P3_Reaction Energies

This leads to a mean absolute error of 62 kjmol and

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Unformatted text preview: o 400 amu. One possibility is the G3(MP2) method that we have used throughout this chapter to supply reference data (in lieu of experimental data). In practice, it is applicable only to very small molecules (with molecular weights below 150 amu). G3(MP2) heats of formation for several hundred small molecules have been compared with experimental values contained in the NIST thermochemical database. This leads to a mean absolute error of 6.2 kJ/mol and an RMS error of 8.3 kJ/mol. G3(MP2) actually involve a combination of several different quantum chemical models, and perhaps is best referred to as a recipe. The first step is to obtain an equilibrium geometry using the MP2/6-31G* model. Next, two energy calculations are performed at this geometry, one an MP2 calculation with the G3MP2large basis set an the other a QCISD(T) calculation with the 6-31G* basis set. The energy differences between the MP2 calculation with the two basis sets and the QCISD(T) and MP2 calculations with the same basis set are summed. This assumes that the changes in energy due to increase in the size of the basis set from 6-31G* to the G3MP2large and improvement in treatment of electron correlation from the MP2 to the QCISD(T) are independent. This assumption is the reason that G3(MP2) is as widely applicable as it is. Were it necessary to perform a QCISD(T) calculation (which scales as the seventh power of the number of basis functions) with the G3MP2large basis set, the procedure would be much more limited. The fact that G3(MP2) heats of formation obtained are in reasonable accord with experimental values validates the assumption. The final step in the recipe involves a HF/6-31G* frequency calculation (preceded by a HF/6-31G* geometry). This allows for calculation of the zero-point energy and for correction for finite temperature. 57 A new recipe, designated T1, has been formulated that requires significantly less computation than G3(MP2), but yields heats of formation that are nearly identical. Both the QCISD(T) and Hartree-Fock frequency calculations have been eliminated and the MP2/G3MP2large calculation has been replaced by a RI-MP2 calculation in which the G3MP2large basis set is approximated using so-called dual basis set techniques. A HF/6-31G* geometry replaces the MP2/6-31G* geometry. Without further modification, these changes to G3(MP2) result in heats of formation that are not sufficiently accurate to be useful in thermochemical calculations. A successful recipe follows by introducing a total of 66 linear regression parameters based on Mulliken bond orders calculated from the Hartree-Fock wavefunction. These have been determined using a training set of more than 1100 G3(MP2) heats of formation. A plot of T1 vs. G3(MP2) heats of formation for this set is provided in Figure P3-3. Table P3-7 compares structural isomer energies obtained from T1 heats of formation for a variety of simple systems with those obtained both from the G3(MP2) recipe and with experimental heats. The mean absolute and rms errors is 6.6 and 9.0 kJ/mol, roughly the same as those for the G3(MP2) recipe. As discussed earlier in this chapter, while the energy of a molecule is one of its most fundamental properties, it is only rarely determined. This means that quantum chemical models (or combinations of quantum chemical models) that were able to provide routine and reliable energies (heats of formation) are of significant value. 58 Figure P3-3: Comparison of Heats of Formation Obtained from the T1 and G3(MP2) Recipes (kJ/mol) 59 Table P3-7: Comparison of Energies of Structural Isomers from T1 and G3(MP2) Recipes with Experimental Values (kJ/mol) formula (reference) isomer T1 G3(MP2) expt. C2H3 N (acetonitrile) methyl isocyanide 102 100 88 C2H4 O (acetaldehyde) vinyl alcohol oxirane 41 113 41 115 43 118 C2H4 O2 (acetic acid) methyl formate 68 70 75 C2H6 O (ethanol) dimethyl ether 49 50 51 C3H4 (propyne) allene cyclopropene -3 91 1 100 7 93 C3H6 (propene) cyclopropane 36 38 29 C4H6 (1,3-butadiene) 2-butyne cyclobutene 1,2-butadiene 1-butyne methylenecyclopropane bicyclo[1.1.0]butane 35 50 43 56 80 113 37 56 51 58 85 120 36 48 53 56 92 108 2-methyl-2-propenal cyclobutanone 2-hydroxy-1,3-butadiene 2,3-dihydrofuran divinyl ether 7 4 25 48 35 96 6 3 23 38 35 97 5 9 23 38 43 102 C4H8 (2-methylpropene) trans-2-butene 1-butene cyclobutane 4 15 46 6 16 47 7 17 46 C5H8 (cyclopentene) 2-methyl-1,3-butadiene methylenecyclobutane 1,4-pentadiene 1,1-dimethylallene 1,2-pentadiene 42 89 69 86 98 37 87 67 90 101 40 86 70 93 105 5 4 - C4H6 O (methyl vinyl ketone) trans-2-butenal mean absolute error 60 The version of Spartan provded with this textbook (Spartan Student) does not provide for calculations using the T1 thermochemical recipe. However, the associated Spartan Molecular Database includes T1 data for all the molecules required for the problems that follow. Double-Bond Disproportionation Reactions: A double-bond disproportionation reaction relates the energy of a molecule incorporating a double bond with the average of the energies of molecules incorporating the corresponding single and triple bonds. For example, the double-bond disproportionation reaction for ethylene relates its energy to the average of the energies of ethane and acetylene. Experimentally, this reaction is endothermic by 38 kJ/mol, meaning that a CC double bond is weaker than the average of carbon-carbon single and triple bonds. 2 H2C=CH2 → H3C-CH3 + HC≡CH Use the T1 recipe to calculate the energies of double-bond disproportionation reactions for ethylene, methyleneimine (H2C=NH), formaldehyde (H2C=O) and thioformaldehyde (H2C=S). (Build the molecules as you normally would and simply retrieve from the Spartan Molecular Database.) Adjust your results for the last three to account for the error in the reaction of ethylene. Note any significant differences among the four disproportionation energies and try to rationalize them. 61 Calculation of Entropy and Gibbs Energy The change in the Gibbs energy (ΔG) for a chemical reaction follows from the change enthalpy (ΔH) by way of the usual thermodynamic relationship. ΔG = ΔH - TΔS T is the temperature in K and ΔS is the change in entropy. The entropy is a sum of translational, rotational and vibrational parts. S = Str + Srot + Svib The translational part, which depends on the total molecular mass, M, and pressure, P (n is the number of moles, and R and k are the gas and Boltzmann constants), cancels in a mass-balanced equation. 3 Str = nR 2 2!MkT + ln 3/ 2 2 nRT P The rotational part depends on the principal moments of inertia, IA, IB and IC, which in turn depend on the geometry. s is termed the symmetry number which is usually unity. 3 Srot = nR 2 ( !vA vBvC )1/2 + ln s vA = h2/8!IA kT, vB = h2 /8!IB kT, vC = h2/8!IC kT The vibrational part depends on the frequencies. It is based on the linear harmonic oscillator approximation, and incorrectly goes to ∞ and not ½ RT as the frequency goes to 0. It needs to be adjusted to approach the proper limit. Svib = nR ! i (uieui – 1)–1 – ln (1 – e –ui ) µi = h!i/kT 62...
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