Thermal enthalpy corrections

The sum of the energy collection for heating the molecule from 0 to 298 K plus RT is called the thermal enthalpy correction (TCH) and yields... 

To compute zero-point vibration and thermal energy corrections to total energies as well as other thermodynamic quantities of interest such and the enthalpy and entropy of the system. 

The raw zero-point energy and thermal energy corrections are listed first, followed by the predicted energy of the system taking them into account. The output also includes corrections to and the final predicted values for the enthalpy and Gibbs free energy. All values are in Hartrees. 

We can use these energies, with the thermal corrections to the enthalpy (above) to calculate the sum of electronic and thermal enthalpies starting with the CAS-MP2 electronic energies ... 

The S H- -N intramolecular hydrogen bond of 8-mercaptoquinoline has been studied recently in the gas phase and in solution [239]. Its strength (difference of sums of electronic and thermal enthalpies including ZPVE corrections) is about 9.6 kJ/mol in vacuum and 6.09 kJ/mol in aqueous solution (MPWlK/6-311-1— -G(d,p)). The barrier height (10.585 kcal/mol) suggests that the proton transfer from S to N occurs with difficulty whilst the opposite process is practically spontaneous. 

Finally, when using a database with enthalpies of formation of ions, one should be aware of the two possible conventions used to derive those values the so-called thermal electron convention or just electron convention, and the stationary electron convention or the ion convention. These conventions are related to the standard enthalpy of formation of an electron gas Af//°(e , g) and its thermal temperature correction from 0 to 298.15 K. A detailed description of the reasoning behind both conventions provided in the introductory chapter of a widely used data compilation. In practical terms, one should be aware that the enthalpy of formation of an ion calculated by the electron convention will be 6.197 kj mol (= 2.5RTat 298.15 K) higher than the value derived by the ion convention. Therefore, we must be alert when using enthalpy of formation data from several sources, because they may have been derived by accepting either of those conventions. 

The quantity experimentally determined is the thermal effect accompanying the mixing in the calorimetric cell of a solubilizate-organic solvent solution with a water-surfactant-organic solvent microemulsion at a given surfactant concentration ([S]). This thermal effect, corrected for the enthalpy of dilution of both solutions and referred to 1 mole of the solubilizate, corresponds to the enthalpy of transfer (AH,) of the solubilizate from the organic to the micellar phase. In order to analyze the calorimetric data (AH, [S]), it is also necessary to develop... 

Geometry and thermal, enthalpy and entropic corrections at B3LYP/6-31-hG(d) and electronic energy with MP2/aug-cc-pVDZ... 

The calculation of the thermal conductivity of gas hydrate using EMD and the Green-Kubo linear response theory was repeated recently. In that work, convergences of the relevant quantities were monitored carefully as a function of the model size. Subtleties in the numerical procedures were also carefully considered. The thermal conductivity of methane hydrate was found to converge within numerical accuracy for 3 x 3 x 3 and 4x4x4 supercells. In the calculation of the heat flux vector there is an interactive term that is a pairwise summation over the forces exerted by atomic sites on one another. The species (i.e., water and methane) enthalpy correction term requires that the total enthalpy of the system is decomposed into contributions from each species. Because of the partial transformation from pairwise, real-space treatment to a reciprocal space form in Ewald electrostatics, it is necessary to recast the diffusive and interactive terms in this expression in a form amenable for use with the Ewald method using the formulation of Petravic. ... 

Nxylylene system, substituents affect it only to a minor extent. AH parylenes are expected to have a similar molar enthalpy of polymerization. An experimental value for the heat of polymerization of Parylene C has appeared. Using the gas evolution from the Hquid nitrogen cold trap to measure thermal input from the polymer, and taking advantage of a peculiarity of Parylene C at — 196°C to polymerize abmptiy, perhaps owing to the arrival of a free radical, a = —152 8 kJ/mol (—36.4 2.0 kcal/mol) at — 196°C was reported (25). The correction from — 196°C to room temperature is... 

Salufian Here are the results for the lithium reaction (E values in hartrees, and thermal correction to the enthalpy in kcal-mol ) ... 

Note that the standard enthalpy of this reaction, Aacid77°(AH), is equal to the proton affinity of the anion, PA(A ). As shown in figure 4.5, this quantity can be related to PA(A) by using the adiabatic ionization energy of AH and the adiabatic electron affinity of A. The result is also expressed by equation 4.28 (derived from equations 4.4 and4.9), where A = (TT g - o)ah+ ( 298 o)ah and A = ( 298 o )a- - ( 298— o )a These thermal corrections are often smaller than the usual experimental uncertainties of proton affinity data (ca. 4 kJ mol-1). 

Let us return to the thermal decomposition of Fe(CO)(l,3-C4H6)2. Once the calibration constant is known, the enthalpy of the net process 9.10 can be calculated as the product of s and the area (A + B). The next step is to correct this value to 298.15 K by using heat capacity data. This exercise is, however, complicated by the cyclobutadiene polymerization. Brown et al. analyzed the reaction products by mass spectrometry and found several oligomers, in particular the dimer (C4H6)2 and the trimer (C4H6)3 [163]. With such a mixture, it is difficult to ascribe the observed enthalpy change to a well-defined chemical reaction. This is discussed in the paper by Brown and colleagues, who were nevertheless able to recommend a value for the standard enthalpy of formation of the iron-olefin... 

If we make the assumption that the reverse of reaction 15.5 is diffusion-controlled and assume that the activation enthalpy for the acyl radicals recombination is 8 kJ mol-1, the enthalpy of reaction 15.5 will be equal to (121 - 8) = 113 kJ mol-1. This conclusion helps us derive other useful data. Assuming that the thermal correction to 298.15 K is small and that the solvation enthalpies of the peroxide and the acyl radicals approximately cancel, we can accept that the enthalpy of reaction 15.5 in the gas phase is equal to 113 kJ mol-1 with an estimated uncertainty of, say, 15 kJ mol-1. Therefore, as the standard enthalpy of formation of gaseous PhC(0)00(0)CPh is available (-271.7 5.2 kJ mol-1 [59]), we can derive the standard enthalpy of formation of the acyl radical Af//°[PhC(0)0, g] -79 8 kJ mol-1. This value can finally be used, together with the standard enthalpy of formation of benzoic acid in the gas phase (-294.0 2.2 kJ mol-1 [59]), to obtain the O-H bond dissociation enthalpy in PhC(0)0H DH° [PhC(0)0-H] = 433 8 kJ mol-1. 

FIGURE 18. Transition structures for the epoxidation of Z-2-butene (a) and ii-2-butene (b) with DMDO, optimized at the B3LYP/6-3H-G(d,p) level of theory. Bond distances in parentheses for ii-2-butene are at the QCISD/6-31G(d) level of theory. Thermal corrections to enthalpy (H) and entropy values have been calculated at the B3LYP/6-31G(d) level of theory... 

In order to compute the enthalpy difference between two stationary points, the difference between their electronic energies must be corrected for the difference between their vibrational energies at 0 K and also for the difference between the amounts of thermal energy that each absorbs between 0 K and the temperature... 

Table 1 summarizes the behavior, in the form of activation enthalpies (AH ), for each of 18 reactions. The values listed are somewhat larger than published values [36], reflecting corrections for unrecognized thermal control errors in the original investigation. As expected from classical Marcus theory, decreases in rate are accompanied by increases in AH. Curiously, however, as the reaction is pushed progressively further into the inverted region, AH increases by... 

The enthalpies of formation for CF3, CFaO, and FO are, respectively, —112.6, —151.7, and between 9.7 and 54.1 kcal/mole (see Sect. II-D-4-a). Thus reaction (3-7a) may be either endothermic or exothermic depending on the value for A/f298 FO. Porter and Cady137 have crudely estimated D CF30—F = 47 kcal/mole. Combination of this value with A if 298 CF3OF permits an estimation of A/f288 CF30 —150.5 kcal/mole (see Sect. II-D-2). If this estimate is correct, then reaction (3-8) is essentially thermal neutral. 

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