Thermal corrections

The thermal corrections in the table are taken from the line labeled Thermal correction to energy in the Gaussian output. 

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

The classical scheme for dichroism measurements implies measuring absorbances (optical densities) for light electric vector parallel and perpendicular to the orientation of director of a planarly oriented nematic or smectic sample. This approach requires high quality polarizers and planarly oriented samples. The alternative technique [50, 53] utilizes a comparison of the absorbance in the isotropic phase (Dj) with that of a homeotropically oriented smectic phase (Dh). In this case, the apparent order parameter for each vibrational oscillator of interest S (related to a certain molecular fragment) may be calculated as S = l-(Dh/Di) (l/f), where / is the thermal correction factor. The angles of orientation of vibrational oscillators (0) with respect to the normal to the smectic layers may be determined according to the equation... 

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). 

Figure 4.5 Thermochemical cycle (T = 298.15 K), showing how the proton affinities of A and A- are related. Fj(AH) is the adiabatic ionization energy of AH, and fea(A) is the adiabatic electron affinity of A. A, A, and X are thermal corrections (see text).

As indicated, only elemental iodine is found in the combustion products of organoiodine compounds [61,62,67]. The iodine formed in a static bomb is mostly in the crystalline state, but some is present in the aqueous and in the gaseous phases. The thermal corrections for dissolution and sublimation are very small and, therefore, static-bomb calorimeters may be used to study organoiodine compounds. However, to avoid the uncertainty in the final state due to the distribution... 

The obtained A 7 a() value and the energy equivalent of the calorimeter, e, are then used to calculate the energy change associated with the isothermal bomb process, AE/mp. Conversion of AE/ibp to the standard state, and subtraction from A f/jgp of the thermal corrections due to secondary reactions, finally yield Ac f/°(298.15 K). The energy equivalent of the calorimeter, e, is obtained by electrical calibration or, most commonly, by combustion of benzoic acid in oxygen [110,111,113]. The reduction of fluorine bomb calorimetric data to the standard state was discussed by Hubbard and co-workers [110,111]. 

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. 

Table 7.6 lists the theoretical BDEs of the M-L bonds in the group-10 Ni(CO)3L, Pd(CO)3L and Pt(CO)3L complexes calculated at the MP2/II and CCSD(T)/II levels of theory [49, 50], The only experimental value known for those compounds is an estimate of ca. 10 kcal/mol obtained for the (CO)3Ni-N2 bond energy at 298 K [59], This estimate is based on kinetic measurements of nitrogen extrusion from the complex. Thermal corrections to the CCSD(T)/II value of D0 = 4.6 kcal/mol yield a theoretical prediction of 6.7 kcal/mol, which is in a reasonable agreement with experiment [49]. The MP2/II BDEs listed in... 

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... 

CCSD(T)/6-31G(d)//B3LYP/6-31G d), basis set extrapolation to 6-311G(d,p) at MP2 level, ZPE correction at B3LYP/6-31G(d) level, no thermal corrections. 

Although this procedure works quite well,159 it is not very satisfactory theoretically. Problems could arise if these methods are applied to transition states where there is one less vibrational frequency. Problems could also arise if zero-point energies of thermal corrections were to change during the course of a reaction. 

Example 4. Calculation of CBS-Q Energy for CH4 The geometry is first optimized at the HF/6-31G(d ) level and the HF/6-31G(d ) vibrational frequencies are calculated. The 6-31G(d ) basis set combines the sp functions of 6-31G with the polarization exponents of 6-311G(d,p). A scale factor of 0.91844 is applied to the vibrational frequencies that are used to calculate the zero-point energies and the thermal correction to 298 K. Next the MP2(FC)/6-31G(d ) optimization is performed and this geometry is used in all subsequent single-point energy calculations. In a frozen-core (FC) calculation, only valence electrons are correlated. 

Figure 3 is an illustration of some calculated [H0M76] thermal correction factors for ground-state neutron-capture cross sections for a number of isotopes near the line of stability. From this figure it is clear that these correction factors can be significant. For the benefit of anyone who might like to attack this problem. Table I summarizes some of what we consider to be the most important quantities to better refine as input to the s-process. 

Nuclei with large thermal correction factors or tne... 

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 first step then is to compute the energy at 0 K for the carbon atom and for the N2, 02, Br2, I2 and 1 molecules. Next the zero-point vibrational contributions are added to the molecular energies, plus the thermal corrections to convert each E(0 K) to H(T), whatever is the temperature of interest. (We will asssume it to be 298 K.) Finally the heat of vaporization of Br2 and the heats of sublimation of graphite, I2 and 1 must be included... 

Optimized (6-31G ) ET (without and with Zero-Point Energy and Thermal Corrections) and Selected Geometric Parameters [28] for amides and Lactams (the Carbonyl-Containing Bridge Is Specified e.g. 3.3.2 Signifies l-Azabicyclo[3.3.2]decan-9-one. (See reference 36.)... 

The nitric acid produced in the combustion was determined by titrating with standardized alkali using a methyl orange indicator. The thermal correction was calculated on the basis 14.0 kcal./mole evolved for each mole of aqueous acid formed. A correction was made for the average firing energy, 12.2 cal. 

Sualitative analysis of the screw heads did show the corroded film on Le screws was the metal fluorides. New screws were used in each run, and the necessary thermal corrections were made on the data for this side reaction. The deficiency of HF was used to make these corrections which amounted to the formation of roughly 0.0015 mole of iron and chromium fluorides. Since the AHf° of iron and chromium fluorides are nearly the same, the correction was made assuming only the formation of iron fluoride (AH/0 = —177.8 kcal./mole). As an additional check, an OF2-H2 run was made with the stainless steel screws replaced by nickel-... 

---