (43)2). Parchment et al. [291] contested this... 

Individual operator sites are denoted O if vacant, or R2 if occupied by a repressor dimer. Pairwise interactions between adjacent occupied sites are denoted ( ) AG 2 and AG23 the free energies of cooperative interaction between adjacent occupied sites, defined as the difference between AG, for any species and the sum of the intrinsic free enei es of binding to occupied sites. 

This protein kinase (known as protein kinase A or PK-A) has an R2C2 quaternary structure that binds 3, 5 -cAMP at its dimeric regulatory (R) subunit with resultant release of two catalytic (C) subunits. The free energy of hydrolysis of the cychc nucleotide activator is large (AG 13 kcal/mol) and allows the 3, 5 -cAMP to be virtually irreversibly converted to AMP by the action of a specific phosphodiesterase. This protein kinase, originally discovered by the Nobelists Edwin Krebs and Edward Fischer, is now considered to be the prototype for over two thousand members of the protein kinase superfamily. 

An ab initio method has been employed to study the mechanism of the thermal isomerization of buta-1,2-diene to buta-1,3-diene. The results of the study have indicated619 that the transformation proceeds in a stepwise manner via a radical intermediate. Experimental free energies of activation for the bond shift in halocyclooctatetraenes have been reported and analyzed by using ab initio MO calculations.620 The isomerization of hexene using a dihydridorhodium complex in dimethyl sulfoxide has been reported,621 and it has been suggested622 that the Pd(II)-catalysed homogeneous isomerization of hexenes proceeds by way of zr-allylic intermediates. A study has been made623 of alkene isomerization catalysed by the rhodium /-phosphine-tin dichloride dimeric complex, and the double-bond isomerization of olefinic amines over potassium amide loaded on alumina has been described.624... 

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